THE STRATEGIC ROLE OF PERIGEAN SPRING TIDES In Nautical History and North American Coastal Flooding, 1635-1976 / / U.S.DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION ,_ if Ji' i't- N^ ,.' • 4 • 1 1 ■ « i { ] ' 1, 'M" 1 F ^1 ^j gF T- ni-n^ rw-. t E. ft I ■ lw _j§»**' Pit 1 Wr= a jii M a Breaching of the famous Steel Pier ( extreme left) and former Million Dollar Pier ( extreme right) at Atlantic City, N.J., by the great tidal flooding of March 6-7, 1962. 'arch 6-7, 1961. Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/strategicroleofpOOwood Courtesy of United Press International Aerial photograph showing the extreme damage to homes along the beach at Point-o- Woods, Fire Island, N.Y., created by tidal flooding associated with the coincidence of perigean (proxigean) spring tides and strong onshore winds. This active coastal flooding persisted throughout five successive high tides, March 5-7, 1962. THE STRATEGIC ROLE OF PERIGEAN SPRING TIDES In Nautical History and North American Coastal Flooding, 1635-1976 Fergus J. Wood Research Associate National Ocean Survey Office of the Director U.S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION UNITED STATES / NATIONAL OCEANIC AND / National Ocean DEPARTMENT OF COMMERCE / ATMOSPHERIC ADMINISTRATION / Survey Juanita M. Kreps, Secretary / Richard A. Frank, Administrator / Allen L. Powell, Director For sale by the Superintendent of Documents, U.S. Government Printing Offico Washington, D.C. 20402 (Papor Cover) No. (MO-IH7 oiMJii- Foreword Within recent years, increasing demands on the shoreline have led to its national redefinition as the "coastal zone." Thus emerged the concept of treating the area as a natural "system" in which multiple uses must somehow be accom- modated. The sociopolitico, economic, and scientific debates that ensued have resulted in what is now known as "coastal zone management." This treatise deals with the natural forces at work in the domain of the coastal zone manager, and perhaps will lead him to ponder on events of Nature that should be con- sidered in his planning. The manager must be aware that the shoreline portion of the coastal zone is a shifting triple boundary, fleeting by nature, and forever seeking a stability with sea, beach, and air that is never achieved. Here, where earth, sea, and sky meet, often to wash hands in mischief, is where the most violent physical action occurs in the coastal zone. The National Ocean Survey, and its predecessor agencies, have lived and worked in the coastal zone for 169 years. Even after so long and active a tenure it still seemed reasonable that we should ask ourselves the question: "Have we overlooked anything that would be useful to the coastal zone manager, the planner, the developer, and the citizens who live in this increasingly popular locale?" For years we have published maps, charts, and tide tables. We have established tidal bench marks and geodetic control around the coasts and across the country, all necessary for the apportionment of appropriate jurisdictions among Federal, State, and local governments, between these governments and private landholders, and between our Nation and the rest of the world. Accordingly, we began to think of other areas that might fruitfully occupy our attention. We examined many natural occurrences including coastal sub- sidence, shoreline erosion, loss of coastal marshlands, coastal development, shifting bottom topography, coastal currents, and tide observing systems, always keeping in mind the idea that something might have been overlooked that could be useful to those concerned with the coastal zone. Coastal flooding came under our scrutiny, which led Fergus Wood to examine what is known about the tides. He kept digging and studying all aspects of the tides, ranging from our batting average on tidal prediction to the historical effects of tides on man. It was out of such analytic studies that this work was born. The tides affect man most adversely when coastal flooding occurs. Not all high tides cause flooding, nor do all coastal onshore storms. Given, however, a set of circumstances wherein uncommon tides, called perigean spring tides, coincide with strong onshore winds from an offshore storm, such as a nor'easter along the Atlantic coast, the coast will be flooded at all lowland points. The catastrophic event of March 1962 along the mid-Atlantic seaboard was such a iv Foreword circumstance and provided a grim reminder that two strong forces of Nature acting in concert can create havoc. During the times of perigean spring tides, the controlling astronomical forces are enhanced. Sun, Moon, and Earth are aligned, the Moon is closer to the Earth, and along with the Sun, is exerting the increased and concentrated gravitational forces due to their alignment. The Moon is moving faster in its orbit, the length of the tidal day is increased, and there is created what Wood refers to as "a window for potential flooding." At these times the tides build up faster, tidal currents increase, and when accompanied by a strong onshore wind, the ocean waters pour into the estuaries faster than they can escape on the ebb. The pileup of water behind offshore bars results in a destructive breaching from the landward side, and the ocean begins to reshape the shoreline, moving whatever is in its path. Fergus Wood is an interdisciplinary scientist. He treats the astronomy, meteorology, and oceanography in this volume in a thorough manner for the attention of the scientist. For the interested nonscientist, he has included a less technical discussion, and for the historian he has exhaustively investigated events of the past that were influenced by perigean spring tides. As a research geo- physicist, he has approached cautiously another aspect of the perigean spring situation — how it affects the solid earth. The same forces responsible for perigean spring tides in the ocean also create enhanced earth tides, the results of which are obscure. In the present state of knowledge, there seems to be no satisfactorily provable connection, for example, between perigean spring tides, earth tides, and seismic events. But curious and openminded geophysicists are beginning to examine the connections, if any, between earth tides and earth movements, especially microseismic swarms. Perhaps this book will encourage them to look carefully at what, if anything, occurred in the solid earth on past occasions of perigean spring tides, notably of the "proxigean" type, which are explained in part II, chapters 3, 4, 5, and 8. It has been my pleasure to encourage Fergus Wood in this work and to participate with him in many discussions on the research that went into it. I hope that the reader will find profitable the result which consumed nearly four years of his unflagging attention. ilnnrkAM T tt t ^ August 2, 1976. Gordon Lill, Deputy Director, National Ocean Survey. Author's Preface Perigean Spring Tides : A Potential Threat Toward Coastal Flooding Disaster This book deals with the origin, nature, and impact of severe tidal flooding of lowland coastal regions resulting from the coincidence of astronomical and meteorological forces. On March 6, 1962, such a catastrophic occurrence struck from the sea in the darkness of predawn, and for the following 65 hours inundated the entire mid- Atlantic coastline of the United States from the Carolinas to Cape Cod. This disastrous event resulted in a loss of 40 lives and over $0.5 billion in property damage. As other representative examples, severe tidal floodings of similar origin occurred in regions of the Atlantic coast on December 30, 1959, March 4-5, 1931, and April 10-12, 1918 — and at points along the Pacific coast on March 6, 1970, February 3-4, 1958, and January 3-5, 1939. Still further floodings were experienced simultaneously on both coastlines on December 11, 1973, March 26, 1971, and January 6, 1931. All of these instances of coastal flooding were caused by a special combina- tion and reinforcement of the gravitational forces of the Sun and Moon producing unusually high tides — which were concurrently lifted onto the land by strong, persistent, onshore winds. Such exceptionally high tides and their accelerated ocean currents — coupled with intense sea-surface winds — accompanied the total destruction of an offshore Air Force radar tower on February 12, 1963. The foundational erosion and subsequent toppling of the Marconi experimental transatlantic radio tower on Hatteras Island on April 4, 1915, was associated with a comparable situation of perigean spring tides and strong onshore winds. The previously mentioned astronomical alignment of Earth, Moon, and Sun — known as perigee-syzygy — also was present (although exerting a more limited influence due to the small tidal ranges encountered in the Gulf of Mexico) during the great Galveston, Tex., hurricane and tidal flooding of September 8, 1900. A computerized search of the scientific literature reveals that none of the above aspects of perigean spring tides has been analyzed and discussed in a thoroughly comprehensive manner. In a more modern concept emphasizing the ongoing risk, this semiregularly recurring type of tide — when supported by sustained onshore winds — obviously can pose a threat to the development of offshore oil storage platforms and pump- ing stations engaged in the transfer or distribution of crude oil to coastal refineries. A potential for inland as well as shoreline flooding is created by the increased amplitudes and strongly running currents associated with these tides, which may Author's Preface bring saltwater far up estuaries beyond the ordinary tidewater reaches. The alternating extreme low waters, if diluted by heavy rain, may exercise a severe detrimental influence on the oyster and hardshell fishing industries. Such tides likewise may impact adversely upon coastal wildlife sanctuaries, and interfere with the normal breeding cycles of freshwater fish. At a low-tide phase occurring near a perigee-syzygy alignment, the ex- tremely low waters both preceding and following the astronomically produced extremely high waters can cause the stranding of deep-draft vessels such as modern supertankers plying coastal waterways. This situation imposes an addi- tional threat of oilspills and irremedial damage to the coastline. These and other influences of perigean spring tides which possess a definite practical impact on maritime commerce, the coastal ecology, and the status of the marine en- vironment are thoroughly treated in this work. A definitive review of these numerous special properties of perigean spring tides and their effects constitutes the raison d'etre for the present monograph. Because of the many different degrees and grades of perigean spring tides, the documentation and analysis of a large number of examples has been necessary. In pursuit of this supporting material, a detailed investigation was insti- tuted, based upon interdisciplinary sources of data. With the cooperation of the U.S. Naval Observatory, a computer printout was prepared, indicative of the considerable variation in astronomical alignments responsible for perigean spring tides throughout the 400-year period from 1600 to 1999. With the dates of such augmented tide-raising forces duly tabulated, a systematic search was begun through heretofore uncoordinated accounts of tidal flooding on the North American coastline as presented in newspaper and other more definitive sources extending historically to the year 1635. The pieces of a complex puzzle began to fall in place. The documentation of more than a hundred of these major coastal flooding events of the past, and a discussion of the associated hazards to maritime com- merce, seashore habitations, and the coastal environment posed for the future by such recurring flooding events have been set down respectively in tabular and case-study form in this work. Part I summarizes the historical, practical, and environmental aspects of perigean spring tides. In the second, scientific part of the work, the precise astronomical factors causing close perigee-syzygy alignments under certain conditions are explained in detail. The associated increased perturbations of the lunar orbit which result in diminished Earth-Moon distances, enhanced gravitational forces upon the Earth's ocean waters, and augmented tidal ampli- tudes are mathematically analyzed and described. A numerical quantifier (known as the delta-omega syzygy coefficient) designed to serve as a predictor term in establishing the relative potential for tidal flooding generated by such astronomically augmented tides (when sup- ported by the necessary meteorological conditions) also has been developed. On December 26, 1973, based on the foregoing research, the first actual warning of potential tidal flooding during a period bracketing a very close perigee-syzygy alignment of January 8, 1974, was announced to the public by NOAA through the press, radio, and television media. A counteracting high Author's Preface atmospheric pressure system and calm winds prevented any further rise of the very high astronomical tides produced along the east coast on this date. How- ever, front-page headlines in the Los Angeles Times for January 9 told of the "tidal assault" supported by the strong onshore winds of the day before. The accompanying news article summarized the extent of coastal damage and the advance opportunity provided for preventing damage to homes and shoreline installations by sandbagging, backfilling, and other precautionary measures. A confirming instance of tidal flooding based on the same very close perigee- syzygy alignment (termed proxigee-syzygy throughout this work), in which the resulting proxigean spring tides were accompanied by onshore winds, occurred along the western and southern shores of Great Britain on January 11-12, 1974. The 3-day time delay is a function of oceanographic factors. A second tidal flooding (related to a similarly announced perigee-syzygy alignment a month later) occurred along the southern coast of England on February 9. Yet another example of active astronomical tidal flooding potential, contributed to by strong onshore winds, materialized on March 17, 1976, when 5 feet of seawater flooded at Halifax, Nova Scotia, following considerable tidal erosion in lowland coastal regions of Massachusetts, New Hampshire, and Maine. Again, on January 8-9 and January 11-12, 1978, perigean spring tides associated with the perigee-syzygy alignment of January 8 were reinforced by strong onshore winds. The resulting high waters caused serious flooding damage both along the lowland shores of southern California and New England, and those of Great Britain, respectively. On February 6-7, 1978, significantly one lunar month later, these incidents were followed by even more severe tidal flooding in nearly identical locations on the east and west coasts of the United States. The documented analysis of such major tidal flooding episodes of the past, and the rational precautionary measures to be taken to prevent extensive damage from such flooding events in the future, constitutes a considerable portion of both parts I and II of this monograph. An analysis of the astronomical principles underlying the production of these tides, the varying forces which create them, and the perturbations in the lunar orbit which modify the amplitude of these forces and the duration of time in which they are active, all are contained in the second, scientific portion of the work. The last chapter contains a tabulation of all dates vulnerable to especially severe tidal flooding (should the weather and wind conditions also conspire) down to the year 1999. A Definitive Scientific Study of Perigean Spring Tides Among the results of the research documented in this publication are : 1. Correlations between more than 100 cases of major tidal flooding — sus- tained over 293 years of history — and the coincident existence of perigean spring tides. This volume also includes separate case studies of outstanding examples of tidal flooding along the North American coastline, supplemented by tidal growth curves, daily weather maps, contemporary news accounts of the flooding damage, and other data. Author's Preface 2. Discussion of certain representative cases of perigean spring tides which have altered the course of naval history. 3. Evaluation of the practical impact of perigean spring tides on such diversified areas as coastal and inshore navigation, marine engineering, hydro- logical runoff, bioecological imbalance, and erosional damage to the coastal environment. 4. Examination of various instances of ship groundings, strandings, and collisions caused by the extreme low-water phase associated with perigean spring tides — or by their accompanying strong currents. 5. Delineation of examples of unusual tidal flooding which reached far inland, as the result of the coincidence of hurricanes and perigean spring tides. A comparison is made between the flooding potential of hurricanes with and without the association of perigean spring tides, also between the flooding damage caused by hurricanes and by onshore winds generated by winter storms occurring coincidentally with perigean spring tides. 6. Expansion of those portions of classic tidal theory involving the mean positions and mean motions of the Moon and Sun to suggest further refine- ments in computed heights and amplitudes based upon the true positions and motions of these bodies and the true motion of perigee. 7. Analysis of the perturbational influences of the Sun on the orbit of the Moon during the critical period resulting from the alignment of perigee and syzygy. The results incorporate entirely new concepts substantiated by U.S. Naval Observatory data which provide a considerable modification of previous theories regarding the direction and speed of motion of the lunar perigee at these times. 8. Formulation of appropriate new terminology for the classification of a range of intensities of astronomically produced perigean spring tides. Included among these developments is the origination of the needed additional descriptor terms proxigee and exogee, and a system for categorizing various degrees of perigean spring tides based upon the lunar parallax. 9. Derivation of a numerical coefficient or index expressing tidal flooding potential — which combines astronomical, hydrographic, dynamical oceano- graphic, meteorological, and other factors. Through auxiliary tables published in the book, the astronomical portions of this multiparameter index at the time of any perigee-syzygy alignment are immediately available to marine weather forecasters, beachguards, harbormasters, Coast Guard officials, civil defense agencies, and others directly concerned with coastal hazards and with protection against tidal flooding. 10. Review of numerous interdisciplinary fields in which the astronomical phenomenon of perigee-syzygy — and the increased gravitational forces it en- tails — might show some causal connection with other geophysical phenomena. The areas cited include the known augmentation of earth tides and ocean load- ing, the possible triggering of earthquakes, influences on geodetic leveling and deflection of the vertical, and geomagnetic effects. The possible excitation of biological tidal rhythms is also considered. Author's Preface A Note of Caution Relative to the Interpretation of Data A brief commentary of purely objective nature is desirable in order to satisfy the author's sense of responsibility to the scientific community concerning the content of this work. The following treatise involves, in part, a comprehensive series of case studies on perigean spring tides covering 341 years of historical record. The analytical deductions made have been rigorously tested against this complex of empirical data. Out of this research effort, certain patterns of con- sistency have emerged which are beyond the realm of random chance and which render scientifically tenable the development of appropriate principles relating to the strong flooding potential of perigean spring tides. Coincidentally, certain definite conclusions are possible concerning the strategic importance of these tides in producing tidal flooding — if reinforced by strong onshore winds. In addition, evidence from this research supports a considerable credibility in the practical significance of these tides resulting from their economic, environmental, and ecological influences. A peremptory note of caution must be sounded, however. It is essential to observe that, because of the complexities involved in tidal prediction, many technical statements in connection with the tides must be accompanied by qualifications, reservations, and limitations — and, upon occasion, by individual exclusions and exceptions. One of the easiest available pitfalls and most in- cautious professional errors it is possible to commit in presenting any aspect of the tides is to allow any overgeneralized statement in connection therewith. The empirical data and analytical procedures used in this volume for determining tidal flooding potential are those applicable specifically to lowland regions on the Atlantic and Pacific coasts of North America. Likewise, although any measure of tidal flooding potential derived therefrom may pertain un- equivocably to a dozen or so related tide stations responsive to the same resonance mode, it may be totally or partially inapplicable to a location possessing different harmonic constants situated, perhaps, only a few score miles from the more consistent stations. In short, making any too general statement regarding tidal responses subject to a purely astronomical influence (in this case, a combined lunisolar influence) is, at best, a dangerous undertaking. Such astronomical forces will inevitably be modified by local oceanographic conditions, by tidal harmonics, and by such other variables as geographic latitude and longitude, sea-floor and coastal hydrography, strong hydrological runoff from the land, climate, season, and weather. In this concept, it would be totally pretentious to make unqualified state- ments for the absolute, permanent validity of either the n factor or the Au-syzygy coefficient forming a part of it (cf., ch. 8) which are both subject to the need for continuing test and evaluation over time (permitting any desirable modification in their constituent parameters). A working hypothesis advanced upon the strength of evidence provided by even a large and diverse number of cases, however widely distributed in terms of time, hemispheric geography, and local conditions, is acceptable only insofar as it can adequately represent all circum- stances throughout the entire period of past history for which observed data are available, and be capable of similar accurate reproducibility of tidal flooding Author's Preface potential in the future — on a worldwide basis. This word of caution is not intended in any sense to weaken the analytic procedures or formulae developed in this investigation, but only to point up that ultimate definitiveness of the method requires consideration to a massive, totally representative, and globally adequate body of tide data. The groundwork, however, is at hand. The rate-of-growth tide curves alone in this project involved the computation and plotting of over 18,000 individual data points. More than 100 years of daily tide tables were available, extending back to the original "High Water Only" predictions of the U.S. Coast Survey (which later became the U.S. Coast and Geodetic Survey and is now the National Ocean Survey, a component of the National Oceanic and Atmospheric Adminis- tration). Separate tide tables were first published by the Coast Survey in 1866, following upon a series of simple tabular data showing the relationship of the tides to the "full and change of the moon" which were issued in the annual volumes of the Report of the Superintendent of the Coast Survey, starting in 1859. All such basic data have come under scrutiny, as appropriate to this study, for the validation of perigean spring tides. On the meteorological side of the research effort, 1 05 years of daily surface synoptic weather maps (published since 1871, successively, by the U.S. Signal Corps, the U.S. Weather Bureau, and the present National Weather Service) were reviewed for the presence or absence of strong, persistent, onshore winds at the established times of perigean spring tide. Evidences of accompanying tidal flooding were then sought from newspaper, journal and special report literature dating back to the early colonial period in American history. From the astronomical point of view, the task of correlating these tidal and meteorological data was made possible through the cooperation of the U.S. Naval Observatory in providing a computer printout of all perigee-syzygy alignments having a separation-interval less than, or equal to ± 24 h , occurring during the 400-year period from 1600 to 1999. The exact method of application of these numerous sets of data, and the principles of random selection utilized to provide a space-saving but statistically valid base of comparison throughout widespread geographic locales on both the east and west coasts of North America, in succeeding decades of history, in different seasons of the year, and distributed at various times of the day, is thoroughly explained on pages 10-14 and 327-331 of this work. The alphanu- meric system for coding individual tidal flooding events, making possible a ready intercomparison between the associated astronomical, meteorological, and oceanographic circumstances — as well as a comparison with documented accounts of the accompanying tidal flooding — is described in these same pages . It should be emphasized from the outset that the evaluations made in this treatise concerning the effects of perigean spring tides do not overlook the possibility that other lesser influences (such as sufficiently strong onshore winds coinciding with ordinary spring tides) may cause tidal flooding of generally smaller degree — nor do they in any way play down the role of hurricanes as a very major source of coastal flooding. However, this study does focus upon the particularly vulnerable role of perigean spring tides, with supporting wind accompaniment, in producing such coastal flooding effects. Author's Preface The inherent danger of misconstrual of scientific information on the part of sources bent on sensationalizing such potentially catastrophic events of Nature through a lack of awareness of the total forces and concepts involved has been fully noted on pages 406-408. Further education and enlightenment of the large segment of the coastal population subject to the effects of such devastating flooding is the most effective method to forestall the unnecessary and costly confusion resulting from this type of misrepresentation. The purely scientific conclusions derived from this study are summarized both in the immediately preceding section of the preface and in the abstract which precedes the main text. ******* Finally, a note of apology is extended to professional colleagues for the author's shortcoming in not more rigorously avoiding certain minor redundancies in the following pages of text — an inconsistency which belies previous experiences in encapsulating some 180 articles written on astronomical and geophysical subjects in seven different encyclopedias and reference sources. Such are the vicissitudes of Government agency reorganization that, early in this project, the author found himself pursuing alone, not only the necessary research aspects, the writing, associated computations, compilation of tables, and drafting of diagrams, but also the editing of his own manuscript — while at the same time racing a deadline for publication before his intended retirement from Govern- ment. Under these demanding circumstances, the inevitable result was a certain duplication between the contents of small sections of different chapters, prepared variously, as the associated analyses were accomplished, over a period of more than 4 years. On the positive side, somewhat salving a conscientious attitude regarding such compositional refinement, these same technical areas of the work may, however, benefit from an additional self-containment helping to minimize cross- referrals between chapters by readers who are less conversant with the subject material. A similar occasional repetition of nomenclatural definitions — useful to a prospective student of the subject in recovering his bearings among the otherwise complex technical development — requires, perhaps, a lesser apology. The author naturally assumes responsibility for any errors of technical nature which may, through the very comprehensiveness of the work, have escaped attention in reviewing proofs on an accelerated time scale. Acknowledgmen ts The number and variety of persons contributing to, and in a very real sense ultimately responsible for, the realization of this complex technical mono- graph over nearly a 5-year period represent a degree of individual effort making regrettable an inability more properly to credit the assistance of each, in fitting detail. Such extensive individual cooperation may, parenthetically, be regarded as indicative of the wide range of personal interests in a subject so meaningful to those utilizing the coastal environment. From the very outset of the investigation as a scientific concept suggested for further study — through its subsequent development into a full-scale project as pieces of the puzzle began to fall into place — and the intensive research Author's Preface endeavor culminating in the present volume — the continuing interest, support, and personal encouragement of Dr. Gordon G. Lill, deputy director of the National Ocean Survey, and the matching confidence of its director, Rear Admiral Allen L. Powell, have provided a staunch undergirding for the work. Over this same period of monograph preparation, the close cooperation, interdisciplinary rapport, and many stimulating hours of discussion with Dr. Thomas C. Van Flandern, lunar specialist in the Nautical Almanac Office, U.S. Naval Observatory, have contributed immeasurably to the technical significance and completeness of the project. Through his assistance, and that of Dr. P. Kenneth Seidelmann, director of the Nautical Almanac Office, and Dr. P. M. Janiczek, the extensive data presented in table 16 became possible — for which the availability of the computational facilities of this observatory is also duly acknowledged. The diligent application of Mr. Aaron S. Blauer, formerly of the U.S. Government Printing Office, now retired, in copy-editing, styling, marking, and otherwise preparing the material for publication — as well as in coordinating the multitudinous aspects of readying the text proofs, graphics, tables, and photoreproducibles before release to the Government Printing Office — warrants an enormous debt of gratitude. The administrative support of Mr. John R. Morrison, deputy director of the Office of Publications, U.S. Department of Commerce, and the staff services of Mr. Armand G. Caron of this same office, are deserving of similar recognition. Mr. James L. Moore, Mr. Irving C. Brainerd, and Mr. Philip Gambino handled publication liaison through the National Ocean Survey, the National Oceanic and Atmospheric Administration, and the U.S. Department of Commerce, respectively. Mr. M. Kenneth Miller of the Office of Publications, DOC, coordinated with the Naval Observatory the linotron preparation of computer printout data. Special appreciation must be extended to Mr. Francis X. Oxley, formerly chief of NOAA's Photographic Section, for his meticulous reduction and com- pilation processing of weather maps and composite overlays providing many of the illustrations for this work. He was assisted by Mr. Harold M. Goodman and Mr. John A. Roseborough. These photographic reproductions were initially made possible through the exacting negative copy work accom- plished by Mr. Joseph E. Bradshaw, and Mr. Robert C. Robey, Jr., under the direction of Mr. William C. Bugbee, formerly chief of the photographic labora- tory in the National Ocean Survey's (Chart) Reproduction Division. Inestimable support in the area of literature search was provided by the late Mrs. Sharlene G. Rafter, reference librarian in NOAA's Marine and Earth Sciences Library, and by Mrs. Bettie L. Littlejohn of this same facility. Mr. Robert Walter conducted a computerized literature search of seven different data banks for relevant citations. Mr. Douglas L. Stein, assistant librarian for manuscripts at Mystic Seaport, Mystic, Conn., substantially aided the project in its historical research phases, as did Mr. Thomas A. Stevens, historian of the Connecticut River, Mr. Thompson R. Harlow, director of the Connecticut Historical Society, Mr. A.W.H. Pearsall, historian, National Maritime Museum, Greenwich, England, plus Mrs. Caroline Rutger and Mrs. Margery Ramsey of the library of The Mariners Museum, Newport News ,Va. Further assistance was Author's Preface provided by the William L. Clements Library of the University of Michigan and the Ships' Histories Branch, Naval History Division, U.S. Navy Department. Mr. Timothy C. O'Callaghan aided with the compilation of the bibliography and index. Contributions of illustrative material were made by the many organ- izations to which individual credits are given as a part of the figure captions throughout the treatise. The Library of Congress provided the source for repro- duction of many early newspaper accounts of tidal flooding. Typing and revision of the extensive manuscript through its numerous stages of preparation was accomplished by Mrs. Mary Lou Lapelosa, to whom appreciation is also due for handling the many secretarial duties attendant upon the project, and for maintaining the considerable quantity of graphic material connected with the publication. A special tribute is owing to Miss Rhonda M. LaSaine, summer employee, for a diligent research application to Library of Congress newspaper sources, and to Ms. Beatrice S. Drennan, NOS, for similar assistance with resource literature. During the early stages of monograph pro- duction, support in preparing certain of the diagrams used was provided by Mrs. Gayle Brodnax. Various members of the Tide Prediction Branch, Oceanography Division, National Ocean Survey — especially Mr. Donald C. Simpson and Mr. Samuel E. McCoy — provided tide data necessary to the project. To all of the above, the author expresses his permanent gratitude. Table of Contents Page Foreword iii Author's Preface v Table of Contents xv List of Tables xxv Abstract xxvii PART I— BACKGROUND ASPECTS Chapter 1. Representative Great Tidal Floodings of the North American Coastline The Evidences From History 1 Case No. 200 — Perigean Spring Tides (near the time of a total lunar eclipse) 1 Technical Commentary 4 Case No. 4— Perigean (Proxigean) Spring Tides (tt=61'26.6", P — S= -6 b ) 7 Case No. 7— Perigean Spring Tides (P-S = -17 h ) 8 Case No. 8— Perigean Spring Tides (P-S = + 10 b ) 8 Case No. 13— Pseudo-Perigean Spring Tides (P — S= — 53 b ) 8 Case No. 36 — Near-Ordinary Spring Tides 9 Coastal Flooding as an Ongoing Risk 10 Methods of Identification and Evaluation of Representative Cases of Tidal Flooding 12 Remarks Concerning the Fundamental Astronomical, Tidal, and Meteorological Data Sources Used in Connection With Computations for this Volume 13 Chapter 2. The Impact of Perigean Spring Tides Upon Representative Events in American Nautical History Perigean Spring Tides as an Aid to Navigation 59 The Fate of the Frigate Trumbull 59 Contemporary Knowledge of Perigean Spring Tides 68 Tidal Analysis 68 Hydrographic Analysis 69 The Second Battle of Charleston Harbor 70 Tidal Analysis 72 Hydrographic Analysis 74 The Battle of Port Royal Sound, S.C 78 Tidal Analysis 82 Hydrographic analysis 84 Data Concerning the Draft of the Wabash 84 The Perigean Spring Tide as an Agent of Coastal Erosion 84 The Hatteras Campaign 85 Table of Contents PART I— BACKGROUND ASPECTS— Continued Chapter 3. The Practical, Economic, and Ecological Aspects of Perigean Spring Tides Page The Effects of Extremely Low Waters 93 Dangers of Explosive Decompression in Submarine Environments 93 Ship Grounding 95 The Effects of Accelerated Currents 95 Impact Upon Marine Engineering Projects 96 Dangers to Navigation and Docking 96 The Influences of Improvements in Navigation Aids 96 The Optimum Dispersal of Engineering Demolition Products 97 Ecological Influences of Perigean Spring Tides 98 Variations in Salinity 99 Variations in Carbon Dioxide Content 100 Variations in Water Temperature 100 The Effect Upon Grunion Runs 100 Miscellaneous Environmental Influences 102 Recapitulation of the Practical Influences of Perigean Spring Tides 103 Influences of Perigean Spring Tides for Which Substantiating Evidence is Available 103 Chapter 4. Survey of the Scientific Literature on Perigean Spring Tides Historical Origin of the Concepts of Perigee-Syzygy and Perigean Spring (Perigee-Spring) Tides 109 18th Century Tidal Literature Ill Early 1 9th Century Tidal Literature 112 The " Saxby Tide" of October 5, 1869 112 Late 19th Century Tidal Literature 114 20th Century Tidal Literature 115 PART II— SCIENTIFIC ANALYSIS Chapter 1. General Background Considerations of Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides Astronomical Factors Significant to Tidal Nomenclature 121 Astronomical Positions 121 Coordinate Systems 121 1 . Equitorial System 121 2. Ecliptic System 123 3. Horizon System 123 General Equations for Transformation of Coordinates From the Equatorial to the Ecliptic System or the Reverse 124 General Equations for Transformation of Coordinates From the Equatorial to the Horizon System or the Reverse 1 24 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 1 — Continued Astronomical Factors Significant to Tidal Nomenclature — Continued Page Astronomical Motions 1 24 The Diurnal Rotation of the Earth 124 The Earth's Annual Revolution Around the Sun 125 The Moon's Revolution Around the Earth 125 The Motions of the Earth and Moon in Elliptical Orbits 127 1 . The Anomalistic Month 130 2. Effect of the Solar Parallactic Inequality 131 Declinational Effects on the Apparent Motions of the Moon and Sun 132 Auxiliary Influences Affecting the Daily Rate of Lunar Motion in Right Ascension 132 The Effect of Parallax on the Moon's Apparent Motion 133 Changes in Right Ascension Associated With the Apparent Diurnal Motion of the Moon 133 The Relationship of the Moon's Motion in Right Ascension to Its Declination 135 Chapter 2. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces Principal Effects 137 The Daily Lunar Retardation 137 1. The Lunar Day 139 2. The Tidal Day 139 Relationship of the Tidal Day to Lunar Transit Times, Hourly Differences in Right Ascension of the Moon, and Other Factors 140 Apparent Diurnal Motion of a Body "Fixed" in Space 141 Apparent Diurnal Motion of a Body Possessing Its Own Motion in Right Ascension 141 Variations in the Tide-Raising Force Associated With Lunar Parallax 141 The Effect of the Parallax Inequality Upon the Comparative Lengths of the Tidal Day 143 Ancillary Effects 147 Lunar Augmentation 147 Regional and Latitudinal Effects on the Tides Resulting from Changing Lunar and Solar Declinations 148 1. Solstitial Tides 149 2. Tropic Tides 149 3. Equinoctial Tides 150 4. Latitudinal Effects of the Diurnal Inequality 150 Subordinate Factors Influencing the Length of the Tidal Day 150 1 . Solar Declinational Effects 1 50 2. Effects Due to Changing Parallax and the Obliquity of the Ecliptic 150 3. Lunar Declinational Effects 150 4. Effect of the Moon's Orbital Inclination to the Horizon 150 5. Supplementary Influences 151 Seasonal Factors Influencing the Production of Heightened Tides 151 Effects of the Phase Inequality and Diurnal Inequality 151 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 3. The Action of Various Perturbing Functions in Establishing, Altering, and Controlling the Amplitudes of Perigean Spring Tides Page The Effects of Perturbations Upon Lunar Distances and Orbital Motions 153 The Lunar Evection 153 The Lunar Variation 155 1. Alternating Acceleration and Deceleration of the Moon's Orbital Motion 156 2. Changing Lunar Orbital Velocity With Respect to the Earth 157 3. Changes in Curvature of the Lunar Orbit 158 The Elliptic Variation 1 59 The Annual Variation 159 The Lunar Reduction 159 Differences Between the Mean and True Astronomical Positions of the Moon and Sun 159 The Derivation of True and Mean Astronomical Positions 161 The Assumption of Mean Positions 161 The Special Perturbative Influences of Lunar Evection and Lunar Variation 162 Summary of the Effects of the Principal Lunar Perturbations in Differentiating Between the Mean and True Orbital Positions of the Moon 164 1. Effects of Elliptic Inequality 164 2. Effects of Evection (combined with the elliptic inequality) 164 3. Effects of Lunar Variation 165 4. Effects of the Annual Equation 165 Corrections for Lunar Perturbations as Used in the Tidal Equations 166 Chapter 4. Identification of the Specific Astronomical Forces and Influences Contributing to the Production of Perigean Spring Tides The Principal Concurrent Tidal Forces 169 The Effects of a Near-Alignment of Perigee and Syzygy in Producing Tides of Increased Ampli- tude and Range 1 69 Basic Force Equation Defining the Magnitude of Tidal Uplift 169 1 . Lunar Evection Effects 1 70 2. Lunar Variation Effects 172 3. Summary Analysis 1 73 The Effect of Perigee-Syzygy Alignment in Increasing the Value of the Lunar Parallax 1 74 1 . Effect of the Elliptic Inequality 175 2. Effect of the Lunar Evection 175 3. Effect of the Lunar Variation 175 4. Summary Analysis 1 76 The Concepts of Mean Motion vs. True Motion in Relation to the Earth, Moon, and Lunar Perigee 177 1. The True Motion of Lunar Perigee 177 2. Short-Period and Long-Period (Averaged) Perturbational Motions of Perigee 177 3. The Special Motion of Perigee Close to the Position of Perigee-Syzygy Alignment 179 4. The Comparison of True and Mean Motions 182 5. The Minor Sinusoidal Variation Between True and Mean Longitude 184 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 4 — Continued Page Subordinate and Counterproductive Effects on Perigean Spring Tides 185 Effects of Declination on the Tide-Raising Forces 186 Maximization of Declination in the 18.6-Year Period of the Lunar Nodical Cycle 189 Aside From a Lack of Onshore Winds, Why Does Coastal Flooding Not Occur With Every Perigean Spring Tide? 191 Combined Effect of Changing Parallax and Large Declination on the Moon's Hourly Motion in Right Ascension 1 92 Effects of Extreme Lunar Declination on Motions in Right Ascension 193 1. Decrease of Motion in Right Ascension, and Shortening of the Tidal Day at Times of High Lunar Inclination to the Celestial Equator 195 2. Increase of Motion in Right Ascension, and Lengthening of the Tidal Day at Times When the Moon Is at an Extreme Declination 1 96 Chapter 5. The Essential Conditions for Achieving Amplified Perigean Spring Tides The General Concepts of Maximization of Perigean Spring Tides 197 Factors Increasing the Intensities of the Tidal Forces Acting 197 A Quantitative Evaluation of the Various Tide-Maximizing Factors 199 Summary of Relative Gravitational Force Influences 199 Astronomical Influences Producting Uneven Heights Among Perigean Spring Tides ; Lack of a Current Procedure for Variable-Intensity Classification 202 Perigean Spring and Other Tidal Equivalents in International Terminology 203 Compensating and Counterproductive Tidal Force Influences 204 Variation in Parallax and Orbital Curvature with Lunar Configuration 204 Comparitive Effects of Various Lunisolar Configurations Upon Lunar Distance From the Earth and the Curvature of the Lunar Orbit 205 1 . Apogee-Syzygy 207 2. Apogee-Quadrature 207 3. Ordinary Syzygy 208 4. Ordinary Quadrature 208 5. Perigee-Quadrature 209 6. Perigee-Syzygy 209 A Quantitative Comparison of the Lunar Parallax at Times of Perigee and Apogee 210 Causes of Variation in the Shape of the Lunar Orbit and in the Consequent Tide-Raising Forces 214 Effects of the Individual Syzygies 214 1. Case One: Full Moon at Perigee 214 2. Case Two : New Moon at Perigee 216 The Effect of Solar Perigee 218 The Effect of Coplanar Lunisolar Declinations 218 The Effect of Nodal Alignment 218 Summary Evaluation of Extreme Lunar Parallaxes 219 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 6. Conditions Extending the Duration of Augmented Tide-Raising Forces at the Times of Perigee-Syzygy Page The General Principles of" Stern Chase" Motion 269 Factors Increasing the Length of the Tidal Day 269 1 . Lunar Parallactic Inequality 269 2. Declination Effects 270 3. The Counterproductive Influences of Solar Perigee (Perihelion) 270 4. Summary 271 Reintroduction of the Concepts of the Lunar and Tidal Day 271 Fluctuations in the Lunar and Tidal Days 27 1 1. Derivation of the Length of the Mean Lunar Day 272 2. Variations in the Lunar Day 272 3. Variations in the Tidal Day 273 Causes of Systematic Variations in the Length of the Tidal Day 273 The Role of the Increased Tidal Day Viewed in Perspective 274 The Effect of Increased Lunar Orbital Velocity Upon the Length of the Tidal Day 274 Quantitative Evaluation of Changing Periods in the Moon's Monthly Revolution 275 Conditions Lengthening the Synodic and Anomalistic Months 275 Maximized Lengths of Those Months Bracketing Perigee-Syzygy 285 Cycles of Alternation in Perigee-Syzygy Alignments 285 The Meaning and Relationships of High and Low Maxima in the Lengths of the Lunar Months . 286 1 . Variation in Length of the Anomalistic Month 287 2. Variation in Length of the Synodic Month 287 The Correlation Between Smaller Perigee-Syzygy Separation-Intervals and Longer Months 287 Analysis of the Relative Gains in the Lengths of the Anomalistic Months Containing a Close Perigee-Syzygy Alignment 288 1 . Anomalistic Month 286 2. Synodic Month 288 Prolongation of a Small Separation-Interval at Close Perigee-Syzygy Alignments 288 Declinational Influences on the Length of the Tidal Day 299 The Effect of the Lunar Apsides Cycle 290 Modification of the Lunar Period by the Lunar Apsides Cycle 292 Other Time-Related Factors Susceptible to Analysis by the Methods of Harmonic Analysis 296 Evaluation of the Principal Harmonic Constituents 296 The Phase Age and the Parallax Age 297 Variation in Tidal Range, and in the Types of Tides 298 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 7. The Classification, Designation, and Periodicity of Perigean Spring Tides, With Outstanding Examples of Accompanying Tidal Flooding From Recent History Page Comparison of Ordinary Spring Tides and Perigean Spring Tides 301 Concepts of Tidal Priming and Lagging 302 Lunar Phase Effects — Qualitative Evaluation 302 Priming and Lagging as Shown in Tide Curves 302 1. Tidal Priming 303 2. Tidal Lagging 303 Quantitative Analysis of the Effects of Tidal Priming and Lagging 306 Relative Tide-Raising Forces at Quadratures and Syzygies 306 Confirmation of the Extended Duration of Peak Tide-Raising Forces at Perigee- Syzygy 306 Examples of Tidal Priming and Lagging 311 1 . Application to Ordinary Spring Tides 311 2. Application to Perigean Spring Tides 312 A Proposed New System for the Quantitative Designation of Perigean Spring Tides 312 Basis for the Classification of Perigean Spring Tides 313 1 . Maximum Perigean Spring Tides (or Ultimate Proxigean Spring Tides) ; Maximum Proxigean Spring Tides 313 2. Extreme Proxigean Spring Tides 316 3. Proxigean Spring Tides 316 4. Perigean Spring (or Perigee-Spring) Tides 317 5. Pseudo-Perigean Spring Tides 317 6. Ordinary Spring Tides 318 Periodic Relationships 318 The Mean Period Between Successive Occurrences of Perigee-Syzygy 318 Short-Period Cycles of Repetition of Perigean Spring Tides 319 The 3 1-Year Cycle of Perigee-Syzygy 32 1 Meteorological Aspects of Coastal Flooding at Times of Perigean Spring Tides 326 Selection of Multidisciplinary Data Sources 327 The Correlation of Meteorological and Astronomical Data 328 Grouping of the Weather Maps 328 Explanatory Comments Concerning the Manner of Designation of Weather Maps and the Concurrent Perigee-Syzygy Data 329 1. The Tidal Flooding of 1931 March 4-5 331 2. The Tidal Flooding of 1939 January 3-5 374 3. The Tidal Flooding of 1959 December 29-30 383 4. The Tidal Flooding of 1962 March 6-7 386 5. The Aborted Tidal Flooding of 1962 October 13 403 6. The Tidal Flooding of 1974 January 8 (N-99) 404 A Note on Storm Tide Announcement Effectiveness 406 Data on Tidal Flooding and Associated Damage 408 7. Tidal Flooding in the British Isles on 1974 January 1 1-12 and February 9 420 8. Tidal Flooding of 1976 March 16-17 424 9. Tidal Flooding of 1978 January 8-9 429 10. Tidal Flooding of 1978 February 6-7 430 Table of Contents PART II— SCIENTIFIC ANALYSIS— Continued Chapter 8. Tidal Flooding Potential, and the Relationship of Perigee-Syzygy to Other Oceanographic and Geophysical Factors and Influences Page Development of a Numerical Index Designating the Astronomical Potential for Tidal Flooding 434 1. The Need for Combined Lunisolar Representation 434 2. Significance of the Aw-Syzygy Coefficient 435 3. Evaluation of the Aw-Syzygy Coefficient 436 Establishment of a Combined Astronomical-Meteorological Index to Potential Tidal Flooding 437 Empirical Support for the Validity of the Delta Omega-Syzygy Coefficient Provided by Predicted and Observed Tidal Height Data 440 The Lengthened Tidal Day as an Indicator of Increased Tidal Flooding Potential 440 Accelerated Rate of Tide Rise as an Indicator of Increased Tidal Flooding Potential 448 1 . Semidiurnal Tide 448 2. Mixed Tides (Affected by the Diurnal Inequality) 474 An Independent Check on the Validity of the Aw-Syzygy Coefficient 475 Summary and Conclusions A. The Tidal Aspects of Perigee-Syzygy Alignment 477 B. The Subsidiary Effects of Extreme High and Low Waters and Strong Tidal Currents at Times of Perigee-Syzygy 482 Representative Instances of Ship Groundings in Shallow Depths Produced at the Low- Water Phase of Perigean Spring Tides 483 Representative Instances of the Effects of Strong Current Flow Associated With Periods of Perigean Spring Tides 485 Extreme Tide and Current Impact on Offshore Platforms in Shallow Ocean Areas 485 Influences of Perigean Spring Tides Upon the Ecology of the Coastal Zone 485 C. Unproven Geophysical Relationships With the Phenomenon of Perigee-Syzygy 485 1. Wholly Conjectural Relationships Between Meteorological Factors and Perigee-Syzygy. 486 2. Other Possible Geophysical Influences 487 D. Geomagnetic Illustration of the Increase in Velocity of Tidal Currents at Times of Perigee . Syzygy 489 Supplementary Comments, Specific Literature Citations and Case Examples in Connection with the Influences of Perigee-Syzygy Alignments and Perigean Spring Tides 490 1 . Storm Surge Models and Tidal Flooding 490 2. Engineering Protection Against Storm Surges and Tidal Flooding 490 3. Possible Coincidence of Tsunamis and Perigean Spring Tides 490 4. Concepts of Earthquake Triggering 490 5. Tidal Loading 493 6. Earth Tides 493 7. Crustal Tilt 494 8. Deflection of the Vertical 494 9. Geomagnetic Effects 494 10. Ecological Aspects 494 1 1 . Internal Waves 494 12. Turbidity Currents 494 13. Fish Migration 494 14. Biological Rhythms 495 15. Breakup of River Ice 495 The Challenge of Geophysical Discovery: An Advocacy of Interdisciplinary Cooperation 495 Table of Contents APPENDIX The Basic Theory of the Tides Introduction Page The Astronomical Tide-Producing Forces : General Considerations 497 Origin of the Tide-Raising Forces 497 Detailed Explanation of the Differential Tide-Producing Forces 498 1 . The Effect of Centrifugal Force 498 2. The Effect of Gravitational Force 498 3. The Net or Differential Tide-Raising Forces: Direct and Opposite Tides 499 4. The Tractive Force 500 5. The Tidal Force Envelope 50 1 Variations in the Range of the Tides: Tidal Inequalities 501 1. Lunar Phase Effects: Spring and Neap Tides 501 2. Parallax Effects (Moon and Sun) 502 3. Lunar Declination Effects: The Diurnal Inequality 503 Factors Influencing the Local Heights and Times of Arrival of the Tides 503 Prediction of the Tides 506 Reference Sources and Notes 511 Bibliography on Tides (in 42 Categories) 517 Index 53 1 List of Tables BLE Page 1. List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds 15 2. A Representative List of North American Hurricanes Occurring Nearly Concurrently With Perigean Spring Tides 26 3. Representative Cases of Coastal Flooding Associated With Ordinary Spring Tides, Coupled With Strong, Persistent, Onshore Winds 29 4a. Representative Cases of the Highest High Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzygy 32 4b. Representative Cases of the Lowest Low Waters of Record Observed at Various Tidal Sta- tions, Within 2 Days of Perigee-Syzygy 33 4c. Examples of Perigean Spring Tides Resulting in, or Contributing to, Coastal Flooding Through Impaired Hydrological Runoff 35 4d. Illustrative Cases of Coastal Erosion Produced at Times of Perigean Spring Tides Coincident With Strong, Persistent, Onshore Winds 36 5. A Representative Sample of Newpaper Articles Covering Tidal Flooding Events Associated With Perigean Spring Tides, 1723-1974 39 6. Comparative Tides at Charleston Harbor, S.C., October 13-19, 1974 72 7. Apparent Daily Motion of the True Sun in Right Ascension and Longitude for Selected Dates in 1975 131 8. Comparison of Geocentric Horizontal Parallax and True Geocentric Distance of the Moon for a Case of Widely Separated Perigee-Syzygy 142 9. The Changing True Distance of the Earth From the Sun 144 10. Approximate Orbital Angular Velocity of the Moon, Expressed as a Difference in Celestial Lpngitude, Showing the Variation at Times of Close Perigee-Syzygy, (Proxigee-Syzygy) Apogee-Syzygy (Exogee-Syzygy), and Perigee-Quadrature 146 1 1 . Approximate Dates on Which Maximum Lunar Declinations Occurred, According to the 6,798.4-Day Nodical Cycle 195 12. Selected Cases of Perigee-Syzygy, Showing the Relationship Between the Equinoctial Posi- tion of the Moon and the Lunar Parallax Over the 400-Year Period 1600-1999 200 13. Compilation of All Cases of Extreme Proxigee-Syzygy Occurring Over the 400-Year Period 1600-1999 201 14. Selected Cases of Perigee-Syzygy Occurring Simultaneously at a Lunar Node (Total Solar Eclipse) and Near Perihelion 202 15. True Geocentric Distance of the Moon 206 16. Computer Printout of All Cases of Perigee-Syzygy Occurring Between 1600 and 1999 Which Have a Separation Interval <24 h (With Accompanying Astronomical Data) 221 17. Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments 276 18. Variation in the Length of the Synodic Month Within the 8.849-Year Lunar Apsides Cycle. . 292 19. Types of Tides (With Index and Range) at Various Locations Along the Atlantic, Pacific, and Gulf Coasts of North America 299 20. Effects of Tidal Priming and Lagging (at Perigee-Syzygy) 309 21. Effects of Tidal Priming and Lagging (at Ordinary Syzygy) 310 22. Proposed Classification System for Perigean (including Proxigean) Spring Tides 313 23. Examples of Scientific and Technical Terminology in the English Language Involving Inter- lingual Combinations of Prefixes and Suffixes 315 List of Tables Table Page 24. Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Align- ments 321 25. Cases of Extreme Tidal Flooding Coinciding With Long-Term Astronomical Cycles of Close Alignment Between Perigee and Syzygy 326 26. Surface Synoptic Weather Maps for Twenty Representative Cases of Coastal Flooding As- sociated With Perigean Spring Tides and Strong, Sustained, Onshore Winds 332 27. Surface Synoptic Weather Maps for Twenty Representaive Cases of Nonflooding Conditions Associated with Perigean Spring Tides Which Were Accompanied by Light and Variable Winds and High Atmospheric Pressure 353 28a. Surface Synoptic Weather Maps for Four Representative Cases of Hurricanes Occurring in Near-Coincidence With Perigean Spring Tides 374 28b. Representative Surface Synoptic Weather Map at a Time During Which a Perigean Spring Tide Caused Blocking and Backup of Hydrological Runoff 374 29. Surface Synoptic Weather Maps for Cases of Tidal Flooding Receiving Special Attention in the Text 387 30. Examples Involving the Use of the A^-S Coefficient in Establishing a Combined Astro- nomical-Meteorological Index (n) of Potential Tidal Flooding 439 Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy (Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-Decem- ber, 1962 441 Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December, 1 962 449 33. Sixteen Instances of Major Tidal Flooding Near a Time of Perigee-Syzygy, Represented (in Figs. 153-163) by Plots Showing the Predicted Rate of Rise of the Astronomical Tide at Nearby Tidal Reference Stations (Listed in the Table) 453 34. A Checklist of the Central Dates (Mean Epochs) of Perigean Spring Tides (P — S< ±24 b ) Occurring Between 1977 and 1999 480 31a, c b. , d. 32a. c 1). ,d. Abstract Tides are caused by the gravitational attractions of the Moon and Sun acting upon the oceans and major water bodies of the Earth. Two times during each month, at new moon (conjunction) and full moon (opposition), the Earth, Moon, and Sun come into direct alignment in celestial longitude and, in the combination of their gravitational forces, enhanced tide-raising forces result. Tides produced at these times are called spring tides. Since the lunar orbit is elliptical in shape, once each revolution the Moon also attains its closest monthly approach to the Earth, a position known as perigee. Ordinarily, the passage of the Moon through perigee and the alignment of Moon, Earth, and Sun at new moon or full moon (either position being called syzygy) do not take place at the same time. Commensurable relationships between the lengths of the synodic and anomalistic months do, however, make this possi- ble. On the relatively infrequent occasions when these two phenomena occur within \){ days of each other, the resultant astronomical configuration is de- scribed as perigee- syzygy, and the tides of increased daily range thus generated are termed perigean spring tides or, simply, perigee springs. Whenever such alignments between perigee and syzygy occur within a few hours or less of each other, augmented dynamic influences act to increase sensibly the eccentricity of the lunar orbit, the lunar parallax, and hence also the orbital velocity of the Moon itself. Such solar-induced perturbations also reduce the Moon's perigee distance in each case by an amount which is greater the closer is the coincidence of alignment between these two astronomical positions, but which also fluctuates with other factors throughout the years. The tide-raising force varies inversely as the cube of the distance between the Earth and Moon (or Sun) . On certain occasions, lunar passage through perigee involves a particu- larly close approach of the Moon to the Earth. To distinguish these cases of unusually close perigee, the new term "proxigee" has been devised, and the associated tides of proportionately increased amplitude and range are designated as "proxigean spring tides." Evidences presented in this technical monograph indicate that the appreci- ably enhanced influences on the tides produced at the time of proxigee-syzygy are revealed, not so much in increasing the height of the tide (usually a maximum increase of about 0.5-1 foot above mean high water springs) but in accelerating the rate at which these augmented high waters are reached. This accelerated growth rate in the height of the tides, together with an increased horizontal current movement, creates a sea-air interface situation particularly susceptible to the coupling action of surface winds. Although the perigean spring tides do not, of themselves, constitute a major flooding threat to coastlines, friction be- Abstract tween strong, persistent, onshore winds and the sea surface can raise the astro- nomically produced tide level to cause extensive flooding of the coast in low- land regions. In addition, at the times of perigee- (proxigee-) syzygy, various dynamic influences combine to lengthen the tidal day, increasing the period within which the enhanced tide-raising forces, effective for some few days on either side of the perigee-syzygy alignment, can exert their maximized effects. In this monograph, covering a 341 -year period of history relative to the coastal environment of North America, a large number of examples of major tidal flooding produced by the combination of the above causes have been collated to provide a detailed case study. A composite table of 100 such cases, including all pertinent astronomical and meteorological source data, has been compiled. Graphic, textual, and mathematical analysis have been used to demonstrate the individual astronomical, oceanographic, meteorological, hydro- graphic, climatological, and hydrological influences which are involved during the production of the phenomenon commonly referred to as a "storm surge." Quantitative correlations between these various factors have been established. A proposed new index of tidal flooding potential based upon the combina- tion of astronomical influences augmenting the tides at the times of perigee- syzygy and known as the Au-syzygy coefficient has been developed. This has been combined with other physical quantities representative of the local and prevailing tidal, meteorological, and hydrographic circumstances to establish a second index known as the n factor. The latter term is designed to provide a quantitative measure of the probability of tidal flooding occurrences along a lowland coast- line, should strong, persistent, onshore winds coincide with perigean spring tides. In contrast to the traditional method which involves a simple consideration to the highest tides of the year to determine flooding potential when such tides are accompanied by strong onshore winds (a procedure which can be shown to be both ambiguous and erratic in numerous instances), the combination of the Aw-syzygy coefficient with appropriate meteorological indicators is demonstrated to be an effective new tool for the evaluation of tidal flooding potential at coastal stations having a daily tidal range of 5 feet or more. The usefulness of this method can be further enhanced by future empirical refinements. The particular vulnerability to tidal flooding exhibited by those perigean spring tides which possess a sharply accelerated rate of growth is one of the primary points of consideration in this monograph, inasmuch as the graphical- analytical methods applied do not appear elsewhere in scientific literature. Separate methods for obtaining a meaningful rate of tide growth in the case of both semidiurnal and mixed tides are shown. Such rate-of-growth tide curves are presented for actual cases of tidal flooding occurring over a wide range of latitudes, on both the east and west coasts of North America. These specially analyzed instances of coastal flooding are randomly chosen throughout all months of the winter storm season for a wide range of stations and are distributed, in each decade, over 80 years of record to permit a scientifically representative basis of correlation between the circumstances of tidal flooding and associated astronomical and meteorological data. Numerous examples of perigean spring tides accompanied by nearly simultaneous tidal flooding on both the Atlantic Abstract and Pacific coasts — and other floodings displaying a definite relationship to various astronomical cycles of perigee-syzygy — are included. The observed and predicted hourly height tide records for selected cases of tidal flooding are compared to show the separate effects of astronomical and wind actions. A selection of daily synoptic weather maps matching the incidents of tidal flooding is used to demonstrate the contributing influence of strong onshore winds ; an equal number of cases of nonflooding on occasions of perigean spring tides which were not enhanced by strong onshore winds is included to emphasize this necessary meteorological accompaniment. Supported by such winds, the far greater coastal flooding potential of perigean spring tides compared with ordinary spring tides or other tidal situations — often exceeding the inundating effects of hurricanes — is clearly pointed out. The always devastating effects of the combination of a hurricane with perigean spring tides is also discussed. Selected cloud-cover photographs made from weather satellites near the time of flooding perigean spring tides are incorporated in the treatise to reveal the exact atmospheric frontal conditions and disposition of each low pressure center responsible for strong onshore winds. In the preliminary chapters, which trace the effects of perigean spring tides upon nautical history, navigation, marine engineering, and marine science, the various practical, economic, environmental, and ecological influences of these tides are outlined. This evaluation includes the combined effects of the elevated high waters, their corresponding low-water extremes, and the accompanying accelerated flood and ebb currents. In the final chapter, various other possible geophysical effects related to the phenomenon of perigee-syzygy and the increased gravitational forces producing perigean spring tides are discussed. Part I — Background Aspects Chapter 1. Representative Great Tidal Floodings of the North American Coastline ITTLE did our colonial forefathers know that, dthin 5 years after they settled in Massachu- setts Colony early in 1630, their New World home would be beset by disaster involving two natural forces of a type with which they had no previous experience, but whose enormously destructive influences upon life, limb, and property they and subsequent genera- tions would have occasion to witness repeatedly through- out ensuing years. This first recorded coastal flooding of catastrophic proportions on the American continent hap- pened in the fall of 1635. Like other early incidents of this type, it has never been thoroughly analyzed from the stand- point of its complex natural origins. Although purely meteorological factors are commonly given as the cause of such coastal flooding phenomena, certain specific astro- nomical tide-raising forces of periodic nature are also def- initely involved, whose specific contribution will form the subject of the present study. The Evidences From History William Bradford, author of History of Plimoth Plan- tation, wrote dramatically of the impact of this early coastal flooding event which occurred on August 14-15, 1635, Old Style Calendar.* A portion of his narrative follows : "This year the 14 [24] or 15 [25] of August (being Sat- urday) was such a mighty storm of wind and raine as none living in these parts, either English or Indians, ever saw. Being like (for the time it continued) to those Hurri- canes and Tuffoons that writers make mention in the Indies. It began in the morning a little before day, and grue not be [sic] degrees, but came with a violence in the beginning, to the great amasmente of many. — It con- tinued not (in the extremities) above 5 or 6 hours, but the violence began to abate. The signes and marks of it will remaine this 100 years in these parts wher it was sorest." 1 An additional account of this great coastal storm and accompanying tidal flooding in colonial New England appears in a contemporary work by Nathaniel Morton titled New England Memorial in which the event likewise is described as a disaster-causing one that : ". . . blew down houses and uncovered divers others; divers vessels were lost at sea in it, and many more in extreme danger. It caused the sea to swell in some places to the southward of Plymoth, as that it arose to 20 feet right up and down, and made many of the Indians to climb into trees for their safety ... It began in the southeast, and veered sundry ways, but the greatest force of it at Plymoth, was from the former quarter, it con- tinued not in extremities above 5 or 6 hours before the violence of it began to abate; the mark of it will remain this many years, in those parts where it was sorest; the moon suffered a great eclipse 2 nights after it." ~ [At 9 :49 p.m., 75° W.-meridian time, on August 27.] Case No. 200 — Perigean Spring Tides (near the time of a total lunar eclipse). The last statement is that which has been generally overlooked in previous accounts, attributing the flooding entirely to winds. As noted in footnote (c), on page 7, a For the purpose of exact comparison of astronomical, tidal, and meteorological events in the historical portion of this work, all dates given in the Old Style or Julian Calendar must be corrected by the addition of 10-11 days to give the corresponding date in the New Style or Gregorian Calendar, our present usage. The New Style date is indicated in square brackets following all such early dates quoted. Some of the cases of coastal flooding under discussion occurred prior to 1752. In this year, a change was made in England and through- out the British Colonies (including America) from the Julian Calendar (Old Style) to the Gregorian Calendar (New Style). This change came about from practical necessity. By the 16th century, because of an astronomical phenomenon known as "precession of the equinoxes," the difference between the Julian Calendar year, invented by the Alexandrian astronomer Sosigenes, and the period of the Sun's apparent annual movement with respect to the vernal equinox amounted to 10 days. Contin- uing divergence threatened to throw out the existing alignment between the calendar months and the seasons. It therefore became necessary to drop 10 days from the Julian Calendar, and by a new system of accounting for Leap Years, to convert from the Julian Calendar to the Gregorian Calendar, (cont. on next page) Superior figures refer to sources listed at end of book. 202-509 0-78-3 Strategic Role of Perigean Spring Tides, 1635-1976 the same alignments of Sun, Earth, and Moon responsible for either solar or lunar eclipses b provide a geometric re- inforcement of the gravitational forces of the Moon and Sun and thereby also augment the tide-raising forces pres- ent. The tidal forces are also sometimes further amplified by a special proximity of the Moon to the Earth resulting from such alignments. What the inhabitants of the Massachusetts Colony did not know was that this great coastal storm very nearly coincided in time with another phenomenon of nature — the astronomical condition known as perigee-syzygy (see page 5 under "Technical Commentary"). In this phe- nomenon, the average between the exact time of full moon and that of the Moon's closest monthly approach to the Earth occurred between August 28 and 29 (Gregorian Calendar), within 2 days of the maximum intensity of the storm. With a significance which will appear in later discussions (see chapter 7), the separation in time be- tween perigee and syzygy on this occasion also was less than 42 hours. This comparatively small difference in time between perigee and syzygy is an indication of the com- bined, nearly coincident application of the tide-raising forces of the Sun with those of the Moon — the Moon being at its monthly position of closest approach to the Earth, and in addition being brought by solar dynamic influences to an even smaller separation from the Earth. In consequence of these enhanced gravitational forces, tides possessing an exceptionally great rise and fall known as perigean spring tides were produced. Subject to the simultaneous action of strong, persistent, onshore winds (serving to reinforce water movement toward and onto the land), severe tidal coastal flooding was a near- certainty. With onshore winds prevailing from southern Massachusetts through Maine to Cape Sable, Nova Scotia, together with exceptionally high astronomical tides, their combined effects were felt over this entire region in severe coastal flooding and extensive damage. At Buzzards Bay, and Providence, R.I., the tides reached heights of 20 ft. With consideration to all related factors, and in main- taining a proper perspective between the combined astro- nomical and meteorological forces responsible for coastal flooding, it is necessary that the meteorological conditions at this time be carefully documented. Governor John Winthrop of the Massachusetts Colony also kept a journal in which, under the date August 16 [26], he cites the meteorological conditions prevailing at the time and notes that, at midnight of this date, a mod- erate southwest wind of the previous week changed sud- denly to a violent northeast gale. He states that the force of the storm was sufficient to destroy houses in Boston, and to separate the cables of ships in the harbor. The strong gale blew steadily off the water for 8 hours, fur- ther heightening the evening high tide, and then shifted as abruptly to the northwest, now blowing offshore. In his diary account, corresponding to the Gregorian Calendar date August 26, Winthrop relates: "About eight of the clock the wind came about to N.W. very strong, and it be then about high water, by nine the tide was fallen about three feet. Then it began to flow again about one hour and rose about two or three feet, which was conceived to be that the sea was grown so high abroad with the N.W. wind, that, meeting with the ebb it forced it back again." 3 The impeding and forced backing up of the outgoing (ebb) tide by the next succeeding incoming and wind- driven (flood) tide resulted in two high tides within far less than a 1 2-hour period — in itself an unusual phenom- (cont. from preceding page) Although this Gregorian or New Style Calendar was adopted throughout most of the Roman Catholic countries in 1582, Protes- tant countries held out, and only in 1752 (because of the steadily increasing time difference) England and her colonies dropped 11 days from the calendar previously used. In comparing dates prior to 1752 with dates on the modern Gregorian Calendar, the difference must be allowed for, and results from the somewhat different pro- cedures used in determining those century years which are Leap Years under the two systems. In the Julian Calendar, all century years divisible by four are regarded as Leap Years. According to the Gregorian Calendar, only those century years divisible by 100 which are also divisible by 400 (or whose first two digits are divisible by four) are considered to be Leap Years. Thus, in the Julian Calendar, 1600, 1700, 1800, and 1900 are all Leap Years. Subsequent to the change in 1752, the difference between the two systems had increased to 12 days by 1800 and 13 days by 1900. However, in chapter 1, only Julian Calendar dates occurring be- tween March 1, 1500 and February 18, 1700 (requiring a 10-day correction) and between February 19, 1700 and September 3, 1752 (requiring an 11-day correction) overlap the computer printout of table 16. Since the latter dates are given in the New Style Calendar, either 10 or 11 days must be added to the Old Style dates to con- vert them to this Gregorian system. The fact that, prior to the year 1752, the calendar year in England and her colonies also began on March 25 rather than January 1, as thereafter, also accounts for the usage of a dual year in conjunction with dates prior to 1752, where the period January 1-March 25 is involved (e.g., February 24, 1722/23). b In Theodor Ritter von Oppolzer's Canon der Finsternisse (1887) all eclipses of the Sun between 1207 B.C. and A.D. 2161 and lunar eclipses between 1206 B.C. and A.D. 2163 are cata- loged together with pertinent astronomical data. This lunar eclipse of August 1635, the midpoint of whose total phase occurred at 0249 G.c.t. on August 28 (New Style Calendar), is listed as having a magnitude of 18.1 on an arbitrary 22.8-point scale repre- senting maximum central totality. This value indicates a well- centered eclipse, with the Sun and Moon in closely opposite (gra- vitationally reinforcing) longitudes and declinations. The tidal forces would be augmented in proportion. Representative Great Tidal Floodings of the North American Coastline enon and, as will be discussed in later instances, one very conducive to tidal flooding (e.g., ch. 7 "Meteorological Aspects . . .," case 4. The sequence of wind shifts noted by John Winthrop was from southwest (for a week) to a strong northeast gale — at midnight of August 16 [26] — swinging around to a strong northwest wind — at 8 a.m. on August 17[27]. He adds that the morning high tide was depressed 3 feet in 1 hour by this strong offshore wind. The storm is described as being felt as far north as Cape Sable, Nova Scotia, but possessing maximum strength south of Boston. William Bradford suggests its similarity to hurricanes and "tuffoons" of the Indies. This violent storm is, indeed, in- cluded among a list of hurricanes occurring historically on the east coast of the United States. 4 So-called "storm-surges" and coastal flooding associated with hurricanes have been widely treated in the scientific literature from a meteorological standpoint (see Bibli- ography) and will not, therefore, be extensively discussed in this work. Hurricanes possess sufficiently strong wind velocities to cause coastal flooding, in varying degrees, at any phase of the tides — although, as will be seen in sub- sequent comparisons between various types of hurricanes involved in coastal flooding, wind damage is of greater consequence where astronomically induced high tides are not an immediate accompaniment. The present and a few subsequent examples are included to show the extent to which the tidal flooding influence of a hurricane may be further augmented by coincidence with a perigean spring tide to produce coastal inundation (in addition to wind damage) of extremely disastrous and destructive propor- tions. The extensive tidal flooding damage experienced in Massachusetts, Rhode Island, and Connecticut in 1635 is a typical example. This strong tidal flooding is the first which was made a matter of record in American history , but was by no means the last, as attested to by subsequent, similarly documented examples. The additional flooding potential resulting from the combination of a hurricane with perigean spring tides — and the extremely hazardous effects of the combination of perigean spring tides with severe coastal storms in winter — are evaluated, in their relative significance, in chapter 7. It is an observed fact that a fast-moving hurri- cane does not usually provide as much time for a buildup of water level by friction at the air-sea interface as does a stagnant, offshore extratropical storm possessing a long overwater wind path. By contrast, the special setup condition provided by perigean spring tides which occur as a protracted, height- ened water-level condition coincident with onshore winds has been shown in contemporary accounts of the 1635 coastal flooding event. Under the action of strong, sus- tained, onshore winds, the previously mentioned backup of water between successive high tides ( occurring as a new flood tide comes in before the preceding ebbtide has had an opportunity to recede) provides a natural condition for land flooding. In an actual recorded circumstance more than 325 years later, this fact was clearly substantiated by the great east coast flooding of 1962, whose intervening low tides were built up by sustained onshore winds to be- come effective high tides (see chapter 7, Case 4) . The preceding 1635 example typifies a case of coastal flooding occurring largely as the result of hurricane-force winds acting upon astronomically augmented tides, which in turn played a very significant role in the extent and severity of the flooding. In the following treatise dealing with coastal flooding produced by onshore wind effects acting on the higher- than-usual waters of perigean spring tides, primary con- sideration v/ill be given to those cases of coastal flooding associated with winter storms. In addition, although meteorologically oriented param- eters are duly considered in all examples given, it will be the principal purpose of this volume dealing with peri- gean spring tides to analyze the astronomical causes con- tributing to severe coastal flooding. It is these astronomi- cal circumstances forming the principal thesis of this work with which the discerning reader should gradually become familiar. To permit appropriate emphasis on the astro- nomical forces present, the various factors creating a setup condition of unusually rapidly rising tidal waters, upon which sustained onshore winds act to produce coastal flooding will, therefore, be introduced, one by one, throughout the remaining historical examples. Signifi- cantly, these involve, in several cases, a winter storm situa- tion familiarly known today throughout New England as a "nor 'easier." Because the fundamental astronomical causes for the high tides which lend themselves to coastal flooding are twofold in nature, the circumstances and tide-raising forces resulting from the simple phase alignment of Moon, Earth, and Sun at syzygy will be considered first, followed by a discussion of the combined astronomical perigee- syzygy relationship which adds appreciably to the bi- monthly syzygian tide-raising forces. In this historical sec- tion — as in part II, throughout the scientific portions of the text — supplementary technical analyses and explana- tory footnotes are included for those interested in greater detail. Strategic Role of Perigean Spring Tides, 1635-1976 Technical Commentary Although the scientific discussion of the cause and effect of perigean spring tides will be reserved for part II, a brief introduction to the phenomenon of perigee-syzygy necessary .to an understanding of its flood-producing potential will be included in this present chapter, couched in descriptive terms, and pointing up the relationship with various his- torical cases of coastal flooding. Such a technical explanation is incorporated in the following 3-page section, supplement- ing the main text and subordinated in smaller type. The reading continuity of the main text is thereby preserved. The astronomical tides are produced solely by the gravita- tional attractions of the Moon and the Sun acting upon large bodies of water. Twice each month, at new and full moon, the Moon and Sun in their respective real and ap- parent revolutionary motions with respect to the Earth, come into direct alignment with the Earth in celestial lon- gitude (see figs. 1-2). In this relationship, the Moon may either lie along a straight line connecting the Earth and Sun, between the Earth and Sun (at new moon or conjunction) or on the far side of the Earth from the Sun (at full moon or opposition). If, in either case, the Moon simultaneously crosses the plane in which the Earth revolves around the Sun, or comes within a limiting angular distance thereof, a solar or lunar eclipse also must take place. However, these events occur, on the average, far less often. The alignment of the Sun and Moon with the Earth in celestial longitude occurs twice in each period of 29.53 days. The resulting combination of gravitational forces of the first two bodies creates higher-than-average tides on the Earth. Either of these two positions of alignment between Earth, PERIGEE-SYZYGY ALIGNMENTS DURING 1974 PRODUCTIVE OF PERIGEAN SPRING TIDES Earth at perihelion January 4, and at aphelion July Inclination of moon's orbit to ecliptic = 5°9' SUN 8=--16 / FEBRUARY 6 FULL MOON 6 , = + 17° SUN 5= -22° J\ JANUARY 8 FULL MOON ff=+21 EARTH'S ORBITJ* EARTH, MOON, AND SUN IN DIRECT ALIGNMENT ON ALL FOUR DAYS (within 1° of longitude in each case) JULY 19 NEW MOON &= +20° SUN G=+21° AUGUST 17 NEW MOON S = +13 c SUN S = +14° Figure 1. — A typical series of close perigee-syzygy alignments occurring in the year 1974. Earth and Moon reach syzygy alignment with the Sun (i.e., at new or full moon) very nearly at the same time the Moon reaches its position of perigee (closest monthly approach to the Earth). The mutually reinforcing gravitational attractions of the Moon and Sun, combined with that of the Moon at its close approach, considerably enhance the tide-raising forces on the Earth's oceans. Representative Great Tidal Floodings of the North American Coastline PERIGEE-SYZYG1 DIRECTION OF MOON'S ORBITAL MOTION APOGEE-SYZYG\ Figure 2A. — Syzygy alignment of Moon and Sun at new moon, with the Moon between Earth and Sun. A near- coincidence of perigee and syzygy can also occur at full moon (fig. 2B). IPOGEE-SYZYG1 SUN S APPAREI THE MOON S ORBITAL VELOCITY ! IS DETERM INED BY ITS DISTANCE FROM THE EARTH AND KEPLER S LAW 1 OF EQUAL AREAS DIRECTION \ OF EARTH'S V- REVOLUTION EARTH & i PERIGEE \ FASTER ANGULAR VELOCITY AND GREATER ORBITAL MOTION OF MOON AT PERIGEE Figure 2B. — Revolution of the Moon around the Earth in an ellipse brings it to perigee each anomalistic month, averaging 27.555 d . It then reaches maximum orbital velocity. Moon, and Sun in celestial longitude is called syzygy (pro- nounced 'siz-3-je) and the increased tides thus produced are called spring tides (which refers to their behavior as they "well" or "spring" up — not to the season of the year) . The Moon revolves monthly around the Earth in an orbit which is slightly "out-of-round," or eccentric, with the Earth occupying one of the two foci (C in fig. 2A) of the geometric ellipse thus produced, and located slightly to one side of its center, (O).At least once a month also (the 27.55-day revo- lution period can actually allow two occurrences in a calen- dar month), as the Moon revolves in this elliptical orbit, it reaches its position of closest approach to the Earth, known as perigee (P) . Generally, the individual phenomena of perigee and syzygy do not coincide in time but, due to numerous approximately commensurable relationships between 29.53 and 27.55, the two events can approach each other within various intervals of close agreement. When this happens, the additional rein- forcement of gravitational forces caused by (1) the solar- lunar alignment and (2) the concurrent proximity of the Moon to the Earth produces .tides whose high- and low-water phases are even more pronounced than those associated with spring tides. The increased tides thus created are termed perigean spring tides. Much less frequently — on the average not more than once in about one and one-half years — the Moon, which is the greatest single influence on the tides, moves into a perigee position which, as the result of additional dynamic influences diminishing the distance of the Moon from the Earth, lies especially close to the Earth. For purposes of distinction in tidal discussions throughout the present work, such a particu- larly close perigee position of the Moon with respect to the Earth, hitherto unnamed in astronomy, will be termed a proxigee, and the especially amplified type of tide produced as this condition coincides with syzygy will be called a proxi- gean spring tide. Such especially close (proxigean) distances between the Moon and the Earth always coincide with a very small sep- aration in time between perigee and syzygy. This results (see part II, chapter 3) in a combination and interaction of the gravitational forces of the Sun and Earth in a manner to change slightly and transitorily the shape of .the Moon's orbit. Because of a dynamic perturbation in the lunar orbit known as "evection," the Moon at perigee-syzygy draws even closer to the Earth than at its ordinary perigee position and recedes to a greater distance from the Earth at apogee, ap- proximately 2 weeks later. The tide-raising force varies in- versely as the cube of the distance between the Earth and Strategic Role of Perigean Spring Tides, 1635-1976 the Moon. Accordingly, as a further immediate consequence of this closer approach of the Moon to the Earth at proxigee, increased gravitational forces come into play which, in turn, augment the .tide-raising influence exerted by the Moon upon the Earth's major water bodies. The progressive buildup of these gravitational forces toward an increasingly significant tide-producing role is treated in successive stages in part II, chapters 3-6. For various reasons, among which are the discrete reso- nance responses of each individual ocean and portions of these oceans to tide-raising forces, the inertia of the moving water mass, friction with the ocean floor, internal viscosity of the water, and the imposition of continental land masses, the maximum heights attained by perigean spring tides do not always coincide exactly with the times of maximum attain- ment of the forces which produce them. As will be brought out in later chapters, two of these very important delays are known as the phase age and parallax age. These various combinations of astronomical forces acting upon the ocean waters, when taken together with supporting meteorological circumstances, may exert a very practical in- fluence in causing flooding and erosion of, and other dam- age to, the coastal environment. The associated impact of such coastal zone changes upon human affairs will become increasingly evident throughout part I, chapters 2-4. If the high-water phase of either the perigean spring or proxigean spring tides occurs while a strong, persistent, on- PERIGEAN SPRING TIDES MAY BE CONDUCIVE TO COASTAL FLOODING NORMAL TIDES HIGH PERIGEAN S^JLme** SPRING TIDE " Figure 3. — Strong, persistent, onshore winds may create tidal flooding on low coasts, as friction between wind and sea lifts amplified perigean spring tides onto the land. shore wind is blowing (fig. 3), a major coastal flood in low- lying areas is almost inevitable. A nonfrozen condition of the surface waters in large bays or the near-shore region is, of course, assumed in this connection. It has been found that over 100 cases of major coastal flooding associated with these conditions have occurred on the North American coastline in the past 341 years. Such a strong, sustained, onshore wind, which tends to pile up the waters along the coast and en- hance the effect of the already high, astronomically produced tides, is an essential ingredient for coastal flooding. Conversely, a continuous, strong, offshore wind tends to lower the tidal water level and to negate the effects of a perigean spring tide. The atmosphere and the ocean act together like an inverted barometer. As .the atmospheric- pressure rises, the water level goes down; as the atmos- pheric pressure diminishes, the water level rises. The adjust- ment in ocean level in either direction is approximately 13 inches for each change of 1 inch in barometric pressure. Only lowland coastal regions and those with a sufficiently large daily range between high and low phases of the tide are subject to the flooding effects noted. (The combined condi- tions of perigee-syzygy add about 40 percent to the tidal range.) Thus, the entire coast of the Gulf of Mexico and much of the southeastern coast of the United States are ex- cluded from this particular influence, except during hurri- canes. Hurricanes possess sufficient wind velocity to lift even relatively shallow waters onto the land. As a result of the continuous frictional effects made possible by the large-scale movement of wind over the surface of the water (the lateral extent of this overwater wind movement is known as the "fetch"), a hurricane passing even well off the coast and producing a strong swell which impacts a low shoreline can cause coastal flooding. In the case of the coastal storm system of August 24-26, 1635, it is difficult because of the ensuing lapse of time — and lacking either manuscript or published weather data — to know whether this system persisted as a true tropical storm originating from energy provided by warm tropical waters, or was partially modified by a contrast of atmospheric air masses in extratropical latitudes. While seemingly maintain- ing — as indicated in the several descriptive accounts avail- able — its basic identity as a true hurricane, nevertheless at this high latitude of occurrence it may possibly have taken on some of the characteristics of an extratropical storm, such as were instrumentally recorded and plotted on the synoptic weather map, 303 years later, during the great New England hurricane of September 21, 1938. s This hurricane began as a tropical storm of comparable intensity and possessed a similar northward movement along the Atlantic coast to New England, accompanied by strong, onshore winds. It was separated by 1 day from the mean epoch of an only approximate perigee-syzygy situation. The corresponding separation between perigee and syzygy was — 69 hours. The flood waters raised at Providence, R.I., in this instance were 18.3 ft above mean low water, compared with approximately 20 ft at the closer perigee-syzygy align- ment accompanying the storm of August 24-26, 1635. Representative Great Tidal Floodings of the North American Coastline Case No. 4 — Perigean (Proxigean) Spring Tides (t = 61'27.0", P-S=-6 h ) At approximately 7 o'clock in the evening, 75°W.- meridian time, on Saturday, February 23, 1722/23 O.S. [March 6, 1723] the Moon in its monthly revolution around the Earth reached a position of direct alignment with the Sun in the angular reference system known in astronomy as celestial longitude. The result was the familiar phenomenon of new moon, d which happens once each month and is of no unusual consequence. As an astronomical occurrence which preceded this one by only 6 hours on the same date, the Moon also passed through its position of closest monthly approach to the Earth, known as perigee — again a regular monthly happening, and by itself of no special significance. However, the near- coincidence of new moon and perigee is of particular sig- nificance. In the combination of these two events, a far less common astronomical circumstance occurred, which was made the more meaningful by the simultaneous, un- usually close proximity of the Moon to the Earth. In the orderly astronomical cycle of events which govern and alter both the distances and motions of the Moon, such a condition of close agreement between the time of the closest monthly approach of the Moon to the Earth (perigee) and the alignment of Earth, Moon, and Sun responsible for the production of a new moon or full moon (either alignment being called syzygy) is termed, appropriately, peri gee -syzygy. The resulting forces created are manifest by their action in producing, within the Earth's tidal waters, the phenomenon of perigean spring tides. On the east coast of the United States, the normal lag time between the occurrence of such a combined astro- nomical event and the resulting perigean spring tides pro- duced is approximately 1 to \ l / 2 days. As it happens, therefore, the force-amplified perigean spring tides which occurred, on February 24 (Old Style Calendar), 1722/ 23, one day after the perigee-syzygy date of February 23, very nearly coincided with the arrival of a very strong coastal storm on the east coast of New England. This storm — although of extratropical origin (i.e., formed out- side of the normal tropical region of hurricanes) — rapidly approached the wind velocities associated with such a tropical disturbance and sent strong, sustained, onshore winds lashing for many hours against the coastlines of Massachusetts and New Hampshire. The ensuing ca- tastrophe was described, in the somewhat colorful lan- guage of the period, in a report by the contemporary American cleric-scientist-philosopher, Cotton Mather, to the Royal Society of London : ". . . It was Feb 24, 1723, when our American phi- losophers observed an uncommon concurrence of all those causes which a high tide was to be expected from. The moon was then at the change, and both sun and moon together on the meridian. The moon was in her perigee, and the sun was near to his having past, [i.e., the closest distance between moon and sun, occurring about January 4] . . . finally the wind was high and blew hard and long . . . Then veering eastwardly it brought the eastern seas almost upon them [these shores] . . . They raised the tide unto a height which had never been seen in the memory of man among us . . . The City of Boston par- ticularly suffered from its incredible mischiefs and losses . . ." G It is significant that without actually being given the name perigee-syzygy, all of the requisite conditions for a close occurrence of this phenomenon were present : ". . . moon was then at the change (new phase) ; . . . moon was then in her perigee ; . . . sun was near to his having past." The Boston News-Letter of that time reported that ". . . the inundation in Boston looked very dread- c Definitions of many of the astronomical and tidal terms used in this publication will be found in the appendix and in part II, chapter 1. To avoid any ambiguity in meaning possible through overgeneralization, extreme caution must be exercised in the exact specification of terminology even in this nontechnical introduction. Thus, for the phenomena of new moon or full moon to occur, only the celestial longitudes of the Moon and Sun need be the same. However, if, at the time of full moon, the Moon's longitude is between 9°30' and 12° 15' of one of the two positions (the so- called "nodes") where, twice each month, the Moon crosses the orbital path of the Earth around the Sun (the "ecliptic") the Moon will also be aligned (within the diameter of its disc) with the Earth and Sun in celestial latitude and a total lunar eclipse will occur. Similarly, at new moon, if the Moon is within 9°55' and 1 1 °50' of one of these same nodes, a central (total) eclipse of the Sun will take place — or, if the Moon is then beyond a certain limiting dis- tance from the Earth, an annular eclipse of the Sun will result. As indicated earlier, a total eclipse of the Moon followed within 2 days of the August 24-26, 1635 coastal flooding event. The conditions of this eclipse resulted in a faster apparent motion of the Moon, a shorter (relative) duration of the eclipse, and a greater duration of the lunar and tidal days (see chapter 6) in addition to more closely aligned tidal forces of the Moon and Sun. ''As previously noted, such an alignment in longitude (or, alter- natively, right ascension) between Sun, Earth, and Moon at either new moon (conjunction) or full moon (opposition) is known in astronomy as syzygy (from the Greek syn "together" and zygon, "yoke"). At conjunction, lost in the glare of the Sun's rays, the new moon is actually invisible to the eye ; too often, people associate the slim crescent appearing immediately before or after the new moon with this descriptive term. a Strategic Role of Perigean Spring Tides, 1635-1976 ful . . . the tide rising to a height of 16 ft ... At Hampton, New Hampshire, the storm caused the great waves of the full sea to break over its natural banks for miles together, and the ocean continued to pour its water over them for several hours." 7 With the causes of such coastal flooding now firmly established, additional important historical examples will be considered in terms of their efTects only, without ex- planatory comments. # * * # * Case No. 7 — Perigean Spring Tides (P-S=-17 h ) A similar severe coastal storm struck Boston and New England on December 4-5 (New Style), 1786. Strong onshore winds again acted upon perigean spring tides resulting from the combination of a lunar perigee reached at 2 p.m. in the afternoon of the 4th, local time, and a full moon occurring 18 hours later. As reported in The Boston Gazette and The Country Journal for December 11,1 786 : ". . . The wind at east, and northeast, blew exceeding heavy, and drove in the tides with such violence on Tues- day, as overflowed the pier several inches, which entering the stores on the lowest parts thereof, did much damage to the sugars, salt, etc. therein — considerable quantities of wood, lumber, etc., were carried off the several wharfs . . ." 8 This great coastal storm, which became known as the December Gale of 1786 — with its associated tidal flood- ing — also was accompanied by subfreezing conditions, and left a 5-6 ft snowfall throughout New England. As the direct cause of numerous cases of drownings and ship- wrecks, it was long remembered as one of New England's worst tidal flooding disasters. 9 ***** Case No. 8 — Perigean Spring Tides (P-S = + 10") Perigean spring tides produced under similar circum- stances (a perigee-syzygy configuration centered around 2 p.m. in the afternoon, local time, on March 24) reached their peak on March 25, 1830. Their flooding potential became manifest the next day when : "A cold, northeast storm of wind, rain and snow raged along the coast of New England . . . producing a great tide, which in some parts exceeded the highest tide re- membered there. The storm began on the morning of Friday, the twenty-sixth, and continued till one o'clock in the afternoon, the tide being at its height at noon of that day. "At Portland, Me., several wharves were carried away, and many vessels lost their fastenings, some being driven on shore and others greatly damaged by being beaten against the wharves . . . 'At Portsmouth, N.H. wharves were injured and sev- eral vessels driven ashore . . . "At Gloucester the water was two or three feet deep on the wharves, and much movable property was washed away, the waves being covered with articles and debris of all kinds . . . "The tide rose at Boston one and one-half inches higher than the great tide of December, 1786, which was ten inches higher than the highest that any person then living remembered. The water broke through the dam along the Roxbury canal . . . sweeping away fences and out- houses, and prostrating buildings. "Much property was set afloat at Charlestown and Cambridgeport. The navy yard was overflowed, and the tide broke through the coffer-dam, about three feet of water coming into the dry dock." 10 ***** Case No. 13 — Pseudo-Perigean Spring Tides (P-S=-53 h ) Between the 14th and 16th of April 1851, a severe case of tidal flooding occurred as a result of an event which has come to be known as the "Minot's Light Storm" — since this famous lighthouse of Boston's Outer Harbor was temporarily destroyed as a result. The associ- ated tidal contribution to coastal flooding provides an example of a type later to be described in this volume as a pseudo-perigean spring tide (i.e., having characteristics generally similar to, but — for lack of an equal gravita- tional force acting — not precisely the same as, those of a perigean spring tide). In this case, the two elements con- cerned, perigee and syzygy, were more than 36 hours, but less than 84 hours apart — the arbitrary limits set as a terminology standard throughout this case study. With perigee occurring at 1 o'clock in the afternoon (local time) of April 13 and full moon at 6 p.m. on the 15th, the gravitational forces of Moon and Sun were not united to the fullest possible extent as when these condi- tions occur within less than a day of each other. How- ever, coupled with a strong, sustained, onshore gale — one of the severest of the century — the tidal flooding potential became extremely high. A vivid account of the disaster has been given in Sidney Perley's book, Historic Storms of New England: "It [the storm] commenced at Washington, D.C. on Sunday [the 13th], reached New York Monday morning, and during the day extended over New England . . . The Moon was at its full, and the water having been Representative Great Tidal Floodings of the North American Coastline blown in upon the shores for several days the tide rose to a greater height in many places than was remembered by the people then living. It swept the wharves and lower streets like a flood, and at Dorchester, Mass., rose nearly seven feet higher than the average tide . . . "On all parts of the coast where the northeast wind could exert its force the tide rose over the wharves from one to four feet. At Provincetown, on Cape Cod, many wharves and salt mills were swept away; and in several places people left their houses, which were flooded, water being six inches on the lower floors in some of them. "At Boston [where the tide averaged 15.62 feet] the water was three or four feet deep on Central and Long wharfs, and the wooden stores on the latter wharf were completely inundated . . . "Deer Island in Boston harbor suffered extensively by the great tide which made a complete breach over the island, covering nearly the whole of it. The sea-wall that had been built there a few years before by the govern- ment was washed away ; and three buildings were carried out to sea, one of them being the school-house . . ." " Excerpted and abridged, in part, from Edward Rowe Snow's work on Great Storms and Famous Shipwrecks of the New England Coast, and somewhat rearranged in terms of the importance of the tidal disaster involved, is the following description of this catastrophe : "The City of Boston actually became an island during the Wednesday high tide as the water swept across the neck, cutting the city off from the mainland completely. On Harrison Avenue the water was four feet deep, and the tide flowed entirely across Washington Street near the corner of Waltham Street. In downtown Boston the waves swept right up State Street, with the area around the Custom House three feet under water . . . Brown Street was partially submerged, the waves continuing up Central and Milk Streets. It is said that Merchants Row was reached by the great tide. The record high tide submerged both the Charlestown and Chelsea bridges ... on Pleasant Beach in Cohasset ... a large three- story hotel was floated right out from its underpinning, with almost a score of guests escaping in time . . . The tide at Dorchester, Mass., rose seven feet higher than usual. . . The boys at Deer Island school . . . were caught in their dormitory with the water steadily rising around them. . . By midnight the water had risen to a height of five feet, and the roof of the building fell in. . . Derby Wharf in Salem was ruined. The railroad track at Collin's Cove and the bridge between Forrester Street and Northey's Point were carried away, and the sea rushed into the tunnel. In Beverly the sea washed over Tuck's Point and over Water Street, while the tide in Gloucester was said to have been the highest in fifty years. . . The passage through Shirley Gut was widened to twice its former size. . . The storm raged all along the coast from New York to Portland, Me. The feeling was general that the storm brought a higher tide and greater gale than any since December 1786. . . Damage to shipping was estimated in hundreds of thou- sands of dollars, while property all along the coast was destroyed. . ." 12 * ■;:- * * *■ Case No. 36 — Near-Ordinary Spring Tides An ordinary spring tide situation in which a moderate 3/ 2 -day proximity to the time of perigee set up an addi- tional potential for tidal flooding occurred on the morn- ing of December 26, 1909, in connection with the so-called "Christmas Gale" of that year. Full moon oc- curred at 4 : 30 in the afternoon on December 26, preceded by perigee at about 4:00 a.m. on December 23, local time, a difference of 84 1 / 2 hours. This is marginal to the maximum separation-interval adopted for a pseudo- perigean spring tide ( 84 hours ) — but the associated tidal flooding took place only some 36 hours from the mean time between perigee and syzygy, computed to be approx- imately 10:00 p.m. on December 24. As will be discussed in note/ table 1, even such a 3 x /i -day proximity between the time of perigee and the time of syzygy (or, more meaningfully, the occurence of a spring tide within l/a days of the mean epoch, or average time between perigee and syzygy) can reinforce, and provide a definite amplitude contribution to, an ordinary spring tide. In every sense of the word, therefore, the spring tide must be regarded as the basic higher-than-usual high tide, to which the effects of a near-coincidence between peri- gee and syzygy are added. The concept of perigean tides standing alone without any contribution from syzygy can only be realized once in any given lunation and during certain nonconsecutive months, when the Moon is simultaneously at perigee and quadrature. The concept of syzygian (spring) tides standing alone without sensible reinforcement from perigee, on the other hand, is valid on twice as many occasions throughout an extended period of time — viz., at those apogee-syzygy positions oc- curring at either new or full moon. The ordinary spring tide is, therefore, more logically the comparative standard for a greater-than-average high tide, upon which the effects of pengee-syzygy are addi- tionally superimposed — rather than the effects of a syzygian tide being thought of as impressed upon those of a perigean tide. 10 Strategic Role of Perigean Spring Tides, 1635-1976 The present case of tidal flooding is an example of the sea surface being raised to comparatively high levels by the joint action of winds and tides (either of which is sub- ject to varying intensities and amplitudes) — a funda- mental principle that will be enunciated many times in the present volume. As reported in the Monthly Weather Review for January 1910: "The morning tide of December 26, 1909, attending the severe storm of this date on the New England coast, was one of the highest ever recorded in Boston Harbor. . . "At Boston Light the predicted time of high tide was 10 : 20 a.m. The wind from the later afternoon of the 25th until nearly noon of the 26th was from the east and north- east over Boston Harbor and Massachusetts Bay, rapidly increasing in force during the evening of the 25th to very high velocities soon after midnight, which continued un- diminished through the morning and day of the 26th. At Cape Cod, Highland Light, the velocity at 8 a.m. of the 26th was 48 miles, northeast [the wind velocities stated are uncorrected values — not adjusted for instrumental error; corrected values are about three-fourths of the values given]; noon, 72 miles; 2:15 p.m., 84 miles; at 5 p.m., 66 miles — all from the east-northeast — and at midnight was 60 miles, north. At Boston the hourly move- ments from midnight to noon of the 26th ranged between 25 and 39 miles, ,the hourly maximum rates between 32 and 45 mph — the latter occurring at 5 : 10 a.m., from the northeast. . . "The increasing and high wind, occurring with the ris- ing tide, together with a high run of tide, caused the water in Boston Harbor to reach approximately the record height of the tide of April 14, 1851 (The Lighthouse Storm), which at the U.S. Navy Yard was 15.0 to 15.1 ft — the height of the tide of December 26, 1909, being, at the same station, 14.98 ft. In general the tide in Boston Harbor and Massachusetts Bay was approximately 3.5 feet above the predicted height. The actual height as given by the U.S. Engineers and other reliable authorities at the following places was as follows: Newburyport, Massachusetts Harbor, Black Rock Wharf, 12.68'; Sand Bay, Rockport Harbor, 13.64'; Boston Harbor, Deer Is- land, 14.56'; Plymouth Harbor, 14.8'; Barnstable Bay, 13.25'; Provincetown Harbor, 14.35'; the tide at all these stations with the exception of Plymouth and Barnstable was approximately 5 feet above mean high water." " -x- -x- -x- -x- # Coastal Flooding As an Ongoing Risk The detailed case-study forming a part of the present research effort shows that the phenomenon of perigee oc- curring either in near-coincidence with, or comparatively close proximity to (i.e., within even several days of), new moon or full moon, has reinforced spring tides on many occasions and in varying degrees down through history. Also, in repeated examples throughout history, perigean spring tides, combined with intense onshore winds, have provided an important source of coastal flooding. Subsequent technical discussions will include an evalua- tion of the increased flood-producing potential of hurri- canes which occur at the same time as perigean spring tides. A proposed intensity scale also will be developed to indicate the comparative degrees of coastal flooding possible from various intensities of onshore wind com- bined with the separate categories of ( 1 ) proxigean spring tides, (2) perigean spring tides, (3) pseudo-perigean spring tides, and (4) ordinary spring tides. In the light of this intensity grouping by classes, the foregoing exam- ples (in addition to their historical significance) have been chosen as being representative of each of these four types of astronomically augmented tides. A more mean- ingful expansion from these few introductory cases is now desirable. Table 1 contains a list of 100 representative examples of major tidal flooding occurring along the North Ameri- can coastlines between 1683 and 1976, associated with the near-simultaneous occurrence of perigean spring tides (as a generic term) and strong, sustained, onshore winds. This list includes, and distinguishes between, cases of proxigean spring, perigean spring, and pseudo-perigean spring tides according to the nomenclatural definitions given in table 22 and the accompanying text. Other representative cases in which landfalling hurri- canes have provided a source of intense winds, resulting in severe coastal inundation in addition to wind damage (and a greater degree of flooding than is experienced in hurricanes occurring at other times than perigee- syzygy) are contained in table 2. Surface synoptic weather maps are included in part II, chapter 7, to match more than 25 cases of tidal flooding. These graphically portray the condition of coastal weather and distribution of the wind pattern at the time the flooding occurred. Because of total space limitations, these examples were chosen at random from the master lists, but include one case in each decade from 1890 to 1970, distributed in latitude from Halifax, Nova Scotia, to Long Beach, Calif., on both the east and west coasts of North America (representing both semidiurnal and mixed tides), in all months from October through April (and with perigee-syzygy separations from ±1 to — 34 hours. Numerous illustrations of the destructive ef- Representative Great Tidal Floodings of the North American Coastline fects of such coastal flooding incidents are also interspersed throughout the latter portions of the text. In this wealth of available previous examples, there is a pattern of recurring significance. On both the At- lantic and Pacific shorelines of the United States, wherever lowland coastal regions exist, perigean spring tides coupled with strong, sustained, onshore winds become an all too frequent harbinger of tidal flooding. On the east coast of Florida, along the coast of the Gulf of Mexico, and at certain other specific coastal locations, as will be seen in part II, chapter 8, limited daily tidal ranges greatly reduce the attendant hazard of tidal flooding except in the case of hurricanes. The most outstanding 20th century example of coastal flooding associated with perigean spring tides, which oc- curred on March 6-7, 1962, will be discussed at length in part II, chapter 7. The more recent tidal floodings, of January 8, 1974 along the southwest coast of Cali- fornia and — allowing for the appropriate tidal delays — 2 to 3 days later along the southwest coasts of England and Wales and on the Islands of Guernsey and Lewis, also will be treated separately in this chapter. Satellite weather photographs revealing offshore cloudcover by day and night (infrared) indicate the frontal and weather patterns that existed during these 1974 incidents of tidal flooding. A further group of cases of coastal flooding which have occurred at times of ordinary spring tides, supported by the necessary wind velocities and varying degrees of proximity to perigee, are listed in table 3. Numerous additional instances of the highest tides of record at various coastal localities are given in table 4. These particular cases were all observed at times of perigee-syzygy, but lacked the simultaneous existence of sufficiently high or sustained onshore winds to cause no- ticeable flooding. A system of scientific controls also has been imple- mented (see table 27 and figs. 70-89), suitable for the analysis of certain cases of strongly potential tidal flooding which failed to materialize. All such cases were associated with a close perigee-syzygy alignment and other astro- nomical tide-raising factors which, although they lifted the water to unusual levels, did not produce flooding. In this control system, an equal number of representative exam- ples has been included for a wide variety of dates and circumstances agreeing in statistical randomness with the cases of active flooding ( table 1 ) in order to provide statistical comparability therewith. As an acid test of principles to be developed in part II, chapters 3-6, they, like the first group of cases, possess properties rendering them especially vulnerable to tidal flooding which, paradoxically, did not occur. As a first and most important consideration, these ex- amples have been chosen on the basis of an extremely small difference between the times of perigee and syzygy (less than 1 to a maximum of 12 hours). Secondly, each has been selected as possessing one or more special features which, in terms of the exceptionally high tides produced thereby, should make the situation one extremely suscepti- ble to tidal flooding. Among these conditions occurring either singly or in combination and contributing in various degrees to the production of exceptionally high tides are : ( 1 ) an un- usually large value of the lunar parallax, indicating an exceptionally close approach of the Moon to the Earth; (2) the location of the Moon directly in the zenith (i.e., at altitude = 90°) ; (3) the position of the Sun very close to solar perigee (around January 1-4 of the year) ; (4) the location of the Moon very near to the vernal or autumnal equinox, around March 21 or September 23, respectively, thus being on the Equator and aligned with the Sun in both declination and celestial longitude; (5) the location of the Moon at, or very near to, one of its nodes (positions of crossing the ecliptic) at the same time the Sun is near this same longitude, resulting in a solar eclipse ( at new moon ) or a lunar eclipse ( at full moon ) ; (6) the new moon being simultaneously at the same high declination, or the full moon at an opposite high declina- tion (in algebraic sign) with the Sun, causing a force alignment in declination as well as an increase in the tidal day; and (7) the presence of the Sun at the summer or winter solstice (greatest annual declination) , increasing its apparent motion in right ascension, and lengthening the tidal day in the same manner as a high declination of the Moon. These various effects will be completely described in part II, chapters 1-4. With such very favorable astronomical conditions add- ing their individual effects to that of the perigean spring tide already present, the immediate question from the standpoint of the premise subsequently advanced (calling for a strong tidal flooding potential under these condi- tions) is why no reported tidal flooding actually occurred. And here again a very definite emphasis must be placed upon the necessity that the two natural forces — astro- nomical and meteorological — work together in close uni- son if tidal flooding is to occur. Neither a powerful offshore winter storm nor an excep- tionally uplifted astronomical high tide — one without the other — can produce the devastating flooding effects abundantly illustrated among the many cases resulting 12 Strategic Role of Perigean Spring Tides, 1635-1976 from the combination of these factors documented in table 5. The considerably augmented astronomical high tide resulting from the condition of perigee-syzygy, which will be discussed extensively in the ensuing chapters — often supported by additional astronomical factors such as those listed above — provides the setup condition for sub- sequent wind action. An active coupling between strong, sustained, onshore winds, if present, and the surface of the sea provides the second factor necessary to cause active coastal flooding. The absence of flooding in these control cases is clearly shown by the accompanying weather maps to be due to high atmospheric pressure and a condition of calm — or offshore (rather than onshore) winds along the coast, act- ing to negate the effect of the astronomically induced high tides. The action of negative (depressed) tides produced by intense offshore winds during the low-water stage of peri- gean spring tides is also duly considered on pages 93, 103, in terms of the threat for ship groundings and strandings. As a followup to the cases of tidal flooding listed in the tables of this chapter, and as an indication of the con- tinuing, open-ended relationship of this historical over- view, facsimile copies of newspaper articles describing tidal floodings which have occurred widely along the North American coastlines are included, in chronological order, on the following pages (table 5). These serve to sum- marize, from an at-once historical and yet contemporary, firsthand point of view, the effects of a quite considerable number of cases of coastal flooding resulting from the co- incidence of sustained, onshore winds and perigean spring tides over a period in history covering the 18th, 19th, and early 20th centuries. Appropriate data for each occurrence are contained in the accompanying captions. The events reported speak for themselves in the intensity of the tidal flooding damage sustained. From the standpoint of the contribution made to such events by perigean spring tides, certain of these cases of coastal flooding will be further individually evaluated in part II, chapter 7. The gradual reduction in the frequency of reported cases of severe tidal flooding in more recent years, as the result of an increased construction of seawalls, breakwaters, groins, and other devices designed to prevent coastal flooding, will also be given appropriate attention in this later chapter. In connection with these reproduced news articles from a fairly extensive range of coastal communities, and cover- ing a span of 251 years, several pertinent comments are in order: Both in the case of very early newspaper accounts and those published in relatively small coastal communities, it is necessary to consider that most of the newspapers in- volved are weeklies. Accordingly, the reporting time of a coastal storm accompanied by tidal flooding which oc- curred just prior to a weekly publication date and too late for inclusion at that time may be delayed as much as a week. It must also be remembered that, in the documenta- tion of such tidal floodings, the news value of these na- tural events as determined by the news editor is at all times in competition with other news of the day, of political, international, economic, or other topical interest. The timing of the flooding in relation to press deadlines and follow-on editions, as well as the writing skills, thorough- ness, and even the working habits of the reporter can all affect the degree of prominence given to one story com- pared with another whose flooding consequences are ostensibly as great. A lack of technical knowledge on the part of the reporter, a desire to achieve a sensational story, or an excessive shortening of the article by a news editor — all can affect the accuracy of the pertinent data. Any quantitative comparison and analysis made from newspa- per accounts is, therefore, subject to some degree of qual- ification in keeping with these considerations. In conclusion, a brief explanation is desirable concern- ing the examples of tidal flooding cited in different chap- ters of this work. Methods of Identification and Evaluation of Representative Cases of Tidal Flooding The 100 representative cases of coastal flooding asso- ciated with perigean spring tides which are listed in table 1 are chronologically arranged and numbered for con- venience in reference. In order to provide for a greater variety in the case-study analysis used in different portions of the text — as permissible within space limitations — the cases variously chosen from among the 100 for individual evaluation are not always the same. However, a common thread of comparison has been maintained by including data for a single, consistent group of cases throughout the volume. To permit a ready means of correlation between such related sets of data covering various aspects and influences of perigean spring tides in different chapters of the text, an alphanumeric system of identifying these common cases has been adopted. The several randomly selected listings of perigean spring tides (distributed widely in time and geography, and both accompanied and unaccom- panied by tidal flooding) which have been mentioned Representative Great Tidal Floodings of the North American Coastline 13 earlier in this section constitute control groups. Each of the events in these individual groupings carries the same identifying number, allocated in chronological order, given to it in the first columns of tables 1-4. In addition, for those cases which appear repeatedly among the tide curves, weather maps, newspaper articles, etc., published throughout the volume, a key letter has been assigned. The keying letter and/or number serve to identify a flooding or nonflooding situation as the same tidal cir- cumstance, no matter where it appears in the text, with- out reference to the accompanying date. In some cases this is a weather map date (usually the same as the date of tidal flooding) , in others, it is the date of the published newspaper article (often a day or so later) relating to the tidal flooding, and in still others represents the mean epoch of perigee-syzygy. Wherever a numerical or alpha- numerical designation is given in the caption accompany- ing graphical or tabular material, these data form a cor- rectable set with any similarly labeled perigee-syzygy data appearing elsewhere in the volume. Due care should be exercised in making all intercom- parisons to check the standard time zone for which the data apply. Most of the synoptic weather map, coastal flooding, or related tide table data are given either for the time meridian of 75° W. (eastern standard time) or 120° W. (Pacific standard time) — depending, in the last two instances, on the coastline involved. All astronomical and ephemeris data relating to the Sun, Earth, or Moon (including the computer printouts) are referred to ephemeris time (e.t.) c . First adopted in- ternationally for use starting in 1960, and based upon the comparison of exact lunar, observations with gravitational data rather than upon the rotation of the Earth, as here- tofore, ephemeris time is the modern form — with some small distinctions and corrections — of Greenwich civil time. Between January 1, 1939 and January 1, 1960, astronomical data were given in universal time (u.t. ), otherwise known as world time or Weltzeit (W.z.) , temps universel (t.u.), or Greenwich zone time (Z) — all of which are equivalent to Greenwich civil time (G.c.t.). In each case, 24 hours constitute the day, starting at midnight (0000 h ) and lasting until the next midnight ( 2400 h ) . Universal time is still used instead of ephemeris time in astronomical applications other than those that relate to the Sun, Moon, and planets, and likewise always refers to an astronomical day starting at Greenwich mid- night, no matter in what year it occurs. 6 This abbreviation should not be confused with that for eastern standard time (e.s.t.) also used in the text. However, several possible pitfalls exist in the compari- son of the times of tidal flooding events taking place in different years, particularly in the past : ( 1 ) Prior to January 1, 1925, Greenwich mean time (G.m.t. ) was used, in which the 24-hour day began at Greenwich mean noon, rather than the preceding midnight. Although Greenwich civil time came into use in the 1925 issue of The American Ephemeris and Nautical Almanac, the des- ignation universal time did not appear until the 1939 edition. In converting to Greenwich civil time or universal time, 12 hours always have to be added to Greenwich mean time; (2) The term Greenwich mean time (but reckoned from Greenwich midnight) also continued in use in the British Nautical Almanac during the' same period that Greenwich civil time was being used in The American Ephemeris and Nautical Almanac and before they both converted to universal time and then ephemeris time ; and ( 3 ) The designation Greenwich mean time is still used today in the navigational and tide publications of some English-speaking countries. Although this other- wise abandoned nomenclatural usage implies a time 12 hours earlier, it pertains to a value which is intended to be the same as universal time or Greenwich civil time, start- ing at Greenwich midnight. To avoid confusion with the similarly named Green- wich mean time which had been used in the United States before January 1, 1925, the more complete desig- nation of Greenwich mean astronomical time should be assigned to any reckoning system which is based upon Greenwich mean noon. In early editions of The American Ephemeris and Nautical Almanac, the meridian of Wash- ington D.C., was also used for various astronomical posi- tion and time determinations, and the exact designation of this meridian has undergone several changes over the years. The lengths of all days (solar or lunar) specified throughout the text are given in terms of their equivalents in mean solar time ( 1 mean solar day= 1,440 mean solar minutes = 86,400 mean solar seconds), based on the ficti- tious motion of the mean Sun. Reference should also be made to the note in connec- tion with Julian (Old Style) and Gregorian (New Style) calendars on page 1 . Remarks Concerning the Fundamental Astronom- ical, Tidal, and Meteorological Data Sources Used in Connection With Computations for this Volume The times of perigee and szyygy, the separation-interval between them, and the mean epoch of this combined phe- nomenon are given for each case of tidal flooding listed in II Strategic Role of Perigean Spring Tides, 1635-1976 tables 1, 2. In the reductions leading to these tabulations, as elsewhere throughout the volume, the data contained in the computer printout of table 16 have been used, for con- sistency, in all instances where P~S>±1<±24 hours. An arbitrary interval of one mean solar day has been set as the separation limit between perigee and syzygy for all cases of perigee-syzygy "alignment" appearing in this latter table. Within this ±24-hour limitation, table 16 (compiled from magnetic tape data by the U.S. Naval Observatory) provides the means for extending such perigee-syzygy data backward in time to historical dates even prior to the exist- ence of published nautical almanacs and astronomical ephemerides. Among the earliest of such published data sources, the French Connaissance des Temps was first issued in 1679, the British Nautical Almanac in 1767, the Italian Effemeridi astronomiche (original Latin title Effemeridi astronomicae) in 1775, the German Berliner astronomisch.es Jahrbuch in 1776, and The American Ephemeris and Nauti- cal Almanac in 1855. Where the P — S separation-interval is greater than ±24 hours, the corresponding data have been obtained from these astronomical ephemerides, within their dates of availability. For earlier dates, these data have been calculated retro- actively on the computer, resorting to the same analytical approach involving the application of periodic terms and coefficients in the solution of the lunar disturbing function which is used in the compilation of table 16. Table 16 is prepared from computer-programmed equa- tions and theoretical methods of analysis which differ, for example, from the standard interpolation method for de- termining the times of perigees from maximum values of the parallax, used in The American Ephemeris and Nautical Al- manac and other ephemerides. Rounding-off procedures in- volving data truncation to the nearest significant figure also have been employed in the computer printouts. As a result, variations of up to one-half hour may exist between corresponding values obtained by the several meth- ods noted above (or, if the rounding-off errors add in the same direction, differences of up to 1 hour may occasion- ally result). These variations are the most critical when P — S is very small, and the solar perturbation of the lunar line of apsides is, correspondingly, at its greatest value. However, the maximum influence of the strong, onshore surface winds required to produce coastal flooding in con- nection with perigean spring tides usually extends over at least several hours. The influences of phase and parallax ages, variable with location, also affect the interval between the occurrence of perigee-syzygy and the production of the maximum perigean spring tides. Such small differences pos- sible in the mean time of perigee-svzygy are, therefore, not detrimental to the accuracy of the present study. In this same connection, a greater uncertainty exists in determining the exact time of perigee than in the case of s y z ygy> an d the former value is now customarily given only to the nearest hour, whereas the time of syzygy is given to the nearest minute. Carried to the accuracy of the less well- known component of the pair, the value of the mean epoch of perigee-syzygy is rounded off throughout this book to the nearest hour only, or — where odd-value separation-in- tervals are involved — to the nearest half-hour. One excep- tion to this procedure exists: In order to separate and emphasize the effects of particularly close perigee-syzygy alignments, where the difference P — S<±l h , its precise value has been computed, in minutes of time, directly from the data in an astronomical ephemeris. Of significance to certain tables contained in later chap- ters of this study are the earliest years in which ( 1 ) for- malized tide data were available, and (2) synoptic weather maps were issued in the United States. Between 1853 and 1867, the first rudimentary tide tables resulting from studies made at certain larger seaports on the east coast of the United States were contained among the text and appendixes of the annual Reports of the Super- intendent of the Coast Survey. These consisted, for the most part, of related tidal data requiring further self-computation and use by the navigator. In 1867, the actual prediction of high tides for 15 stations on the east coast of the United States was begun. Because of the special demands made necessary for safe navigation over shoals, bars, and reefs, the prediction of daily low waters for the west coast of Florida as well as for the Pacific coast of the continent was begun in 1868. In 1887, the prediction of both high and low waters for 16 stations on the east coast also was inaugurated. In 1885, the use of the first tide-computing machine in the United States, devised by William Ferrel of the U.S. Coast and Geodetic Survey and utilizing 19 harmonic constants, was instituted. In 1896, such tidal predictions were extended to include 70 standard reference stations throughout the world, together with tidal differences for an additional 3,000 stations. In 1912, annual tide tables were computed for the first time by USC&GS tide-predicting machine No. 2 (developed by Rollin A. Harris and E. G. Fischer of this organization in 1910, and utilizing 37 harmonic constituents). Beginning with the tide tables for 1966, the use of an elec- tronic computer was introduced, by which all tide predic- tions published by the National Oceanic and Atmospheric Administration/National Ocean Survey are now calculated. In connection with the availability of various meteorologi- cal sources cited in part II, chapter 7, the first issue of the Monthly Weather Review was published (by the Signal Service, U.S. Army) in June 1872; the earliest issue of the U.S. Weather Bureau publication Climatological Data — National Summary appeared in Tanuary 1950 (vol. l,No. 1). Information concerning individual coastal storms was first tabulated in a section designated "Severe Storms" in the latter publication from January 1950 until December 1953. This section was retitled "Storm Data and Unusual Phenomena" from January 1954 to December 1958. There- after, and to the present, similar information has appeared in a separate publication titled Storm Data, whose first edi- tion (vol. 1, No. 1) was issued in January 1959. The first daily surface synoptic weather map of the United States, including adjoining waters of the Atlantic and Pacific Representative Great Tidal Floodings of the North American Coastline 15 oceans (but of course lacking synoptic weather data from ships at sea until the advent of marine radio) was published as a War Department Weather Map by the Signal Service, U.S. Army, on January 1, 1871. The first representation of weather fronts on these maps was not begun until Au- gust 1, 1941. Other data are given in the explanatory com- ments preceding the appropriate groups of weather maps included in part II, chapter 7. Data on storm surges are also available in many sources, including those listed in the bibliography at the end of this volume. However, it is important to note in connection with the list of tidal flooding events contained in tables 1, 2 that the existence of a storm surge does not necessarily imply tidal flooding unless the amplitude of the surge exceeds the land- flooding level at the point under consideration. A storm surge is defined as an additional increment to the observed tide as meteorological factors cause the water level to rise above that of the predicted astronomical tide. The specific meteoro- logical contributions in this case are a strong, sustained, onshore wind and/or decreasing atmospheric pressure. A surge therefore represents the positive residual in the total height of the observed tide in excess of the height ap- pearing in tide tables for that date and time. f In order for coastal flooding to occur, the combined water level from these two causes must be higher than the level of the adjoin- ing land. The height of the storm surge above mean sea level must be considered in terms of the elevation of the shoreline with respect to this same datum plane in order to establish the possibility for coastal flooding. Bv the same token, the use of observed (recorded) hourly height data for the tides is not meaningful until referenced to the actual flood level for the point in question. All such cases of shore- line inundation cited in tables 1, 2 are confirmed by pub- lished eyewitness accounts. Table 1 List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976 Explanatory Comments Table 1 consists of a compilation of 100 cases of severe coastal flooding caused by the combined action of perigean spring tides and near-coincident, strong, persistent, onshore winds. As indicated by the reference sources given in the table, almost all of these instances of tidal flooding are of a magnitude to warrant mention in contemporary local or regional newspapers and/or to be cited as of considerable consequence among historical accounts, monthly and annual meteorological reviews, coastal storm summaries, or other technical sources of marine data. The documented examples of tidal flooding listed are, therefore, semantically distinct from the more restricted category of meteorological storm surges. As described in the foregoing section on meteorologi- f Conversely, a negative storm surge refers to the depression of local water levels below those predicted from the existing astro- nomical forces; it is caused by a strong, persistent, offshore wind and/or rapidly increasing atmospheric pressure. cal data sources and nomenclature, storm surges may or may not be accompanied by coastal flooding. The arrangement of items in table 1 which, as a master listing, will be referred to repeatedly throughout this volume is: ( 1 ) the key number of the flooding event, as explained in complete detail on page 13 (col. 1), and in the Ex- planatory Comments preceding table 5 ; (2) the date(s) of tidal flooding at the locations in question. Both Old Style and New Style Calendar dates are given where applicable, according to the procedure for reckoning these dates specified in the aforementioned por- tion of the main text; (3) the cities, towns, seaports, coastal or beach loca- tions at which tidal flooding is documented by the reference sources as having occurred ; (4) the date and time (to the nearest hour) of the lunar perigee occurring closest in time to (either preceding or following) the instance of tidal flooding. For convenience in reference, the times given are uniformly converted from the Greenwich civil time or ephemeris time of astronomical tables to 75°W. -meridian time (since 1884, designated as eastern standard time). If a location on the west coast of North America is given in col. (3), an additional 3 hours must be subtracted from those given in cols. (4) , (5) , and (8) to obtain 1 20° W. -meridian time (Pacific standard time) ; (5) the date and eastern standard time (specified to the nearest minute) of the syzygy alignment (either new moon or full moon) closest to the occurrence of the tidal flooding; (6) the algebraic difference in time between the oc- currences of perigee and syzygy nearest to the flooding event, taken in the sense perigee minus syzygy, and rounded off to the nearest hour; (7) the particular phase of syzygy represented — either new moon (NM1 or full moon (FM) ; (8) the mean epoch of perigee-syzygy, obtained by adding one-half the difference in hours given in col. (6) (without regard to algebraic sign) to the time of the earliest of these two phenomena ; and (9) documentary sources of the flooding event, given variously as a citation to a contemporary newspaper (with newspaper title coded, plus date, page, and columns) or a professional journal, book, or other reference in which a more detailed description of the flooding event occurs. The coding numbers used for each reference source are listed at the end of table 4d. With the single exception of Case No. 70 ( P - S = - 87 h ) , all accompanying perigee-syzygy alignments have a separa- tion-interval between the two components not exceeding ±84 h (±3.5 days). This is the arbitrary limit of separation established in this study in order to include pseudo-perigean spring tides as well as perigean spring and proxigean spring tides. Among the data of table 1, a comparative summary is available indicative of (1) the possible divergences of the times of flooding from the mean epochs of perigee-syzygy within which the special tide-raising influences of this dual alignment are felt, and (2) the greatest separation-interval between perigee and syzygy at which the combined gravita- tional action has a distinct effect. 16 Strategic Role of Perigean Spring Tides, 1635-1976 I" 5 d 52 gj a,' * a o CI h» fcg CM CO ,_» a w l/) o c ,_, ,n"!5 in T ,o c — ' "■" <■<-. C5 d ^ 00 © m <£> a. — - -' o — u '£ in r< r^ ~1 > c ■o§2 u . £?'*^ a 8 ts .s S ! 1 c^ I. ^ I £ «;~ -S ^ o n s © -5 2 s^s s s s z z e bog >.o acfc^tc »&•« £<*« -8 £§ . ? §~§ „§ "S3 ^> 5 --3 ~ ° o a o u o O it O u O m [/J r-~ Q m 15° S 5r 3 -Q O D. O v a u o h oi w ts c o U 8 a -D | 1 = | I If = ■/ . a M i ^ c/3 Z c j^ « ."2 > ^ £ EQ -° " a I 3 tf T) 5 o S O 8- * a m I ^Q 2 I I 3 § I°TfJ tf 2 8.ffi 5. b G pj 2 Jrt "o" c" "he ° » 3 hS -b J2 o -^ >• .a "o Z 3 U^X. Z ~-^ O) CT) — — CN cnO'«* - «nO<^Z'? r O , nZcsrO M Zo Representative Great Tidal Floodings of the North American Coastline jo <£, |C CO — < > co «J 3 O O O o < £ D.8 us m .8,8 H w * co o O - % 3§ |8 § ^ 2 ■S 3 5 ^ -2 4J > a £ =rt: <*> ~ ■g "3 C a "a « g Co* T) 3 — rS B ' S o- «j *J to M U O K 3 s -gz § w is s -g z 1,9 2 -S S ga- O ^>T3 96 V ■s £ 5 ^ Hint •s i tj K c b Q «i j;0 fcg § 8.-B J 2gj§T s s 8 g I 2 . < .2 £ 1! 1 H Strategic Role of Pcrigean Spring Tides, 1635-1976 1 o ^ -5 - '- "2 ~f- . 10 a, o a- c co en 1-1 * ^ -UD CM CM * d d a ?3 rj-"cn v -' ^fg * - — C J2 CO •t . - to" d -_- u m <£ ,_ — CM O J3 O - o o en 3 n " cn a th2 Z En -D O H O «J o J: o fcoflw Z m Q en ^ cm O o m cm ■* * - ID N S O 3> S § -s, Z fa ai •< «"" '? ^ "2 -S;~ § ^ .> »« g - § i8 O 3 o 00a < — CM z£ Q c S fa © Q I» a I c £ g 8 „ M -o -- Q -a s > u Ml s « x > w S t -a &X <3 £ £ 5 ° 3 ^ I J3 < <°G uX — & . -J> — CM Representative Great Tidal Floodings of the North American Coastline ID r>T r-" gT 01* iff °P — ' f"-" — " ^3 t>T i CM CM rvi CM J~ (N CO ™ (N •* O. 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K S H « u If S T3 S O •^3 6 ' w Q j* 5 " g Q Is Representative Great Tidal Floodings of the North American Coastline 21 E E fa (T, CM $.2 - fa 8 ^ CO o CO ai 0) t> ~ rri CO ;n - a o -r- CM a a _- ' ' o m m — !' CO CO CO ti CM og «-% -T <> <-> m ^ m CO — *-' ~" d CM °? o •-D m CM fa m t — „ ~ L> d IS 1 d 6 d 01 rr, > in fO u ^ to £2 P 8 § CM 11 o ^ co u CO •8 8 8 8 a to fafafa^fa^Zfa + + - 1 o N o odofi° c o —i co ^8 fa ■» <£ 8 8 P P. ■^ bo «•} ri ■rf 8 * - 1 w i S IS s ^ m "0 03 _ ■a S a C - !B " t) I) . w I "£ "S •£ 2 c S 3 Q < PQ o f s -o I >i £ o o !S z "8 £ -a" tf « v §:§ fa i£ c Q c fa (« 3 T3 — J? 31^ 8 .-S5 S iTpq i ~ J ^ « -o -5 < ° C 3 — , ij a o « I 1 J 1 ■a 5 ! 3 U ffi a V U C3 pq p fa S S cod c fa ^5 .3 3 'SLg U g S5 6 22 Strategic Role of Perigean Spring Tides, 1635-1976 <% -71 V 'O 1 'n c o. ±. o U r j <-. <■ R . g = H M .2" rt u (D ti ffl - e^ ^- J2 _2 » • io m cm „ I miP-n o o— '" 5 3 2 5 o 13 o ■y >< s s £ 'S J -"B £ < Si 13 £uK *->ll Si* ^^ g| jj o'.^a P tt| >J ^„- fulfil sis 3 C- - "3 Q. s n 8 If » S ^ U S Representative Great Tidal Floodings of the North American Coastline m o . J" a a, cm" cm" ' 2 Sf g d o" o « X, o p ^ o ^ -; s _ — Sr „- S. • - ~ ^ 2 3 £d-^ Wo O ■* O CM O „ « g- d cm d cr •-£ ^ < S ™ « 7 d3 -^ o n 5 ": cm" *}- a d cm" •> f]- & ^ to 4 1 d Sf £ . K CM CM „; ■ - d . "(N . UO^TCM S 2~o ^ oo g 10 CM -a ' g ° .a « c ^ & co- co"^ r- CM a ^ ■J CM * — ^ .<■£> ^ ^ 's< n S 5 © £ o Q en - CM CT> — S2| o " 1^- Q - Q ° S ~ | „ CM O CM O CM CM ' T? u ■* .J CO 8-8 CO co CO -H 15 § Q 3s P co Q co «T3 Si a -a 3 j3 C X, >6 'if Cl, o c U g. m £? S u£> J sq g § < is "8 « c o cm ° X < O D f* 3 o a ^ s g § 4-T - o '< a C 2 ^ 3 C) £ £-P "2 -a - ■a * U '5. = M 3 a U s 2-1 Strategic Role of Perigean Spring Tides, 1635-1976 to C 7 ° <5 I |0 {2 If"* 8 If - IS 1 I*- $<&h XI O O — E;o <2 — °S o . g tf s .s (25c) v. 18, No. 3, p. 8; (65) 3/19/76, p. 1, cols. 1-6, (66) 3/17/76, v. 93, No. 133, p. 1, cols. \-A\ (67) 3/17/76, v. 12, No. 11, p. 1, col. 1; (68) 3/17/76, v. XC, No. 143, p. 1, col. 1. 9" bObo Type of Syzygy Separation- Interval : Perigee Minus Syzygy (h) us + ~* o u ° 3 a u j> ij SfcQ 2»H be C ■a 8 S 1 Ogunquit, Cranberry Island, Popham Beach, Saco, and Kennebunkport, Me.; New Castle, Rye, Hampton Beach, and Portsmouth, N.H.; Marblehead, Provincetown, and Plum Island, Mass.; Halifax, Nova Scotia. a ■a o E Q £ to 2 ;T6 o o 6 m £ o * 3 -a" " ) — .5 «|-H-§ c .-'> boco 5 1 1 6 S 'w CO go — « CD fev| 1 9 a "> w ° - & "5 co ■S ^ &C-H ■? s a.S-| n) J •5 ° -C L° s — (8 y [t, co O " Oi u .2 >; •5 o"2 «13 * H 53 i bo.o o 111 "5 bo h g.S a 2 « « 8 8 ° OS StS-H i^z u - c £ 2 s o 5 -a tf boo 5 •^ <-■ c .5 >. O JJ u ill 3 Sn.itJ if" 3 « e a g 3 u r -a 5 G §^ Eg §1 a a § S ♦* - <° C T3 •- n c s -S i • S.SP^ So £ O „,.£,_£ gen c S 3 c w 3-23 8 1-S * Oh vJ _, 3 -52 *8 c ^ » li £ | I s &-T3 £ a ^ -3 "H lo <« -g. ' ■ 3 ij > JT3 f J O &.S c ■a 3 o .2 Oh g -3 o-E o .2^^-h: OC .ou 3^2cgj3 E" 3tJ U boO ,2lJ-i > S « a m « 1 1|5 m 3< g< ! S **% M .5 a 8 '8 5 E.SP ? S2 S3 £ "S3 ^ -O J3 O 3 -I 'till 3 CT> c 3 rtio 3 rt S,^ o.y 'E ^^ I 3 bo U .22 «d S. 3 g ° I >.-S a Representative Great Tidal Floodings of the North American Coastlint 25 Accordingly, although a few of the examples given may seem to exceed, by a day or so, the tolerance limit in which the influence of perigean spring tides would normally be expected, a comparison with the circumstances of the astro- nomical alignment and the predicted daily tidal ranges around this time reveals that: (1) such apparently more divergent examples are still especially close to perigee, although possibly several days removed from syzygy ; ( 2 ) the predicted tidal level is above that of mean high water springs; or (3) the height predicted is of a magnitude approaching — and therefore over a 19-year cycle of compilation, contribu- tory to — the upper limit of this averaged value of maximum high tides for the station in question. A representative few such more divergent cases are, accordingly, included in the table for completeness. These serve to show the tidal life- span of perigean spring tides in terms of their permissible divergence from the epoch of maximum perigee-syzygy in- fluence — particularly in the case of those examples of tidal flooding that last over several successive days. A significant factor of event correlation between the in- dividual entries of this table is indicated in col. (2) by the brackets connecting instances of tidal flooding related within the principal short-range cycles of perigee-syzygy alignment. These relationships may involve the circumstances of suc- cessive floodings coincident with : ( 1 ) the approximate 28.5- day repetition of perigee-syzygy alignment, once attained (the average between the anomalistic and synodic months) ; (2) occasional double or triple multiples of this period; or (3) the 6.5- to 7.5-month average interval between perigee- syzygy occurrences discussed in chapter 6. The contributing role to tidal flooding provided by the heightened astronomi- cal tide-raising influences at times of perigee-syzygy is sub- stantially confirmed by this evidence. Table 2 A Representative List of North American Hurri- canes Occurring Nearly Concurrently With Perigean Spring Tides Explanatory Comments In the modern precise definition of the word hurricane, only two principal criteria are involved: (1) that the sur- face winds within the intense, low-pressure cyclonic system forming the hurricane shall, at the time of its being so desig- nated, have a sustained velocity equal to 74 miles per hour (64.3 knots) or greater; and (2) that the incipient hurri- cane shall have an origin over tropical or subtropical waters. The expression hurricane applies to storms possessing the above characteristics and occurring either on the east or west coast of North America, in the Gulf of Mexico, or the Caribbean Sea. In all cases, the hurricane originates over tropical or subtropical waters. On the east coast, the hurri- cane may penetrate to middle or even high latitude before recurving eastward, moving inland, or, with a loss of ther- mal energy at high latitudes, dissipating completely. On the west coast, the hurricane only infrequently moves out of sub- tropical waters to landfall on the California shoreline (usu- ally not traveling farther north than the Gulf of Lowei California). However, the term hurricane is used in connec- tion with all such storms occurring in lower latitude por- tions of the North Pacific Ocean, east of the international dateline. The word typhoon characterizes similar storms found in the China Sea and in the North Pacific Ocean, west of the international dateline. The term tropical cyclone properly refers to such storms originating in the Indian Ocean to the south of India, off the southeast coast of Africa, in the Bay of Bengal, or the Arabian Sea. Baguio is the expression used for hurricanes in the Philippine Islands. Although the four preceding terms are synonymous, it is important to note that a tropical depression has not yet reached the intensity of any of these storms — or, alternatively, after a filling and weakening of the low pressure center, has been downgraded from hurricane strength. Gordon E. Dunn and Banner I. Miller in their book on Atlantic Hurricanes 4 " (appendix B) have included the fol- lowing relative intensity scale for hurricanes, based upon the maximum winds and minimum atmospheric pressure as- sociated with them. Since both these quantities are lacking in connection with early American hurricanes, the intensity ratings in these cases have been inferred or extrapolated from contemporary eye-witness accounts of the apparent strength of the storm, judged from observed wind-damage and tidal flooding effects, including destruction of property and any loss of life involved. The Beaufort scale for esti- mating relative wind intensities did not become available until 1806. The Intensity Classification of Hurricanes Intensity Maximum winds Minimum central classification pressure Minor <74mph «64kn) >29.40in. (>996 mb) Minimal 74 to 100 mph 29.03 to 29.40 in. (64 to 87 kn) (983 to 996 mb) Major 101 to 135 mph 28.01 to 29.00 in. (88 to 117 kn) (949 to 982 mb) Extreme > 136 mph (>118kn) <28.00in. (<948 mb) A list and description of "Hurricanes Affecting the United States, by Sections," 1635-1963, is contained in ap- pendixes B, C of the aforementioned work, and hurricanes, 1493-1951, are described in chapters XII-XV and ap- pendix of Ivan R. Tannehill's book on Hurricanes 14 . In ad- dition, such hurricanes are discussed, and documented with both contemporary and later sources, in David M. Ludlum's Early American Hurricanes, 1492-1870. 5 In the present work, the purpose of table 2 and item A-2, "Summary and Conclusions," chapter 8, is to consider the coastal flooding potential added to hurricanes by their coin- cidence or near-coincidence with perigean spring tides. With a few uncertain examples, table 1 likewise contains only cases of coastal flooding generated by the combination of perigean spring tides and offshore storms. Because of the previously mentioned, often completely subjective methods of wind ve- locity appraisal, it is difficult to establish with absolute cer- 2h uT3 N ~' ^ — - § S CT> "" CO c j^ . .« o. 1 ill |s- Strategic Role of Perigean Spring Tides, 1635-1976 CM CM a d = % c- 1 1 ^ •— > CN ~ """' 6 «? I 'E 1' £ ■a « .5 -" C l~~ CO '« "~ "2 ^ 3 3 "S, T c-v « ? o o e .2 ^ o r^ U X U CM Q. _- o c '■a "^ 11 o£ 8-8 5 8 8*8 &8 § § 8- CflCO-^g^CM^CO ^O M s s 2 2 o ■ o • o v n z ■;- *-; oSpoq.oq.ocOq.o 5Po i^030iT0ir030g-0 Jo 0± ! ri (d o ~j m u 4- .4- I CO :.__;_ .^CM^^^cm^csj-^CM^;^ _ ri be' 7 ' W)"^ too C/D ti)^ *J OT 4-i ^ w ^ > ^ kV, CO CO CO CO CO o co co oi ■* o — §£■* ago Representative Great Tidal Floodings of the North American Coastline 27 .00- 3- c r~- co m o rf" -S - S — © i * r. . * o CO TJ O C " in o ■« , joi a d n" S S £! - a. .2 £ « org ^■3 « 2 -9 —So m u 3 w i: o "- 1 .5 Z r- — f«: a ~ < bo c O ■— I — en co a, o y o u O p, CO en co U m &8 =^3 M CO < o ^ co ^ en t en ^ O in ■* ™ C c ,0^0 •o " IT. m co 2 s 2 " s § x; 5 S /, Ph fe Uh X z tn Ph \n eo o m o — c m <* o - o q© boo >• en < I— . w CO o >*S 030 cm ST — ' S S° ag z g u o o o en m U cm -CO Q.O — 1 Jj o ag a g ag 51 a. <=> r, o o o " o en co o w • T3 T) ex „ ; fl TJ o ^ £ B « tJ to ^S ~ O O Ph » 0-2 •£ * U O r u CM (fl IO ft (O Sq CD ■* 2 8 S~ q. CM y CO .Q CM fl" *J o o s y> - - > o _q o 60 > o Oo uO^oOo r-. 0"> O co "* Tj- LO iO Ci Gi 01 O bO ■ ^ Jo g < £ - is S c y >• c c «J o o w rt JS 2 U ^ U J « ^ - u y (fl O ■O -C mill .H T3 m 2c2 g !? o ■- -s ^ £ j: _ bi ^ u rt >< 4? o.pt| cq 2 £ 3 i J3 > 2 Z CT r^ cc £ "- c\ u- M) Strategic Role of Perigean Spring Tides, 1635-1976 G u u X c E J2 I- -o <2 5 £"0 3 w c (2 (51) 10/15/55, p. 1, col. 1; p. 34, cols. 2-4. (51) 1/11/56, p. 33, cols. 2-4. (25e) HYDRO-32, p. 8. (51) 10/30/73, p. 1, cols. 5-7; p. 47, cols. 3-6. (51)8/25/27, p. 3, col. 1. (51) 10/16/47, p. 31, col. 1. "56 s s s s s s 2 2 2 2 2 2 ^« Q Oct. 15 1432 1956 Jan. 12 2201 Apr. 10 2139 Oct. 25 2217 Aug. 27 0146 Oct. 14 0110 u C3 55 1955 Oct. 5 0600 1955 Dec. 28 1900 1956 Apr. 15 1700 1973 Oct. 15 2000 1927 Aug. 15 1042 1947 Oct. 9 1300 c '-3 E c _o Lowland coastal regions from Cape Hatteras to Maine, including Staten Island, N.Y. ; and entire Connecti- cut shoreline. Cape May, Atlantic City, and along north shore and Raritan Bay, N.J. Monmoulh Beach, N.J., to northern New Jersey and the Rockaways, N.Y. C3 If O 6 « a Is 8 1 S l| ■S § g w C T3 « C (3 t/3 c '-5 E t5 Q -1- Z ir c c c 1— c < m cr 0- Cs - i * -: 3 ■a H L u < ^ " m *■ T) \- : Representative Great Tidal Floodings of the North American Coastline 31 winds and their contribution to coastal flooding. The reason is that the phenomenon of syzygy occurs twice in each synodic month (new moon and full moon) or approximately 25 times in each calendar year. This frequency of disposition must be compared with the usual occurrence of only 2 cases of perigee-syzygy in each year which possess separation- intervals of ±12 hours or less (or, at most, 5 cases which have separation-intervals of up to ±24 hours. The possible range of opportunity for securing the coincidence of a sustained, strong, onshore wind is proportionately greater at syzygy alone than at perigee-syzygy. Despite this fact, the number of cases actually recorded involving severe tidal flooding at times of ordinary spring tides is far less in terms of justified proportion to those pro- duced at times of perigee-syzygy. This is because of the greater tidal amplification occurring from the combined alignment of perigee-syzygy, and the resulting increased potential for tidal flooding if the necessary supporting mete- orological conditions are also present. A representative group of examples of coastal flooding accompanying ordinary spring tides is given in table 3. One further lunisolar configuration is deserving of com- ment in connection with its relative tide-raising forces. This is the situation in which the Moon, while located at its perigee and closest monthly approach to the Earth, is simultaneously at its greatest possible orbital angular distance from either of the two syzygies (i.e., at one of its two positions of quad- rature). The resulting tides produced (called perigean neap tides) are always of much smaller amplitude and range than perigean spring tides. Thus, even in the presence of strong, persistent, onshore winds, it is an uncommon circumstance in which major tidal flooding accompanies perigean neap tides. Instances of coastal inundation at such times are correspondingly rare throughout history, unless extraordinarily high winds asso- ciated with an active coastal storm or a severe landfalling hurricane have prevailed. However, for the record, a typical prototype of one such flooding tide uplifted by an unusually strong, onshore wind was that which took place on 1894 April 11 along the coast- line of New York State (as recorded on page 1, col. 2 of the New York Times for April 12). In this month, perigee occurred on April 10 at 2244 h e.s.t. (the additional lag due to parallax age before the peak of the high waters was reached being approximately 1.5 days). The first-quarter moon occurred on April 12 at 1933 h e.s.t. Under the force of a strong, northeasterly gale, tidal flooding was experienced at such locations as New Brighton, South Beach, and St. George, Staten Island, and at Riverhead and Babylon on Long Island, N.Y. Tables 4a-4d Miscellaneous Factors of Dynamic Influence Asso- ciated With Perigean Spring Tides, in Cases Variously Lacking, or Reinforced by, the Pres- ence of Strong, Persistent, Onshore Winds Explanatory Comments Tables 4a-4d quantitatively depict four supplementary but revealing tidal phenomena associated with the predic- tion of perigean spring tides. These are : (a) the attainment of water levels of record-establish- ing height for astronomically produced tides (the corre- spondingly named highest astronomical tide for the locality) at the times of perigee-syzygy; (b) The creation of extreme low waters of record, pro- duced by the same amplified gravitational forces at the low- water phases of these tides ; (c) The occurrence of cases in which extraordinarily high waters are raised near the times of perigee-syzygy, but do not actually produce flooding of themselves because of insufficiently strong supporting winds. However, at high- water phase, they effectively block the hydrological runoff created by heavy precipitation, ice and snow melt, or simi- lar freshets on the land. The result is a greatly augmented flooding of the coastal regions. The same type of flooding situation may occur as the result of tidal blocking of storm drains or elevated sewerage outfalls — even those supposedly remote from the land; and (d) The production of conditions unmarked by severe flooding of the coast, but accompanied by extreme scouring and erosion of beaches, berms, estuaries, and inlets along wide stretches of the shoreline. 'SI Strategic Role of Perigean Spring Tides, 1635-1976 Table 4a. — Representative Cases of the Highest High Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzygy (Resulting from astronomically induced perigean or pseudo-perigean spring tides, without coincident strong onshore winds or significant coastal flooding.* See table 1 for wind-supported cases of tidal flooding.) Extreme Mean High Perigee Epoch Date Place Water Minus of (ft Syzygy Perigee- >MHW) (h) Syzygy (75°W.) ATLANTIC COAST Claries Point, Mass Rockland, Me Boston Light, Lighthouse Island, Mass. Bath, Me Bath, Me Boston Light, Lighthouse Island, Mass. Bar Harbor, Me Deer Island (Fort Dawes), Mass Port Clyde, Me '1932 Mar. 24 1932 Apr. 21. 1940 May 20. ■1942 May 31. 1942 June 29 1952 Aug. 5. . '1953 Feb. 15. 1953 Apr. 13 1954 June 2.. 2. 1 + 21 2.4 -1 2.3 -67 1. 9 + 9 1.9 -11 2.3 +20 mm. 3.9 + 9 3.3 -37 3.0 -39 Mar. 22 1730 Apr. 20 1530 May 19 2330 May 30 0530 June 28 0130 Aug. 5 1530 Feb. 14 0030 Apr. 12 2030 May 31 0330 Extreme Perigee Mean High Minus Epoch of Date Place Water Syzygy Perigee- (ft (h) Syzygy >MHHW) (75°W.) PACIFIC COAST Seward, Alaska Santa Monica, Calif Skagway, Alaska Los Angeles, Calif Sweeper Cove, Adak Island, Alaska. . Neah Bay. Wash Crescent City, Calif 1927 Oct. 13. . . 1936 Dec. 27.. . 1945 Oct. 22. . . 1948 Jan. 25-26 1951 Jan. 5-6. . '1951 Nov. 30... 1951 Dec. 29.. . 4. 1 + 7 2.3 -55 5.8 +8 2.2 +4 2.6 -31 4.0 + 36 3. 1 + 11 Oct. 10 1930 Dec. 26 1930 Oct. 21 0500 Jan. 26 0400 Jan. 6 2330 Nov. 29 1400 Dec. 28 1230 * Note: The east coast cases cited also occurred prior to the great mid-Atlantic coastal storm of March 6-7, 1962. This event, in the combination of meteorological and astronomical effects, set many new tidal height records and was accompanied by major coastal flooding (see table 1 and chapter 7). Note the cyclical perigee-syzygy relationship between four pairs of these maximum high tides, bracketed above. Representative Great Tidal Floodings of the North American Coastline 33 Table 4b. — Representative Cases of the Lowest Low Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzvgy Extreme Perigee Mean Low Minus Epoch of Date Place Water Syzygy Perigee- (ft (h) Syzygy u m in S J- 3 7" CM c/^ O Oi to" ^ u u: d. c~r ri.H Pm ~ o o * =9 _r CO ,-. CM CO 10 . ^ 5^. in "o to <2 *"" g IN "° ^ ° 2 t v c £'* 3.2 — . CM a en" - d fa co" _r dc a 3 CM „« « a ce; C/3,0 cm" *-. "i to a- d cn".2 m *S eo J JO a u >- gS 8 2 g ^ rt"" CO '> j-j CO CO 1 co in r 1 o o n> ID CM cLS(^ >< cc to ~^ ^ Is p4 <* lO ■* CO s X, CM CO r m CO ~<3 CM CM 3 0-hDhn Gj O i = 5?o too « o ■*-, v3 CO w CO CO 3 o " CO 1 CM to CM — CM 2 s 1° S ° Ol -o z in CT) to o o £ 'o >j l>D 2 s s 2 s & >» Ph 2 Pi ta fa ~S Htfl o 1 a ■■ O -75 U a> >. ^3 '2 J U 3 kn CM m r^ o ID CM s a> « & c&i2 cc + + 1 + 6 1 U cT $ w CM CM „ m CO N o vS o <" O r: -■- J2 cm r r o> CD a 3 i 3. « E o 2 ^ 2 - 1 £ >H o J2 2 in 1 ^ u "2 ■S c £ ■6 *i ■- c * o o o J S J E !* rs S - ** c 1 o .^0 t 1 | c o o -a . - c C a; u « > tf g S c^ p. — 3 01 S lis > 1 c m Z V pa fS 1. cj 5D +r 3 n '-3 o CM ~ c- Lr c < E t; u till ^J h *S 1 S 1 ^ CM ~ C CM CM CO lO Q Ol CT> r CJi ~ "" " ~* "- CO to - CO t£> m z r-^ CO V o ■* '•* t * *Z 36 Strategic Role of Perigean Spring Tides, 1635-1976 V to li v a §1 CO o C jJ (51) 11/15/62, p. 39, col. 8. (29) pp. 52, 250, 256, 259. (29) pp. 248, 251. (21) p. 6. (21) p. 6. (32) 1/19/74. local news section. 1U 1962 Nov. 11 0100 1967 Jan. 27 0600 1967 May 22 1800 1969 Feb. 15 0500 1969 July 28 1300 1974 Jan. 8 0700 S S % £ 3S s tn fa in 2 ta fa Separation- Interval: Perigee Minus Syzygy (h) CM tO CM O CO CM co m Tt- to — Nearest Syzygy Date Nov. 11 1704 Jan. 26 0141 May 23 1523 Feb. 16 1126 July 28 2200 Jan. 8 0800 fc-g fa 1962 Nov. 10 0900 1967 Jan. 28 1000 1967 May 21 2100 1969 Feb. 13 2300 1969 July 28 0400 1974 Jan. 8 0600 c 1 W "o a p o o Fire Island to Montauk Point, Long Island, N.Y. East side of Plum Island, Mass East side of Plum Island, Mass South spit of Pawleys Island, S.C. . . . Closure of existing south inlet of Paw- leys Island, S.C, by erosion, and creation of a new inlet farther north. Recreational beaches at Oceanside, Calif. c .0 o W Q 1962 Nov. 10-14... 1967 Jan. 27-28. . . 1967 May 25-26... 1969 Feb. 15-16.. . 1969 July 29 1974 Tan. 8 v 6 K-87 489 490 491 492 N-99 Representative Great Tidal Floodings of the North American Coastline 37 Reference Sources for Tidal Flooding Reference Code No. (1) William Bradford, Of Plymouth Plantation, 1620-1647, A New Edition, with Notes, Etc., by Eliot Morison, New York, 1952. (2) Governor John Winthrop's Journal, entry for August 16 (O.S.), August 26 (N.S.), 1635, subsequently published as History of New England from 1630 to 1649, James K. Hosmer, ed., 2 vols., New York, N.Y., 1908. (3) Nathaniel Morton, New England's Memorial, Cambridge, Mass., 1669. (4) Fitz-Henry Smith, Jr., Bostonian Society Publications, vol. II, Second Series, "Storms and Shipwrecks in Boston Bay and the Record of the Life Savers of Hull," Boston, Mass., (n.d.). (5) The Pennsylvania Magazine, Cambridge, Mass., December 1775. (6) Sidney Perley, Historic Storms of New England, Salem, Mass., 1891. (7) W. Bell Dawson, Survey of Tides and Currents in Canadian Waters, Government Printing Bureau, Ottawa, Ont., 1896-1903. (Note: The appropriate fiscal year of each annual survey listed among the reference sources usually precedes the actual date of publication by 1 year.) (8) W. Bell Dawson, Tides at the Head of Bay of Fundy, Dept. of the Naval Service, Ottawa, Ont., 1917. (9) W. Bell Dawson, Tide Levels and Datum Planes in Eastern Canada, Dept. of the Naval Service, Ottawa, Ont., 1917. (10) Edward Rowe Snow, Great Storms and Famous Shipwrecks of the New England Coast, Boston, Mass., 1943. (11) David Stick, Graveyard of the Atlantic: Shipwrecks of The North Carolina Coast, Chapel Hill, N.C., 1952. (12) Ben Dixon McNeill, The Hatter asman, Winston-Salem, N.C., 1958. (13) Transactions of the Canadian Institute, vol. IX, University of Toronto Press, Toronto, Canada, 1913. (14) Dorothy Franklin, West Coast Disaster, Columbus Day, 1962, Gann Publishing Co., Portland, Oreg. (no publication or copyright date). (15) David M. Ludlum, Early American Hurricanes, 1492-1870, Boston, Mass., 1963. (16) Ivan Ray Tannehill, Hurricanes, 9th ed., Princeton, N.J., 1956. (17) Gordon E. Dunn and Banner I. Miller, Atlantic Hurricanes (rev. ed.), Baton Rouge, La., 1964. (18) David M. Ludlum, Early American Winters I, 1604-1820, Boston, Mass., 1966. (19) David M. Ludlum, Early American Winters II, 1821-1870, Boston, Mass. 1968. (20) William E. Clark, ed., Naval Documents of the American Revolution, vol. 2, Washington, D.C., 1966. (21) U.S. Army Engineer District, Charleston Corps of Engineers, Charleston, South Carolina, Reconnaissance Report on Beach Erosion, Pawleys Island Beach, George- town County, South Carolina, October 1972. (22) Beach Erosion and Damages to the Ventura County Shoreline, Department of Public Works, Ventura County, Calif., June 1972. (23) Annual Report of the Superintendent of the Coast Survey for 1847, Washington, D.C., 1847. Reference Code No. (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65) «><>) (67) National Oceanic and Atmospheric Administration (NO A A), Environmental Data Service, Washington, D.C.: Mariners Weather Log National Oceanic and Atmospheric Administration (NOAA), National Weather Service (formerly U.S. Weather Bureau), Silver Spring, Md.: (a) Climatological Data — National Summary (b) Monthly Weather Review (c) Storm Data (d) NOAA Technical Reports, NWS Series (e) NOAA Technical Memoranda, NWS Series Weatherwise (bimonthly publication for the American Meteorological Society and others), Boston, Mass. Shore and Beach (periodical publication of the American Shore and Beach Preservation Association), Miami, Fla. The National Geographic magazine, Washington, D.C. Coastal Research Group, Department of Geology, Uni- versity of Massachusetts, Contribution No. 1, Coastal Environments, N.E. Massachusetts and New Hampshire, 1972. The Los Angeles Times, Los Angeles, Calif. The Pacifica Tribune, Pacific a, Calif. The San Diego Union, San Diego, Calif. The San Francisco Examiner, San Francisco, Calif. The San Francisco Chronicle, San Francisco, Calif. The Evening Telegram, Saint John's, Newfoundland, Canada Bridgeport Sunday Post, Bridgeport, Conn. The New Haven Journal-Courier, New Haven, Conn. Delaware State News, Dover, Del. Every Evening, Wilmington, Del. Daily Kennebec Journal, Augusta, Me. Maine Sunday Telegram, Portland, Me. Portland Press-Herald, Portland, Me. The Bar Harbor Times, Bar Harbor, Me. The Boston Evening Globe, Boston, Mass. The Boston Gazette and Country Journal, Boston, Mass. The Boston Herald, Boston, Mass. The Boston Journal, Boston, Mass. The Boston News-Letter, Boston, Mass. The New Hampshire Gazette, Portsmouth, N.H. The Newark Star-Ledger, Newark, N.J. The New York Times, New York, N.Y. The Savannah Morning News, Savannah, Ga. The News and Observer, Raleigh, N.C. News-Observer Chronicle, Raleigh, N.C. The Oregon Daily Journal, Portland, Oreg. The Oregonian, Portland, Oreg. The Philadelphia Inquirer, Philadelphia, Pa. The Norfolk Virginian-Pilot, Norfolk, Va. The Times-Dispatch, Richmond, Va. The Virginian Pilot, Norfolk, Va. The Virginian Pilot and the Norfolk Landmark, Norfolk, Va. The Seattle Daily Times, Seattle, Wash. The Seattle Post-Intelligencer, Seattle, Wash. The Evening Star, Washington, D.C. Biddeford-Saco Journal, Biddeford, Me. Evening Express, Portland, Me. York County Coast Star, York County, Me. ■w Strategic Role of Perigean Spring Tides, 1635-1976 Reference Sources for Tidal Flooding — Continued Reference Code No. (68) The Portsmouth Herald, Portsmouth, N.H. (69) Raymond Herald and Advertiser, Raymond, Wash. (70) The Savannah Daily Advertiser, Savannah, Ga. (71) M. P. O'Brien and J. W. Johnson, "The March 1962 Storm on the Atlantic Coast of the United States," in Proceedings, VHIth Conference on Coastal Engineering, Council on Wave Research, The Engineering Founda- tion, Richmond, Va. 1963. (72) Civil Works Branch, Construction-Operations Division, North Atlantic Division, Corps of Engineers, U.S. Army, Report on Operation Five-High, March 1962 Storm, August 1963. Reference Code No. (73) Charles L. Bretschneider, "The Ash Wednesday East Coast Storm, March 5-8, 1962; A Hindcast of Events, Causes, and Effects," in Proceedings of the Ninth Con- ference on Coastal Engineering, Lisbon, Portugal (1964), 1964. (74) Massachusetts Geodetic Survey, Works Progress Ad- ministration Project No. 165-14-6085, "High Water Data, Flood of March 1936 in Massachusetts," Boston, Mass., November 1, 1936. (75) Fitz-Henry Smith, Jr., "Some Old-Fashioned Winters in Boston," vol. 65, Proceedings of the Massachusetts Historical Society, Boston, 1940. Table 5 A Representative Sample of Newspaper Articles Covering Tidal Flooding Events Associated with Perigean Spring Tides, 1723-1974 Explanatory Comments The following reproductions of news articles, covering 50 major tidal flooding events that have occurred on both the east and west coasts of North America in association with perigean spring tides, comprise one-half of the total list of representative events listed in the master catalog (table 1) . In practically all cases, considerable additional information was contained in the original full-length news article. These news accounts have been shortened, and considerable detailed material relating to individual prop- erty losses as the result of tidal flooding has been deleted. The excision of material is indicated by the use of ellipses. News photos which, in many cases, accompanied the orig- inal stories and illustrated the considerable extent of flood- ing damage have been eliminated, for technical reasons. However, no substantive editing involving any altera- tion of the original content has been employed. Every attempt has been made to preserve all possible information on the preceding and concurrent meteorological condi- tions pertinent to the tidal flooding, the observed and recorded heights of the tides, and other factual data. Care also has been exercised to include all newspaper datelines or, where these are lacking, other textual references to the time of the flooding event (the clay of the week, etc.) through which an accurate correlation may be made with the corresponding perigee-syzygy data. The exact source of each article is identified by news- paper name, day of the week and date of publication (or the period of coverage for weeklies) , and the page and column for each article used. The initials "O.S." stand for Old Style Calendar and "N.S." for New Style Calendar, whose exact meanings are explained in a technical note at the beginning of chapter 1. (References to columns start with that at the extreme left hand side of the page as col. 1 and proceed progressively to the right.) Although news- papers may have changed their titles over subsequent years, the contemporary title is used in all cases. The arti- cles are chronologically arranged. The boldface number following each newspaper article is a key number for use in cross-referencing the article to the listing of the flooding events and their associated astro- nomical conditions given in table 1, where the same serial numbers are used. The presence of a capital letter preceding this number indicates that a corresponding synoptic weather map and/ or tidal curve relating to this event (and carrying the same alphanumeric descriptor) are to be found in part II, chap- ters 7 and 8, respectively, of the text. Where tidal flooding occurred simultaneously on both the east and west coasts, a small letter "e" or "w" following the key number indi- cates which coast is represented. The figures printed in the lower left corner following each news article provide information relating to the perigee-syzygy alignment with which the reported tidal flooding was associated. The first such entry gives the date and time of the mean epoch of perigee-syzygy, specified to the nearest hour or half-hour in the respective eastern standard time (e.s.t.) or Pacific standard time (P.s.t.) zone concerned. All times given are standard times, despite the occasional historical intervention of daylight time or war time. The number in parentheses is the separation, in hours, between the times of perigee and syzygy, in the algebraic sense perigee minus syzygy. This grouping of data conforms exactly with the data given in similar slant- lettering on the reproduced synoptic weather maps, tide curves, or other graphical representations throughout the volume, with which these data may be rigorously com- pared. The morning-final or evening-final editions of the news- papers concerned were used in nearly all cases. Where another edition was used and this fact is known, it is so indicated. Since many of the original newspaper articles were not reproducible in their aged condition, all articles have been uniformly reset, in abridged form. Although some of the earliest news accounts lack headlines, and other such heads have been eliminated because of their multiple-column widths or large point sizes, an effort has been made to retain significant headings wherever possible. Additional news articles relating to unusually large coastal flooding events which are given special attention in the main body of the text are contained in chapter 7. 39 10 Strategic Role of Perigean Spring Tides, 1635-1976 The Boston News-Letter (New England - Weekly) Thurs., Feb. 21-Thurs., Feb. 28, 1723 (O.S.) Page 2, Col. 2 Boston, Febr. 25. — Yesterday, being the Lord's Day, the Water flowed over our Wharff's and into our Streets to a very surprizing height. They say the Tide rose 20 Inchest higher than ever known before. The Storm was very strong at North-east . . . The loss and damage sustained is very great, and the little Image of an Inunda- tion which we had, look'd very dread- ful . . . 1722/23 Feb. 23 (O.S.) 1723 Mar.6(N.S.) 16h e.s.t. (-6) Islands were submerged by the waves, and many docks were so badly shattered that it will be necessary to rebuild them. The Harlem flats resembled an inland sea . . . . . . The tide rose to a great height and washed out many manufacturing places . . ■. Much damage was done to buildings by the wind, and to the docks by the very high tide. The meadows between Williams- burg and Greenpoint were flooded by the wind backing the water up East river, and a number of buildings were inundated . . . 7878 Oct. 25 9.5h e.s.t. (17) 19 The Boston Herald Wed., Nov. 25, 1885 Page 1, Cols. 4-6 A MIGHTY TIDE. Old Neptune Baptizes the Shore. An Unprecedented Rise of Water. The Boston Gazette and Country Journal Mon., Dec. 11, 1786 (N.S.) No. 1690, Page 3, Col. 1 Boston, December 11. — On Monday evening last came on, and continued without inter- mission until Tuesday evening, as severe a snowstorm as has been experienced here for several years past . . . . . . The wind, at east, and northeast, blew exceeding heavy, and drove in the tide with such violence on Tuesday, as over- flowed the pier several inches, which en- tering the stores on the lower part thereof, did much damage to the Sugars, Salt, &c. therein — considerable quantities of wood, lumber, &c. were carried off the several wharfs . . . 7786 Dec. 4 23.5h e.s.t. (-17) The Philadelphia Inquirer Thurs., Oct. 24, 1878 Page 1, Cols. 2, 3 High Tide at New York and Shattered Shipping, Docks and Buildings. New York, Oct. 23— The tide which ac- companied the eastern gale of today was <>tic of the highest remembered, and caused extensive damage along the city's eastern front. The sea walls around Ward's, Ran- dall's and the upper end of Blackwell's The New York Times Fri., Sept. 29, 1882 Page 5, Col. 2 HIGH TIDES AT LONG BRANCH Long Branch, Sept. 28. — The storm on the New Jersey coast has increased in in- tensity since midnight yesterday, the gale continuing from the north-east . . . ... At high tide this morning — 8 :30 o'clock — a terrific sea was coming over the Long Branch Ocean Pier, the black waves touch- ing the floor of the pier 20 feet above the ordinary tide . . . . . . The heavy sea washed over the land and into the Shrewsbury River, the water reaching the first floors of the elegant cottages and flooding the stables. Car- riages were sent to higher ground on the mainland. The Pennsylvania Railroad was badly cut at Seaside Park, and passengers were sent by way of the New-Jersey Cen- tral to New-York. At Branchport, Little Silver, and Red Bank at low tide the waters were within eight inches of the floors of bridges, and much alarm was felt as to the effects of the high tide to-night. This tide is the highest ever known here . . . . . . The high tide of yesterday morning has not been surpassed in several years. Late last evening the tide was rising rapidly, and there was every indication that this morning it will reach the same height as yesterday, if it does not surpass Picturesque Commingling of Wind and Wave. 7882 Sept. 26 79/7 e.s.f. (-10) 20 Great Damage to Property in New York. The Jersey Coast Strewn with Wreckage. . . . Yesterday's storm proved one of the severest that has visited this section of the country, its effect being most perceptible along the coast and water front of the city. In the upper harbor at noon, when the tide was full, the sight was a grand one . . . ... At the South city ferry the tide over- flowed to the entrance gates on Lewis street on the East Boston side, and the Eastern-a venue entrance in the city proper was all awash for a short time. The ticket boxes on the East Boston side were sub- merged to the depth of several inches by the encroaching element. At the North ferry the extreme high tide made matters unpleasant for the pedestrians, as the water worked its way up through the east- erly end of the new headhouse on the Bos- ton side. The ferry employes say that the tide was the highest that has been known here for a great many years. The tide at midnight was considerably higher, it rising 11 ft. 7 in., but owing to the decrease of the wind, its effects were not so severe as those of the noon tide . . . . . . The waves at noon broke over the high wall of the State dock. South Boston, and sent their spray high in air, Representative Great Tidal Floodings of the North American Coastline 41 the foam from which was blown several hundred feet inland. The sea wall between Jeffries point and Wood island, which has Towered Above the Angry Waves since the destructive gale which washed Minot's light away in 1851,— was yester- day overtopped by the briny elements, and large sections of it were wholly submerged, while on all parts the sea made heavy breaks at frequent intervals . . . Along the North and South Shores. The tides ran unusually high at Lynn. There was much damage at some of the wharves. The water nearly reached the Nahant roadway. The Boston, Revere Beach & Lynn railroad's outward tracks were badly washed for a fourth of a mile between the Point of Pines and Oak Island . . . The tide was the highest at Salem that has been known for years. It filled the North river canal to the top. The tide at Edgeworth and in the marsh on Charles street was the highest ever known. A large number of cellars were flooded, and a lot of lumber floated off. The water covered the Saugus branch track of the Boston & Maine railroad, causing some inconvenience to trains. The tide also covered Charles street, making it impassable. A large number of tons of hay was floated off on the marshes at Welling- ton, causing a considerable loss. At Cohasset the tide was the highest since April 16, 1851, the day of the destruc- tion of Minot's ledge lighthouse. The streets and meadows in the vicinity of the harbor were overflowed, and the wharves were covered to a depth of 18 inches. NEW YORK AND VICINITY Great Damage to Property — The Highest Tide Ever Known New York, Nov. 24, 1885. Never before has such a high tide rolled in upon the city, and incalculable damage has been done along the water front. At 10 o'clock, when the tide was at the full, the water was said by the ferry authorities to be nearly three feet higher than it had ever been known before. The bridges in the ferry houses on the North river were tilted up by the tide to an angle of 30°, and the incoming boats scraped along on the top of the rack guards. When the boats were made fast to the docks, the passengers, in many cases, had to be hoisted upon the bridge . . . ... A telegram from Rockaway Beach says "Great damage has been done all along the beach. The tracks of the New York, Wood- haven & Rockaway railroad have been washed out, and trains cannot proceed. The spile work across Jamaica bay is totally submerged, and, for safety's sake, no trains are allowed to cross it. The docks at the different hotels have all been dam- aged, and are likely to break up entirely unless the wind shifts soon. The families living in small houses along the ocean and bay have been obliged to move out. The cellar of the great hotel is flooded. The wind is blowing a gale" . . . . . . At Hunter's Point, the tide rose to an extraordinary height, water to the depth of several feet having covered the docks and street for a distance of a hundred yards, rendering foot travel to the ferries and railroad impossible. Wagons cannot get aboard the ferry boats, the latter being several feet above the ferry bridges. The lower parts of Astoria and Ravenswood are also flooded. The meadows at Flushing are under water, and the railroad trestle is covered in places. Several wagons and small outhouses have been carried off and are floating in the bay. The cellars and first floors in the lower part of the village are flooded, and the inmates of the houses have been compelled to move upstairs. At Atlantic City, N. J., the tide was the highest for years. The damage to property was considerable. Much of the board walk along the ocean front is washed away, and the railroad tracks are washed out near the inlet. Many of the streets are flooded. Boats are being used to convey residents up and down some of the streets . . . . . . Prom Barnegat bay to Sandy Hook the beach is covered with boards torn from bulkheads and summer houses. The ocean promenade and pavilions of James A. Bradley, the founder of Asbury Park, were damaged to the amount of $1000. Several elegant cottages at Elberon have been badly damaged. At Bridgeport, Ct., the tide reached the highest point known in that vicinity for many years, wharves, warehouses and cel- lars along the water front being over- flowed to the depth of several feet, causing much damage . . . 7885 Nov. 23 22h e.S.t. (+59) 21 The New York Times Wed., Oct. 14, 1891 Page 1, Col. 5 DAMAGE BY HIGH TIDES Long Branch, N. J., Oct. 13.— The severe northeast wind and rain storm which has been raging for the past twenty- four hours has done considerable damage all along the New Jersey coast, and par- ticularly between Sandy Hook and Point Pleasant. For twelve hours the wind along the seaboard has blown from forty to fifty miles an hour and the sea has been un- usually high and strong . . . . . . The foundation and platforms of the Ocean Hotel bathing pavilions, just south of the pier, were this morning smashed into kindling wood by the high tide and carried out to sea. Between the Surf House, just north of the pier, and Chelsea Avenue nearly eight feet of sand have been carried away, and the bluff has been badly washed and inundated . . . . . . Minugh's Hollow, at Seabright, is flooded by the high tide in the Shrewsbury River, and several small houses there have been badly undermined. The tide there is so high that the first floors in several houses are submerged. At Highland Beach the tracks of the New-Jersey Southern Railroad are covered with water . . . . . . Point Pleasant, N. J., Oct. 13. — The high tide this evening cut the beach badly at Seabright. At this place the large pavil- ions of W. T. Streets and Dr. Knox were surrounded by water and both houses were washed away. The seas ran down all At- lantic and Arnold Avenues and the board walks are afloat. At Bayhead 300 feet of bulkhead and board walks were cut out and went to sea. At Barnegat City the railroad is torn up to the beach and rail- road communication to the city is cut off. At Atlantic City and Ocean City the sea is very high, and the railroad from Cape May to Sewell's Point is under water. The sea came in like a tidal wave. It is the worst surf in years. . . . 7897 Oct. 16 23h e.s.t. (—20) 23 The New York Times Sat., Feb. 9, 1895 Page 3, Col. 4 TKEMENDOES TIDES UN THE COAST Wharves, Streets, and Buildings Flooded . . . enormous high tides prevailed along the entire coast . . . BIG TIDES ALONG NEW-ENGLAND. Streets, Wharves, and Buildings Badly Flooded. BANGOR, Me., Feb. 8.— The tide here today was the highest since the freshet of \2 Strategic Role of Perigean Spring Tides, 1635-1976 1S4(I. There is from one to three feet of water in the cellars of stores on Exchange, Broad, Central, and Front Streets. The damage caused is from $15,000 to $20,000. The tide is rive feet higher than flood. The railroad bridge across Kenduskeag stream is weighted down with freight cars and locomotives to prevent it from being carried away. PORTLAND, Me., Feb. 8.— To-day's tide was the highest known here for years. In some cases the water rose to the flooring of the wharves, and it flooded many cel- lars. BATH, Me., Feb. 8.— The tide to-day is the highest ever recorded here, necessitat- ing the stopping of work in several build- ings along the wharves. PROVIDENCE, R. I., Feb. 8.— The tide at this port was the highest since the fam- ous storm of September, 1869. The water ran over docks and wharves and sub- merged cellars of warehouses. In some parts of the Narragansett Electric Light- ing Company's plant 6 feet of water were measured. The damage to the company will amount to thousands. NEW-BEDFORD, Mass., Feb. 8. — The tide here was never known to rise so high as it did to-day. Water covers the wharves to the depth of two feet. Front Street was inundated to the depth of eighteen inches. On Water Street the New-Bedford Ma- chine Company and the Smith & Carlton Iron Foundry were obliged to close, and several of the mills were forced to close down because of the large amount of water in the basement. HIGHLAND LIGHT, Mass., Feb. 8.— Such a gale as swept Cape Cod to-day has not happened before since the great bliz- zard of 1888. The wind at 9 A. M. reached a velocity of sixty miles an hour. The tides in the bay were higher than ever known before, washing the banks and threatening the destruction of twenty fish- ing houses along the shore. Roads were washed in every direction. NEWPORT, R. I., Feb. 8.— A tremen- dous high tide, accompanied by great seas and heavy ice, is doing great damage along the water front to-day. Two barges are ashore. At the beach, a part of the sea wall is gone, and the roadway is washed away. At the naval station, several thousand dollars' damage was done to walls. 7895 Feb. 9 10h e.s.t. (-4) 25 The New York Times Sun., Feb. 10, 1895 Page 1, Cols. 3, 7 . . . SANDY HOOK, N. J., Feb. 9.— The large four-masted steamship Patria of the Hamburg-American Packet Steamship Company, while proceeding to sea this evening, grounded in the main ship chan- nel, near the southern edge of Palestine Shoal . . . LOWEST TIDE IN TWENTY YEARS Ferryboats Blockaded by let Lines in Operation. -Few A northwest wind, an extremely low tide — the lowest in twenty years, old boat- men say — and the heavy ice conspired yesterday to tie up all the ferries on the East River from the Battery to Thirty- fourth Street . . . 1895 Feb. 9 10h e.s.t. (-4) 25 The New York Times Sun., Feb. 10, 1895 Page 2, Col. 1 . . . The Staten Island ferryboats were all running, but their trips to and from St. George were eventful. The Southfleld had a severe encounter with an ice floe at 6 o'clock in the morning. She was on her first trip from Staten Island, and she had a number of passengers on board. She came up the bay without much trouble, but between Governor's Island and the Battery she got stuck in a heavy icefield that was swept by the current around from the North River into the East River toward the bridge. The Southfleld tried hard to escape from the ice, but her wheels were clogged and she was forced to drift with the floe . . . . . . The boats of the Staten Island line ran all day, but late in the afternoon the tide was so low that the ferry bridges were far above the decks of the boats, and the ascent and descent were so dangerous that teamsters did not dare to risk their horses on the steep planks, and wagon traffic had to be suspended . . . . . . The Shackamaxon, that plies between Ellis Island and the Battery, made several trips, and every one was eventful. She encountered immense cakes of ice, through which she had to plow her way, and the northwest winds that swept in gales across the bay helped to impede her progress . . . . . . The Fulton Ferry boats Fulton and Farragut ran until 4 o'clock yesterday afternoon. From 6 to 9 A. M. they had much difficulty in getting across, but after noon they made trips more regularly. At 4 P. M. the tide was so low and the ice on the Brooklyn side became so bad that it was necessary to stop running the boats 7895 Feb. 9 10h e.s.t. (-4) 25 The Richmond (Va.) Dispatch Fri., Aug. 18, 1899 Page 1, Col. 7 THE TIDE UNUSUALLY HIGH NEWPORT NEWS, VA., August 17.— (Special.) — James river at this point is higher to-night than it has been since the great storm of 1889. It is believed the tide has risen five feet above average high water. The water is up in the car-tracks, in the bottom of the piers, and within a foot of the pier-floors . . . 7899 Aug. 20 20.5h e.s.t. (-7) 30 The New York Times Mon., Nov. 25, 1901 Page 1, Col. 7 Heavy Tide Overflows East and West River Fronts. . . . The northeast gale, that started to blow in this neighborhood Saturday even- ing, did not abate to any appreciable ex- tent, until well in the afternoon of yester- day. Its maximum velocity was nearly sixty miles an hour. It blew with unabated furv all night Saturday and yesterday . . . Not only the winds made life miser- able from a marine standpoint, but the fides as well. According to veteran mari- ners long familiar with everything that had to do with New York Harbor, a tide such as has not been seen in these parts in nearly a score of years washed upon the shores of the city and nearby islands yes- terday morning. It swept over the Battery wall, deluged the piers along the river fronts, finally ending in the cellars under I be bouses on South. West, and other af- Representative Great Tidal Floodings of the North American Coastline 43 fected streets, soaking and in many cases ruining, the merchandise or other things contained in them . . . ... In Manhattan the greatest damage, of course, was along the streets fronting on the rivers and in the subway. On West Street produce merchants were busy hail- ing the water out of their cellars. From Warren Street to Park Place, on West Street, the shops, saloons, and restaurants were flooded. A restaurant at 16.") West Street was so completely surrounded with water that the proprietor was unable to get to it when he arrived to open up early in the morning. The Fall River steamer in arriving at Pier IK, at the foot of Murray Street, had to keep her passengers on hoard owing to the water, which was about two feet deep, that Hooded the street outside. . . . ... In the East River there was a serious amount of damage, due to a tide, which river men insist has never been equalled in their experience. The lighthouse on the north end of Blackwell's Island, usually high above flood tide, was wrapped in spray, the platform of the house being but little above the water. The entire north side of the island was flooded at 9 o'clock, and several small frame buildings were carried away. In the upper west side the greatest damage was in the rapid transit tunnel, the excavations extending through Lenox Avenue north from One Hundred and Thirty-fourth Street to the Harlem River . . . This trench is eighteen feet wide and forty feet deep, and is to go under the river at a depth of sixty feet below its bottom. The contractor had sunk a coffer dam at the river bank. This held, but the water poured over it and into the tunnel, tilling it. The banks were softened and caved in at many places, but the tunnel is not seriously damaged. The loss to the contractors is about $10,000 . . . 7907 Nov. 25 75.5/7 e.s.t. (-9) 34 The New York Times Mon., Nov. 25, 1901 Page 2, Cols. 3, 4 HAVOC AT KEYPORT KEYPORT. X. J., Nov. 24.— The tide rose until the docks along the water front were several feet below the water. More than a hundred large sloops were in Key- port harbor, besides a large number of smaller craft. Owners of the vessels stood upon the shore this morning and were powerless to save their property, as the vessels dragged their anchors and burst from their moorings. The tide and wind swept oyster boats and handsome sloops in a wrecked mass upon the shore and meadows. The Golden Gate, a large sloop owned by ("apt. William E. Woolley of this place, was dashed upon the shore here, and crashed through a large storehouse building owned by Bauer & Hopkins . . . were lifted from their foundations and curried away with the tides . . . . . . Thomas Browns dock at Lock port was almost completely wrecked by the tide . . . MUCH DAMAGE ON THE CONNECTICUT COASTS. XEW HA VEX. Conn., Nov. 24— At Ship- pan Point, in Stamford, several docks con- nected with Summer residences were car- ried away by the unusually high tide, and the cellars of a number of buildings near the water front were completely sub- merged. Along the canal the water rose over the banks and a considerable part of the lower end of the city was inundated. The freight offices of the North and East River Steamboat Company were flooded, as were many of the shops on the canal . . . . . . Milford probably suffered more than any other town on the Connecticut shore, and the damage there is estimated at $10,- 000. The seawall at Burwell's Beach, re- cently built, was completely carried away. At Fort Trumbull Beach every bathing house was washed away, and the banks and lawns of the Summer homes were destroyed . . . . . . At Greenwich the tide was live feet higher this morning than usual, and every- thing on the low lands was carried away. Lumber yards were flooded, and huge piles of lumber toppled over and floated out into the harbor. At Belle Haven two docks owned by John 1'. Lafflin and John B. Barrett were swept away and carried on to Byram shore, and the macadam roads were damaged to such an extent that it will take from $3,000 to $4,000 to repair them. The total damage in this vicinity will reach at least $7,000 . . . SCENES OF DESTRUCTION AT OLD CONEY ISLAND Bulkheads and Boardwalks Smashed Into Kindling Wood. . . . Coney Island breezes yesterday were of the cyclonic sort, and came from the northeast, meeting unusually high tides, so the waves rose high, worked havoc with the strongest bulkheads, and tossed about boardwalks with a playful madness ren- dering them fit only for kindling wood . . . . . . The fl 1 tide at 5:36 o'clock in the morning came tearing in and tearing up . . . . . . The Manhattan Beach Hotel suffered severely on its water front. The plank walks were torn away. 010 feet being destroyed, and the bathing pavilion was very nearly destroyed. At the Oriental Hotel the hoard- walk was torn to bits. The iron lamp posts were twisted and bent, and the embank- ment cut into. It will not be possible to fix the loss until the storm has subsided and an examination can be made. The waves breaking over what was the boardwalk rolled in on the lawn and scattered over it the debris of its earlier destruction. The total loss at Coney Island is estimated at $25,000 . . . CHATHAM, Mass., Nov. 24.— The life savers along the shore from Monomoy Point to Provincetown report the gale as very severe, with a high tide which has washed away miles of the beaches and made bad inroads into the headlands. At South Beach the high tide and heavy seas have cut away the sand embankment for many years . . . 7907 Nov. 25 75.5/7 e.s.t. (~9) 34 The Evening Telegram Saint John's, Newfoundland Tues., Feb. 3, 1908 Page 4, Col. 2 . . . The railway track was washed away about eight miles this side of Port aux Basques so that the Bruce express was not able to leave there this morning. The sea swept in with terrific violence and inundated the track for several hundred yards. The tide is not expected to subside till this afternoon, about 3 o'clock . . . 7908 Feb. 2 Oh e.s.t. (-8) 35 44 Strategic Role of Perigean Spring Tides, 1635-1976 The Los Angeles Times Fit, Dec. 18, 1914 Pt. 2, Page 1, Cols. 4, 5 Destructive. The Virginian-Pilot and the Norfolk Landmark Norfolk, Va. Sun., April 4, 1915 Page 5, Col. 3 SEAS LASHED BY GALE BATTER COAST TOWNS Houses Destroyed, Bulkheads Shattered, Sewer and Gas Mains Severed by Pounding Breakers on Crest of High Tide— More Trouble Feared Today— Loss of Property Many Thousands— No Casualties. Lashed to a fury by a heavy on-shore Kale that lent impetus to an unusually high tide, the sea battered the southern coast early yesterday morning with fury and destroyed property worth many thou- sands of dollars. From all along the shore came the same story, of huge waves leaping over harriers and carrying destruction with them. At Long Reach $s< >.<>(>< I damage was done, while at Balboa the loss was also heavy. Railway tracks were washed out at the harbor and traffic delayed for hours. One fatality due to the storm was reported from the sea. There were no casualties ashore. The off-shore breeze that accompanied the rain of Wednesday night switched to the southeast early in the day, and blew at places forty-five miles an hour. Xo damage was done here. Further trouble at coast points is feared for this morning's high-tide period. TERROR AT LONG REACH. \Vashing houses into the sea, tearing up concrete bulkheads and cement promen- ades, and spreading terror and damage along the ocean front, the wind, aided in its work of destruction by an extremely high tide and heavy rain, paid a terrifying visit to Long Beach early in the morning. Many persons had narrow escapes from ilrowning in their seaside bungalows, one of which was completely destroyed, and four are partially washed away. Great anxiety is felt along the washed- out portions of the beach over this morn- ing's high tide, when more buildings and works are expected to go. A tide of 7.3 feet is expected at 0:15. Many of the houses on the east beach are hanging over a bluff caused by the waves, and, although the owners and occupants of these build- ings worked feverishly last night with bags of sand and timbers, they cannot hope to stem the huge tide expected . . . 1914 Dec. 16 Oh P.s.t. (-36) 38 The Los Angeles Times Fri., Dec. 18, 1914 Pt. 2, Page 6, Cols. 3-5 PENINSULA INUNDATED. In the wake of a forty-five mile gale, the tide rose to unprecedented height at Balboa Beach yesterday morning, broke over the bulkheads, cut 100 feet off the tip end of the peninsula, inundated Collins Island, damaged or wrecked a score of residences and receded, leaving many thousands of dollars damage in its wake . . . Although the storm was accompanied by a gale from the southeast and the high- est tide in nearly twenty years, there was no damage to shipping at the harbor . . . . . . The tide at 8 :50 a.m. reached 7.5 feet, and with the storm behind it backed up the water in the channel and the bay to a hitherto-unknown height. About 200 feet of the Salt Lake track at Ostend was washed out by the high tide, and train service was demoralized for several hours. Repairs were completed last night and service resumed . . . 1914 Dec. 16 Oh P.s.t. (-36) STORM SEVERE AT VIRGINIA BEACH . . . More damage was inflicted by the storm at Virginia Beach than that resort has suffered in the past 30 years. Swept by the 75-mile gale of Friday night and early yesterday morning, the beach front suffered in a number of places, both from wind and water . . . . . . Practically all of the board walk in front of the site of the old Princess Anne hotel was torn up by the surf which broke over the sea wall . . . 1915 Mar. 31 22h e.s.t. (+42) 39 38 The New York Times Thurs., April 11, 1918 Page 15, Cols. 5, 6 Sixty-Mile Blow from the East Piles Twelve-Foot Tide Over Piers and Streets. Beach Hotels and Bungalows Flooded and New Cement Shore Walk Undermined ... A sixty-mile easterly gale, blowing directly from the sea, pushed a tremen- dous tide against the whole length of the south shore of Staten Island late yesterday afternoon, submerging piers from four to six feet, inundating streets and business property, and tearing several small ves- sels from anchorages and throwing them ashore. It was estimated that the property loss would reach $100,000 . . . . . . All along the waterfront from Simon- son Avenue, at Clifton to Fort Wadsworth, a distance of two miles, the piers were under water, and the ships which had been loading or discharging cargo had to be moved to outside anchorage last night to prevent them pounding to pieces. In Clifton the water was four feet deep in the streets, and boats were used to move about. Summer hotels and bungalows at South Representative Great Tidal Floodings of the North American Coastline 45 Beach and Midland Beach were damaged severely. The flood swept over the first floors of most of these places. Long stretches of the new concrete walk at both beaches were undermined by the tide ... At 10 o'clock last night it was said the tide had reached eleven feet above normal high tide, the highest for years . . . . . . SEABRIGHT, N. J., April 10.— Row boats were used in Ocean Avenue tonight at high tide. The crest came at 11 :30 after which it subsided a little after threaten- ing to inundate several buildings . . . 7978 Apr. 10 14.5h e.s.t. (-19) A-43 The New York Times Sat., April 13, 1918 Page 11, Col. 3 Unusually High Tide Drives Water to Station Entrances in Jersey City. Homes at Sea Bright Inundated— $50,000 Damage at Sea Gate. water. Families, fearing the water would rise above their living quarters, sought refuge in the upper stories. Finucan's Hotel, facing the sea, was so undermined ,by water that it was feared it would collapse. The boulevard at Edgemere was covered with water and several bungalows were washed away. . . . According to the city gauge at Pier A, North River, at 10 o'clock Thursday night the card registered a height of water of eight and fifteen-hundredths feet above mean low water. This is the highest tide since the records were established in 1886 . . . SEA FLOODS ATLANTIC CITY ATLANTIC CITY, N. J., April 12.— A record tide did much damage along the sea front today. For the first time in years the sea flooded the lawns of the big hotels, smashed doors and flooded cellars, drown- ing out fires in some of the apartment houses and causing loss of property in store rooms. The water put the plant of the electric company out of service, and the entire city was in darkness last night. 7978 Apr. 10 14.5h e.s.t. (-19) A-43 makes a difference of, say, a couple of feet as compared with moon at the quarter. On the 18th, then, wind and moon favored an exceptional high tide. On Nov. 18 my barometer showed a sea- level reading of approximately 28.7 inches, perhaps, with one exception, the lowest I have ever happened to observe. When the barometer is low — that is, when the air pressure on top of the water is lessened — the water tends to rise. In support of this let me quote from William M. Davis's book 'Whirlwinds, Cyclones, and Torna- does,' where he speaks of this phenomenon in the Bay of Bengal. "The diminished atmospheric pressure about the storm centre allows the heavier surrounding air to lift the water, and for every inch that the mercury falls in the barometer the water will rise a foot, . . . and if a strong tide conspires with these other causes a great flood is produced." The same rule that works in the Bay of Bengal works in New York Bay, I should think. CHARLES VEZIN, Jr. Yonkers, Nov. 22, 1918. 1918 Nov. 17 12.5h e.s.t. (-29) . . . The high east wind and the unusually high tide yesterday caused great damage all along the Atlantic Coast . . . . . . On the waterfront the water piled up by the wind flooded streets, undermined houses, interfered with ferry traffic, and caused discomfort to thousands of persons. In New Jersey the water came up so high that it flooded the waiting rooms of the railroad stations and interfered with the handling of freight in the Erie and Penn- sylvania railroad yards. When the tide came up water began to run down the steps of the entrance to the Hudson tunnel in the Lackawanna station in Hoboken. It soon became so bad that the entrance had to be closed to the public, and a barricade of boards was hastily raised to stop the water from flooding into the tube and interfering with the traffic. As the tide came higher the water rose in the ferry houses and more poured into the tunnel . . . . . . Wind and tide wrought destruction along the shore from Long Beach to Sea Gate. At Coney Island, Brighton, and Sea Gate the police last night estimated the damage at .$50,000 . . . ... In the district around Far Rockaway streets were flooded, small buildings car- ried away, and larger ones damaged. Train and trolley service was practically stopped. Near Howard Beach parts of the Long Island Railroad tracks were covered by The New York Times Mon., Nov. 25, 1918 Page 12, Col. 6 Remarkable Tides on Nov. 18 To the Editor of The New York Times : Your issue of Nov. 19 contained this paragraph : "The south wind caused an unusually high tide. Many of the ferry bridges were lifted until vehicles had to go up a sharp incline to make the boats, and in some cases the water flooded the ferry houses." Your issue of the 20th reproduced a dispatch from Quebec, dated Nov. 19, which read in part as follows : "The tidal wave . . . swept up the St. Lawrence last night, causing damage esti- mated at $1,000,000. Part of the village of Batiscan was submerged by the flood tide." The above accounts went on to ascribe the abnormal tides to the south and east winds, which, of course, had an effect, but there were two other unmentioned causes — the moon, and the low barometer pres- sure. The moon was full Nov. 19, and it is a familiar phenomenon that, other things being equal, tides always run higher and run lower at full moon. Frequenters of the seashore may have noticed that this The New York Times Sat., Nov. 8, 1919 Page 5, Col. 1 HIGH TIDE FLOODS STREETS AT FERRIES Unusual Rise Causes Delays on the Jersey Side for More Than Three Hours UPPER PLATFORMS USED Pilots Make Slips with Difficulty — Water Enters Cellars on New York Side An extraordinarily high tide on the North River yesterday morning, said by the water front experts to have been caused by the northeast wind and the full moon, flooded the streets and cellars of the houses, interfered with the power If. Strategic Role of Perigean Spring Tides, 1635-1976 plants of the Grand and Desbrosses Streets surface ear lines, and partially tied up the Hudson River ferry services, which caused a good deal of inconvenience to the early morning commuters. The passengers managed to board the ferryboats from the upper platforms on the Jersey shore, but the water was so deep in the streets below that trucks had to wait two hours before it subsided . . . . . . The Brooklyn shore suffered, too, from the exceptionally high tide, and two men were marooned all Friday night on a jetty running from the Municipal Baths . . . . . . The pilots on the Brooklyn ferryboats had considerable difficulty in making their slips on account of the tide, and many of the piers along the front were flooded. In Newtown Creek the water rose three feet in the early forenoon and flooded both shores. Pilots said these exceptionally high tides come about once every five years, and the exact cause has never been deter- mined . . . 1919 Nov. 8 2b e.s.t (±14) 45 Seattle Post-Intelligencer Sun., Dec. 9, 1923 Page 16 HH, Col. 3 PACIFIC COUNTY IS HIT BY TIDE SOUTH BEND, Dec. 8.— Pacific County is still estimating its losses and trying to repair them after the worst combination storm and tide the Willapa Harbor district has known for more than fifteen years . . . . . . The long and narrow Willapa Bay acted as a gigantic funnel with the wind and tide pushing the water far above the scheduled 10.5 mark and inundating tide- lands, the lower lying farms of the county and portions of South Bend and practically the entire city of Raymond . . . 1923 Dec. 7 6.5/7 P.S.t. (-23) 47 The San Francisco Examiner Sun., Feb. 14, 1926 Page 1, Col. 4 COAST TIDES ATTACK FILM STARS' HOMES Ventura Wharf Crumples Under Battering Highways and Bridges Blocked; Long Beach Sea Wall Is Washed Out LOS ANGELES, Feb. 13.— ( AP)— South- ern California was slowly emerging tonight from the three day raging of elements, in which gales and driving rains vied with al- most unprecedented high tides, leaving in their converging wakes death, injury and property damage estimated in tens of thou- sands of dollars . . . . . . mountainous seas, whipped into fury by off-shore gales, have resulted in three deaths by drowning, one injury and the destruction of one wharf, damage to num- erous piers, beaching of many small fish- ing craft, and wholesale undermining of dwellings, cabins and strand walks on the water fronts . . . . . . The loss of the Ventura wharf ties up shipping activity entirely at that city, all cargoes having been discharged on the one wharf. Six hundred feet of the structure collapsed . . . . . . The Coast highway to San Diego was rendered impassable by washouts near San Juan Capistrano and farther south near Oceanside . . . 7926 Feb. 12 6.5h P.s.t. (-5) 48 The Boston Evening Globe Thurs., March 3, 1927 Page 1, Col. 3 Wharves in Boston Under Water Foot Deep various places attained a velocity of 75 miles an hour, lashed practically the entire New England Coast line last night and this morning, compelling ships to seek shelter, and wharves to be submerged, and causing much damage . . . ... an exceptionally strong, high tide swept in at 10:46 this morning. The tide reached such a height that the water was on a level with the base of the caplogs of practically all the wharves along Atlantic av. At Long Wharf, T. Wharf and several others the water seeped underneath the caplogs and the floorings, flooding the wharves with water that averaged about one foot deep . . . Tide 13 Feet or Higher Under normal conditions the tide today should have risen 11 feet at its highest, but the indications were that it went to the 13-foot mark or higher. Large, docked ships loomed high above the wharf struc- tures . . . 1927 Mar. 3 21.5b e.s.t. (±15) B-50 High, i he'av nigh seas, whipped into fury northeasterly gale, which at The New York Times Sun., April 3, 1927 Page 19, Col. 2 Atlantic City Streets Flooded— ATLANTIC CITY. N. J., April 2.— Driven up the beach and over the bulk- heads by a fifty-mile northeaster, a heavy sea flooded parts of the Inlet section at high tide tonight. Although the high seas did not reach the proportions of the February flood, water stood a foot deep in sections of Maine Avenue ; waves lashed across the trolley tracks at the Inlet loop and gigantic comb- ers washed over the bulkheads at the ocean ends of Vermont, Rhode Island and Gramercy Avenues . . . 1927 Apr. 1 20b e.s.t. (-6) C-51 Every Evening Wilmington, Del. Tues., April 5, 1927 Page 3, Col. 4 LIGHTHOUSE KEEPER MAROONED BY WATER . . . Due to the heavy tides caused by unsettled weather conditions of the past Representative Great Tidal Floodings of the North American Coastline 47 few weeks, the river embankment, 300 yards above the lighthouse, on the gov- ernment reservation at the junction of the Delaware and Christiana rivers, suffered a break and the rush of water through the Assure virtually made the keeper, W. H. Johnson, a prisoner. The water, at high tide, is two feet deep on the reservation . . . 7927 Apr. 1 20h e.s.t. (-6) C-51 The New York Times Fri., April 12, 1929 Page 5, Col. 2 HIGH TIDE CARRIES OFF A JERSEY BUNGALOW . . . Although the southeasterly wind which prevailed most of the day showed a maxi- mum velocity of twenty-four miles an hour in the city, it did considerable damage along the Jersey coast. Accompanied there by unusually high tides, it drove the sea waters inland for several hundred feet at some places. At Point Pleasant Coast Guards and volunteer workers put in a busy day trying to save bungalow colonies threatened by the rising waters. But de- spite their efforts one bungalow was carried out to sea, while five others were wallow- ing in shallow water close to shore and 000 feet of boardwalk was converted by the waves into driftwood. The damage there is estimated at $30,000 . . . 1929 Apr. 11 4h e.s.t. (+73) 53 The New York Times Tues., Nov. 19, 1929 Page 20, Col. 3 13-F00T TIDE SWEEPS BOSTON'S WATERFRONT BOSTON, Mass., Nov. 18.— A record tide, driven four feet beyond its normal height by the easterly storm, inundated Boston's waterfront today, causing heavy damage. The tide reached its highest point in many years with a rise of 13 feet 6 inches at 11 :45 A. M. An unusual rise had been expected, but the water rose two feet beyond the mark predicted, flooding cellars and food stores piled up in wharf sheds. The flood condition lasted for two hours, an hour before and an hour after the tide reached its peak. Half the length of Long Wharf from Atlantic Avenue was covered with seven inches of water . . . . . . The Eastern Avenue approach to South Ferry was inundated with more than a foot of water and foot passengers unable to board the ferries were taken aboard on trucks. Winthrop's seaside suffered much dam- age as the big waves battered the break- water and crashed over the Shore Drive . . . The tide was the highest ever wit- nessed at the Boston airport, rolling up over the southern bulkhead and covering about a third of the runway . . . 1929 Nov. 17 22h e.s.t. (+54) (tivc also chapter 7.) 54 The New York Times Wed., Jan. 7, 1931 (Last Ed.) Page BQ 27, Col. 8 Tides Cause Huge Damage . . . Dense fog delayed vehicular traffic and harbor shipping and caused several mis- haps in and near New York yesterday, while the highest tide in a score of years, stirred up by a full gale which battered the New England coast, caused extensive damage . . . New England Coast Battered . . . All along the New England coast the angry seas pounded wharfs, undermined cottages and flooded storehouses, The As- sociated Press reported. Occupants of of- fices along the Boston waterfront were forced to use ladders to get in and out of their places of business, while those using the harbor ferryboats were forced to use improvised gangplanks. Several cottages were washed from their foundations at Hampton, N. H., where the tide was the highest known since 1909, and between thirty and forty Summer homes were surrounded by water . . . The streets of the Indian village of Taholah on the Quinault Reservation in Washington were flooded by the highest tide ever known there . . . 1931 Jan. 5 9h e.s.t. (+50) 56e The New Haven Journal-Courier Thurs., March 5, 1931 Sect. I, Page 2, Cols. 7, 8 REVERE HARD HIT BY EXTRA RISE OF TIDES Many Homes Flooded, Forcing 200 Persons To Seek Shelter Elsewhere. Revere, Mass., March 4(AP)— The Red Cross tonight came to the aid of civic authorities in supplying food and shelter to more than 300 persons left homeless by the battering of a storm tossed ocean. With more than 75 cottages and homes flooded or demolished, scores of persons sought refuge from the city . . . . . . About 25 pupils at the cities schools were forced to appeal to police when the unchecked tide inundated their homes or tore them to wreckage. All police and fire reserves were called on duty and stationed at Revere Beach for the purpose of aiding sufferers and watching for further damage by the re- turn tide. Police believed the midnight tide would be at least as severe as that of the day . . . . . . Representatives Augustine Airola and Thomas F. Carroll told the governor the damage here was estimated at $1,000,000 and that greater loss was anticipated with the rising tide . . . 7937 Mar. 4 5.5h e.s.t. (-1) (See also chapter 7.) D-57 The New York Times Fri., March 6, 1931 Page BQ 48, Col. 2 THIRD GREAT TIDE LASHES BAY STATE BOSTON, March 5. — Towering seas con- tinued to lash the coast of New England early today despite the fact that the wind and snow storm which accompanied yes- terday's record-breaking tides had moved off-shore . . . IM Strategic Role of Perigean Spring Tides, 1635-1976 . . . The waves of the third consecutive abnormal tide, though somewhat abated, swept in at noon today and toppled several beach houses which had been weakened by the previous more savage onslaughts. The loss is expected to run into the millions . . . . . . The finale to the most destructive storm since 1898, today's tide ripped apart crumbling seawalls, again inundated sev- eral communities and tore more cottages from weakened foundations . . . . . . great swells broke over seawalls an hour before high tide . . . . . . Firemen started pumping out the inundated section of Beachmont, where water lay from three to seven feet deep, surrounding scores of houses. The nearest estimate of the loss is $3,000,000 . . . HALIFAX, X. S., March 5.— Damage estimated at a million dollars has been caused by the violent storm and record high tides along the coast of Nova Scotia during the last thirty hours . . . . . . Wharves were carried away, at least one deep-sea cable twisted and torn, and bridges were smashed when a peaceful countryside received the worst battering by mountainous seas in the memory of its oldest inhabitants. Devil's Island, standing like a sentinel off Halifax Harbor, where the snug homes of its fishermen nestle together, appeared to have borne the brunt of the attack. The tide was unusually high and as the spray, borne before the fierce wind, drove clean across the island, the women and children of the place fearfully watched the island men hauling their boats to safety. Seas swept over the sheds housing the lifeboats, there being a life-saving station on the island, and for a time inhabitants of the island feared for their lives as the giant seas threatened to carry away the breakwater . . . 793) Mar. 4 5.5h e.s.t. (-1) D-57 The New Haven Journal-Courier Fri., March 6, 1931 Page 20, Col. 1 EASTERN COAST STORM PASSES AFTER DAMAGE Boston, March 5, (AP)— The storm which yesterday lashed the northeast coast, causing damage estimated in the millions, blew itself out today. There was no recurrence of the extreme high tide, which was responsible for the greater part of the destruction. As the sea rolled back it left in its wake a shore line streamed with splintered dwellings and summer cottages and up- rooted and undermined seawalls and break- waters. Highways and roadbeds of electric and steam railroads were washed out in many places and road gangs labored to re- pair the damage. Although the force of the tidal storm was felt all along the North Atlantic states the most destructive blows fell on the Massachusetts and New Hamp- shire coasts. Numerous summer cottages were demol- ished at Revere, popular greater Boston summer resorts, and at Hampton Beach, N. H. Fear that today's tide would approach the record high of yesterday to multiply the damage already inflicted was found without foundation. The wind that had been blowing from the northeast, driving the sea upon the land, shifted to the north- west, serving to abate the heavy seas. Many sections that were flooded yesterday remained comparatively dry . . . Revere Hard Hit The Beachmont district of Revere, bat- tered by three successive tides, tonight escaped further assault. The after mid- night tide officials believed would be minus the fury of its predecessors which left the greater part of the district under water. Acre upon acre of land on which homes or summer cottages rested were covered tonight with black placid water. The land being of the marsh variety failed to soak up the water . . . Travel by Rafts Those families who declined to leave their water surrounded homes were forced to go about on rafts or in row boats. The water in some areas reached a depth of six feet . . . ... At Highland Light, Mass., a shift in wind saved the Peaked Hills Coast Guard station and four cottages at Ballston Beach from tumbling into the sea. The beach was battered incessantly from Tues- day night until this noon when the change in wind was noted. The tide there was higher than anytime during the past ten years . . . 7937 Mar. 4 5.5/7 e.s.t. ( 1) D-57 The New York Times Tues., March 10, 1931 Page 18, Cols. 1, 4 PORTLAND, Me., March 9 (AP).— A howling overnight southeaster, bringing heavy snow, sleet, rain and lightning, to- day had caused some damage along the Maine coast . . . ... An unusually high tide switched the mouth of the Goose Fair River, dividing line of Old Orchard and Saco, 100 feet to the south . . . . . . NEW HAVEN, Conn., March 9.— Damage to the Connecticut shorefront from yesterday's storm will total $1,000,- 000, according to estimates compiled from reports received today. The shorefront suffered heavily from Greenwich to Madi- son. Record-breaking high tides were re- corded over this area. In practically every colony cottages or bath houses were wash- ed away and wreckage was strewn over lawns and roads . . . . . . For the first time in recorded history the Housatonic River overflowed its banks . . . Beachfront communities in New York and New Jersey were busy repairing the damage done by the tides and gale over the week-end. On Fire Island bar, opposite Centre Moriches, the new inlet cut by the raging seas seemed to be filling in again . . . (See also ehapter 7. 1931 Mar. 4 5.5h e.s.t. (-1) D-57 Millions Of Harm Done By High Tides Sweeping Far Ashore Upon Towns. The New York Times Thurs., April 2, 1931 Page 2, Cols. 2, 3 HIGH TIDES MENACE NEW ENGLAND WITH A HEA VY GALE BLOWING BOSTON, April 1.— April rode in to New England on the crest of a northeaster which tonight caused uneasiness along shore for fear of damage by high tides. Three high tides are scheduled in eight- een hours. The first this noon ran a foot higher than the predicted stage, despite the fact that the wind was only just be- ginning to rise. As the day advanced the gale increased . . . Representative Great Tidal Floodings of the North American Coastline 4'j High Tides Wreck Summer Home at Southampton . . . Blinding sheets of rain swept the streets of New York and its vicinity yester- day, while high tides and a strong north- east wind caused damage along the north- eastern coast of the country . . . . . . The Summer home of William F. Ladd, member of the New York Stock Exchange, at Southampton, L. I., was wrecked when a heavy sea undermined the house, which had been pounded by waves for several weeks. . . . All along the Jersey coast bulkheads were battered and Summer homes dam- aged by the wind and tide . . . . . . Trains on the North Shore division of the Long Island Railroad were held up for eighteen minutes by an open drawbridge at Main Street, Flushing, which had been opened to permit the passage of a tug and then could not be closed at once because of the wind and tide . . . Tides Shatter Bulkheads. LONG BRANCH, N. J., April 1 (AP).— rounding waves, driven before a forty- five-mile northeast gale, shattered portions of bulkheads today between here and Highlands, threatening hundreds of cot- tages. A sudden shift of the wind to south before high tide, saved coast resorts from greater damage . . . 7937 Apr. 2 4h e.s.t. (-22) E-58 The New Haven Journal-Courier Thurs., Dec. 1, 1932 Page 7, Cols. 7, 8 Huge Tide In Boston Area waters and piers along the New England coast causing damage estimated at thou- sands of dollars. Scores of persons em- ployed in Boston waterfront offices were marooned during the peak period of the tide and in Winthrop, flooded streets kept students in a school during the noon lunch period. At Truro on Cape Cod and along the New Hampshire coast in the Hampton Beach area, damage to cottages was re- ported. The summer cottage of Osborne Ball of Boston at Truro tumbled into the sea when the thundering surf undermined the cliff on which it stood. At high water time, about 12:30 p. m., the tide reached a height of 13.66 feet and unofficially was reported to have reached a height of more than 15 feet. The normal tide is 11 feet, four inches . . . ... In Boston the tide inundated the low Lying piers of the Atlantic avenue section. The water seeped into the approaches at many of the famous old wharves, includ- ing Central, India, Long and T., and many trucks were stranded on piers. Ferry boat slips were flooded and many passengers were delayed for a short time until the water receded. A sight that attracted much attention was that of ships lifted almost to street level by the rising waters. Meanwhile, crews worked vigorously to keep mooring ropes from snapping under the strain. All along the north and south Massa- chusetts shores beach cottages were sur- rounded with water and in many instances serious damage was done to the structures by the beating of the surf. For the first time since 1909, the town of Nahant was isolated when the waters of Lynn harbor inundated the narrow pe- ninsula connecting the town with the mainland . . . 7932 Nov. 27 15h e.s.t. (-10) 60 The Oregon Daily Journal Mon., Dec. 18, 1933 Page 1, Col. 2 Does Damage Coast Area Pounded by Rains, Tides Water Rushes Over Roads And Shore Towns Are Partly Submerged. trict, Grays Harbor attempted today to take stock of damage clone by a great storm driven tide which flooded major por- tions of Aberdeen, Hoquiam and Cosmo- polis Sunday. A survey of the business district this morning indicated a loss in merchandise and fixtures of between $50,000 and .$100,- 000. Flooded homes, street damage and road washouts will augment the total loss. The port of Grays Harbor tidal gauge measured the rise at 15.8 feet, four feet above the predicted high tide mark and nearly a foot higher than any previous tide in history here . . . . . . the chief cause was declared to be the great tide, supplemented by the 90- mile southwest gale . .- . . . . Eastbound traffic was threatened again this morning when another tide of over 11 feet began backing water over the low- land road between Aberdeen and Monte- sano. The series of 11 -foot tides will con- tinue until Thursday . . . 7933 Dec. 16 23. 5h P.s.t. f+9j 63 The San Francisco Examiner Wed., Aug. 22, 1934 Page 1, Col. 4 HUGE MYSTERY WAVES FLOOD L A. BEACHES Forty-foot Water Walls Strike; Two-Story Apartment Swept From Foundations; No Wind Boston, Nov. 30 (AD— The highest tide >f the season today swept over break- Aberdeen, Dec. 18. — (AP)— While soggy skies continued to pour rain on this dis- NEWPORT BEACH, Aug. 21.— (AP) — A strangely acting Pacific Ocean, which has been running waves 30 and 40 feet high during the day, got out of bounds at high tide at 6 :10 tonight and swept a two-story apartment building from its foundation and damaged other buildings. Part of the city was inundated a few feet . . . 50 Strategic Role of Perigean Spring Tides, 1635-1976 . . . The waves threatened for a time to cut a new channel across from the ocean to Newport Bay, ripping out a large cut in the sand under the apartment building and across Central avenue . . . . . . Portions of the Central avenue pave- ment, the only connecting link between the city and the fashionable residential section on Balboa Peninsula, were torn up, isolating for a time the residents on the peninsula . . . . . . No wind was reported and no explana- tion for the unusual waves could be given by weather officials . . . 7934 Aug. 24 Oh P.s.t. (-24) 64 The New York Times Wed., July 17, 1935 Page 14 L-f , Col. 7 Highest Seas in Years Threaten Oak Beach, L.I. . . . OAK BEACH, L. I., July 16.— One of the highest seas in years, driven by a strong southeast wind for two days, pound- ed this village of twenty homes on the outer bar tonight, partly undermining the foundations of three cottages . . . . . . After 10 P. M., when high tide had passed, the danger lessened. An automo- bile parking space on the beach was under more than a foot of water. The waves had dashed up within forty feet of the Coast Guard station here . . . 1935 July 16 23h e.s.t. (+46) The Oregon Daily Journal Wed., Jan. 4, 1939 Page 2, Cols. 3-6 . . . Aberdeen, Jan. 4. — (AP) — A sudden halt in the southwest gale and rain del- uge which had hammered Grays Harbor for 4K hours until shortly before noon Tuesday temporarily ended a serious flood threat, in Aberdeen and Hoquiam. Water had backed up through sewers in parts of South Aberdeen and had just started over the Chehalis river dikes in two places, when the rain and wind halted and the high tide which had been pushed four feet above its predicted 10% foot peak started to recede. Water had been backing into Hoquiam streets through sewers also . . . Storm Floods Neskowin; Many Homes Damaged Neskowin, Jan. 4. — A heavy sea follow- ing in the wake of a stormy night which saw the wind reach a 75-mile-an-hour velocity, flooded Neskowin Tuesday morn- ing, causing an estimated damage to homes and buildings of from $50,000 to $75,000. The turbulent sea water, which poured into the city between 9 and 11 :30 a. m., wrecked the community kitchen, restau- rant and warehouse and undermined the Neskowin store. Neskowin apartments and about 30 per cent of the homes were damaged . . . 1939 Jan. 5 20h P.s.t. (+14) F-68 The Oregon Daily Journal Thurs., Jan. 5, 1939 Page 1, Cols. 4, 7 . . . Four women were injured, one perhaps fatally, Thursday noon near Seaside as the northern Oregon coast suffered a re- currence of attacks by huge swells accom- panying a high tide. The women were standing on a log when a swell picked it up and slammed it about . . . . . . Marshfield, Jan. 5. — (AP) — A tide so high that many persons described it as a "tidal wave" moved houses, damaged small craft and destroyed cabins in the Coos Bay area Thursday. Three houses were shifted on their foundations at Charleston and 15 cabins wrecked . . . . . . High water forced the International Cedar Mill to shut down here . . . 7939 Jan. 5 20h P.s.t. (+14) F-68 The Oregon Daily Journal Fri., Jan. 6, 1939 Page 1, Col. 4 . . . Apprehension felt regarding another high tide along the coast today was al- layed when the first community reporting, Nelscott, announced that the Lincoln county crest had passed shortly before 1 p. m. and that the extreme height of the tide was 12 feet, two feet lower than that of yesterday. It is believed this relative figure will indicate the situation at other points, as the tide visitations yesterday were similar at all of them. Tide gauge readings at Delake during the storm and high tides which ensued, were 15 feet Wednesday, when most dam- age was inflicted; 14 feet yesterday, and 12 feet today. A normal high tide reading of 9.8 had been scheduled for today. Two lives are known to have been lost in the augmented tides which hammered the Oregon coast yesterday . . . Resorts Flooded Again Fog prevailed this morning at Astoria and south as far as Wheeler. Nelscott re- ported the sun shining. There was no wind at either point . . . . . . Damage was less yesterday than dur- ing Tuesday's storm, the tide being as high, but not driven by a gale. The Tilla- mook beaches seemed to lie harder hit yes- terday, but resorts again were flooded as far south as Coos Bay . . . The Oregon Daily Journal Fri., Jan. 6, 1939 Page 1, Col. 7 Sea Unruly in California Three Homes Washed Into Pacific; Others Damaged Long Beach, Cal., Jan. 6— (AP)— Three modest beach homes in the Alamitos pe- ninsula area southeast of Belmont shore were washed to sea today as giant break- ers, riding in from the Pacific on high tide ground swells, crashed over the low sea wall . . . . . . The tide also brought extensive dam- age to Manhattan and Hermosa beaches, where the highest water in years flowed as far as ISO feet inland. But the Alamitos peninsula below Long Beach was hardest hit. William E. Ross, boat builder there, said the tide was the worst in bis 35 years' ex- perience. Mrs. I). H. Collins stood by and watched the tide carry her two-story dwelling into the Pacific . . . . . . More than two feet of water roared in at some Santa Monica bay points, sweeping out the board walk along the strand between Manhattan and Hermosa beaches . . . (Sec also chapter 7. i 1939 Jan. 5 20h P.s.t. (+14) F-68 Representative Great Tidal Floodings of the North American Coastline 51 The New York Times Mon., April 22, 1940 Page 1, Col. 2 (Late City Ed.) GIANT WAVES LASH NORTHEAST COAST Hundreds Marooned in Towns Near Boston— Blizzard Hits Maine and Vermont BOSTON, April 21— Scores of persons were marooned today and the coast was hammered hy mountainous waves whose spray washed over Minot's Light, 114 feet high, and lifted surf to a height of 130 feet at Deer Island, as a northeast storm, continuing from yesterday, brought to New England heavy rain, sleet, hail, snow and a gale blowing fifty-one miles an hour . . . ... A family of four and three other per- sons on Bassing's Island off Cohasset Har- bor fled to the mainland in dories when the sea swept over the island for the first time since the storm of '98, in which the steamer Portland went down . . . . . . The sea, lashed by the gale, sur- mounted seawalls, undermined streets and flooded cellars. Hundreds of persons were temporarily marooned in churches in Winthrop and Beachmont by flooded streets, and services had to be called off tonight at one in Winthrop . . . . . . Several hundred Summer homes at Hull were damaged by wind and sea. The tide late tonight was 11 feet 3 inches, six inches higher than the morning tide and the continuing gale increased the floods and coastal damage, driving waves and surf against cottages many yards from the ocean front . . . 1940 Apr. 21 7h e.s.t. (-34) G-69 The New York Times Mon., April 22, 1940 Page 34 L, Col. 1 who recently refused to let it be dredged out because anti-aircraft guns might have to be rushed to the island overland in event of war. Tip of Maine Is Isolated BOSTON. April 21— The northeast tip of Maine and its 7,000 residents were isolated tonight as a 50-mile-an-hour northeaster sent a high surf pounding against New England waterfront roads and property . . . . . . An incoming tide, driven by the gale, flooded Quincy Shore Boulevard, main highway between Boston and Cape Cod, for three miles and halted automobile traffic. Squantum, a Quincy peninsula of 1,500 residents and home of a Naval Reserve air base, was cut off temporarily as the tide swept across its only outgoing high- 1940 Apr. 21 7h e.s.t. (-34) G-69 Shirley Gut, formerly a strait between Winthrop and Deer Islands, but long since closed by storms, was nearly reopened by the sea, to the concern of army engineers The Oregon Daily Journal Thurs., Dec. 26, 1940 Page 1, Col. 7 (Final Ed.) High Tide, Wind Create Damage In Coast Region ... A nine-foot tide Wednesday, pushed by a 50-mile-an-hour wind, damaged sea- walls and flooded Tillamook farms and the ('oast highway. Hammond, on the Columbia estuary be- low Astoria, reported today that the tide washed out the approach to the Hammond beach road Wednesday, but that there was no other damage . . . 7940 Dec. 26 17.5h P.s.t.( 87) 70 The Oregon Daily Journal Fri., Dec. 27, 1940 Page 1, Cols. 1-4 (Final Ed.) HIGH TIDES SPECTACULAR ON OREGON COAST DP]LAKE, Dec. 27.— North Lincoln resi- dents, under bright skies and a span of ocean rainbows, today estimated damage of a two-day Christmas beating by wind, rain and high tides. Taft had the worst, with damage to the seawall that protects Pacific street along Siletz bay. Mountainous waves drenched that street, littered door yards, dug holes in lawns and removed 200 yards of filling back of the wall. Nelscott reported damage to the seawall, removal of stairways to beach from Over- look property and piling of logs on the ramp . . . Angry Seas Still Batter California LOS ANGELES, Dec. 27.— (AP)— An angry ocean continued today to pummel portions of the California coastline, aim- ing its severest blows at the little town of Redondo Beach. A house and a liquor store, normally, even at highest tide, 50 feet away from the water, were undermined in today's assault. Both collapsed. Two houses which were dropped into the surf yesterday by the gnawing action of 25-foot combers and ground swells were being battered into debris today. Damage estimates run as high as $250,- 000 .. . 1940 Dec. 26 17.5P.s.t.(-87) 70 The Oregonian Sun., Dec. 29, 1940 Page 6, Col. 2 Coast Awaits New Storms . . . SAN FRANCISCO, Dec. 28 (AP) — The Pacific seaboard, battered by recent storms, braced itself for more onslaughts of wind and rain Saturday night, while high water flooded many roadways . . . . . . Winter tides were at high peak. Salt water stood so deep on highway 101 south ">2 Strategic Role of Perigean Spring Tides, 1635-1976 of San Rafael that many cars were stalled, and high-wheeled trucks were used to tow or push them to higher ground . . . 1940 Dec. 26 17.5P.s.t.(-87) 70 The New York Times Fri., Dec. 1, 1944 Page 25 L, Col. 1 HIGH WINDS, TIDES LASH THE CITY AREA Third Wettest November Bows Out With Gusts Hitting 57 Miles and Snow Flurries Commuters Delayed as Tracks, Ferry Slips and Roads Are Flooded— Planes Grounded . . . The third wettest Novemher on record hlustered to a close amid snow flurries yesterday as winds reaching fifty-seven miles an hour swept the metropolitan area, disrupting railroad, ferry and air services. The tempestuous weather, the Weather Bureau predicted last night, would con- tinue in strong to gale strength until some time today . . . . . . The wind velocity started to increase about 9 A. M., when it was measured at 23 miles an hour, and ranged between 45 and 50 miles an hour in. the afternoon, with gusts up to 57. It had subsided last night to 32 miles an hour and was expected to range about there throughout the night . . . The sea was whipped into almost record tides along New England's coast, causing damage estimated in the millions of dollars. Cape Cod bore the brunt of the storm. Coast Guardsmen evacuated per- sons on Nantucket Sound from Falmouth to Chatham, and dozens of homes that have withstood the September hurricane were wrecked. Provincetown reported eleven-foot tides inland, the worst in forty years. In New Bedford, floods crippled several industrial plants. In many coastal communities electric and telephone lines were down. Fishermen suffered large losses in gear. Thousands of New York commuters were delayed in reaching work when high tides stranded them in Long Island and New Jersey. Long Island Railroad service was discontinued between 8 :50 and 11 :25 A. M. over Jamaica Bay between Hamilton and Howard Beaches when the tides covered the railroad trestle. Trains between Long Beach and Island Park were delayed. The tide backing up into the Erie Rail- road yard in Jersey City covered road approaches to the ferry line with three feet of water, and for the first time in eighteen years ferry service was suspended at 8 :30 A. M., resuming at 10 o'clock. Water rose more than two feet above the ferry slips and flooded Pavonia Avenue, stalling many buses and trucks. While the Central Railroad of New Jersey said that it had had no difficulty in loading its ferryboats, high tides north of Sea Bright overflowed tracks at several points, resulting in delayed service. The high tide in Jamaica Bay cut off vehicular traffic on the Cross Bay Park- way and Rockaway Boulevard routes from the peninsula to the mainland, which were flooded from 8 A. M. until noon . . . 1944 Nov. 28 9.5h e.s.t. (-69) 71 The Daily Kennebec Journal Augusta, Me. Wed., Nov. 21, 1945 Page 1, Col. 8 Record Tide, 70 Mph Gale, Heavy Snow Portland, Me., Nov. 20— (AP)— A fierce southeast gale whipped the Maine coast today causing waterfront damage running into hundreds of thousands of dollars. . . . Sweeping up the coast, the gale, which recorded wind gusts of 70 miles an hour here, drenched southwestern Maine . . . . . . In Machiasport, numerous sardine boats, hauled up for the winter, were set adrift by the high tide. An estimated 28-foot tide at Eastport, on Passamaquoddy Bay, exceeded a previ- ous high there of 27.1 feet, moving build- ings from their foundations and wrecking wharves and waterfront bulkheads. Dam- age in Eastport alone was estimated un- officially at $100,000. When the water flooded the Northern Herring Company wharf at Eastport, five women employes of the U. S. Customs and Immigration offices in a three-story wharf building were taken down ladders to safety. Tidewaters of the Machias River wash- ed out the Maine Central railroad tracks at four places between Machias and East Machias, interrupting travel from Bangor to Calais. Rails were torn up for a dis- tance of 600 yards at one place. A paral- leling highway was damaged but remained passable. Reports of extensive damage to wharves, fishermen's "shops," and industrial plants came from Cutler, Camden, Bar Harbor and other "downeast" points . . . 1945 Nov. 19 3.5h e.s.t. (-13) H-72 The San Francisco Examiner Mon., Jan. 26, 1948 Page 1, Col. 7 Tides Flood Bay Area S.F. BOY DROWNS; ROADS BLOCKED An unprecedentedly high tide flooded por- tions of three Bay area counties yesterday and was blamed for the drowning of a San Francisco boy - . . . . . Small craft warnings were hoisted on the Bay for northeasterly winds up to thirty-five miles per hour due this morning. FLOODS ROADS The tide spilled onto several Marin County roads, including Highway No. 1 at Dolans Corner, south of Mill Valley, and a service road between San Quentin and San Rafael. Some autos stalled on the latter. The water almost overlapped High- way 101 just south of San Rafael. Representative Great Tidal Floodings of the North American Coastline .7.5 In San Francisco, sewers backed up in the south of Market area, flooding several streets . . . . . . The tide rise, six feet eight inches, was described by the Coast Guard as the high- est due this year, although today's high tide, at 10:52 a. m., will reach six feet seven inches . . . 1948 Jan. 26 1h P.S.t. (+4) 74 The New York Times Wed., Oct. 19, 1949 Page 59, Col. 1 Jersey Shore Streets Flooded LONG BRANCH, N. J., Oct. 18 (AP) — Rising tides and high waves pounded beaches and flooded some streets in the shore area tonight. Thirty-foot-high waves were reported at Seabright, where water inundated parts of Ocean Avenue six to eight inches deep. Police said that not much damage was done but that Ocean Avenue was expected to be closed to traffic for about twenty- four hours. 1949 Oct. 21 13h e.s.t. (~6) 75 The Los Angeles Times Thurs., July 19, 1951 Page 1, Col. 1 (Final Ed.) Tide Floods Long Beach; Boat Saves 9 . . . Two expectant mothers and five chil- dren were among a number of persons evacuated by lifeguard boats from homes flooded by sea water at record high tide last night in the Long Beach Harbor area. ... A battery of pumps worked throughout the day yesterday to eliminate sea water which rushed into the area affected by the earth's subsidence. More than 100 homes in a six-block- square area of the district were flooded following the third record high tide in three nights. Tides of 7.2 feet swept through harbor area storm drain systems Tuesday night and sent water gushing through streets to flood small homes with as much as 14 inches of water . . . . . . Some automobiles were left in the flooded streets and others were pushed or towed out of the path of the water. Each day since Monday, residents said, the tides sent water into the area between Seaside Blvd. and Water St. . . . . . . The piers at Berth 32 and Berth 33 on the harbor waterfront also were flooded by sea water during the high point of the tide. The flooding is basically due to the land subsidence in the harbor area, although failure of some sandbag dikes and the plugging of pumps in the area also are blamed for the condition . . . 7957 July 18 1h P.s.t. (-20) 76 The Seattle Daily Times Mon., Dec. 3, 1951 Page 16, Col. 6 New Storm Causes Flood Damage In North California SAN FRANCISCO, Dec. 3.— (AP)— A new storm, on the heels of one which closed the Golden Gate Bridge Saturday for three hours, caused flood damage in Northern California today . . . . . . Water stood three feet deep in sections of Sonoma, 35 miles north of San Fran- cisco. A dozen ranches in Sonoma County were isolated. Eight schools were closed. Flood waters entered Burlingame, 15 miles south of San Francisco, and marooned people in stores . . . 7957 Nov. 29 11 h P.s.t. (+36) 77 The Seattle Daily Times Mon., Dec. 3, 1951 Page 13, Col. 2 Tide Spills Over Bank Of Duwamish A high tide of 12.7 feet spilled over the west bank of the Duwamish River about 9 o'clock this forenoon. Water inundated lawns of three residences in Riverside Drive, a foot deep near Webster Street. Occupants said little damage resulted, and the water receded by noon. Another 12.6-foot tide is due about the same time tomorrow . . . 7957 Nov. 29 11h P.s.t. (+36) 77 The San Francisco Chronicle Sat., Dec. 29, 1951 Page 1, Cols. 7, 8 (Final Ed.) Bay Area Gets a Soaking High Tides Flood Marin; Valley Situation Eases Except for the few dozen Bay Area families, whose homes have been flooded, this will be a wonderful week end to stay home. The storm so far has been persistent, but relatively benign. Heavy rainfall has been general, but temperatures have been mild for this time of year, even in the mountains, and there have been no de- structive winds. High tides and a break in the dike north of San Rafael flooded Railroad avenue which leads to the San Francisco Bay Airport. The tide rose 6.9 feet above mean low tide. The road to Mill Valley was under water at Dolan's Corners. So was Highway 101 south of Richardson's Bridge during the high tide. 7957 Dec. 28 9.5h P.s.t. (+11) 78 54 The New York Times Fri., Oct. 23, 1953 Page 1, Cols. 1, 2 (Late Ed. Strategic Role of Perigean Spring Tides, 1635-1976 Lower Manhattan Wetted by Tide As Full Moon Pays Us Close Call Early commuters in downtown New York found the water curb-deep in a few spots off South and West Streets yesterday morning-. A high perigee tide, possibly aided by the winds, had pushed sea water up into lower Manhattan storm sewers and out into the streets . . . ... A few cellars were flooded downtown and in coastal Brooklyn, and traffic was delayed by deep water in several New Jersey points. But there was no report of damage from the unusual tide . . . . . . The high tide at 7 :34 yesterday morn- ing coincided with the full moon at 7 :56 A. M. and came only a few hours after the moment when the moon was in perigee — its closest approach to the earth. The moon travels an irregular path as it moves around the earth. At perigee, the closest point, when the moon's gravita- tional pull on the oceans exerts its great- est influence, the tides are high. The co- incidence of perigee with the beginning of a full moon — the moment when the earth, the sun and the moon are in a straight line so both the sun's and the moon's gravitational pulls work together on the oceans — occurs twice each year, Joseph M. Chamberlain of the Hayden Planetarium explained . . . . . . The Coast and Geodetic Survey which calculates for each day a tide forecast, had placed the tide yesterday morning at the Battery at 5.9 feet above the mean low water level, which is the "normal" low water level for the day. Low water yesterday was 0.8 feet below normal, so the range of the tide yesterday morning was 6.7 feet, a figure far above average, the agency reported . . . 1953 Oct. 21 21. 5/7 e.s.t. (-21) 79 The New York Times Sat., Oct. 24, 1953 Page 9, Cols. 5, 6 TIDE AGAIN SPILLS INTO CITY STREETS Floods Caused by a Full Moon Close to Earth Disrupt Rail and Ferryboat Service For the second day, a perigee spring tide caused tidal waters to overflow some city streets and low acres in the suburbs. In addition to a few downtown Man- hattan streets, the water affected areas along the New Jersey coast, both shores of Long Island and occasional points along the New England coastline as far as East- port, Me. A perigee spring tide occurs twice every year, when the full or new moon (a spring tide) happens to be nearest to the earth (the point of perigee). At this time both sun and moon simultaneously exert their strongest gravitational pull on the oceans. The full moon entered perigee on Thurs- day morning, while the semimonthly spring tide occurred yesterday. The Army Corps of Engineers meas- ured high tide at 8 :22 A. M. yesterday off Fort Hamilton at the Narrows at 8.2 feet. This was 2 feet above average and one- half foot above high tide on Thursday morning. Water Backs Up Drains High water in the harbor backed up storm drains into Grand Street, West Broadway and West and Barclay Streets. Between one and two feet of water lay in the cellars of 200 homes along Jamaica Bay in Hamilton Beach and Howard Beach in southern Queens. The Long Island Rail Road could not run trains to those stations until 10 :20 A. M. because of flooded tracks. The Long Beach Bridge to Island Park, L. I. was closed at 8 A. M. as Reynolds Channel overflowed the northern approach road . . . . . . Ferryboats of the Erie Railroad floated so .high above their slips in Jersey City, N. J. that no automobiles could board until 11:25 A. M. Commuters on foot, however, embarked by using upper ramps, while the rejected cars went to Manhattan by bridges and tunnels. High water also hampered commuters on the Lackawanna ferryboats and Hudson and Manhattan tube trains in Hoboken. 150 in Jersey Evacuated The police and Coast Guardsmen evacu- ated a dozen residents and 150 employees of oyster-shucking sheds when the surf invaded Wildwood, N. J. Two schools in Union Beach, N. J., and one in At- lantic City were closed for part of yester- day by flood conditions. Five square blocks of Atlantic City were flooded by Absecon Inlet backing up in storm sewers and trolley service was disrupted there. Artists living in converted sail-lofts on the Boston wharves had to evacuate yes- terday morning with hip boots or in row- boats as salt water came over the sea wall. There were overflowing tides all along the Maine coast, but that is an old story there. The United States Coast and Geodetic Survey predicted that the great tides would taper off today. This part of the coast was spared much damage, the ocean- ographers said, because we did not have strong east winds . . . 7953 Oct. 21 21. 5h e.s.t. (-21) 79 The New York Times Thurs., April 12, 1956 Page 63 L+, Col. 2 HIGH TIDES CAUSING FLOODS IN NORFOLK NORFOLK, Va., April 11 (AP)— The highest tides in twenty years started flash floods in low-lying Hampton Roads areas tonight and isolated two communities. The rising water halted ferry service across Hampton Roads, blocked highways, forced closing of the James River Bridge at Newport News and seriously interfered with coastal shipping. The towns of Poquoson and Willoughby were cut off. The Army dispatched a fleet of amphibi- ous vehicles from Fort Eustis on an emer- gency mission to restore communications with them. The floods were precipitated by strong northeast winds that raged up to seventy miles per hour in gusts . . . 1956 Apr. 13 7.5h e.s.t. (+115) 80 (Alternate) Representative Great Tidal Floodings of the North American Coastline r ). r ) The Los Angeles Times Tues., Feb. 4, 1958 Part 1, Page 1, Col. 3 Tide, Surf Hit San Diego Bay Community By a Times Correspondent IMPERIAL BEACH. Feb. 3— High tides and pounding surf smashed at homes and the boardwalk at the height of today's storm, creating an emergency condition that led to proclamation by Gov. Knight of a state of disaster in this South San Diego Bay community. At least four families were prepared to evacuate their ocean-front homes. One was partly undermined as the boardwalk in front collapsed. City crews rushed truck-loads of rock and sand to the beach front in an effort to protect property. Mayor Cecil Gunthorp telegraphed Gov. Knight that "the City Council has declared a local emergency, wherein all cash re- serves have been used and financial as- sistance is needed.'' Under Knight's proclamation, the State will provide aid . . . 7958 Feb. 4 19.5 P.s.t. (+39) 81 The Boston Herald Wed., April 2, 1958 Page 1, Cols. 6-8 (Late City Ed.) Giant Waves, 82-mph Waves Lash Coast, Cape A roaring northeast storm at sea sent winds up to 82 miles an hour through Nan- tucket last night and pounded waves against the Winthrop sea wall that tow- ered 50 to 75 feet into the air. Low roads in several coastal communi- ties between Chatham and Portsmouth, The Los Angeles Times Wed., Feb. 5, 1958 Part 1, Page 2, Cols. 4, 5 High Tides Batter at Southland Coast Areas High tides, lashed by the same Pacific storm that brought heavy rains to the Southland, battered at Southern California coasts yesterday. At Oxnard Beach, northwest of Port Hueneme, Navy helicopter and crash-boat crews reported they failed to find the body of a 17-year-old Santa Paula girl who was washed into the sea late Monday. The teen-ager, Judith Lou Nasalroad, was caught by a huge wave while walking on the beach. The tumbling waves swept her into the sea. On the Alamitos Bay Peninsula near Long Beach, two feet of salt water dam- aged lawns from 56th to 59th Place along the bayfront. Crews blocked off Ocean Blvd. at 50th Place after a high tide pushed water over a 30-inch cement sea- wall. A U.S. Coast and Geodetic Survey team said a 7.1-foot peak tide at 9:50 a.m. caused the flooding. City crews piled sand- bags atop the seawall in preparation for a similar tide peak this morning. In Seal Beach, bulldozers piled up an 8-foot sand dike along Seal Way east of Municipal Pier to guard a row of apart- ment houses. In San Diego County, work crews labor- ed in a rainstorm to pile rocks along a section of Imperial Beach waterfront where four homes were undermined by high tides Monday. Gov. Knight declared the beach front a disaster area to make State funds available to work crews . . . 7958 Feb. 4 19.5h P.s.t. (+39) 81 NT. II., were flooded, but damage was less than feared. Revere street in Winthrop and Wessa- gussett road in Weymouth were among in- undated thoroughfares between 8 and 10 p.m. when the seasonably high tides were pushed three feet higher by the storm. Water on T Wharf During the storm evening tides in Bos- ton ran several feet higher than normal. More than 50 residents of apartments on T Wharf were marooned when the tides swept over wharf stringers. Fishing boats tied up to the wharf, and at adjacent wharfs were at doorstep level while the tides were high. A number of automobiles parked on the wharf were also marooned by the excep- tionally high tides and some of them had their electrical systems soaked as high winds swept the water across the wharf planking . . . 1958 Apr. 3 19h e.s.t. (-8) 82 The Boston Herald Thurs., April 3, 1958 Page 1, Col. 3 (Late City Ed.) 2 Big Tides Rip Walls Main Roads The 18th northeast storm since Decem- ber kept hammering at New England last night, causing coastal damage from tides four feet above normal that marooned communities and smashed waterfront property twice in one day. Again at 9 o'clock last night high tides thrashed exposed locations, casting up more sand, rock, sections of cottages. Ash- ing and lobster gear and other debris. The unusually high morning tide was whipped by 70-mile-an-hour winds. Nahant Isolated Nahant again was isolated as Lynn Shore Drive, leading to this town from Lynn and the only means of getting to Nahant, was under three feet of water for a second time at 9 p.m. Nearly 100 families were marooned in their homes on Surfside and Beach roads in Lynn by last night's high tide. Water again was licking the sides of the Metropolitan Police station and the amusement stands on Revere Beach Boule- ->h Strategic Role of Perigean Spring Tides, 1635-1976 vard, which was closed to traffic, and was gushing downward into Ocean avenue, in the rear of the beach area. Winthrop Shore drive was closed and 400 families in the Point Shirley section of Winthrop were marooned, as were many more in the Beachmont area of Revere . . . 1958 Apr. 3 19h e.s.t. (-8) 82 The New York Times Wed., Mar. 7, 1962 Page 1, Cols. 2, 3 (Late City Ed.) Snow, Rain, Gales, Tides Lash Mid-Atlantic States The New York Times Wed., Dec. 30, 1959 Page 6, Col. 4 NEW ENGLAND HIT BY SAVAGE STORM Near-Record Tides Strand Scores BOSTON, Dec. 29 (UPD— A savage storm swept into New England from the Midwest today. Carrying snow, sleet and rain, it churned up the highest tides in 108 years and stranded hundreds of per- sons. Boston harbor's tide rose about two and a half feet above normal. Wind -lashed breakers surged over beaches and seawalls on the highest tide since 1851 when an April storm carried away a stone light- house. The unofficial reading by the Coast and Geodetic Survey was 14.3 feet above mean low tide as compared with the 108-year- old record of fifteen feet. Huge seas, born of gale-lashed winds, pounded the coast and inundated low sea- side areas. Roads and cellars were flooded. Two bridges in Maine were awash and telephone and power lines were knocked out. Boats Rescue 300 Three Coast Guard boats rescued 300 men, women and children from flooded homes in Hull on Massachusetts' south shore. The sea surged over two bridges at Kennebunkport, Me., marooning some eighty families. Two feet of water covered the bridges but officials said the families were in no danger. 7959 Dec. 29 5h e.s.t. (-18) (Sec also chapter 7.) l-83e A savage storm lashed the mid-Atlantic states with snow, rain, gales and high tides yesterday from Virginia into New England. At least nine persons were killed and six were missing last night. Flooding forced thousands of persons out of their homes and electricity was cut off from 85,000 users. The damage in the Atlantic City area alone was estimated at more than $1,000,000 . . . . . . winds up to sixty miles an hour roared in between 2 P. M. and 2 :50 P. M. The Weather Bureau warned that high winds would continue today, bringing tides three to Ave feet above normal and caus- ing new flooding of low-lying areas. Railroad and ferry travel was hampered in New Jersey and Long Island. A Hudson and Manhattan Railroad train with 494 passengers, many of them standing, was stalled for more than three hours at Kearny, N. J., by the flooding of the Passaic River . . . 7962 Mar. 6 4.5h e.s.t. (-31 min.) J-85 (See also chapter 7.) The Los Angeles Times Fri., March 6, 1970 Page 10, Cols. 1, 2 WINDS, HIGH TIDES Two Beach Areas Pounded by Surf Two sections of the Orange County coastline suffered heavy damage Thursday morning from a combined attack by high tides and storm winds. Seawalls valued at more than $75,000 were battered down by waves which then chewed at the foundations of several lux- ury homes on the shores of Capistrano Beach. At Newport Beach, heavy surf again took a mile-long bite of sand from an area of which the pier is the center, and threat- ened to undermine lifeguard headquarters at the foot of the pier . . . . . . High tide, cresting at 6.3 feet just before 8 a.m. Thursday, was pushed by westerly winds of 25 to 30 m.p.h. Heavy surf at Capistrano Beach pounded against several hundred feet of wooden seawall protecting homes on Beach Road and smashed it into splinters. Breakers then chopped away beach sand and sloshed against the foundations of several residences . . . . . . Anticipating another high tide of about 6.4 feet this morning, residents or- dered an emergency haul of rocks and boulders to replace the seawall. Orange County Weather Central said, however, Thursday's strong winds should be diminished by today . . . 7970 Mar. 6 18h P.s.t. (-32) 92 Representative Great Tidal Flooding of the North American Coastline 57 The Virginian-Pilot Norfolk, Va. Sat., March 27, 1971 Page 1 , Cols. 2-4 . . . The season-mocking snowstorm which ushered in the sixth day of spring for much of the Atlantic Seaboard pushed tides above normal and plunged thermom- eters below average Friday. Tides crested at Sewells Point at 9 p.m. at 6 feet, 2.8 feet above normal and the highest since the Ash Wednesday storm of 1962, the weatherman said. High tide at Virginia Beach measured 7.6 feet, or 4 feet above normal. Willoughby and Ocean View appeared hardest hit by the wind-driven tides, al- though scattered flooding was reported throughout the area from Colonial Place in Norfolk to Wolfsnare Plantation in Virginia Beach. Water was knee-deep in the parking lot of the Quality Court Motel at Willoughby Spit. The wooden pier at Virginia Beach reportedly suffered damage . . . towns before spreading slowly across the rest of the state . . . . . . The famed pier at Old Orchard Beach, for example, gave way before the rolling sea. The large arcade section at the end of the pier was torn away and the wreck- age washed up on the beach. In Kennebunk, selectmen will seek state aid for what they describe as a disaster area. About 30 families were evacuated along Kennebunk Beach and in the Great Hill section near the beach. Severe flooding washed out roads, and high seas crushed a portion of the granite and wood sea wall along the Kennebunk beaches. A couple was rescued from their Kenne- bunk Beach home after surf began pour- ing through the front windows . . . 7972 Feb. 16 4.5h e.s.t. (+67) 96 water a foot deep throughout town. Flooding caused by the tide and winds also was reported at nearby Raymond and South Bend. Police said water reached depths of four feet in the streets of the two communities. No injuries were re- ported. The touchy period came between 2 and 3 p.m. at the peak of the high tide when winds of 75 miles per hour were reported at Seaside. The wind-caused flooding at Tokeland pushed a large trailer house out into a street and washed another house off its foundation. Waves breaking over the seawall near the general store and post office threw logs against the store and littered the road with rocks, driftwood and debris. 1973 Dec. 10 4.5h P.s.t. (+21) M-98w . . . Norfolk police said the worst flooding Friday occurred at Ocean View, on May- flower Road in Colonial Place, Olney Road, West Main Street, Boush Street, and Mowbray Arch. The 7900 block of Hamp- ton Boulevard was impassable for a time because of high water, police reported . . . 7977 Mar. 26 9h e.s.t. (-10) L-93e Maine Sunday Telegram Portland, Me. — Final Ed. Sun., Feb. 20, 1972 Page 1, Col. 3 ... A wild northeast blizzard, with snow taking a back seat to high tides and winds, wreaked havoc on southern Maine coastal The Oregonian Wed., Dec. 12, 1973 Page 24, 3M, Cols. 4, 5 Tidewaters flood Washington towns; winds to ease off Strong coastal winds Tuesday blew water from a near-record 16-foot tide over the seawall at Tokeland, Wash., leaving The Los Angeles Times Fri., April 23, 1971 Part 1, Page 3, Cols. 1, 2 Heavy Surf, Tides and Winds Batter Oxnard Shores Homes A combination of unusually high tides, heavy surf and strong winds Thursday caused considerable damage to six expen- sive homes along a three block stretch of Mandalay Beach Road at Oxnard Shores, north of Oxnard Beach. According to officials, the crescent- shaped beach area, which is annually pounded by the wind and sea, has been under its latest, and perhaps greatest, on- slaught for several days. Thursday, a section of beach 60 feet wide and 12 feet deep disappeared into the ocean. The damage left the six homes, valued at between $60,000 and $80,000, either hanging over a weak, sandy cliff or strand- ed on pilings that have "only 5 feet of sand to go before there's nothing to hold them up," Police Capt. Jack Snyder said 7977 Apr. 24 3h P.s.t. (-34) 94 The Los Angeles Times Wed., Jan. 9, 1974 (CC Ed.) Part I, Page 1, Cols. 2, 3 Giant Waves Pound Southland Coast, Undermine Beach Homes Sandbag Barriers Erected to Ward Off Tidal Assault. Giant wind-driven waves riding on surg- ing high tides battered the Southern Cali- fornia coast Tuesday, damaging homes and flooding nearby areas. Occupants of many beachfront homes from Santa Barbara to San Clemente erected sandbag barriers throughout the day in preparation for the next high tide at 10 :08 a.m. today. The wave and tidal assault came as rainfall from a five-day storm tapered off after dropping 7.69 inches in the Los Angeles Civic Center. In Orange County, supervisors proclaim- ed a "local emergency" for wave-battered coastline sections. (See also chapter 7.) 7974 Jan. 8 4h P.s.t. (-2) N-99 Chapter 2. The Impact of Perigean Spring Tides Upon Representative Events in American Nautical History Without pragmatically asserting a total and absolute causality of relationships in any of the following circum- stances, there is, nevertheless, ample justification for the fact that, on certain occasions, perigean spring tides have played a significant role in determining or altering the course of nautical history. A few episodes researched from American naval annals will serve to indicate the strategic importance of these tides. Since the increases in ampli- tude a associated with these tides (and winds) may occur in rather widely varying degree, the influences of such amplitude variations can be either detrimental or desir- able. Perigean Spring Tides as an Aid to Navigation Numerous cases have been mentioned in the preceding chapter in which destructive coastal flooding resulted from perigean spring tides that occurred in conjunction with strong onshore winds. Additional instances also can be cited in which moderate but navigationally important increments in tidal heights have had a direct impact upon historical events. These lesser increments were provided by perigean spring tides reinforced by light but steady on- shore winds, generally insufficient to cause flooding. Ap- propriate examples are given below. a The term "amplitude" is sometimes used in this volume in a general physical sense to designate the magnitude of either a positive or negative displacement of the tide with respect to mean water level, in preference to the more restrictive words "rise" or "fall" of the tides. The expression "increased amplitude" collectively allows for the algebraic increment in both the high and low waters asso- ciated with perigean spring tides. Strictly defined in tidal nomenclature, the value of the amplitude is equivalent to one-half the range (see fig. 6 in appendix), and may differ quantitatively from either the rise or fall (the vertical displacement of the surface of the sea respectively above or below the local chart datum) at times of high or low water. The word amplitude is also used as a mathematical coefficient (i.e., "ampli- tude of a constituent") in the harmonic analysis of tides. The quantitative information provided by accompany- ing eyewitness accounts, when coupled with supporting data from modern tide tables, point realistically to the fact that occurrences of this particular type involving perigean spring tides do not necessarily require the alignment of perigee and syzygy within the close limits of agreement in time possessed by the cases of severe coastal flooding previously described. The Fate of the Frigate Trumbull At the outset of the Revolutionary War, the American colonies had no organized navy, and much of the burden of the war effort was borne by privateers and by ships provided by the individual new States. However, limited funds were shortly authorized by the Continental Con- gress for the establishment of a small complement of Federal Navy vessels, and existing shipyards along the coast were given the task of constructing these new ships of war. Early in the year 1776, at the Connecticut River (Brainerd Quarry) shipyard of John Cotton in East Mid- dletown, Chatham Township (then consisting of several parishes ranging from present-day Portland to East Hamp- ton), work was started on the frigate Trumbull of 28 guns. Lofting was begun near the end of February 1 and the ship was launched on September 5. 2 The ensuing activity can only be described as involving the ultimate in misplanning as well as a classic blunder in shipbuilding. In the lack of present-day information concerning the exact outboard profile of this ship, the body plans used in construction of the Trumbull can only be assumed to be those specified for the official design of a Continental frigate. 3 If this conjecture is correct, the Trumbull had a full-load draft of 18 ft 4 in. which, allowing for an addi- tional navigational safety factor of 2-3 ft of keel clear- ance, was still in excess of the minimum water depth at 59 1,0 Strategic Role of Perigean Spring Tides, 1635-1976 the mouth of the Connecticut River at any ordinary high tide. The Trumbull ran aground on a bar. b The original of the accompanying early chart of the mouth of the Connecticut River (fig. 4), titled "Captain Parker's Chart of Saybrook Barr" [sic], with engraving done by Abel Buell, Connecticut's first engraver, is in the possession of the Connecticut Historical Society. A helio- type copy made from a very exact tracing of the fragile chart (from which published version fig. 4 was repro- duced) occurs in "The Public Records of the Colony of Connecticut, May 1768-May 1772." 4 The date printed on Captain Abner Parker's chart is 1771. However, information provided by the Connecticut Historical Society and published in a professional paper of the society 5 dealing with this early chartmaker reveals that the Governor's House shown on the chart was not actually built until 1 784. Accordingly, the chart must have been several times revised and updated from its original publication date, which the Connecticut Historical Society states could not have been earlier than 1784. 6 A further search reveals that no earlier British or Amer- ican chart exists in the Geography and Map Division of the Library of Congress, and even the contemporary Atlantic Neptune charts do not extend west of Newport, R.I., in this section 'of Long Island Sound. With these explanatory comments, it may safely be as- sumed that Abner Parker's chart provides an accurate and at least very representative contemporary indication of water depths in the vicinity of Saybrook Bar during the period under discussion. On this chart, the shallowest water depth in the principal navigation channel at the mouth of the Connecticut River is given as 6-8 ft, with that over the closely adjoining bars being only 4-7 ft. The earliest available nautical chart (fig. 5) for which detailed hydrographic soundings were made of this river mouth and its associated bars by the Coast Survey (the forerunner of the present National Ocean Survey) is chart No. 360 (1st edition) of the Connecticut River, published in 1853. Soundings on this chart (figs. 6-7) clearly show that the least depth of water anywhere directly along the designated ship channel or over im- mediately adjacent bars is 5/ 2 -7 ft, which is quite similar to that shown on Captain Parker's chart 79 years later. On the Coast Survey chart, the height of mean low water above the chart plane of reference is 0.6 ft, and the rise of highest tide observed above this plane of reference up b Considerable confusion seems to exist in modern reference sources concerning whether the Trumbull actually grounded or was simply blocked by the rivermouth bar; however, compare the direct contemporary quotations in references 14 and 16 which follow. until the publication date of the chart is given as 5.4 ft. From modern data, the mean range of ordinary spring tides at Saybrook Jetty at the mouth of the Connecticut River is 4.2 ft, and that at Old Saybrook Point is 3.8 ft. With consideration to the preceding ship-draft and hydrographic sounding figures, together with others to be discussed later in this same section, the Trumbull obvi- ously could not get off the rivermouth bar on which she had grounded at any ordinary high waters (including spring tides). As a result, she was prevented from taking any part in naval actions throughout the entire early por- tion of the Revolutionary War. Although those involved were repeatedly prodded by admonishments from militarily interested parties in Con- gress 7 and in Connecticut, 8 including an appeal to presi- dent-to-be John Adams (at that time delegate to the Continental Congress from Massachusetts and member of the Board of War) , all efforts to get the Trumbull off the bar were without success. An indication of the existing state of despair and of the fact that the shoalness of the water constituted the principal problem to be overcome showed in this same letter from William Vernon to John Adams, dated December 17, 1778. The letter quoted the opinion of a New England mariner aspiring to command the new frigate, one Captain Hinman. This authority claimed that only by the use of a "camel" (the name given to a type of special flotation gear) was there appar- ently any hope of clearing the bar. 9 With the Trumbull a firm captive within the Connecticut River, the vessel was in danger of "sitting out" the entire Revolutionary War. On August 1 1, 1779, an unusually high water occurred associated with a perigean spring tide. The tide was pro- duced by a close alignment (difference, -20 hours) be- tween perigee and syzygy, with the mean incidence of the two phenomena taking place at approximately 7 : 00 a.m., 75° W. -meridian time, on that date. The resulting peri- gean spring tide could, of course, have been enhanced by sustained, strong, onshore winds. Although contemporary weather records from this immediate vicinity are lacking, a diary account of local weather conditions at New Haven, Conn., during the Revolutionary War period, preserved in the vault of the National Climatic Center, NOAA, indicates that the wind conditions were calm there on this date in 1779. This would tend to indicate the presence of high atmospheric pressure over the area. Simi- lar contemporary records show that no strong hydrologi- cal runoff from recent severe rainfall, or melting snow or ice, occurred to swell the height of the waters at the river mouth. Impact of Perigean Spring Tides on American Nautical History 61 Cs i) J - ^ 5s^st U S ^ & c 4 ^ | l| i I i « s p .3 X CO 3 rt 1° C o 03 Jh pq a r * #. f. _Xr- 9 ■"•, m 5 ! IVJ r ; *i ii ^ITy** // V o ' '' 1 /. V <• f * ,j '' '' ***, -"-'f •"■■"•;; . V '/V** ■ :. t , ■■ : s : • MO ITU OF CONNECTICUT RIVER illlVKY OK'I'HK COAST OK TIIK I Ml'KII STA'I'I- Figure 5. — U.S. Coast Survey Chart No. 360 (1st ed.) of the mouth of the Connecticut River, published in 1853, including basic tidal data. Boxed areas are enlarged in figs. 6 and 7. fi-1 Strategic Role of Perigean Spring Tides, 1635-1976 Divkeison 's tg <» I jr, lX Whtu-f \ tf hi n Li trt jkenvrii k •' 1 TO aS (bisuflils ;;i V^ / '< »< »/ ,y Ac™ AW' v a r o * t-m H , /*,//>/ :i t» *i*« *H >.;i 1($ .]/, f.'"' IL ^^ JZ jfi &^f-}:, yl'Li^it House 3? 4« ..- ,6s ght 1. »8o Fl. above the sea 11 visilJtfifci Miles , 7 7« 5 Figure 6.— Enlarged section of the U.S. Coast Survey Chart No. 360 (1st ed.), showing soundings at the mouth of the Connecticut River between Fort Fenwick and Lynde's Point made in 1849 and 1851. Impact of Perigean Spring Tides on American Nautical History 02 65 ' feat, l&BBfl / ,: „ ,80 N. abovo the sea : • V- *S ..^^J^ 1, / -' visible i4* Miles , 7* 9i ./«>/.. y. -i . 7* 02 *•,;. mi,.-., -.m,.. 7 X 7 7 7- » 7 i. 5 1 Beacon 8 » ^4^ % 7<*~ 7 .*//„/ 6? hr.l.S. 8 ft .%«/. 12 » « 6 4-i Bi -,. 7* 7 * i!2 1-- m m hr,l.S. ■* 4i *5 - <>* I3i i4i i4 13 i4 1 4 _ rj 11 i. r » 7 «h a ffl G ^o *"■ a; ^S ~£ 1 g a — i ,*~ a S C 8" C o >, o § 5 s I H* O S a rn R3 m §il S g« "^ rt o g U 05 ffl box I .SH co ga> "^ Strategic Role of Perigean Spring Tides, 1635-1976 Nicholson, to proceed to Havana with despatches, letters, and a cargo of flour. The 'Trumbull' had scarcely cleared the Capes of the Delaware on August 8, when she was chased by the frigate 'Iris' 32, Captain George Dawson. Encountering a storm, the 'Trumbull' was dismasted, and thus crippled she was overtaken by the 'Iris'. The 'Trum- bull's' crew were a sorry lot; some of them were British deserters, and others were cowardly and disaffected. It was late in the evening when the fight began. Many of the crew now put out their battle lanterns and flew from their quarters. Captain Nicholson and his officers, with a handful of seamen, bravely defended their ship against impossible odds for an hour before they surrendered. "... A letter from New York dated Aug. 11, 1781, informs us that 'this day arrived the celebrated rebel frigate named the 'Trumbull'." 25 This terminated her war service. CONTEMPORARY KNOWLEDGE OF PERIGEAN SPRING TIDES In considering various other reasons why a possible practical advantage was not taken of earlier perigean spring tides to accomplish the release of the Trumbull from Saybrook Bar, it is important to recognize the gen- erally rudimentary knowledge of the tides in this colonial period. First and foremost, there should be taken into account the almost certain lack of technical awareness of either the causes or effects of perigean spring tides at this early date. To this must be added a rather limited familiarity by navigators with the technical principles underlying even ordinary spring tides. This knowledge rarely ex- tended beyond the fact that, in accordance with a well- known rule-of-thumb, higher (spring) tides were associ- ated with the "full and change of the Moon." Therefore, any case of perigean spring tides would not likely have been regarded as being any different from ordinary spring tides, which already had presented repeated opportunities for floating the ship free, without avail. Whether those concerned actually knew in advance of the favorable op- portunity presented by this particular perigean spring tide in terms of a water level considerably above that of ordinary spring tides is, accordingly, very much a matter of conjecture. In evaluating the comparative dearth of tidal knowl- edge in this early period, it is worthy of note that neither the astronomical phenomenon of perigee-syzygy nor the practical effects resulting therefrom in the form of peri- gean spring tides are anywhere mentioned in early edi- tions of Nathaniel Bowditch's American Practical Navigator, the generally accepted epitome of navigational knowledge in this country, first published in 1802. How- ever, the basic principle of these tides is described, together with their practical advantage to navigators in getting in and out of shallow harbors, in John Hamilton Moore's The New Practical Navigator, a British mariner's hand- book which, although having gone through 12 English editions by 1796, was first published in the United States only in 1799. Although this work contains errors in its tables which Bowditch subsequently sought to correct, Moore precisely summarizes the nature of perigean spring tides in the following words which, because of their direct application to navigation, are appropriate both to the immediately preceding and succeeding examples of the practical importance of these tides : "When the moon is in her perigaeum, or nearest ap- proach to the earth, the tides rise higher than they do, under the same circumstances, at other times; for, ac- cording to the laws of gravitation, the moon must attract most when she is nearest the earth . . . Some of these effects arise from the different distances of the moon from the earth after a period of six months, when she is in the same situation with respect to the sun; for if she be in perigee at the time of the new moon, she will, in about six months after, be in perigee about the time of full moon. These particulars being well known, a pilot may chuse [sic] that time which will prove most convenient for con- ducting a ship out of any port, where there is not a suf- ficient depth of water on common spring-tides." 26 Other references indicating an awareness of perigean spring tides by early philosopher-scientists — although a knowledge not necessarily shared by navigators — are given in a survey of pertinent tidal literature in part I, chapter 4 of the present work. The fact remains that, whether the Trumoull's rescuers knew the exact cause of this tidal phenomenon or not, they took advantage of it, with posi- tive results. TIDAL ANALYSIS It will be observed that the portion of the previously mentioned condition of tidal enhancement used occurred on exactly the same day as perigee-syzygy. In the light of subsequent discussions in this volume concerning "phase age" and "parallax age" in relation to perigean spring tides (see chapter 8) , it is desirable to point out that each tidal situation possesses its own local timing response to gravitational forces which must always be individually considered. This circumstance, as will be repeatedly em- phasized throughout this volume, prevents the application of any too positive, all encompassing or generalized rules Impact of Perigean Spring Tides on American Nautical History f» f ) in connection with even closely adjoining coastal areas subject to the same tidal action. Such "station differences" become a function of harmonic constants (table 19), which are representative of local tidal responses to astro- nomical effects. Additional deviations from the tidal con- ditions which prevail at certain standard or "reference" tide stations, expressed as time and height variations in the high and low waters, also may be either positive or negative. Tides at the mouth of the Connecticut River initially react more rapidly in their response to the influence of perigee-syzygy than do coastal locations farther south (compare with the tidal analysis following "The Battle of Port Royal Sound, S.C.," below). The peak of the perigee-syzygy tidal influence at the Connecticut River outlet actually occurs sometime prior to the near-coinci- dence of perigee and syzygy. A modern example based on actual data available from tide tables appropriate to this location for a situation corresponding to the same time of the year, possessing nearly the same separation in time between perigee and syzygy, a similar declination of the Moon, and other factors will serve to substantiate this statement. The peri- gean spring tide involved in the Trumbull's release oc- curred on August 11, 1779, in connection with a near- alignment between perigee and syzygy which took place at approximately 8:00 a.m. (75° W. -meridian time) on this date. The time difference between perigee and syzygy was — 20 hours (with perigee preceding syzygy) and the Moon, at new phase, was in declination +21.4. A closely similar circumstance existed at the entrance of the Connecticut River at approximately the same time of the year, with almost exactly the same interval between perigee and syzygy ( —20 hours), with perigee preceding syzygy, and the new moon in nearly the same declination ( + 17.6°) at the time of perigee-syzygy on July 15, 1920 — for which date tide tables are, of course, readily available. In practice, the predicted tide heights for Saybrook Light, at the entrance to the Connecticut River, and a so- called "subordinate" tide station, are referred to the pri- mary tide station at New London, Conn., at which regular tidal measurements are made. As a further source of data, the earliest available hydrographic chart of the Connec- ticut River (chart No. 360 of 1853) previously referred to (fig. 5) indicates that the rise of the highest tide ob- served above the chart plane of reference prior to the chart's publication date was 5.4 ft. From appropriate annual tide tables, the first of two maximum daily tidal ranges (lower low water to higher high water) at Saybrook Light around the preceding 1920 date was predicted for July 15, 1920 and was 4.8 ft, which is 0.5 ft in excess of the mean spring range, 4.3 ft, for this station. On July 13, 14, 15, 16, 17, and 18 the predicted maximum daily ranges for this station were 4.5, 4.7, 4.8, 4.8, 4.7, and 4.5 ft, respectively — above the mean spring range for 6 successive days, and still in excess of this value even 3 days after the occurrence of perigee-syzygy at 5:24 a.m. (e.s.t.) on July 15. It is noteworthy that, in this very comparable case to that of 1779, the perigean spring tidal range not only was predicted to remain above the mean spring range for 3 days after perigee-syzygy, but the first case in excess of this range occurred even 2 days before perigee-syzygy. (Within this series, the first case of such a condition in excess of the mean spring range for Saybrook Light oc- curred at 7:54 p.m., e.s.t., on July 13, approximately 33/ 2 hours before the mean epoch of perigee-syzygy.) As indicated earlier, the first instance of a maximum daily tidal range in this series was predicted for July 15, or on the same day as perigee-syzygy. This situation provides a contrast with the longer phase and parallax ages noted in connection with Port Royal Sound, S.C., on page 84. HYDROGRAPHIC ANALYSIS An additional technical evaluation of the Trumbull's design draft and the actual water depth necessary for this ship to have crossed the bar at the mouth of the Con- necticut River is in order. The previously mentioned 1771 chart (fig. 4) of the Connecticut River shows the least depth of water along that portion of the channel (indi- cated by anchorage symbols) between the present light- house on Lynde's Neck and Fort Fenwick on Saybrook Point to be 18 ft (3 fathoms) . However, the water depths over the bars located just outside the mouth of the river are much less. To the southeast of the ship anchorage, the water depth averages 10 ft, and over numerous bars out- side the entrance it shallows to 4-7 ft. Although shifting bottom sands make the water depth at the river entrance extremely subject to change, possibly even within a few days, the sounding data given on this early chart of 1 77 1 ( 1 784 ) are at least broadly representa- tive of the situation as it existed on the Connecticut River in 1776. The hydrographic data of this chart, indicating navigational impediments subject to a partial offsetting by high tides, are further reinforced by data on the Coast Survey chart of 1853, which indicate a similar least depth of 7 ft at many places along the outer portions of the channel. The chart datum for the 1853 chart corresponds to the mean low water of spring tides which, because of the ad- 70 Strategic Role of Pcrigean Spring Tides, 1635-1976 ditional depression of the low-water stage produced in these tides, is a little lower than the mean of all low waters used in the compilation of present-day nautical charts. However, this datum is considerably more representative in the case of perigean spring tides. The height of mean high water with respect to this spring tide datum plane as noted on the 1853 chart is 4.5 ft, and the height of mean low water is 0.6 ft, giving a mean range of 3.9 ft. By con- trast, the mean spring range is listed as 5.0 ft, and, since the mean low water of spring tides has been set as the arbitrary zero point on this 1853 chart, the rise of ordinary mean high water springs according to these chart data is 5.0 ft. Thus, realizing that the Trumbull would have to navigate water depths shoaling at the places previously mentioned to within 7 ft or less of the latter datum plane, and allowing for a mean rise of spring tides to 5.0 ft above this datum, only a ship having a draft of 12 ft (7 ft + 5 ft) or less could cross these bars even at ordinary spring tides. Although profile plans for the Trumbull have been determined by the present writer to be unavailable from either U.S. Navy or British Admiralty sources (late in the Revolutionary War, as previously noted, the ship was captured by the British) it is stated in Howard I. Chapelle's The History of the American Sailing Navy that it may be assumed she was of the standard design for a 28-gun frigate approved by the Marine Committee of the Continental Congress. 27 A sister ship of this class was the frigate Virginia constructed at the shipyard of George Wells in Baltimore in 1776, and which, after being blockaded by the British for more than a year, also ran aground in the Chesapeake Bay in 1778. Outboard pro- files for this vessel are available in Chapdle's previously mentioned book. Scaling from the waterline on these plans gives a full-load draft (ready for service) of 18 ft 4 in. Without stores, provisions, or armament, and stripped of all extraneous weight other than that neces- sary to make the ship sailable, the draft, in the opinion of a NOAA naval architect, would probably have been reduced to a maximum of 14 ft. However, in the narrow confines of the upper reaches of the Connecticut River, the square-rigged vessel, if under sail, would not be able to tack, and a following wind would also mean an offshore wind which, if strong, would depress the height of the tides at the river entrance. To negotiate the narrow, curving portions of the river, she would have to be towed by small boats. This would permit the ship to be initially stripped of top hamper, rigging, and sailing gear (some control ballast would have to be re- tained), and would reduce her draft to about 1 2 f t 8 in., but spars, sails, and other heavy gear would subsequently again increase the draft in the sea-ready condition in which she grounded on the bar. From a consideration of the tidal data specified earlier, the maximum depth of water available across the bar at the river mouth, even at ordinary spring tides, would be 12 ft. Assuming a forward trim and negligible pitch move- ment of the ship, it would still be necessary, in these only poorly sounded and as yet basically unsurveyed waters, to ahow 2 to 3 ft of keel clearance to accommodate local channel-bottom variations and to ensure a safety precau- tion against grounding. Considering the extra buoyancy that could have been provided by a "camel," a rudimen- tary calculation shows it would have required more than 250 water-tight hogsheads (63-gallon capacity) first par- tially filled with water, and then successively submerged, lowered into position beneath the ship, and pumped com- pletely free of water, to raise the Trumbull by only 1 ft. Even allowing for the buoyancy provided by such an ex- tensive flotation gear, therefore, it is evident that the addi- tional water depth created by a perigean spring tide would be necessary to allow the Trumbull to clear the bar — and this is, obviously, the opportunity that was utilized in 1779. The Second Battle of Charleston Harbor The bar outside the harbor at Charleston, S.C., — like that of the previous example (and another at the entrance to New York Harbor) — was instrumental recurrently throughout the Revolutionary War in impeding the sail- ing, activities of deep-draft men-of-war. In the case of Charleston, tidal circumstances connected with the astro- nomical phenomenon of perigee-syzygy played an im- portant role in the second siege of this city in 1780. (The first British attempt to lay siege to Charleston on July 4, 1776 had failed.) Although a matter not directly ac- counted for in history, the second attempt by the British to capture this southern port was undoubtedly aided by a perigean spring tide. Arriving off Charleston Harbor at the beginning of March 1 780 after needed ship repairs at Savannah, Ga., the British found that, because of the deep drafts of their vessels, the depth of water in the entrance channel (fig. 9) was such that it was impossible to cross the offshore bar. They were compelled to stand off the coast for more than 2 weeks, hopefully awaiting a better opportunity at the next high water springs. Probably unaware of the special nature of the circumstance, but taking advantage Impact of Perigean Spring Tides on American Nautical History 71 of the augmented high waters resulting from a pseudo- perigean spring tide occurring on March 20, 1780, they succeeded in negotiating the bar with a major naval attack force, including a 50-gun frigate, two 44's, and four 32's. The significant aspects of this naval engagement were told in a subsequent report by Vice-Admiral Marriott Arbuthnot to the British Admiralty, dated May 14, 1780: ". . . Preparations were next made for passing the squadron over Charles-town bar, where [at] high water spring tides there is only 19 feet water. [Compare with actual sounding data appearing on the two charts (figs. 10 and 1 1 ) compiled by different sources shortly after this siege.] The guns, provision and water were taken out of the Renown, Roebuck, and Romulus to lighten them, and we lay in that situation on the open coast in the winter season of the year, exposed to the insults of the enemy for 16 days before an opportunity offered of going into the harbour, which was effected without any accident on the 20th of March, not withstanding the enemy's galleys con- tinually attempted to prevent our boats from sounding the channel . . ." 28 The perigean spring tides of which use was made on this occasion occurred as a result of a pseudo-perigee- syzygy situation having a mean date of March 1 9.65, 1 780, with a separation between perigee and syzygy of approxi- mately — 37 hours. Significantly, the British had been un- able to make use of the preceding set of spring tides about March 6, which would have occurred near lunar apogee Courtesy of William L. Clements Library, University of Michigan Figure 9. — Hydrographic chart of Charleston Harbor, S.C., prepared by the British engravers, Sayer and Bennett, as a documentation of the tide-assisted penetration of harbor shoals and second siege of Charleston by the British, 1780. 72 Strategic Role of Pcrigean Spring Tides, 1635-1976 and whose high-water levels would, therefore, be even somewhat less than those of ordinary spring tides (the average situation at perigee-quadrature, discussed at length in part II, chapter 5 ) . The March 6 tides were also accompanied by quartering offshore winds, as noted below. The attendant circumstances were described in editions of the Pennsylvania Packet for April 25 and May 2, 1 780 : "March 19. — The British under General Clinton, now encamped on James Island, seem to wait for the shipping which lay off the bar, and have been disappointed at the last springs by south-west winds, which kept down the tides so that they cannot get over. This day the springs are at the highest, but the weather so hazy that they will scarcely attempt it, and it will probably clear up with unfavorable winds. We begin to hope that Province [Prov- idence] has interposed a second time to prevent their getting over until we are ready. If they should get over either now or hereafter, there will probably be the hottest contest that has happened this war, just off Fort Moultrie. The British ships destined to come in are said to be the Renown, fifty guns; Roebuck, forty-four; Blond, thirty- two; Perseus, twenty and Camilla, twenty . . ." 29 "March 20. — This morning the British got their ships over the bar. They consist of ten vessels of force, from twenty guns to a sixty-four, as some say, others a fifty. . . ." 30 This successful passage over the Charleston bar and subsequent victorious attack by the British upon the American fleet confined within the harbor — followed by the second Siege of Charleston — resulted in the capitula- tion of the American ground forces under General Ben- jamin Lincoln on May 12, and the capture of the Con- tinental ships Providence, Boston, and Ranger, compos- ing major elements of Commodore Whipple's squadron. American naval vessels destroyed and sunk were the Briscole, 44 guns, General Moultrie, 20 guns, and Notre Dame, 16 guns. TIDAL ANALYSIS A modern 1 974 tidal circumstance possessing conditions approximately comparable to those encountered in the second Siege of Charleston will serve to illustrate the tacti- cal importance of the tides in this 1780 occurrence for which tide tables are not available. Around the date October 13, 1974, a pseudo-perigean spring tide similar to that of March 20, 1780 occurred, related to a phenomenon of perigee-syzygy whose mean alignment took place at 9 : 06 p.m. (e.s.t.), on October 13, with a separation of —68 hours (perigee preceding syzygy by this amount) . It is noteworthy that even this considerably larger separation-interval (selected purposely, in this early chapter, as a test case for the practical range of perigean spring tide influence) is still sufficiently small to produce significant amplitude increments in the tides. This may be seen by comparing the high water and daily range data of table 6 with the corresponding values for mean high water springs and mean spring range in the second following paragraph. The wider separation-interval in the test case, com- bined with other dynamic factors is, in turn, responsible for the circumstance that the lunar geocentric horizontal parallax at the mean epoch of perigee-syzygy on Octo- ber 13.88, 1974 was only 59'48.55" compared with 60'43.8" on March 19.65, 1780. These facts give tacit but demonstrable support to the assumption of yet further increased tide-raising effects from the smaller — 37 1 ' interval which occurred in March 1780. As will be established in subsequent chapters, the Moon's proximity to the Earth and the astronomical factors which lessen this distance are the foremost causes for augmentation of tidal heights. The data of table 6 for October 1974 are, therefore, values safely on the small side in terms of the enhanced astronomical tidal situation in March 1780. At Charleston Harbor, the corresponding predicted higher high waters (HHW's) , lower low waters (LLW's), and maximum daily ranges given in the tide tables were : Table 6. — Comparative Tides at Charleston Harbor, S.C. October 13-19, 1974 Maximum Date Time HHW LLW Daily Range (e.s.t.) (/<) c/o (ft) October 13 0542 6.4 -0.2 6.6 October 14 0634 6. 7 —0.4 7. 1 October 15 0725 6.8 —0. 5 7.3 October 16 0815 6.8 —0. 5 7. 3 October 17 0901 6. 7 —0.4 7. 1 October 18 0948 6.4 —0. 1 6. 5 October 19 1034 6. 1 + 0.2 5.9 It will be observed that the first of two maximum heights (HHW's) for these perigean spring tides was pre- dicted for October 15 at 7:25 a.m. (e.s.t.), approximately 34 hours after the perigee-syzygy that occurred at 9:06 p.m. (e.s.t.) on October 13. This accords very closely with the circumstances under which the British crossed the Charleston bar at HHW on March 20, 1780, the next day after the pseudo-perigee-syzygy on March 19. Impact of Pcrigean Spring Tides on American Nautical History 73 Courtesy of Library of Congress Figure 10.— Hydrographic chart of Charleston Harbor, S.C., published by the House of Fayden in Philadelphia, May 27, 1 780, 2 months after the successful navigation of the entrance shoals by British frigates at the time of a perigean spring tide, March 20, 1780. On the chart (fig. 10) published by the House of Fayden in Philadelphia on May 27, 1780, 2 months after the second Siege of Charleston, the datum for mean high water spring tides at Charleston is given as 5.6 ft above the mean low water chart datum. Corroborating this early value, the figure given for mean high water springs at Charleston (Custom House Wharf) in modern tables is also 5.6 ft above the same chart datum. The corrections to the height of HHW for North Jetty, at the entrance to Charleston Harbor and nearby points on the outer coast of South Carolina are, consistently, 0.0 ft. The mean spring tidal range at Charleston is 6. 1 ft. In this comparative situation, the predicted higher high water at Charleston Harbor therefore remains in excess of the value for mean high water springs — and even above that representing mean spring range — for periods of 7 and 6 days respectively, around perigee-syzygy. Likewise, the maximum predicted tidal range at Charleston remains above the mean spring range for 5 days after perigee- syzygy, even under these conditions involving a compara- 7! Strategic Role of Pcrigcan Spring Tides, 1635-1976 tively large (—68-hour) separation in time between the two components. The separation-interval for the 1780 example was somewhat smaller, approximately — 37 hours, a factor contributing still further in this case toward the raising of high tides. Closely supporting the above analysis is the footnote of tidal information contained on the earliest chart of Charleston Harbor prepared by the Coast Survey (Chart No. 432, 1st edition, 1855) where the highest tide of record at Castle Pickney on Charleston Harbor up to that date is given as 7.32 ft (observed on April 15, 1851 — accompanying another pseudo-perigean spring tide). On this same Coast Survey chart, the mean daily tidal range at this location is given as 6.01 ft. The level of mean low water springs is specified to be —0.19 ft below that of mean low water ( the chart datum ) , and the mean range of spring tides is given as 5.81 ft. Hence, the rise of mean high water springs above mean low water is 5.82 — 0.19 = 5.63 ft. The minimum navigable water depths past the bar outside Charleston Harbor just prior to the second Siege of Charleston can now be correlated with these tidal data. HYDROGRAPHIC ANALYSIS A second chart (fig. 1 1 ) , of the water depths inside and outside Charleston Harbor, prepared by the British en- gravers Sayer and Bennett in 1780, within a few months after the second siege of this city, is more specific in its hydrographic data than is the Fayden chart. According to a premetric practice in nautical chart representation, all water depths up to 18 ft are given on the chart in units of feet; depths in excess of 18 ft (3 fathoms) — and, spe- cifically, those along designated navigation channels — are specified in fathoms (1 fathom = 6 ft). However, the depths of water over shallow bars or submerged reefs (which are indicated on the chart by stippled areas out- lined by dotted lines) are also given in feet, printed along- side the submerged features. Having been prepared long before this standard procedure went into effect, the two 1 780 charts utilize a slightly different manner of presenta- tion. With the exception of a few shoal-water passages where the water depth is specifically indicated as being in feet, all soundings thereon, regardless of location, are given in fathoms. Thus, the shallowest water depths between two bars bracketing the designated Ship Channel (which the British used) leading into Charleston Harbor are seen to range from 2 to 3 fathoms (12.0 to 18.0 ft), with the water depths over the bars being only 8 ft. The first values appear on the chart shown in fig. 10; the second value is given in fig. 1 1 . These quantities are also generally confirmed on the same portion of the earliest Coast Survey chart of Charleston Harbor published in 1855 (figs. 12, 13), where the minimum channel depth is shown to be 3J4 fathoms. Despite the constantly drifting bottom sand, both inside and outside the harbor, these charts provide an interesting comparison of the general bottom config- uration at two epochs 75 years apart. Their general similarity is also germane to the assumption of an average reproducibility of sea-level datums over extended periods of time, necessarily employed throughout these various analyses. To provide the most accurate information possible con- cerning the ships involved in this siege, an inquiry was directed to the National Maritime Museum in Green- wich, England, relative to the drafts of the ships Renown, Roebuck, and Romulus. The report indicates that: "Unfortunately, the official lists of ships in possession of the Admiralty do not give the drafts of 1780, but do so in the 1790's, by which time the Renown was out of service. Her sister ship, the Portland, is stated in a list of 1795 . . . to have a draft of 10'6" forward, 15'7" aft. . . . The Roebuck and the Romulus were somewhat similar ships, draft 10'8y 2 " forward, H' 1 /^" aft. It is not, however, specified exactly what these measurements de- scribe, except that they are 'light'." :il The latter statement would imply an out-of-service draft, discounting any load of gunpowder, stores, shot, or cannon. The previously quoted memorandum from Vice-Admiral Arbuthnot indicates that guns, provisions, and water were taken out of these ships before Charleston to lighten them. No mention is made in Admiral Arbuth- not's account relative to the ships making rendezvous to refit, for example, in the available Five-Fathoms Hole after crossing the bar. Inasmuch as a combat status was resumed immediately on crossing the bar, it is unlikely that more than the bare minimum of tactical gear, shot, and ordnance was removed, and that the major portion of the ship's heavy combat-readiness equipment remained. Certainly it would be impractical, under the contingen- cies of time and a hostile environment, to remove more than the guns located on the top deck. It is, therefore, clearly mandatory that (in a directly opposite case to that of the Trumbull) an additional 1 to 2 ft must be added to the previously specified light drafts of the Renown, Roebuck, and Romulus under such con- ditions of near-combat readiness, to compensate for their considerably stripped-down conditions when out of serv- ice. A minimum operational draft for the Renown before Charleston of 16/2 to 17 ft aft can, therefore, safely be assigned. Impact of Pcrigcan Spring Tides on American Nautical History 7 r ) ClullWl a** a vJi^^^Vf ^ y /y J, ^ fr ^ 'J (///}t/fSBL>- /' ^ >h :r h /'<<■/ 4 Ship .-Ctvuin. Courtesy of William L. Clements Library, University of Michigan Figure 11. — Enlarged portion of Sayer and Bennett chart of Charleston Harbor (fig. 9), emphasizing the shoals at the entrance through which the deep-draft British frigates were forced to pass. Comparison of water depths with those of figure 10 shows a close agreement between these charts published respectively in England and America. In addition, subject to the small-boat harassment which Vice-Admiral Arbuthnot mentions, and to prevent any further buildup of resistance by American forces, there was the necessity for the British to accept those weather and tide conditions which offered the earliest possible opportunity for crossing the bar, in contrast to a permis- sible period of waiting for favorable conditions in the Connecticut River example. Choppy seas coupled with a possible light ground swell might readily be produced by the unfavorable winds men- 71) Strategic Role of Perigean Spring Tides, 1635-1976 CHARLESTON HARBOR AMi 11 s APPROACHES ^#1 "" ill **; \ Figure 12. — Preliminary chart of Charleston Harbor and its approaches (C&GS Chart No. 431, ed. No. 1) published by the U.S. Coast Survey in 1855, containing significant tidal data and datum planes. The small boxed area indicates the portion of the chart enlarged in figure 13. Impact of Perigean Spring Tides on American Nautical History 77 TX sT mmm: i;v «a j3 ?6, ; ; 3t« ta .'■V.V. trie S, & Sh i4 .«: l4 t4 & i4 Bfa:20 .11 : - : /::r:!ii;i;^-: ; :mvA- « 55 5t;": .6 34 ^ M.sml.Sk, & 9y- s i$\\U3i$ 4i iH 3*. 3* 4* |> i& 4i^ n •V 3t brk.Sh. 4$ 4t 11 ^ :'".6 IV s : s. . *■ ia ^ i* i4 i4 $ll$lt* 4t 14 i3 ; &////m&(; 5^1 v^"- -?:• i4 i3 i$ 15 lit 11 S£$k *3i •/^/.••/Vvita- Figure 13.- ift 1$ 34 E*. o. ; • A,.- ■ ' £■■■£■■■■■■■<&'■ ' /fc 3t *> i3 3* 34 ia BrtJ^f 3t 37 3* 4; 3t M,S.' 3i 4i U 3£ « :h Mzsh.*** 3t ,6 13 i3 -Enlarged section of C&GS Chart No. 431, ed. No. 1, of Charleston Harbor (fig. 12), showing soundings in the southern portion of the main ship channel, with a minimum depth of ?>)\ fathoms. 7;; Strategic Role of Perigean Spring Tides, 1635-1976 tioned in the previously quoted Pennsylvania Packet ar- ticle. The movement of this swell over the prominent shoals in this area could cause "blind rollers." These, in turn, would cause the entering ships to heave and pitch and would require additional keel clearance to prevent running aground. Thus, in order to ensure a reasonable margin of safety in these little-known waters, the largest British ship, the Renown (even with a partially lightened condition) would have needed a water depth of at least 20 ft to negotiate the channel. Choosing, for the sake of impartiality, that contempo- rary British chart which shows even the greater of the two values (2^4 fathoms or 13.5 ft) for the shoal-water depth in the channel, the required tidal height above mean low water for safe navigation must, therefore, have been 20 _ 13.5 = 6.5 ft. This is a condition which, according to the data appearing on the 1855 Coast Survey chart, is not attained even at ordinary spring tides, whose mean height at Castle Pickney on Folly Island is given as 5.63 ft. Modern tide tables indicate that the difference in high waters between Folly Island and Sullivans (Sulivan's) Island on the outer coast is 0.0 ft. The necessary additional rise in tide height to provide a navigable water level of 6.5 ft (or 8.0 ft, according to the second British chart) above mean low water could have been provided only by the perigean spring tide at this second Siege of Charleston. ***** Two further episodes in U.S. naval history, the one similar, the other involving a different operational appli- cation, but both related to the amplitude-increasing as- pects of perigean spring tides, occurred during the Civil War. The Battle of Port Royal Sound, S.C. This third instance in which perigean spring tides un- questionably exercised an important influence upon an event in American history forms a desirable technical ex- tension of the preceding example. It is characteristic of a tidal property derivable from table 19 that, on the south Atlantic coast of the United States, perigean spring tides tend to follow, by 1 to 1 l / 2 days in time, the near- coincidence between perigee and syzygy which produces them. On October 29, 1861 , a contingent of the Union Fleet, known as the South Atlantic Blockading Squadron, sailed southward from Norfolk, Va., subject to sealed orders. This largest naval armada ever constituted in American history, up to that time, consisted of 50 fighting ships under the command of Flag Officer Samuel Francis Du Pont. Its destination, Port Royal Sound, S.C., had been determined by the Federal Government to have the great- est possible strategic value in pushing the war against the South. The armada was peremptorily scattered en route by the first lashings of a violent coastal gale (some historical sources have variously described it as a hurricane) which, moving northward, subsequently struck inland and caused severe tidal flooding along the New Jersey coast. (See the list of historic tidal floodings of North America in table 1 under the date November 2, 1861.) The date of mean perigee-syzygy upon this particular occasion (with only 1 hour separating the two compo- nents) was November 2, 11.5 hours, 75° W. -meridian time (eastern standard time not yet being in use). This very near-coincidence of perigee and syzygy was com- bined with an extremely close proximity in the distance of the Moon from the Earth at the time, represented by the large geocentric horizontal parallax of 61 '2 7. 6" (see table 16) — yielding a proxigean spring tide. As explained in the subsequent tidal analysis of this event, because of the normal "phase age" and "parallax age" between the close alignment of perigee and syzygy and the associated increased tidal effects in these southern coastal waters, the maximum augmented tidal effects could be expected approximately 1 day after perigee- syzygy — or in the early morning hours of November 3. As further confirmed by data taken from modern tide tables available for this location, the accompanying increased tidal ranges caused by the perigee-syzygy alignment would also continue for several days thereafter, through November 4, 5, and 6. Thus, paradoxically, the same perigean spring tides which, in conjunction with strong onshore winds, resulted in tidal flooding and severe coastal damage in New Jer- sey, served an advantageous purpose in the attack on Forts Walker and Beauregard, commanding Port Royal Sound. This advantage resulted from the relatively high navigational waters associated with these perigean spring c In the interests of scientific objectiveness, reference should be made to the discussion concerning the necessary uncertainty in desig- nation of early North American hurricanes — and the often more-or- less arbitrary classification thereof by experts (among whom opin- ions differ) — that precedes tabic 2. It is not the purpose of this treatise to exercise any partiality. The disturbance in question had moved on northward from the scene of action in the present case. Hence, the exact type of storm earlier represented has no direct bearing upon the navigational im- portance of the astronomically produced perigean spring tides. These alone aided the tactical circumstance at Port Royal Sound described above. Remotely produced swell or waves were not a contributing factor. Impact of Perigean Spring Tides on American Nautical History 7<) tides as approximately 40 ships which were not too badly scattered or disabled by this same storm off Cape Hatteras made rendezvous some 10 miles off Port Royal Sound early on Monday morning, November 4. 32 (Several other- wise reputable historical reference sources give this date as November 5 and the date of crossing the bar as Novem- ber 7, both of which are incorrect.) All artificial aids to navigation (position-fixing targets, buoys, lighthouses, etc. ) already had been removed by the rebel forces and, on this low coastline, no significant features of natural topography were available to serve as identifying navi- gational landmarks. Much battered by the gale, the remnants of the original fleet assembled one by one, and anchored outside Port Royal Sound (fig. 14), where the passage of these deep- draft vessels across the bar at the entrance now posed a serious operational problem. In the months of prepara- tion that had preceded this great combined deployment of naval and army forces to the south, it obviously had been planned to arrive and enter the harbor at the time of the spring tides associated with the new moon of No- vember 2. It is questionable whether, in the existing state of knowledge, it was recognized, or definitely brought into consideration, that this date also represented an occasion of perigean spring tides. The storm had delayed the mission by 2 days. Al- ready the lifespan of the presumed ordinary spring tide (which normally reaches a maximum and declines within a day or two) was fast disappearing. This undoubtedly explains the sense of urgency for immediate passage across the bar indicated in the eyewitness account given below. However, as shown in the subsequent tidal analysis of this episode, perigean spring tides last considerably longer. The hydrographic survey vessel Vixen, a side-wheel steamer which had been obtained by the Union Navy from the Coast Survey for inshore sounding operations, was ordered into action. It had been brought along to Port Royal Sound (then known as Port Royal Bay or simply Royal Bay) for just such a contingency as they now faced. During the ensuing activities of making sound- ings by leadline, buoying the channel, and leading the fighting ships across the bar, the influence of the perigean spring tide soon became known, as is referred to obliquely and without elaboration in the official reports of the ex- pedition. Charles O. Boutelle, Assistant, U.S. Coast Sur- vey, was in charge of these sounding activities and, in a letter dated November 8 from Port Royal Bay, he wrote to the Superintendent of the Coast Survey as follows: ". . . The R.B. Forbes came to me [on Monday, No- vember 4] to say that the Augusta and Dale, steam gunboat and sloop-of-war, were outside. I reported the fact to the commodore, and he expressed so earnest a wish to get them in before the attack that I determined to bring them in at once, though night had already come on. The Augusta draws 15 and the Dale 16 feet. We ran down about 8:00 p.m., and anchored a boat, with a Fresnel lantern in it, at the entrance of the channel. I then went to the two vessels and communicated the commodore's orders. Both captains were ready to go in if I would take the responsibility of leading them. The Augusta took the Dale in tow, and we passed in without trouble, having no cast less than 19 feet [the evening lower high water associated with the perigean spring tide would have been about 9:25 p.m. on this date], and I had the satisfaction of reporting to the flag-officer their arrival at half past eleven p.m. Running outside again I anchored the Vixen at the entrance in readiness to bring in the Ericcson and the Baltic, drawing 20 and 22 feet . . . ". . . At sunrise [Tuesday, November 5] we anchored a large spar buoy at the entrance of the south channel. Mr. Piatt and Mr. Jones, 1st and 2d officers of this vessel, were then sent on board of the Baltic and Ericcson, respectively, and I led in with the Vixen at half flood [the morning higher high water for the perigean spring tide of this date would have been about 9:50 a.m.]. We had no cast less than 27 feet, and I can say with certainty that vessels drawing 25 feet may come in at all ordinary tides [an oblique reference to the fact that, at 27 feet and more, the existing tides were in excess of "ordinary" (including spring) high tides — see be- low] . . . ". . . The Wabash started for the batteries at 8:30 a.m. . . ." 33 As recounted above, during the lower high water in the late evening of Monday, November 4, the Vixen guided two smaller ships over the bar. On the morning of Tuesday, November 5 (with higher high water about 9:50 a.m.), aided by the effects of the perigean spring tide, she led the remainder of the large-draft vessels of the fleet, with the flagship Wabash (fig. 15) second in line, across the bar, "with only a foot or two to spare." 34 ". . . As they ran past vessels that already had crossed, cheers rang out over the water. . . After this came some delay until buoys could be placed around the dangerous shoal. . . Even then, as the next succeeding low tide [deepened by the effect of perigean springs] ap- proached . . . the Wabash, trying to fix the outiines of Strategic Role of Perigean Spring Tides, 1635-1976 ', '.'".'■■". L- 3* '"&% '.*W Transport* l/ %WfWK «■ --•■■- ■, \ , ***** .^{■'(i iV ****** ; / I .. v\ \ - S~k.ttdl of PortTloyCll, S. C, .**«£ to tht, Navy Dtp ! from tluFLut Nov 1861 AutoyraphU, Copy by H LUuLenkM.,CoaJl Survey Offlcr.. Figure 14. — Sketch of Port Royal Sound, S.C., and the Union naval maneuvers before Fort Walker, prepared by a Coast Survey technician aboard the hydrographic survey ship Vixen during this Civil War engagement in November 1861. The chart shows the location of the entrance channel between Gaskin's Bank and Martin's Industry depicted in greater detail in figure 16. Impact of Perigean Spring Tides on American Nautical History 81 % -a ~0 aj §1 ^1 « O ■g.g J* 45 M (8 O O L O 3 ;;j Strategic Role of Pcrigean Spring Tides, 1635-1976 the fort before dark, pushed on too rapidly and grounded. By the time she was free again, Du Pont decided it was too late to proceed, and the squadron was signaled to with- draw out of gunshot for the night. . -" 3: Although the planned attack was delayed on the next day by bad weather, on November 7 Fort Walker was captured, and later, Forts Royal and Beauregard. Through this success at Port Royal, the Federal Navy secured access to, and control of, all inland waterways between Savannah and Charleston. The naval blockade of the South was thereby greatly enhanced. TIDAL ANALYSIS The depths of the actual soundings made on Novem- ber 4-5 empirically confirm that a perigean spring tide was present and that its effects extended several days after the time of mean perigee-syzygy at this particular loca- tion on the east coast of the United States. Supplementary tidal data contained on the contempo- rary nautical charts mentioned in the next section sup- port this statement. Descriptive notes accompanying the preliminary chart, of which fig. 1 6 is an enlarged section, indicate that the mean rise and fall (i.e., the mean range) of high water springs in Port Royal Sound is 7.3 ft. The average fall of low waters associated with spring tides below the chart datum (plane of reference) of mean low water is —0.9 ft. This gives a reduced value for mean high water springs of 7.3-0.9 or 6.4 ft above the chart datum of mean low water. The rise of the highest observed high water above the chart datum prior to the date of the chart is given as 8.6 ft, and the fall of the lowest tide observed below this same plane of reference is -2.0 ft, indicating a rise of 8.6-2.0 or 6.6 ft above mean low water. The latter values provide an essentially accurate means of determining the incremental variations (8.6- 6.4 = 2.2 ft) and (— 2.0— ( — )0.9 1.1 ft) caused by perigean spring tides. These differences were probably supplemented in the extreme instances noted above by the effects of onshore and offshore winds, respectively. Based on the sounding data provided for mean low water on the aforementioned preliminary chart, the sum of this low water depth and the height of the high water, both subject to the effects of a perigean spring tide (i.e., 19.5 + 8.6 = 28.1 ft) is, in fact, necessary to account for the water depth measured by the Vixen at Royal Bay near the time of higher high water on the morning of November 5. The statement contained in the hydrographic report "nowhere less than 27 feet" also conforms with, and con- firms the existence of, a perigean spring tide. An ordinary spring tide would provide only 19.5 + 6.4 = 25.9 ft at mean high water springs. As before, actual tide data for Port Royal will be taken from available modern sources for a situation having ex- actly the same time difference between perigee and syzygy as occurred on November 2, 1861. A comparison of the data for Port Royal and Saybrook Light will reveal, for these respective cases, a basis for individual analysis of ( 1 ) the lag-time influence between perigee-syzygy and the oc- currence of the maximum influence of perigean spring tides, and ( 2 ) the total duration of time over which the effects of these perigean spring tides are felt. These two factors are the combined result of geographic location, hydrography, and astronomy. In order to establish tides at Martin's Industry at the mouth of Royal Bay which are similar to those of Novem- ber 2, 1861, a closely comparable perigee-syzygy situa- tion occurring on January 8, 1974, has been chosen. On this date, perigee-syzygy had a separation of — 2 hours, the geocentric horizontal parallax was 61 '30.0", and the dec- lination of the Moon was +20.4°. Very closely spaced times between perigee and syzygy and close proximities of the Moon to the Earth, among other factors, are seen to be common to both the 1861 and 1974 instances. Both will later be described as proxigean spring tides. Daily high- and low-water predictions for Martin's In- dustry are calculated by reference to Savannah River En- trance, the most representative tidal station at which reg- ular measurements are made. From the tide tables, the mean spring range at Martin's Industry is 7.6 ft. However, responding to the effect of the close perigee-syzygy which took place on January 8 at 6 : 48 a.m. ( e.s.t. ) , the predict- ed maximum daily ranges for the perigean spring tide occurring at Martin's Industry on January 8, 9, 10, 11, 12, and 13 were, respectively, 9.6, 9.8, 9.6, 9.1, 8.3, and 7.3 ft. The corresponding predicted high waters for these dates were, respectively, 8.0, 8.0, 7.8, 7.5, 7.0, and 6.5 ft. The value of mean high water springs previously given is 6.4 ft. Therefore, for this almost exactly comparable situation to that of 1861, the higher high water would have re- mained in excess of mean high water springs on, and for fully 5 days after, the date of perigee-syzygy. This accounts for the fact that the necessary height of waters required for navigation over the bar at Port Royal still existed on November 5, 1861, a full 3 days after perigee-syzygy, a situation which would not have occurred in the case of an ordinary spring tide. Similarly, at Martin's Industry, the maximum response in tidal range to the phenomenon of perigee-syzygy took Impact of Perigean Spring Tides on American Nautical History iV) U' f Ait*JT*. rtjL buoy Figure 16.— Enlarged section of a Preliminary Chart of Port Royal Entrance (Sketch No. 26 in the annual Report of the Superintendent of the Coast Survey for 1862 ) based on soundings executed in 1855, 1856, and 1862. The area represented is in the South Channel lying between Gaskin's Bank and Martin's Industry. 81 Strategic Role of Perigean Spring Tides, 1635-1976 place, a day later, on January 9, 1974. The first of two maximum higher high waters in this series occurred on January 8, at 7:04 a.m. (e.s.t. ), approximately }4 hour after perigee-syzygy — whose mean epoch was 6:48 a.m. (e.s.t.) on January 8. Even this small delay is in contrast with the situation at the mouth of the Connect- icut River in the previous example, where the first maxi- mum higher high water occurred 33 / 2 hours earlier than the mean epoch of perigee-syzygy. The fact that the pre- dicted high tides at Port Royal Sound remained in ex- cess of the value of mean high water springs (6.4 ft) for a full 5 days after perigee-syzygy also illustrates the effect of perigee-syzygy in extending the duration of spring tides, and corroborates the similar 5 -day extension at Saybrook Light, Conn. (MHWS = 3.8 ft). HYDROGRAPHIC ANALYSIS A Preliminary Chart of Port Royal Entrance published in 1862 by the U.S. Coast Survey and based upon sound- ings executed in 1855, 1856, and 1862 (of which fig. 16 is an enlarged portion) shows the least depth of water (for a chart datum corresponding to mean low water) along both the South Channel and the Southeast Chan- nel at the entrance to Port Royal Sound to be 3^4 fathoms (or 19.5 ft). The South Channel was used by the attacking fleet. The Southeast Channel is somewhat narrower and contains contiguous shoals shallowing to 3 fathoms. The bar itself is about 10 miles from the headlands forming the entrance to Royal Bay. A major shoal just to the east of the South Channel and lying between it and the Southeast Channel forms the most seaward part of the bar, and is called Martin's Industry. The water shoals to a depth of 6 ft here at mean low water (even less, if offshore winds prevail ) and, because of the effects of in- creased range, falls to 4 ft at low water associated with ordinary spring tides. To the west of the South Channel lie the Gaskins Banks, with depths as shallow as 14 ft, decreasing to 11 ft (at mean low water) further north where the two entrance channels converge. DATA CONCERNING THE DRAFT OF THE WABASH Precise figures on either the full-load or lightened drafts of the ship Wabash, flagship and largest in the fleet which crossed the bar on the morning of November 5, are not directly available. The only draft figures obtainable in connection with this vessel are those established in 1897 when the ship was stripped down and housed over as a receiving ship in the Boston Navy Yard, with her gun batteries and deck armament removed. The mean draft to the keel was then given 36 as 22 ft 9 in., which is matched by statistical data on Civil War ships contained in Official Records of the Union and Confederate Navies in the War of the Rebellion. 31 Here the draft figures are given as "loaded, forward, 22'6"; aft, 23'." These values are obviously low, however, when the weight of guns and armorplate is considered. Top hamper also would have added considerable displacement, bringing the full- load draft of the Wabash certainly somewhere more near- ly in the range of 24 to 26 ft. The South Channel traversed by the Union Fleet is 10 miles to sea from the entrance to Royal Bay. In intensified swell at such offshore distances, the heave and pitch of the vessel alone would require a safety margin of several feet for keel clearance. Thus the total depth of water required for safe passage of the Wabash over the bar would have been at least 28 ft. With the exception of hurricane-lifted seas, this water depth is available only as the result of the perigean spring tide conditions de- scribed in the section on "Tidal Analysis," together with favorable onshore winds. The Perigean Spring Tide as an Agent of Coastal Erosion Because of the added onslaught against the land pro- duced both by increased current velocity and greater range in water level associated with perigean spring tides, low-lying and potentially submersible coastlines are sub- ject to greater erosional influences under these circum- stances. The actions of strong onshore winds, high waves, and swell may likewise tear at coastlines wherever these meteorologically produced factors are present. When such wind-induced conditions also reinforce a higher- than-usual tide, a greatly increased erosional influence is almost certain to occur. Marked coastline attrition may then result from both astronomical- and wind-accelerated tidal current velocities, larger sedimentary particles main- tained in suspension in the water, and enhanced transport of eroded sediment away from the shoreline. The effects of tidal erosion also are related to more forceful water impact against the shoreline, and wave scouring at greater heights and distances onshore than us- ual. These influences may be combined, during each re- duced stage of the tides, with foreshore-undercutting at points which are lower, farther offshore, less compacted through constant shifting, and hence less resistant to ero- sion. Because the same intensified astronomical forces as- sociated with perigean spring tides act upon both the low Impact of Perigean Spring Tides on American Nautical History }>,:, and high waters, this phenomenon is characterized by ex- ceptionally low tides as well as exceptionally high tides. When these are combined with powerful wind action, the erosional effects of such an alternation of extreme high and low waters may be highly destructive, or even catastrophic, in contrast with the steady, degradational action of the sea which occurs continuously on all coastlines during or- dinary tides. If perigean spring tides are accompanied by strong, onshore winds and swell, large portions of beachline, as well as sections of the foreshore, may be gouged and torn away. An interesting example of the effect of coastal erosion upon an important episode in history occurred during the Civil War. The Hatteras Campaign Both the bold planning and ultimate success of the Hatteras Campaign undertaken by Union forces at the very outset of the Civil War are a matter of detailed his- torical record. It is not generally known, however, that certain definite portions of this planning, as well as a con- siderable degree of success in the operational aspects of the campaign, were the indirect consequence of two earlier astronomical occurrences of perigee-syzygy and their as- sociated perigean spring tides. These precursory factors will be briefly reviewed. On March 1, 1846, as documented in the annual Re- port of the Superintendent of the Coast Survey for 1847, 38 a severe coastal storm swept the vicinity of Bodie's Island, N.C., and the resulting tidal flooding produced several breaches on the seaward side of this narrow spit — one of a line of barrier islands composing the Hatteras Outer Banks. The sea piled onto the land and inundated numerous portions of the Hatteras Banks. This first of a series of three severe coastal storms in the same year followed some 3 days after the maximum influence of a perigean spring tide centered around February 26 (allowing for a 1-day phase- and parallax-age at this location, as normally ex- perienced ) . This tide was associated with a condition of perigee-syzygy having an approximate alignment very early in the morning of February 25, and a difference in time between its astronomical components of just over — 30 hours. Because of at least a 3-day separation in time from the maximum of the perigean spring tides, the flood- ing produced on March 1 only started to form the pre- viously mentioned breaches in the land. However, a second major coastal storm occurred on September 7-8, 1846, as mentioned also in the Coast Sur- vey annual report. 39 The Coast Survey brig Washington, commanded by Lt. George M. Bache, brother of the sec- ond superintendent of the Coast Survey, together with 10 seamen, were lost in this storm off the coast. Although re- ferred to in some historical sources as a hurricane, neither Ivan R. Tannehill in his book Hurricanes (8th ed., 1952 ) nor Gordon E. Dunn and Banner I. Miller in their work Atlantic Hurricanes (rev. ed., 1964) include this storm among their comprehensive catalogs of true hurricanes and tropical storms. d The accompanying gale swept the coast- line, adding its effects to a perigean spring tide whose max- imum rise on this occasion had occurred less than 1 day before, as a result of a perigee-syzygy alignment having a mean date of September 5.0 (with components sepa- rated by only —15 hours). A sustained gale-force wind from the northwest on the 7th and 8th, coupled with high perigean spring tides, lifted the waters of Pamlico (then spelled "Pamplico") Sound to a height of 2 or 3 ft over almost the whole of Bodie's Island. 40 In consequence of this violent flooding action, Oregon Inlet was formed. This inlet is still called "New Inlet" in the first edition of a nautical chart of Pamplico Sound, compiled by the U.S. Coast and Geodetic Survey in 1883 (fig. 17). Portions of the barrier spit to the south similarly were breached at a point where a comparison map of North Carolina prepared by Brazier and MacRae in 1833 (fig. 1 8 ) shows no previous permanent passage. Near Hatteras village, a variably inundated tidewater area was rendered navigationally passable overnight by the force of the ram- paging waters washing back from Pamplico Sound. Still another severe coastal storm occurred during October, further scouring this southern inlet. Previously, the waters forming this narrow channel had been too shallow to per- mit the passage of deep-draft vessels. The larger inlet formed now possessed a sufficient depth of water to ac- commodate rather sizable vessels, a circumstance condu- cive to the development of active maritime commerce. Hatteras village provided a port for the transshipment of goods to smaller intracoastal craft more suited to ply the coastal waterways and rivers. Accordingly, Hatteras Inlet, as it was called, gradually came to outrank Ocracoke In- let and its commercially declining town of Portsmouth in shipping importance. The least depth of water at the en- trance to this newly created inlet (which persisted, despite shifting sands, over the intervening 15 years until the Civil War and thereafter) was 14-16 ft. Fig. 19 is an enlarged portion of the U.S. Coast and Geodetic chart of 1883. d Again, with objective awareness that the defining conditions and criteria for hurricanes have varied widely over history, see the Ex- planatory Comments preceding table 2. Cf. also David M. Ludlum's Early American Hurricanes, 1492-1870, pp. 131-132. :;t, Strategic Role of Perigean Spring Tides, 1635-1976 Figure 17. — Coast and Geodetic Survey Chart No. 142 (ed. 1) of Pamplico Sound (now known as Pamlico Sound), N.C., published in 1883. The small boxed area indicates the location of the present Hatteras Inlet, enlarged in much greater detail in figure 19. Impact of Perigean Spring Tides on American Nautical History •M Courtesy of Library of Congress Figure 18. — Enlarged portion of a "New Map of the State of North Carolina" drawn by Brazier and MacRae in 1833. At this time, although Ocracock (Ocracoke) Inlet is clearly present, there was no breach in the Outer Banks at the present location (indicated by the curved arrow) of Hatteras Inlet. Compare with figure 19. As acknowledged in various historical reference sources, 11, 42 Hatteras Inlet had, through this single for- mative process of Nature occurring a decade and a half earlier, achieved a tactical significance which would en- able it to play a definite role in the Civil War. With ready access to the open sea provided for privateers and block- ade runners through this inlet, Pamplico Sound became an integral part of a network of inland waterways main- tained by the South to transport supplies to the Confed- erate Army. These waterways, in turn, formed a connect- ing artery of .communication which made possible a con- siderable flow of needed supplies through Virginia, North Carolina, and other States of the South in almost com- plete defiance of the Union naval blockade. Toward the end of August 1861, the Union forces were in need of a bold maneuver to counteract the in- glorious defeat suffered at Bull Run some 5 weeks earlier. In an active planning stage was the first major offensive by the Federal Navy in the Civil War. Hatteras Inlet became a key element in a coordinated plan to invade this hh Strategic Role of Perigean Spring Tides, 1635-1976 &i & & &n Sh b k 6* S- G «r« ...v. 1% ib & |- -n 2 3 3 .r a tr 4-1 2 3 T3 c — ~ 43 3 3 >. s E a, "C 3 _- -f be r E 3 P ^-< -Q a u s_ "3D c £ -s ^ *-" u 2 6-s > > s I SI o m c CM W O U .3 o Impact of Perigean Spring Tides on American Nautical History 9! s£ -a S 2 P .-2 gO Oh ra b be W S 3 III U 3 £ §2-2 bfi o i ~ '^ >._G Hi to«& w G >, <+H E s~ O 3 ^ C« 3 C <~ G j5 ° ° C <~ G S c u O -3 S cm 1 1 m 3 U rt p O Chapter 3. The Practical, Economic, and Ecological Aspects of Perigean Spring Tides In addition to the previously demonstrated potential for coastal flooding, many outstanding examples exist in which the production of perigean spring tides or their accompanying phenomena (such as strong tidal currents) has exerted a prominent influence upon projects in coastal engineering, shoreline reclamation, seawall or groin con- struction, and other functions, activities, or events of a technological nature. In the historical development and continuing application of both marine and maritime technology, in particular, as well as in various phases of intracoastal and harbor navigation, numerous circum- stances have arisen in which the occurrence of perigean spring tides has exerted a special impact. Typical of such an historical tidal influence upon engineering projects was the complete destruction of Guglielmo Marconi's experimental transatlantic radio tower by the combination of a windstorm and perigean spring tide in 1915. This incident occurred as the result of erosion and undermin- ing of the tower by tidal flooding at Cape Hatteras, N.C., on April 4 of this year (see table 1, chapter 1 ). Although the role of these tides may have been ob- scured in the details attendant upon a particular activ- ity — or the tides may have affected only a partial phase thereof — their practical contribution to the ultimate suc- cess or failure of the activity can only be described as of major significance. Among the wide range of available examples, a representative few will suffice, and these are given below. As in all previous instances cited of relationships de- pendent upon the existence of perigean spring tides, it must be remembered that the astronomical forces respon- sible for their production are worldwide in scope. Accord- ingly, although the present work deals geographically with the influence of perigean spring tides in North America, the addition of a few appropriate examples to retain these tides in their proper global perspective is desirable, and will serve to emphasize their far-reaching importance. Such examples of international nature in- cluded among the following may readily be extended by analogy to the coastal waters of North America. The Effects of Extremely Low Waters The same augmentation of astronomical tide-raising forces which, at times of perigee -syzygy, produces above- average high tides is responsible — in the low-water stages approximately 4-8 hours preceding and following — for the production of tides which are exceptionally low. In the first case, enhanced tractive forces amass additional quantities of water near the sublunar point on the surface of the Earth (and its antipodal position) to create the in- creased high waters of perigean spring tides. At the same time, these increased forces draw additional quantities of water from source regions along a great circle approx- imately 90° from the common meridian of the first two positions. All points on this second great circle are sub- ject to low tides. Because of the rotation of the Earth, these exceptionally high and low waters alternate, some 4-8 hours apart, at the same location during appropriate por- tions of the tidal cycle. Dangers of Explosive Decompression in Submarine Environments The building of bridges across bays, inlets, or tidewater estuaries and rivers connecting to the sea is an activity much affected by such possible alternations of extreme high and extreme low waters, and as such constitutes an area of extreme practical importance in connection with perigean spring tides. In the construction of large bridges, supported by piers whose foundations extend deep into the soil beneath and along the water channel in order to 93 94 Strategic Role of Perigean Spring Tides, 1635-1976 reach bedrock, an engineering procedure is used which is particularly sensitive to tidal changes. In these projects, a device known as a pneumatic cais- son is customarily employed to provide a pressurized at- mospheric environment in which bridge construction workers, familiarly called "sandhogs," can work at nec- essary depths below the waterline without being flooded out by infiltration of water through the soil and into the open bottom of the caisson. The pressure of the water is exerted equally in all directions, and increases directly with depth according to the hydrostatic formula P is the latitude of the place of observation : sin z sin A = cos z = sin z cos A = cos 8 sin H = sin 8 = cos 8 cos H = cos 8 sin H sin 5 sin + cos 5 cos H cos 4> sin 8 cos — cos 8 cos H sin and sin z sin A cos z sin 4- sin z cos A cos cf> cos z cos — sin z cos A sin

W./- EARTH'S ORBITAL\ 29 " 5 REVOLUTION \ APPROX. 1VDAY \ REVOLU- TION , DURING THE TIME THE EARTH ROTATES FROM T 1 TO T 2 ,THE MOON REVOLVES FROM M 1 TO M 2 ,AND THE SUN APPARENTLY MOVES FROM S-, TO S.,. THE j CELESTIAL I SPHERE, \ APPROX. | 1°/DAY / PLANE OF PAPER IS THAT OF THE ECLIPTIC, SEEN FROM ITS NORTH POLE Figure which the Earth revolves around the Sun. This results in an apparent motion of the Moon in the same direction as that of the Sun, but of greater magnitude because the Moon is both closer to the Earth and moving faster. It must also be remembered that the basic revolutionary motion of the Moon is a real one rather than an apparent one conjugate to the annual motion of the Earth as in the case of the Sun. The true revolution of the Moon around the Earth in a period of one sidereal month, from alignment with a given star to alignment with that same star again, requires 27.321661 days. The tropical month (the period between two successive alignments of the Moon's position with the longitude of the vernal equinox) is 27.321582 days. Because of the slow westward (retrograde) movement of the vernal equinox caused by the precession of the equinoxes, this 22 month is shortened by 0.000079 day with respect to the sidereal month. The draconitic or nodical month (measured by two successive transits of the Moon through the longitude of the Moon's ascending node — or position of intersection between the northward-inclined lunar orbit and the eclip- tic) is equal to 27.212220 days. It is likewise shortened with respect to the sidereal month by the regression of the lunar nodes subject to gravitational perturbations induced by the Sun. The synodic month is the period of time between align- ment of the Moon and Sun in identical longitudes (or right ascensions) and the next succeeding occurrence of this same syzygy position. It is thus equivalent to the inter- val between two successive conjunctions (new moons) or oppositions (full moons) and is equal to 29.530589 days. This considerable lengthening of the synodic month over the period of the sidereal month is explained by the Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 127 fact that, at the same time the Moon revolves around the Earth, the Earth revolves around the Sun, carrying the Moon with it, bound together by their mutual gravita- tional tie. As the Earth physically revolves around the Sun in its annual motion, the Sun appears to revolve around the Earth in the same period, at the same angular velocity, and in the same easterly direction. Accordingly, the ap- parent annual motion of revolution of the Sun occurs in the same direction as the actual monthly revolution of the Moon around the Earth. Although the velocity of the Moon in its orbit is much faster than the apparent motion of the Sun along the ecliptic, the Moon must each month travel somewhat farther in its orbit to catch up with the motion of the Sun and achieve alignment with it at posi- tion of syzygy. The extra period of time required in this catch-up motion is 2.208928 days longer than the sidereal period, which accounts for the longer synodic month of 29.530589 days. If one were to consider only the motion of the Moon with respect to the stars and the length of the sidereal month as previously defined, the Moon would appear to drop back in its daily westward motion of rising and setting (i.e., drift slowly eastward in the sky) by approxi- mately 360°/27.321661 days, or 13.176396°/day— later defined as the lunar mean daily motion. However, as will be seen, factors exist to alter this average angular velocity of the Moon, both with respect to the Sun and relative to any point on the surface of the rotating Earth. Because of the Earth's motion in orbit around the Sun, and the Sun's consequent apparent easterly motion in the same direction as the Moon, the Moon appears to move at the somewhat reduced average angular velocity with respect to the Sun given by 360°/29.530589 days, or 12.190749°/day. It is this apparent motion of the Moon in catching up and passing, and thus moving respectively toward and away from the Sun in angular elongation, that produces the continuously changing lunar phase relationships. It is important to note that the apparent motions of both the Moon and the Sun in the sky (the former caused by the Moon's orbital motion, the latter by the Earth's annual revolution) are in a direction opposite to the mo- tion of rising and setting which results from the rotation of the Earth. The apparent daily motions of the Sun and Moon caused by these respective two factors are, how- ever, in the same direction as that of the rotating Earth. This fact is very significant in connection with a further daily catch-up motion of the rotating Earth with the posi- tions of the Moon and Sun. The corresponding influence of the apparent eastward drift of the Moon in the sky, causing it to transit the celestial meridian some 50 minutes later each day, will be discussed in an ensuing section on the lunar retardation. THE MOTIONS OF THE EARTH AND MOON IN ELLIPTICAL ORBITS It previously has been indicated that the orbit of the Earth around the Sun is not circular, but elliptical in shape, with the Sun occupying one of the two foci of the ellipse. (See fig. 4 in the appendix.) It may be noted by direct analogy that the Moon also revolves around the Earth in an elliptical orbit, with the Earth at the occupied focus of the ellipse (fig. 23). The dynamic principles of orbital motion are exactly the same in each instance, and a single discussion of the general forces involved will suf- fice for both. By definition, an ellipse is a geometric section con- structed by passing a plane obliquely through a cone. The linear circumference of the resulting figure has an "out- of-round" configuration whose greatest diameter is de- scribed as the major axis and the least diameter (bisecting, and at right angles to, the first) is designated as the minor axis. By definition, the mean distance of any celestial ob- ject moving in an ellipse is equivalent to the semimajor axis. The extent of out-of-roundness is described as the eccentricity, whose value varies from for a true circle, through very high values for a thin, very greatly extended ellipse, to infinity for a straight line. The eccentricity is defined by the ratio OC/OA in figure 23. The so-called angle of eccentricity is represented by the angle OBC in this same figure, and the sine of this angle is often used in astronomical computations. Kepler's First Law of Planetary Motion states that all planets (and satellites) in the solar system move in ellip- tical orbits, with the less massive or secondary object revolving around its more massive or primary object. Kepler's Second Law states that the distance of the secondary object from its primary is always such that the radius vector or line drawn from the primary object to its secondary will describe equal areas in equal intervals of time. It is clear from figure 24 that, no matter where in the ellipse a body is located, an area is defined between two radius vectors drawn to different positions of the ob- ject in orbit and the arc of the orbit along which this secondary object travels. The area circumscribed by these two lines and the arc joining the two positions of the object will always be the same. For example, in figure 24, Ai = A 2 . 1 2H Strategic Role of Perigean Spring Tides, 1635-1976 DIRECTION OF M SUN'S APPARENT MOTION ON CELESTIAL SPHERE TO SUN t PERIGEE-SYZYGY NM DIRECTION OF MOON'S ORBITAL MOTION RECURS AT NEW MOON EITHER 6-1/2 OR 7-1/2 SYNODIC MONTHS AFTER PERIGEE-SYZYGY AT FULL MOON FM APOGEE-SYZYGY Figure 23 Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 129 TO SUN t APOGEE-SYZYGY NM SLOWER ANGULAR Dl RECTioN OF SUNS APPARENT MOTION ON /^ CELE ST 1 AL s' SPHERE / \ / A / \ / \ APOGEE "\. SMALLER ORBITAL i j \. MOTION OF MOON j i \^ AT APOGEE JAlj \ / \ \ i \ \ DIRECTION \ OF E ARTH'S \ REVOLUTION ! j THE MOON'S \ ! j ORBITAL VELOCITY Si IS DETERMINED BY J J ITS DISTANCE FROM J ! THE EARTH AND j) KEPLER'S LAW !; OF EQUAL AREAS. 1 /earth\ -A \ AROUND SUN \ ' « M W L U ^^ / 1 * / \ \ 1 A 2 \ \ \ 1 / \ \ J \ / FASTER ANGULAR DIRECTION \\ / \ V E L C 1 T Y A N D OF MOON'S ^^^^PERIGEE \^^^ G RE ATE R R B 1 TAL ORBITAL MOTION \ ^^^ -©"" MOTION OF MOON M— J— ► FM AT PERIGEE PERIGEE- S YZYGY NOTE- FOR CLARITY OF PRESENTATION, BOTH THE ORBITAL ECCENTRICITY AND DAILY MOTION OF THE MOON ARE EXAGGERATED IN SOME DIAGRAMS OF THIS WORK. Figure 24 202-509 O - 78 - 11 no Strategic Role of Perigean Spring Tides, 1635-1976 Kepler's Third Law states that the period of revolution of the secondary object revolving around its primary (or of two secondary bodies revolving around their individual primaries) will vary according to the relationship: P?IP 2 2 =d?ld 2 (corrective terms for the masses are omitted) In words, the square of the period of revolution varies from one time to another (or one object to another) as the cube of the mean distance between the object and its primary during the interval concerned. The direct implication of these three astronomical laws is that, as the Moon revolves around the Earth in its monthly orbit, at one position in its orbit known as perigee it will reach its closest monthly approach to the Earth and, approximately one-half month later, will reach its greatest monthly distance from the Earth known as apogee. Similarly, in the Earth's annual motion around the Sun, about January 2—4 it will pass through a position of closest approach to the Sun known as perihelion and, around July 3-6, 6 months later, will pass through a posi- tion of greatest distance from the Sun known as aphelion. Since, in each case of closest approach (perigee or perihelion) of the less massive object to its primary, the gravitational force of attraction exerted between the pri- mary and secondary is greater, the secondary object will also "fall" faster toward its primary at this point. With this increased inwardly directed gravitational or centrip- etal force being balanced by a correspondingly enhanced outwardly directed centrifugal force, the secondary object remains constrained to move in a closed elliptical orbit. Because of the increased gravitational force involved at this closer distance of approach, the speed of the second- ary object in its orbit also will be greater, and the resulting angular distance the object will travel in any unit of time will be larger (fig. 24). Just the opposite is true at apogee or aphelion, with the secondary object revolving at a considerably slower speed in orbit and covering a much smaller distance (this applies in either a linear or angular sense ) . The maximum and minimum daily angular velocities of the Moon are about 15.4° and 11.8°, respectively; those of the Sun are approximately 1.016° and 0.983°. The length of the anomalistic month (from perigee to perigee) is 27.554551 days, and that of the anomalistic year (from perihelion to perihelion) is 365.25964134 days. The differences between both these values and the corresponding sidereal periods are the result of perturba- tions which cause a net forward motion of perigee and a retrograde motion of perihelion, respectively. With these new concepts in mind, it is necessary to return to the previously mentioned elliptical motions of the Moon around the Earth and the Earth around the Sun. The next step is to discover how such continuously changing, rather than constant, apparent angular motions of both the Moon and Sun, together with their positions of closest approach to the Earth, affect various astro- nomical configurations and alignments, and the mean or average time intervals between successive such alignments. The procedures by which these different intervals are quantitatively evaluated also will be indicated. 1. The Anomalistic Month The period of time between two successive passages of the Moon through the position of perigee is known as an anomalistic month. Determination of the mean length of this month is analytically complicated by the fact that the perigee posi- tion of the Moon's orbit oscillates periodically, but by unequal amounts, in a direct and retrograde sense, due to perturbations produced by the Sun. A simplified repre- sentation of the length of the mean anomalistic month may, however, be achieved from the arbitrary assumptions that : ( 1 ) the perigee position is moving constantly and uniformly around the lunar orbit in the same direction as the Moon ; and ( 2 ) this average daily forward motion of the lunar perigee along the Moon's orbit is +0.1 1 1404°/ day. Since the perigee completes one revolution around the lunar orbit in a period of 3,231.48 days (as calculated from observations secured over many years), this corre- sponds with the average rate of 360° /3, 23 1.48 days, or 0.1 1 1404°/day specified above. The Moon revolves in its orbit at a mean sidereal rate (see below) of 13.176396°/ day, a much faster angular velocity. In a recurring catch- up motion, which is not a part of the Earth's diurnal rotation, the Moon as seen from the Earth therefore moves once each month from a position to the west of ( follow- ing) the lunar perigee, successively overtakes, draws in line with, and passes this position, and then advances to the east thereof. The mean daily motion of the Moon in its orbital revo- lution around the Earth, as measured with respect to the "fixed" stars is given by: 360° 3fi0° 13.176396°/day sidereal month 27.321661 days This means that, with respect to the previously assumed, steadily advancing position of perigee, the Moon moves at a relative angular speed of: Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 131 13.176396%lay-0.1114047day=13.0649927day By means of the latter value, the mean anomalistic period of revolution (from perigee to perigee) may be calculated as: 360° 27.554551 clays 13.064992°/day However, as previously indicated, this average figure is derived from the dual assumptions of : ( 1 ) a perigee posi- tion which moves continuously in a forward direction, and at a uniform speed, along the lunar orbit ; and ( 2 ) a hypothetical or mean moon, which is moving constantly at the same speed in its orbit. At the times of a close perigee-syzygy alignment, very different conditions actually hold true. At such times ( later to be described as proxigee-syzygy ) , the perturbed motion of perigee is considerably different in both magni- tude and direction from the mean value of +0-1 1 1404°/ day given above. (See "The Special Motion of Perigee Close to the Position of Perigee-Syzygy Alignment" in pt. II, ch. 4.) At such times also, the orbital angular velocity of the Moon may attain an actual value as high as 15.4°/ day. 2. Effect of the Solar Parallactic Inequality The quantity known in tidal theory as the solar paral- lactic inequality is that associated with the elliptical shape of the Earth's orbit. It arises from the fact that, revolving in this elliptical orbit, once in each half-year the Earth reaches its respective positions of closest annual approach to, and greatest distance from, the Sun, previously defined as perihelion and aphelion. As also noted earlier, the Earth is traveling at a considerably greater orbital velocity at perihelion, and a correspondingly diminished velocity at aphelion. The fact that the actual orbital motion of the Earth results in a precisely similar, apparent motion of the Sun in the sky makes it possible empirically to evaluate the changing magnitude of this apparent solar motion by means of data tabulated in The American Ephemeris and Nautical Almanac. These data give the daily apparent positions of the Sun throughout the year. If the reflection of the Earth's own orbital motion were the only factor in- volved in the apparent velocity of the Sun's movement, the angular distance covered by the Sun in its apparent daily motion would be greatest near the time of perihelion and least near aphelion. It will be seen (table 7) that, in terms of right ascension, this is not entirely true. Since the apparent daily motion of the Sun along the ecliptic is sufficiently representative to illustrate such ef- fects of the Earth's position in orbit, the changing angular accelerations can be obtained simply by taking successive daily differences in the longitudes of the Sun. Subse- quently, in applying the meaning of these different veloc- ities of motion to tidal phenomena, allowance also will be made for the daily catch-up motion of the rotating Earth with the Sun. It will then be necessary in place of these motions in apparent or true (as distinct from mean) longi- tude to consider the corresponding motions in right ascen- sion (thereby referring them to the equatorial plane of the Earth's rotation). The apparent daily motion of the Sun does not vary widely from year to year and, to the order of accuracy required for the present purpose, may be obtained from The American Ephemeris and Nautical Almanac for any year. Thus, the average daily motions of the Sun in degrees of arc in celestial longitude and in seconds of time in right ascension, bracketing the perihelion of 1975 January 2 and the aphelion of July 6, as well as at the two solstices and two equinoxes, are given in table 7. Table 7. — Apparent Daily Motion of the True Sun in Right Ascension and Longitude for Selected Dates in 1975 Nearest inclusive tabular dates Apparent daily motion True distance of sun, averaged for ecliptic Circumstance In«W InX(°) of inclusive tabular dates (mean distance, 0=1) Perihelion: Jan. 2. Aphelion : July 6. Winter solstice: Dec. 22.5. Summer solstice: June 22. Vernal equinox: Mar. 21. Autumnal Jan. 3-2.... July 6-5.... Dec. 23-22. June 23-22. Mar. 22-21 . Sept. 24-23 . 264. 60 247. 16 1.0190 0. 9536 0. 9832890 1.0167433 17.44 266. 36 249. 49 0. 0654 1.0182 0. 9537 0. 9836583 1.0163006 16.87 218.67 215.45 0. 0645 0.9931 0. 9785 0.9961315 1.0033977 Sept. 23.5. 3.22 0.0146 It is apparent from the preceding table that the greatest difference in the apparent daily motions of the Sun occurs when comparing the respective angular velocities at peri- helion and aphelion. This is due to the greater orbital speed of the Earth and increased apparent motion of the Sun when the Earth reaches its closest annual approach to this massive body, and the corresponding decrease in apparent velocity of the Sun at aphelion. 1 :-!2 Strategic Role of Perigean Spring Tides, 1635-1976 However, as seen also from the second pair of examples, the difference in the Sun's apparent daily motions be- tween the summer and winter solstices runs a very close second — since these dates occur within less than 2 weeks of aphelion and perihelion, respectively. Moreover, and even more important in terms of the subsequent descrip- tion of solstitial tidal peaks (pt. II, ch. 2), the individual values of the daily apparent angular motions of the Sun at the times of the summer and winter solstices are higher than those at aphelion and perihelion, respectively. This indicates the effect of minimum daily motion in declina- tion and a maximum motion in right ascension, as will be discussed in detail in various subsequent sections — with an introductory explanation under the immediately fol- lowing heading. Finally, the daily motion of the Sun at the times of either of the equinoxes is seen to be the least of all — evidence of a minimum motion in right ascension and maximum motion in declination. In the third set of data representing the apparent motions of the Sun at the times of the vernal and autumnal equinoxes, the small differ- ence between the respective daily solar motions on these dates results from several possible causes : ( 1 ) an asym- metry in the Earth's orbit produced by a slow regression of the ascending and descending nodes along the ecliptic — such that the equinoxes are not necessarily symmetrically arranged with respect to the line of apsides joining peri- helion and aphelion ; ( 2 ) the recognized slow progression of the Earth's line of apsides along the ecliptic will have a similar effect; and (3) the date of the vernal equinox, around March 21, is closer to the perihelion date, about January 4 (and its effect in increasing the orbital velocity of the Earth) , than the autumnal equinox, approximately September 23, is to this same perihelion date. In consequence, within a day or two of the summer and winter solstices, as the positive and negative solar declina- tion angles reach their respective maximum annual values, the daily differences in right ascension of the Sun also attain their greatest values and the daily differences in declination their least values for the year, as confirmed in table 7. Similarly, at those times, twice each lunar month, when the Moon reaches its maximum declination, either north or south of the celestial equator, the daily difference in the lunar declination becomes zero. Within a few days of this same date, the daily change in the right ascension of the Moon approaches a maximum value for that lunation. Conversely, as the Moon and Sun in their apparent motions cross the Earth's Equator, their declinations be- come zero and change sign. At such times, especially for the Moon ( due to its large parallax ) and, to a lesser ex- tent, for the Sun, the paths of their movements in declina- tion have their greatest inclinations to the Equator and the differences in declination change the most rapidly. This situation is especially marked in terms of topo-centric motions as the Moon reaches its extreme declinational values in the 18.6-year nodical cycle (see pt. II, ch. 4, "Effects of Extreme Lunar Declination . . ."). DECLINATIONAL EFFECTS ON THE AP- PARENT MOTIONS OF THE MOON AND SUN In dealing with the changing tidal forces resulting from the varying positions and motions of the Moon and Sun. one factor is noteworthy as accelerating the apparent mo- tions of these two bodies in right ascension. This, in turn, increases the Earth's necessary rotational catch-up time, lengthens the tidal day, and provides a greater opportunity for enhanced tide-raising forces to operate. The effect in question is that of a maximum lunar (or solar) declina- tion angle in contributing to an increased motion of these respective bodies parallel to the celestial equator. Each of the apparent motions represented, when declination is plotted against increasing right ascension ( or the passage of time) as in the top of figure 44, reveals a series of curve maxima and minima in declination. Any such near-maximum value in declination means that the Moon or Sun, in attaining its greatest angular distance north or south of the celestial equator, is at a point where the slope of the curve is very nearly zero. Practically all of the movement of the body is in right ascension and very little, if any, is in declination. As the slope becomes zero at the peak of the curve, the daily differences in declination contrastingly become the small- est and, as they pass through zero, change their sign. Auxiliary Influences Affecting the Daily Rate of Lunar Motion in Right Ascension In the interests of completeness, it must be noted that several counterproductive astronomical forces exist, capa- ble of altering the extra tide-raising potential created by situations in which the relative motions between Earth, Moon, and Sun are slowed down. As will subsequently be demonstrated, it is subject to this latter condition that augmented gravitational forces produced by the mutual alignment of these three bodies are exerted over a greater period of time in a lengthened tidal day, and enhanced tides result. Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides \:vs The Effect of Parallax on the Moon's Apparent Motion In addition to the effects upon lunar motion associated with the two solstitial and two equinoctial positions previ- ously described, another astronomical factor contributes to the respective circumstances that : ( 1 ) the Moon's ap- parent motion in right ascension often attains its largest value and the declinational motion reaches a minimum when the Moon is at or near its greatest declination ( either north or south of the celestial equator); and (2) the Moon's greatest motion in declination and least motion in right ascension occurs when it is on or near the celestial equator. (All such comparisons of extreme motions refer specifically to the lunation in which the Moon is at the moment. ) This second contributing factor involves the consider- able difference in the Moon's motion' as calculated in ( 1 ) geocentric and (2) topocentric coordinates (i.e., as this motion would be observed respectively from the center of the Earth and from a point on its surface) . The differ- ence in apparent motion is caused by the relatively close distance to the Earth and large parallax angle (see figs. 41, 25 A) of the Moon. Two other factors which must be considered as an integral part of the present discussion are ( 1 ) the apparent diurnal motion of the Moon, as a reflection of the rotation of the Earth, and (2) the indi- vidual or actual motion of the Moon in its own orbit, creating a positional displacement which is only vec- torially related to the motion of the rotating Earth. Changes in Right Ascension Associated With the Apparent Diurnal Motion of the Moon The first of these two motions will now be discussed, employing the equatorial system of coordinates for refer- ence, in order to illustrate the particular influence of lunar declination upon one of several possible variable motions of the Moon in right ascension — that is, the di- urnal motion as seen from a topocentric position. (The diurnal motion of the Moon as used for purpose of com- parison in the present connection has been defined as that occurring in a diurnal circle and resulting purely from the rotation of the Earth. In this usage, it does not contain the daily component of the Moon's own orbital motion. The term topocentric — referring to measurements made from the surface of a planetary body — also has been dif- ferentiated from the expression geocentric, referring to the Earth's center.) The apparent diurnal motion of the Moon as seen from any given location on the surface of the Earth is, in topo- centric terms, and as expressed in the equatorial system of coordinates, a function of two quantities which serve to relate the lunar position to this particular point of observation. These quantities are the geocentric latitude () of the place and the hour angle {h) of the Moon. The latter value represents the angular distance of a ce- lestial object east or west of the local meridian, measured at right angles thereto and, in this usage, expressed in equivalent units of time. Its value is positive when the object is west, and negative when it is east of the meridian. An additional parameter which is necessary to transfer the lunar position from a geocentric to a topocentric refer- ence system is the distance of the Moon from the center of the Earth (given by tt, the geocentric horizontal paral- lax at the time of observation ) . The first two of the above quantities are different for each location on the Earth's surface, and the third changes continuously with time. The two remaining astronomical variables involved are denoted by Aa (the hourly rate of change of the Moon's position in right ascension) and 8 (the instantaneous value of the Moon's declination) . The geometric relationships between these various quantities are expressed approximately by the formula given below. This represents the geocentric motion im- posed on the Moon by the Earth's diurnal rotation, plus topocentric corrections to this motion introduced by : ( 1 ) the hour angle and parallax of the Moon ; ( 2 ) its altered declination as seen from the Earth's surface rather than its center; and (3) the latitude of the observer. , , . , . ir" cos e/> cos h Aa (topocentric) = Aa (geocentric) + 57 . 3 o /radian cos 5 The analytic evaluation of Aa (geocentric) is given by Aa (geocentric) =g] c -[f] r At this point, a substantial technical digression is de- sirable, as a supplement to the main text, to explain the alternative method of positional representation in the equatorial system of coordinates, and at the same time quantitatively to evaluate the unknown analytic terms in the above equation. In the equatorial system of coordinates, the Earth's axis is the primary reference, and its extension to the points of intersection with the celestial sphere demarcates the north and south celestial poles. The celestial equator lies in a plane perpendicular to this rotational axis and midway between the poles. It is around this axis that the diurnal motion constituting the immediate topic of discussion occurs. The apparent "rising and setting" motion caused by the rotating Earth changes the Moon's position with I'M- Strategic Role of Perigean Spring Tides, 1635-1976 respect to the local meridian and hence its hour angle (see next paragraph), but does not alter its right ascension, since the established origin of this coordinate is, as far as the diurnal motion is concerned, also moving at the same angular rate. If the effect of the Earth's rotational motion were alone to be considered and the Moon's own actual motion due to its revolution in orbit disregarded, the lunar body would appear to move across the sky in a circle very nearly parallel to the celestial equator. These small circles in which most celestial objects (other than those located directly on the celestial equator) appear to move, subject only to the diurnal rotation of the Earth, are called parallels of declination. Great circles perpendicular to the plane of the celestial equator, spaced 1 hour apart, and passing through the celestial poles, are designated as hour circles. That hour circle which co- incides with the vertical circle of the horizon system of coordinates, and passes through the zenith, nadir, north and south celestial poles, as well as the north and south points on the horizon, is termed the meridian. And it is here that the first distinction is found affecting the motions of relatively close astronomical bodies such as the Moon and Sun, because of the different positions in which these would be seen from the center of the Earth and from its surface. The difference is a direct function of the geocentric parallax. A changing parallax angle of the Moon relative to the Earth occurs as the Moon suc- cessively regresses toward, transits, and falls behind the meridian due to the Earth's faster rotation in the same direction as that of the Moon's orbital revolution. At any particular latitude of observation on the Earth's surface, a greater distance is involved in the side of the parallax triangle joining the Moon and an observing posi- tion on the far side of the meridian than in the case of an observing position on its near side. When the Moon is west of the meridian, the effect of parallax is, therefore, to increase the hour angle; when the Moon is east of the meridian, the effect of parallax is to reduce the hour angle. The coordinate of right ascension is measured in the plane of the celestial equator and, although it is subject to geocentric and topocentric differences in the same manner as the hour angle, the right ascension of a body does not vary with the geographic longitude of the observing posi- tion on Earth, while the hour angle of the object does. Because the change in parallax with position in hour angle is different from the change of parallax with right ascen- sion, the diurnal motions in hour angle and in right ascension of a close celestial body are not the same. The difference is of some consequence in the case of the Moon, whose apparent motion results from a combination of the Earth's diurnal motion and the Moon's own orbital motion. Whereas any change in the Moon's position caused by the diurnal rotation of the Earth alone would occur in a path which, over a short period of time, would remain parallel to the celestial equator, the lunar body actually appears to move along a track on the celestial sphere which is a composite of the Moon's own orbital path and the diurnal circle produced by the Earth's rotation. It is often found to be more convenient to measure such apparent motion by means of an available alternate in the equatorial coordinate system. This variation employs the celestial meridian rather than the vernal equinox as a point of reference and thereby becomes more meaningful in establishing the effects, upon motion in right ascension, of topocentric position on the Earth. The corresponding adaptation of the equatorial system is termed the hour- angle subsystem. That component of the Moon's apparent movement which is parallel to a declination circle and takes place between successive hour circles or fractional parts thereof in a standard unit of time is termed, in the discussion which follows, the rate of change in hour angle. The specification of apparent motion in either geocentric or topocentric systems is denoted by adding a subscript "G" or "TV' respectively. The value of the mean diurnal geocentric motion of the Moon in hour angle h and time t, resulting from the rotation of the Earth, is given by the differential function LdtJo 15.04100 o/h This figure is derived by a transformation from time to angular systems of measurement. It represents the slight excess (3,609.856473 s ) over the length of the mean solar hour (i.e., l h =60 m X60 s =3,600 s X 1-003) resulting from an average decrease, by atmospheric refraction, of the rate of change in hour angle. The corresponding value when converted into radian measure is 'dhl Jt\ c 0.26252 rad/h Similarly, the value of the mean diurnal topocentric motion of the Moon in hour angle, exclusive of the Moon's own orbital motion, is 'dhl _dt_\ T l4.49208 o/ Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 1!55 which is equivalent to ldtj 7 0.25294 r It will be seen that when the next-to-the-last value is multiplied by 24 h/d , giving 347.808°, it is less than the 360° defining one rotation of the Earth, since it contains the effects of the Moon's eastward drift resulting from the Earth's orbital revolution described a few sections earlier. If the additional 50.4 15 m (0.84025 h ) of the mean daily lunar retardation (see pt. II, ch. 2) is multiplied by the same rate of lunar motion, it gives 12.177°, and if this is added to the rotation during 24 h , the full 360° comprising the daily angular rotation of the Earth from one lunar transit to the next is obtained. Substituting these quantities (in radian measure) in the second of the preceding equations : Aa (geocentric) =0.26252 rad/h - 0.25924 rad/h = 0.00958 rad/h ; 0.00958 rad/ 70.01745 rad/o = 0.54900 o/h = 134.7 8/h . Assuming, by way of example, that the Moon is on the celestial equator (5 = 0°) and is just transiting the local meridian (h=0°) at the latitude of the U.S. Naval Observatory in Washington, D.C. ( = 38°55'14.0" N.) and, for simplicity, that -k = 60 , = 3,600 // . Then: Aa = 134.7 3/h + 3600" cos 38 o 55'14.0" cos 0° 57.3° /rad cos 0° : 134.78/h + 2^09 = 18368 57.3 The effect of the Moon's additional component of motion in right ascension resulting from its own orbital motion will be discussed in connection with the extreme lunar displacement caused by the lunar nodical cycle, as shown in fig. 36 (pt. II, ch.4). The Relationship of the Moon's Motion in Right Ascension to Its Declination In the basic equation evaluated above, involving only the effect of the Earth's diurnal rotation upon the change in right ascension of the Moon, it will be observed that the cosine of the declination occurs in the denominator. Hence, as the declination increases from 0° to 90°, the influence of this factor upon the change in right ascension varies from ( 1 ) the minimum value produced by the other parameters h, v, and <£, through ( 2 ) larger values introduced by the presence of a decimal fraction in the denominator, to (3) infinity at 90° (any motion in right ascension is indeterminate at the celestial poles) . From an analysis of the spherical trigonometry rela- tionships in figure 25B, it is also obvious that the ap- parent motion of the Moon along any portion of a parallel circle of declination (whose radius must decrease toward the poles) will likewise vary from a maximum on the celestial equator to zero at the poles. That is, the ap- parent change in right ascension ( Aa )p, along any paral- lel circle will, as caused by the Earth's diurnal rotation alone, be approximately equivalent to the change in right ascension at the equator ( Aa ) e, multiplied by the cosine of the declination of the Moon (i.e., (Aa)p = (Aa)s cos s). At the Equator, all of the Moon's apparent diurnal mo- tion occurs in the coordinate of right ascension, and hence the length of the lunar day is increased a greater amount. The precise relationships which variously modified lunar motions in right ascension have with respect to the Moon's declination actually are quite complex. Further- more, the significance of the declination-induced magni- tudes of these apparent motions in right ascension result- ing from the Earth's diurnal rotation as they influence the tide-raising potential should not be confused with other effects associated with the Moon's own orbital mo- tion. Those purely dynamic aspects of the tide-raising forces which are related to lunar declination will be described in part II, chapter 4. Chapter 2. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces The preceding chapter describes the continuously changing positions and motions of the Moon, Earth, and Sun which, taken together, result in correspondingly varying astronomical forces responsible for the produc- tion of the tides. In the present chapter, attention will be focused upon certain closely related factors operating to increase both the magnitude and duration of these tide- raising influences. Principal Effects Various alignments and combinations of the gravita- tional forces acting, as well as the relative distances be- tween Earth, Moon, and Sun, and the angular positioning of the latter two bodies with respect to any observing posi- tion on the Earth's surface, collectively exercise a very important influence in producing tides of considerably increased amplitude and/or range. Similarly, the relative speeds of motion of these same three bodies, the inclina- tions of the apparent paths of the Moon and Sun to the celestial equator, and the lengths of their arcs of move- ment across the sky, affect the period of time during which such augmented tides exist. In general, the enhanced astronomical forces creating perigean spring tides are of relatively short duration. Plots of these tides are marked by more steeply sloping curves of tidal growth and decline (see part II, chapter 8) asso- ciated with the transient reinforcement of the tidal forces. These amplified crests and troughs occur at appropriate times of high and low water during the tidal day. As a result, a very important factor of determination in connec- tion with the relative intensity of perigean spring tides involves the changing lengths of the tidal day within which such transitorily increased tidal forces are exerted. Two important concepts affecting the duration of the tidal forces acting which will appear repeatedly in future analytic discussions throughout the text are those of ( 1 ) lunar transit times, and (2) the necessary "catch-up" times between a point on the rotating Earth and various apparent motions of both the Moon and Sun in the same direction. Other dynamic factors of consequence to the period of application of augmented gravitational forces involve the instantaneous geometric figure and varying rotational motion of the orbit of the Moon. These are both subject to small disturbances known as "perturbations" caused by the changing gravitational attraction of the Sun, and such perturbations may, in turn, give rise to corresponding variations in the length of the tidal day. The perturbations produced in the lunar orbit will form one of the principal topics for discussion in part II, chap- ter 3, and the further description of their associated effects will be reserved until then. However, with consideration to the duration of time in which augmented tide-raising forces can act, it is desirable to provide an immediate introduction to the close connection between lunar transit times and the length of the lunar day (as loosely desig- nated, before various modifications and differences indi- cated in the present chapter cause it to become the tidal day). Significantly, certain changes in the length of the tidal day may also cause variations in the catch-up times of the rotating Earth. Foremost among the variable quantities affecting the length of the lunar day and, through it, the tidal day, is the daily lunar retardation. The actual magnitude of the daily lunar retardation also bears a very close relationship to the daily differences in motion of the Moon in right ascension, introduced in the preceding chapter and con- tinued in the present one. The Daily Lunar Retardation As has been previously noted, the period of revolution of the Moon in its orbit around the Earth from conjunc- tion or alignment with a star to conjunction with that 137 i:w Strategic Role of Perigean Spring Tides, 1635-1976 same star again is known as the sidereal month. Its mean value is 27.321661 days. This figure represents the average period of revolution, obtained from the individual, real motion of the Moon in space. It is independent of either the Moon's combined revolution with the Earth around the Sun (annual orbital motion) or the rotation of the Earth on its axis (diurnal motion.) which causes the Moon to rise and set, and to move daily across the sky with respect to any location except one in extreme polar lati- tudes on the surface of the Earth. Both of the motions named above in parentheses, and others as well, do, how- ever, introduce modifications in the apparent speed of movement of the Moon. Through corresponding altera- tions in the length of the lunar day, they also affect the length of the tidal day and, with this, the magnitude of the tides. Thus, continuing from the sidereal or true month, the average period of time between two successive conjunc- tions (or oppositions) of the Moon with the Sun (i.e., at new moon or full moon, respectively) is termed the synod- ic month. Because the Earth's own mean (orbital) motion around the Sun carries the Moon with it approximately 0.985647° eastward each day and this same amount farther away from the next succeeding alignment between Earth, Moon, and Sun at time of syzygy, a necessary catch-up motion is required. The synodic month is, there- fore, 2.208928 days longer than the sidereal month, or 29.530589 davs. actually revolves around the Earth. Thus, the Moon must, during each month, catch up with the current position of the Sun to achieve a direct alignment between Earth, Moon, and Sun at times of either new moon or full moon. In the following equation M si a = the length of the sidereal month, in mean solar days (measured by the revolu- tion of the Moon through 360° from alignment with one star to alignment with that same star again) . In one day, the Moon will, therefore, move through 360° /M sUi . Similarly, Y si( i= the length of the ordinary (sidereal) year, in mean solar days. In one day, the Earth will move through 360° /y s id- As the Earth revolves in its annual orbit around the Sun, the Sun appears to move forward in the same direction in the sky. Accordingly, the quantity 360°/T si a also represents the apparent daily motion of the Sun, caused by the Earth's revolution. Since the average (mean) orbital motion of the Moon is 12.190749°/day and the mean apparent motion of the Sun (the equivalent of the Earth's mean orbital motion) is only 0.985647 °/day, the Moon appears to move much faster in its daily eastward motion in the sky than does the Sun. (This motion is not to be confused with the daily rising and setting motions of both the Sun and Moon in a westward direction across the sky, an apparent motion caused by the oppositely directed rotation of the Earth.) In its fictitious eastward motion with respect to the Earth, the Sun appears to be moving in the same direction in which the Moon The mean period of time, in days, between two such successive occurrences of either new moon or full moon has been defined as the synodic month (M eyn ). The mean daily gain of the Moon on the Sun is given by the equation : 3607M BW -360°/F -ld =3607M W B. Therefore l/M Byn = 1/27.321661 -1/365.25636042 = 0.036600996 - 0.002737803 = 0.033863193 or M 8yn = 29.530589 days. With respect to the Sun, the Moon advances in one mean solar day through the previously mentioned average angular distance of 360 o /29.530589 d =12.190749 o . In terms of its times of transiting the celestial meridian, the Moon is retarded daily through this angle, on the average, throughout the year. Because the apparent angular motion of the mean sun is only 0.985 647° /day and that of the Moon with respect to the Sun many times greater, the Moon is constantly gaining on, and passing the Sun. At the same time that the Moon and the Earth are revolving in their separate orbits, at mean angular veloci- ties of 0.549°/mean solar hour and 0.041°/ msh , respec- tively, the Earth is rotating on its axis and at a very much faster angular rate given by 360 o /24 h =15.0 o / ms \ In con- trast with the Earth's revolutionary motion around the Sun, this results in an apparent motion of the Sun in a direction opposite to that in which the Earth is rotating. Accordingly, as a reflection of the Earth's daily axial rota- tion, but subject to a small eastward component of motion equal to the daily portion of the Earth's eastward revolu- tion around the Sun, the Sun appears to move westward in the sky and transits the upper meridian of any place once each apparent solar day. The period of time between two successive transits of the true Sun is extremely variable throughout the year. However, at a very early time, this apparent motion of the true Sun became the basis for timekeeping by means of sundials. Later, for purpose of convenience, the motion of an hypothetical or fictitious mean sun was chosen, and this concept has persisted, although the method of determining extremely precise clock time has changed. The mean sun is assumed to move uniformly with a constant, average rate of motion along the celestial equator instead of along Factors Affecting the Magnitude and Duration of the Tide-Raising Forces i:;<) its apparent true path, the ecliptic — and without any variation due to the Earth's changing velocity in orbit around the Sun. The time between two successive upper transits of this mean sun across the local meridian of any place is defined as the mean solar day of 24 mean solar hours. 1. The Lunar Day The Moon is likewise caused to transit the upper merid- ian of any place on the Earth's surface once each day as a result of the Earth's axial rotation. However, the Moon is revolving in its orbit in the same direction as that in which the Earth is rotating on its axis, and this results in an extra amount of time required for a position on the Earth's surface, subject to its rotational motion, to catch up with the Moon's changing position. In relating the daily apparent gain in position of the Moon to the corre- spondingly delayed time at which the Moon reaches the upper meridian of a place, and hence the amount of this delay, the following reduction is used: Daily mean synodic motion of the Moon in orbit = 12.190749°. Mean solar day = 24 mean solar hours. Thus, the mean synodic motion of the Moon per hour is 12.190749° per day/24 hours per day =0. 507948° per mean solar hour. Since the Earth rotates through 15° in one mean solar hour, the preceding hourly motion of the Moon in its orbit (or, when the Moon is on the celestial equator, the instantaneous motion in right ascension ) involves a time- delay factor of : =0.507948° per mean solar hour. =0.033863X60 minutes/hour X 24 hours/day =48.73008 minutes = 48 m 45.8 s . However, as the Earth rotates through 360° on its axis, the Moon moves through 12.190749° in its own orbit around the Earth. Allowing for this catch-up motion of the Earth's rotation upon the changing position of the Moon, the average daily delay between two successive transits of the Moon across the celestial meridian of a place on the Earth's Equator is 360° + 12.190749°=372. 190749° 48.762996 m X372.190749°/360°=50.414267 m =50 m 24.9 s . Since the lunar day is defined as the period of time be- tween two successive upper transits of the Moon across the local meridian, the length of the mean lunar day at the Equator is, therefore, 24 h 50" 1 24.9 s . The amount above 24 hours is known as the mean daily lunar retarda- tion. 2. The Tidal Day It must be noted that the angular velocity of the Moon from which the above value of the mean lunar day is derived is steadily changing. These changes are caused by the elliptical shape of the Moon's orbit, its inclination to the celestial equator — with consequent continuously vary- ing declinations — and by perturbations produced within the lunar orbit. Other local fluctuations in the Moon's apparent angular velocity across the sky result from the latitude of the position of observation and the Moon's varying zenith distance. The average value of the daily lunar retardation in transit times may, accordingly, range from 38 to 66 minutes, but may be quite different from the corresponding retardation times in the Moon's rising or setting. Various factors — notably the seasonal changes in the inclination of the ecliptic to the celestial equator and the continuously varying angle between the Moon's orbit and the local horizon — cause the lunar retardation times in these respective positions to be different. Sim- ilarly, only in transiting the meridian are the Moon's angular motions in right ascension, hour angle, and azi- muth the same. At increasingly larger angles from the meridian, greater divergences appear among these three motions. The mean lunar day has been defined above. For cer- tain general purposes, and where only average values are concerned, the mean tidal day may be regarded as synon- ymous with, and equivalent in length to, the mean lunar day. This does not apply where considerable deviations in the length of the tidal day, dependent upon tidal re- sponses to reinforcing astronomical conditions, are a mat- ter of immediate concern. By contrast, a more exacting interpretation of the ac- tual tidal day (see appendix, fig. 6), as used generally throughout this volume, involves the period of time be- tween the larger maxima (or minima) of two tides of the same type (ordinarily measured between one higher high water and the next ) . The differences between any specific lunar day and the corresponding tidal day are obvious : Lunar transit times used in the determination of the lunar day consider only the instant of passage of the Moon across the upper or lower branch of the meridian, and are, therefore, re- Mil Strategic Role of Perigean Spring Tides, 1635-1976 stricted to the meridian altitude of the Moon a ; large numbers of intermediate occurrences of tidal peaks, with the Moon being at different altitudes and azimuths, would not be included under this definition of the tidal day, since the times of lunar transit and those of the maximum rise of the tide do not bear a one-to-one correlation. Moreover, the length of the tidal day as used in the second and more restrictive sense involves numerous addi- tional variable quantities. These are associated with the relative positions, motions, and forces of both the Moon and Sun, perturbations of the Moon's orbit by the Sun, and other specific circumstances relating both to hydrog- raphy and dynamic oceanography. (See pt. II, chs. 4, 6.) This more exact usage is especially applicable in the com- parison of tidal actions at localized observing stations which are subject to ( 1 ) different high-water lunitidal intervals (i.e., specific time intervals between lunar transit and the highest rise of the tide, attributable to hydro- graphic and other causes), and (2) varying delays in attaining a maximum tide rise after transit of the Moon (associated with unequal phase and parallax lags at the individual stations). These effects are discussed further in part II, chapter 6. Relationship of the Tidal Day to Lunar Transit Times, Hourly Differences in Right Ascension of the Moon, and Other Factors A comparison of data tabulated in The American Ephemeris and Nautical Almanac shows that the greatest difference in time between successive upper and lower transits of the Moon occurs when the difference between successive hourly right ascensions also reaches a maximum value (i.e., the Moon is moving eastward in right ascen- sion by its greatest amount). The agreement between these two factors is very close. An increase in the differ- ences between the values of hourly right ascension and an increase in the differences between the retardation times affecting the transit of the Moon are, in fact, directly correctable. Conversely, the least difference in time between im- mediately succeeding upper and lower transits (or two " It should be noted at this point also that a small distinction exists between the meanings of "culmination" and "meridian transit" due to variations between the angles at which parallels of declination (equatorial system) and almucantars (horizon sys- tem) cross the celestial meridian. Thus the Moon may transit the meridian, yet not be exactly at its maximum angular altitude above the horizon, as implied by the word "culmination." In the Northern Hemisphere, as the Moon moves toward greater declinations, it culminates following its transit of the meridian. succeeding upper transits ) of the Moon occurs when the difference between successive hourly right ascensions at- tains a minimum value. Other possible correlations, par- ticularly any sought between the motions of the Moon in either right ascension or declination and the correspond- ing length of the tidal day (as distinct from the lunar day) are not as well defined. The greatest and least values of the hourly differences in right ascension usually occur, in a directly opposite relationship, at times very close to those of the least and greatest values, respectively, of hourly change in declina- tion. However (since other factors also affect the two coordinates), these opposing maximum and minimum values of hourly change in right ascension and declination do not necessarily occur even on exactly the same day. Similarly, the time of maximum retardation in transit of the Moon does not necessarily agree exactly with an increase in the length of the tidal day as defined in the second concept given above and determined from tide tables. This is because various other astronomical circum- stances, including the gravitational influence of the Sun, are also effective in altering the period of time between successive high waters, and hence the length of the tidal day. Among those circumstances which tend to increase the Moon's apparent motion in right ascension as seen from the Earth are: ( 1 ) proximity of the Moon to the position of perigee-syzygy, causing an acceleration of the Moon's direct motion in orbit ; and ( 2 ) proximity of the Moon to its largest values in declination, positive or negative, re- sulting in a maximum forward motion in right ascension. Circumstances which tend to decrease the Moon's ap- parent motion in right ascension include : ( 1 ) proximity of the Moon to the position of apogee-syzygy, with the decreased gravitational force of the Earth causing a re- duction in the Moon's forward velocity in orbit; and (2) creation of the maximum possible angle of inclination between lunar orbit and the celestial equator (±28.5°) during the appropriate phase of the 18.6-year lunar nodi- cal cycle (pt. II, ch. 4), thus markedly increasing the inch- nation of the Moon's topocentric path in declination, augmenting its apparent motion in this coordinate and, to a certain extent, decreasing its apparent motion in right ascension ; this effect is in addition to the greater inclina- tion between the declinational motion of the Moon and the celestial equator, and the relatively reduced motion in right ascension which occurs when the Moon is near to, or crossing, the celestial equator compared to that when it is near its semimonthly position of maximum declination. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 111 Apparent Diurnal Motion of a Body "Fixed" in Space When a very distant and hence, in terms of its actual space motion, essentially stationary celestial object such as a star is subject to the Earth's diurnal rotation, it will apparently move through the same distance in hour angle in the same period of time, no matter at what declination it is situated. The reason is a geometric one. Although hour circles converge toward the poles, a point on any given hour circle is located exactly one hour in time from its counterpart position (i.e., one located at the same declination) on an immediately adjacent hour circle. In viewing, from a suitable position on the surface of the Earth, any such celestial objects having declinations rang- ing from 0° to 90°, those objects located at greater decli- nations will appear to move more slowly ( in linear veloc- ity) across the celestial sphere than those on or near the celestial equator, but their angular velocities are the same. Apparent Diurnal Motion of a Body Pos- sessing Its Own Motion in Right Ascension In the case of a relatively nearby celestial object such as the Moon, which also possesses its own orbital motion, positional displacements result that are quite different from those of the preceding section. Where, as in the example of the actual motion of the Moon and the ap- parent motion of the Sun, the movement of these bodies is in the same direction as that of the Earth's rotation (i.e., a direction eastward, or counterclockwise as viewed from the respective poles of revolution and rotation), a special catch-up motion is involved which will be exten- sively discussed in subsequent chapters. ( The only excep- tions to this statement occur in the cases of a few asteroids and comets that revolve around the Sun in a retrograde direction, as well as those planets of the solar system that are relatively close to the Earth and may, on occasion, exhibit apparent retrograde motions. ) Following upon the meridian transit of a celestial body having its own direct motion, as observed from a par- ticular location on the Earth's surface, the Earth must rotate through more than one complete rotation to bring this body into direct alignment over this same point on its surface again. Any nonpolar point on Earth rotates in a plane either in, or parallel to, the celestial equator. In considering the motion of any other body relative to this plane, the body's apparent daily displacement must be converted to an equivalent component of motion in the equatorial plane. Unless the body remains in the plane of, or parallel to, the celestial equator (i.e., exhibits motion only in a diurnal circle) during the entire period of one rotation of the Earth, as in the case of a "rixed" star, a trigonometric reduction is necessary to obtain the object's individual motion in, or parallel to, the celestial equator. Although the Sun is a star, its distance from the Earth is relatively so close that it also exhibits the simulation of the Earth's annual orbital motion previously described. Only for a short period of time around the equinoxes where the ecliptic crosses the celestial equator and the Sun's declination is zero is its motion in longitude very nearly equal to its motion in right ascension. Hence, only in these positions is the Sun's westerly displacement in hour angle ( caused by the Earth's diurnal rotation ) in the same plane as the Sun's easterly motion in longitude, produced by the Earth's annual revolution. At all other times and positions, the daily angular difference in the Sun's longi- tude must be converted to a corresponding daily motion in right ascension by the use of transformation equations or, more simply, can be obtained directly from tables of right ascension of the Sun. The tabulated daily difference in the Sun's apparent motion in right ascension (caused by the annual revolution of the Earth) is then subtracted from the oppositely directed component of apparent motion in hour angle, measured in the same equatorial plane, and caused by the diurnal rotation of the Earth. The resulting difference indicates the necessary additional time required for a given point on the Earth's surface to catch up to a position of alignment with (i.e., a meridian transit of) the Sun. Similarly, except at the two positions each month where the Moon crosses the Earth's Equator, the changing lunar longitudes must be converted to a daily difference in right ascension, or the necessary equatorial coordinate values can be obtained from tables of lunar right ascension. The daily difference in right ascension caused by the Moon's motion in orbit is then subtracted from the amount of the Moon's motion in hour angle produced by the Earth's rotation to determine the necessary catch-up time for a given point on the Earth to regain a meridian transit posi- tion with the Moon. The principle of this catch-up time will be extensively elaborated upon in the next chapter. Variations in the Tide-Raising Force Associated With Lunar Parallax It has been specified previously that, in accordance with Sir Isaac Newton's Universal Law of Gravitation, the gravitational attraction between two celestial bodies varies directly as the product of their masses and inversely as the square of the distance between them (i.e., the closer the two bodies are to each other the greater is the interact- 142 Strategic Role of Pcrigean Spring Tides, 1635-1976 ing gravitational force; as they draw farther apart, this force decreases as the second power of the distance sep- arating them. However, as noted in the appendix ("The Effect of Gravitational Force"), tide-raising forces vary inversely as the third power of the distance. In the motion of the Moon in its orbit around the Earth, the gravitational force of the Earth is at all times directed at right angles to the lunar orbit, causing the Moon to fall constantly toward the Earth. However, an equal and oppositely directed centrifugal force resulting from the revolution of the Moon in orbit resists the infall- ing motion and keeps the Moon from plunging toward the Earth. Although the Moon's own gravitational force upon the Earth is directed along a line connecting their centers, two components of this total force exerted upon the Earth's surface, and known as the horizontal (or tractive) component and the vertical component, respec- tively, act to produce tides in the Earth's waters. Variations in the Moon's tide-raising force as a result of its changing distances from the Earth form the basis for the phenomenon of parallactic inequality. Because the Moon revolves in an elliptical orbit around the Earth with the Earth located at one focus of the ellipse (fig. 23 ) , once each lunar month the Moon comes to its closest approach to the Earth at perigee and, approx- imately 2 weeks later, reaches its greatest monthly dis- tance from the Earth at apogee. As was seen in connection with the earlier discussion of Kepler's Second Law of Planetary Motions, the radius vector — or center-to-center axis joining the Moon and the Earth — sweeps out equal areas at any portion of the lunar orbit within equal intervals of time (fig. 24). The lunar distances delineated by the two sides of the elliptical sector so formed are continuously varying. In order that the radius vector may describe equal areas in the same period of time, the angular velocity of the Moon also must be variable at different portions of the orbit. In that half of the lunar orbit between apogee and perigee, as the Moon nears its position of closest monthly approach to the Earth, it speeds up in response to the increased gravitational force of the Earth which results from the diminished lunar distance. Conversely, between perigee and apogee, the Moon's angular velocity becomes less. Near the exact position of perigee, the Moon is mov- ing at its maximum angular velocity; at apogee, it is moving the slowest. Each of these latter two positions in the lunar orbit is called an apse, and the axis connecting them is correspondingly termed the line of apsides. The changing distance of the Moon from the Earth is measured by the angle subtended by the equatorial semi- diameter of the Earth as it would be seen from the Moon — thus in a position very nearly on the local hori- zon. b This is equivalent to the angle (viewed at the center of gravity of the Moon) between a line drawn from the center of the Moon to a semidiametrical position on the surface of the Earth and another line drawn from the center of the Moon to the center of the Earth (fig. 41). It is also equal to the apparent angular difference in the Moon's direction in the sky as it would be seen from these two positions on the Earth. This angle — larger when the Moon is closer and smaller when it is farther away — is termed the equatorial geocentric horizontal parallax. Hence, the effect of the changing distances of the Moon in altering the tides, as well as in producing variations in the daily retardation of the tidal day from this cause, is termed the parallactic inequality. Table 8 shows a comparison between the continuously varying values of the geocentric horizontal parallax (t) and the distance (p, in Earth-radii) of the Moon from the center of the Earth during an ordinary lunation in the year 1974 (i.e., a period of one synodic month including all lunar phases, but containing no close perigee-syzygy alignment ) . These data may be contrasted with the data of table 15, which show the values of p for various alignments of perigee-syzygy, perigee-quadrature, and apogee-syzygy during 1973 and 1974. The geocentric dis- tance p is related to the value of the geocentric horizontal parallax tt through the relationship p = cosec 7r=l/sin n. Table 8. — Comparison of Geocentric Horizontal Parallax and True Geocentric Distance of the Moon for a Case of Widely Separated Pengee-Syzygy Date 1974 Horizontal Parallax True distance, Earth-radii ' Apr. 14.0 54 19. 3409 63. 286 841 14.5 54 15.9150 63. 353 427 15.0 54 15. 1045 63. 369 201 15.5 54 16. 9068 63. 334 137 16.0 54 21.2810 63.249 196 16.5 54 28. 1483 63. 116 302 17.0 54 37. 3921 62. 938 300 17.5 54 48. 8577 62. 718 903 18.0 55 02. 3534 62.462 612 " Where a semidiameter of the Earth perpendicular to any local horizon is considered, a variation in geocentric parallax occurs with altitude of the Moon above the horizon. This "parallax in altitude" is zero in the zenith and maximum on the horizon. Because the Earth is neither a true sphere nor an oblate spheroid (possessing an irregular figure known as a geoid) , for astronomical purposes the equatorial semidiameter is chosen and adjustments are made, as necessary, for the Moon's altitude and the latitude of observation. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 14:', Table 8. — Comparison of Geocentric Horizontal Parallax and True Geocentric Distance of the Moon for a Case of Widely Separated Perigee-Syzvgy — Continued Date 1974 Horizontal Parallax True distance, Earth-radii " Apr. 18. 5 55 17.6508 62. 174 627 19.0 55 34.4869 61.860 729 19.5 55 52. 5668 61.527 153 20.0 56 11. 5681 61. 180 433 20.5 56 31. 1469 60. 827. 238 21.0 56 50. 9457 60.474 199 21.5 57 10. 6026 60. 127 721 22.0 57 29. 7624 59. 793 806 22.5 57 48. 0878 59. 477 884 23.0 58 05.2716 59. 184 663 23.5 58 21.0468 58.918 010 24.0 58 35. 1964 58. 680 873 24. 5 58 47. 5589 58.475 242 25.0 58 58.0316 58. 302 170 25.5 59 06. 5696 58. 161 827 26.0 59 13. 1813 58.053 612 26.5 59 17.9206 57. 976 289 27.0 59 20. 8770 57.928 159 27.5 59 22. 1638 57. 907 235 28.0 59 21.9064 57.911 420 28. 5 59 20. 2310 57. 938 670 29.0 59 17.2549 57.987 138 29.5 59 13.0796 58. 055 274 30.0 59 07. 7856 58. 141 895 30.5 59 01.4311 58. 246 210 May 1.0 58 54.0530 58. 367 799 1. 5 58 45. 6704 58. 506 561 2.0 58 36.2901 58. 662 622 2.5 58 25. 9142 58. 836 220 3.0 58 14. 5475 59.027 578 3.5 58 02. 2061 59.236 760 4.0 57 48. 9244 59.463 541 4.5 57 34. 7619 59. 707 284 5.0 57 19.8070 59. 966 844 5.5 57 04. 1801 60. 240 488 6.0 56 48. 0338 60. 525 864 6.5 56 31.5511 60.819 988 7.0 56 14. 9420 61. 119 275 7.5 55 58. 4383 61.419 595 8.0 55 42. 2877 61.716 360 8.5 55 26. 7474 62. 004 632 9.0 55 12.0776 62. 279 239 9.5 54 58. 5348 62.534 916 10.0 54 46. 3669 62. 766 435 10.5 54 35.8074 62.968 744 11.0 54 27.0717 63. 137 100 11. 5 54 20. 3533 63. 267 191 12.0 54 15.8210 63. 355 255 12.5 54 13.6163 63. 398 183 13.0 54 13.8510 63. 393 611 13.5 54 16.6051 63. 340 003 14.0 54 21.9245 63.236 719 perihelion and closest to the Sun in its annual motion, the Moon is also nearly so, and is then subject to the maxi- mum gravitational influence of the Sun, including those forces producing perturbations in the lunar orbit. This relationship is, therefore, often referred to as solar perigee (i.e., the Sun reaches a position near solar perigee or apogee as the Earth reaches its position of perihelion or aphelion, respectively ). c In order quantitatively to illustrate these combined lunisolar effects, the next-to-the-last column in table 9 shows the relative geocentric distances of the Sun from the Earth corresponding to an astronomical circumstance chosen to accord with the close perigee-syzygy of 1974 January 8. The values are expressed in terms of the mean distance of the Sun from the Earth (equal to the semi- major axis of the Earth's orbit) considered as unity. The Effect of the Parallax Inequality Upon the Comparative Lengths of the Tidal Day The average speed of the Moon in its orbit is about 12.2°/day. However, for the reasons given in the previous section and as partly evident in tables 10, 20, the lunar angular velocity increases to an extreme maximum of approximately 14.2° _ 15.4°/day d at very close perigee- syzygies, diminishes to about 14.1°-14.2°/day at perigee- quadrature, and to 11.8°-12.0°/day at apogee-syzygy or apogee-quadrature. Sensible differences are introduced both in the daily lunar retardation and in the length of the tidal day as the result of these changing lunar veloc- ities. An interesting comparison can be made between the considerably increased daily lunar retardation produced as the result of such accelerated lunar velocities at the time of perigee-syzygy and the lesser retardation produced subject to the previously computed mean orbital velocity of the Moon (pt. II, ch. 2, "The Daily Lunar Retarda- tion"). Using the same calculation procedure as in the earlier example, involving the mean synodic motion of the Moon : Maximum daily angular velocity of the Moon in orbit (at the representative close perigee-syzygies of May 2.5 and Nov. 10.5, 1950) =15.28°/day. It is also important to note that, because the Moon is bound gravitationally to the Earth, when the Earth is at c However, the fact that the Earth is at perihelion does not neces- sarily imply that the Moon is at its absolute minimum distance from the Sun. In order for this condition to be achieved rigorously, the Moon must also be located at its position of apogee (with respect to the Earth) at this time. See chapter 5. A At an occurrence of proxigee-syzygy having a mean epoch of 1918 March 12.39 G.m.t. (P-S=+29\ 3=1.56°, T ma x=61'27.- 08"), the Moon's average daily motion between March 12.0-13.0 was 15.3566°. 144 Strategic Role of Perigean Spring Tides, 1635-1976 Table 9. — The Changing True Distance of the Earth From the Sun (Expressed as a Decimal Portion of the Mean Astronomical Distance of the Earth From the Sun — i.e., the Length of the Semimajor Axis of the Earth's Orbit — Considered as Unity) These distances are chosen to accord with the period of time around the close perigee-syzygy alignment of 1974 January 8, and indicate the Earth's least annual distance from the Sun at perihelion on 1974 January 4. The table also shows the corresponding increase in, solar semidiameter at perihelion, together with the effect of the Sun's slow daily change in declination and rapid change in right ascension at the winter solstice (1973 December 22). Date Apparent right ascension Apparent declination True distance of the Earth from the Sun Semi- diameter 1973 Dec. 20 h 17 m 51 s 05.47 A 8 266. 41 23 25 37.0 42.4 I .983 ; a .u.=i 8173 652 16 16.99 21 17 55 31.88 266. 50 -23 26 19. 4 — 14.2 0.983 7521 -614 16 17.06 22 17 59 58. 38 266. 54 23 26 33. 6 + 14. 1 , 983 6907 574 16 17. 12 23 18 04 24.92 23 26 19.5 .983 6333 U, 17. 17 24 18 08 51.47 266. 55 266. 51 23 25 37. 1 42.4 7(1. 7 .983 5797 536 4MB 16 17.23 25 26 27 18 18 18 13 17 22 17.98 44.43 10. 76 266. 45 266. 33 266. 19 23 -23 23 24 22 20 26.4 47.5 40. 4 98.9 + 127. 1 155. 1 . 983 0. 983 . 983 5299 4839 44 1 8 460 -421 381 16 16 16 17. 28 17. 32 17. 36 28 18 26 36.95 266. 00 23 18 05.3 183.3 .983 4037 540 16 17.40 29 L8 31 02.95 265. 78 23 15 02.0 211.2 . 983 3697 298 li. 17.44 30 18 35 28. 73 265. 53 23 11 30. 8 239.0 . 983 3399 2:14 16 17.46 31 18 :i'i 54.26 -23 (17 31.8 0.983 3145 16 17.49 1974 Jan. 1 18 44 19.50 265. 24 23 03 05. +266. 8 .983 2937 -208 It, 17. 51 2 18 48 44.42 264. 92 264. 57 22 58 10. 6 294.4 321.7 .983 277') 158 107 li, 17. 53 3 18 53 08. 99 264. 18 22 52 48.9 349. 1 . 983 2672 - 52 li, 17.54 4 18 57 33. 17 22 46 59. 8 .983 2b2H 16 17.54 5 19 ill 56.95 263. 78 -22 40 43. 7 376. 1 0.983 2626 + 6 16 17.54 <» 19 06 20.30 263. 35 262. 89 22 34 00.6 +403. 1 429.8 .983 2694 + 68 130 It, 17.53 7 19 in 43. 19 262. 40 22 26 50. 8 456.2 . 983 2824 197 16 1 7. 52 8 19 15 05.59 22 19 14.6 . 983 3021 li, 17.50 9 19 19 27.48 261. 89 22 11 12.0 482.6 .983 3284 263 It, 17.48 10 19 23 48.85 261.37 -22 02 43.4 508.6 0.983 3614 330 16 17.44 11 19 28 09.67 260. 82 260. 25 21 53 48. 9 + 534. 5 560. 1 .983 4010 + 396 460 16 17.40 12 19 32 29.92 21 44 28. 8 .983 4470 16 17.36 13 19 36 49. 58 259. 66 259. 06 21 34 43.3 585.5 610. 7 .983 4')!!') 519 .177 It, 17. 31 Factors Affecting the Magnitude and Duration of the Tide-Raising Forces Table 9. — The Changing True Distance of the Earth From the Sun etc. — Continued i r> Date Apparent right ascension Apparent declination True distance of the Earth Semi- from the Sun diameter 1974 h m s A 8 / // A" ( l.U.= l) A / n Jan. 14 19 41 08.64 258. 45 21 24 32.6 635.5 .983 5566 631 It, 17.25 15 19 45 27.09 257. 80 -21 13 57. 1 + 660. 0.983 6197 +682 If. 17. 19 16 19 49 44.89 257. 15 21 02 57. 1 684.3 .983 6879 729 16 17. 12 17 19 54 02.04 256. 47 20 51 32.8 708.2 .983 7608 775 16 17.05 18 19 58 18.51 255. 77 20 39 44.6 731.8 . 983 8383 817 If, 16.97 19 20 02 34.28 255. 07 20 27 32.8 755.0 .983 9200 858 16 16.89 20 20 06 49.35 -20 14 57. 8 0.983 0058 16 16.80 Mean solar day=24 mean solar hours. Hence, the mean hourly motion of the Moon at its maximum orbital velocity is 15.28° per day/24 hours per day=0.6367° per hour. Since the Earth rotates through 15° in one hour, this represents a corresponding time delay factor of 0.6367° per hour/15° per hour =0.0424X60 minutes/hour X24 hours/day =61.1232 minutes=61 m 7.39 s . Since the Moon revolves through 15.28° in its own orbit while the Earth rotates through 360° on its axis, the Moon's right ascension increases by this same amount. 360°+15.28°=375.28° 61. 1232X375.28°/360°=63.7175 m =63 m 43.0 s . Thus, subject to these maximized conditions in the Moon's orbital velocity at the time of a very close perigee-syzygy, the actual daily lunar retardation has increased from its mean value of 50 m 24.9 s to 63 m 43.0 s , a gain of more than 13 minutes. The increase in the value of the daily lunar retardation and corresponding extension of the tidal day also result in an increase in the time required for a point on the rotating Earth to catch up with the additional advance- ment of the Moon in its orbit made possible in this length- ened interval and at the Moon's greater orbital velocity. As before, the revolution of the Moon around the Earth in the same direction as the Earth rotates on its axis means that, for the Moon to undergo two successive transits over any one location on the Earth's surface (in the first defini- tion of the lunar day) the rotating Earth must catch up through the angle the Moon has moved in the sky during the time the Earth has rotated once through 360° with respect to the Sun (i.e., the mean solar day). As seen earlier, this extra angular distance through which the Moon will have moved eastward across the sky during the lunar day may range from 11.8°-15.4°, depending upon the Moon's position in its orbit. Although the tides, in general, quite closely follow the motions of the Moon, it will be seen in chapter 6 (cf., "The Phase Age and Parallax Age") that, under certain astronomical and hydrographic situations, their maximum amplitudes may occur either before or after lunar transits. While the time of lunar transit is not, therefore, an ac- curate indicator of the time of high water, any change which affects the apparent transit time of the Moon will, in one way or another, affect the times of the tides. When the Moon is traveling faster in its orbit at times of perigee-syzygy, the value of the daily lunar retardation is greater, and the interval required for the Earth's rota- tion (in the same direction) to catch up with the position of the Moon is longer. The interval between two successive higher high waters (the second definition of the tidal day) is increased in proportion. Conversely, when the Moon's orbital velocity is reduced, as it approaches apogee, the daily lunar retardation is decreased and the tidal day is shortened. Repeating the previous computations, but substituting the data for a near-minimum velocity of the Moon in orbit (11.82° per day) at a situation of apogee-quadra- ture on April 13, 1974 gives: 1 1.82° per day/24 hours per day=0.4925° per hour 0.4925° per hour/ 15° per hour =0.0328X60 minutes/hour X 24 hours/day =47.2320 minutes=47 m 13.9 s 360° + 11.82 o =371.82° 47.2320 m X37l.82°/360°=48.7828 m =48 m 47.0 s . The effect of parallactic inequality thus results in a difference of more than 15 minutes, on the average, be- 202-509 O - 78 Mb Strategic Role of Perigean Spring Tides, 1635-1976 Table 10. — Approximate Orbital Angular Velocity of the Moon, Expressed as a Difference in Celestial Longitude, Showing the Variation at Times of Close Perigee-Syzygy {Proxigee-Syzygy), Apogee-Syzygy {Exogee-Syzygy), and Perigee-Quadrature Apparent Average Apparent Average Alignment Date 1 inar daily Alig nment Date lunar daily longitude motion in longitude motion in longitude longitude 1974 o o 1974 o Jan. 1.0 1.2803 12. 8622 Jan. 27.il 345. 7534 12.4004 2.0 14. 1425 13.2472 28.0 358. 1538 12.6104 3.0 27. 38' )7 13.6763 29.0 10. 7642 12.8613 4.0 41.0660 14. 1238 30.0 23. 6255 13. 1566 5.0 55. 1898 14. 5529 31.0 36. 7821 6.0 69. 7427 14.9174 Apr. 24.0 53.5013 13.9751 7.0 84. 6601 15. 1697 25.0 26.0 67. 4764 81. 5680 14.0916 Proxigee-Syzygy 8. 9.0 10.(1 99. 8298 115. 1003 130.3009 15.2705 15.2006 14. 9678 27.0 28.0 29.0 95. 7270 109.9131 124.0944 14. 1590 14. 1861 14. 1813 1 1. i) 145. 2687 Perigee-Oi adrature 14. 1491 14. 6046 (1st quarter) 12.0 159.8733 14. 1593 30.0 138. 2435 14. 0889 13.0 174.0326 13.6833 May 1. ii 2.0 152.3324 166. 3292 13. 9968 14.0 187. 7159 13.2216 3.0 180. 1960 13. 8668 15.0 200. 9375 12.8066 4.0 193.8909 13. 6949 16. 213. 7441 12.4582 Nov. 2.0 63. 1558 17.0 226. 2023 12. 1847 3.0 76. 7768 13.6210 18. ii 238. 3870 11.9868 4.0 90.5619 13. 7851 19.0 250. 3738 11.8588 5.0 104. 4857 13.9238 20.0 262. 2326 11. 7929 6.0 118.5252 14.0395 21.0 274. 0255 1 1. 7790 7.(1 132.6568 14. 1316 22.0 285. 8045 Perigee-Qi tadrature 14. 1961 11.8078 (3d quarter) Exogee-Syzygy 23. 297. 6123 8.0 146.8529 11.8711 9.0 161.0778 14. 2249 24.0 309. 4834 11.9631 10.0 1 75. 2854 14. 2076 25.0 321.4465 12.0811 11.0 189.4193 14. 1339 26 (> 333. 5276 12.2258 12.0 203.4170 13.9977 Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 117 tween the respective values of the daily tidal retardation as they occur at perigee-syzygy and at either apogee-syzygy or apogee-quadrature. The smaller value of the retarda- tion, occurring at apogee-syzygy, averages about 49 min- utes per day. This difference of approximately 15 minutes, permit- ting a longer application of the combined gravitational forces of the Sun and Moon, and at a time when the latter is exerted from a relatively close distance — together with certain other factors to be developed in ensuing chapters — add measurably to the greater tidal flooding potential at times of perigee-syzygy. Ancillary Effects Lunar Augmentation In figure 25A, which represents the position of the Moon on the celestial sphere as seen in the horizon system of coordinates, it is very obvious that, when the Moon is in the zenith, it is a distance equal to the equatorial radius of the Earth (6,378.388 km or 3,963.530 mi) nearer to the surface of the Earth than when it is on the horizon. This amounts to a gravitationally significant portion (0.017 ) of the average distance of the Moon from the surface of the Earth (378,000 km or 234,900 mi). Since the tide-raising force increases rapidly as the third power of any diminished distance of the Moon from the Earth, this quantity is of measurable importance in deal- ing with tidal phenomena. The same geometric principle is true for the Sun-Earth configuration, but the change in distance here represents but an insignificant portion of the mean distance of the Earth from the Sun ( 149,500,- 000 km, or 92,900,000 mi). The effect of the lunar augmentation impacts upon those aspects of tidal prediction which relate to the instan- taneous distance of the Moon from the Earth and it can, LUNAR AUGMENTATION EFFECT LUNAR DECLI NATION A L EFFECT ON MOTION IN RIGHT ASCENSION AND THE LENGTH OFTHETIDAL DAY PLANE OF PAPER IS THAT OF THE CELESTIAL MERIDIAN c. B a2 ,4 2 IN ABOVE, /a = i Aa p = Aa e COS 6 o 1 ,6o A SEE TEXT to"- : C d2'6o Figures 25 A, B in-; therefore, be considered as a correction to the lunar hori- zontal parallax. The computation necessary to evaluate the quantitative influence of this phenomenon as it affects the tides follows. To the second order, neglecting the flattening of the Earth, 6 while assuming that the Earth's semidiameter r=\, and that the Moon is transiting the local meridian (/z=0° ) , the amount of the augmentation in lunar semi- diameter (S — So) is given approximately by: S~S =So sin Ho cos z'+S sin 2 H (1 — / 2 sin 2 z') where ( all values are for the Moon ) S =the observed (topocentric) angular semidiameter So =the geocentric angular semidiameter Ho =the equatorial horizontal parallax z' =the topocentric zenith distance (from the geodetic zenith). From The American Ephemeris and Nautical Almanac, the value of S is given by : S=0.0799"+0.272453 tt or the topocentric parallax is = £-0.0799" * 0.272453 In order to determine the maximum possible effect of the lunar augmentation arising from a favorable com- bination of circumstances, the extremely close perigee- syzygy situation of 1974 January 8.5 has been selected, having the following ephemeris values: #o=61' 30.0009"= 1.025000250° 5o=16' 45.43" =0.279286111° Assuming that these large geocentric values had oc- curred simultaneously at a time in the lunar nodical cycle at which the Moon had reached its maximum declination of ±28.5°, and selecting also the geographic latitude $=28.5° north or south, respectively, where the Moon would be seen in the zenith: Strategic Role of Perigean Spring Tides, 1635-1976 Therefore : Since : =0° ; cos z'= 1 ; sin z'=0 sin //o=0.01 7888675 sin 2 #0=0.000320005 ° The exact equation for determining the topocentric parallax w from the equatorial horizontal parallax Ha, at any latitude [) Strategic Role of Perigean Spring Tides, 1635-1976 3. Equinoctial Tides The Moon crosses the ecliptic twice each month, once from north to south, and once from south to north, and is never more than 5° 20' from the ecliptic (its maximum possible inclination, due to perturbations). The Sun, moving in the ecliptic, crosses the celestial equator twice each year at the vernal and autumnal equi- noxes, about March 21 and September 23, respectively. When the Moon comes close to the true equinox positions, it must also lie very nearly in the plane of the celestial equator, at a time when the Sun is crossing this same great circle. Thus, at times close to the equinoxes, the Sun and Moon are in almost the same declination plane (i.e., approximately 0° ) as the Earth's Equator. The Sun's semidiurnal component of gravitational force will then add an extra 27 percent to the lunar force to provide a greater amplification of the Earth's tides. The tides result- ing are known as equinoctial tides. The effect of adding a close perigee-syzygy alignment to this already gravitationally reinforced tidal situation will be discussed in connection with high equinoctial spring tides in chapter 5, in describing those astronomical factors which lead to the maximization of perigean spring tides. 4. Latitudinal Effects of the Diurnal Inequality The more common situation involving, for example, a differing height between higher high water and lower high water — and referred to as the diurnal inequality — is described in the appendix. Briefly, this phenomenon is created by a high declination of the Moon. The diurnal inequality also renders unequal the period of time between higher high water (HHW) and lower low water (LLW) compared with that between lower high water (LHW) and higher low water (HLW), and hence affects the duration of each. The effects of diurnal inequality usually increase with latitude and, to a greater degree, in the hemisphere to which the Moon's declinational motion carries it alternately during each half-month. However, the absence of any diurnal inequality when the Moon is over the Equator is general for all latitudes. Subordinate Factors Influencing the Length of the Tidal Day Certain definite relationships exist between the chang- ing lengths of the apparent solar day and those of the lunar (and tidal) days which are a direct function of the positional changes of the Sun and Moon. 1. Solar Declinational Effects When the Sun is on the celestial equator, the lengths of the day and night are very nearly equal at the Equator (although the length of the day increases slightly with geographic latitude) . With the Sun at the summer solstice, the lengths of day and night remain approximately the same at the Equator, but the length of the day is as much as 6 hours longer at latitude -(-60°. The same situation applies in the Southern Hemisphere at the winter solstice. As the Sun moves away from the celestial equator, its maximum (meridian) altitude above the horizon also becomes greater. In consequence, since the Sun must move over a longer daylight path from horizon to horizon — although its apparent daily motion in right ascension is larger — the duration of daylight is extended. 2. Effects Due to Changing Parallax and the Obliquity of the Ecliptic Because of the effects of the Earth's orbital eccentricity and inclination on its daily motion, the apparent solar day may be approximately 15 minutes longer or shorter than the mean solar day ( this constantly changing differ- ence is designated as the "equation of time"). The simi- larity between this "equation of time" (caused by the difference between the Sun's actual and mean motions) and a second tide-influential pattern existing between the motions of the true and mean moons will be described in part II, chapterS. 3. Lunar Declinational Effects The same influences specified in connection with the Sun in ( 1 ) above hold approximately true for the Moon's position with respect to the celestial equator, although not to such a close degree, since the effects of large parallax and other factors are of greater consequence in altering the apparent orbital motion of the Moon. As the declina- tion of the Moon increases, the period between moonrise and moonset remains approximately the same at the Equator, but this interval increases very significantly at higher latitudes. The lunar (and tidal) days are length- ened in proportion. 4. Effect of the Moon's Orbital Inclination to the Horizon Near the time of the autumnal equinox, with the full moon at the vernal equinox opposite the Sun, the Moon's orbit is inclined at a very small angle with respect to the horizon at middle and high latitudes in the Northern Hemisphere (particularly, if the Moon's ascending node also coincides with the vernal equinox). This circum- Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 151 stance results in the fact that the full moon rises above the horizon very slowly and with only a slight daily re- tardation for several successive nights. By rising at essen- tially the same time and hanging low in the sky for an extended period of time on consecutive evenings, it pro- vides extra illumination for fall harvesting. Accordingly, this phenomenon has been given the name "harvest moon," and the full moon following a month later under nearly the same circumstances has been designated "hunter's moon." From a tidal point of view, the slowly moving Moon possessing but a small daily lunar retardation implies an accompanying fast catch-up time between a point on the rotating Earth and the orbiting Moon. This results, in turn, in a relatively short tidal day, and a reduced period of application of any amplified tidal forces. 5. Supplementary Influences In succeeding chapters, the extension of the lunar and tidal days will be seen to be of importance in providing extra periods of time within which augmented tide-raising forces such as those associated with perigee-syzygy can act. This influence applies in particular to those cases in which the Moon is near its maximum possible declina- tions. As will be noted in this same connection, the tidal flooding potential may, therefore, also be increased by the diurnal inequality. The influence of a combined, two-dimensional align- ment of the gravitational forces of the Moon and Sun in both right ascension and declination as the Moon crosses one of its two nodes coincidentally with the attainment of new moon or full moon, producing a solar or lunar eclipse, will be treated in chapter 5. Seasonal Factors Influencing the Production of Heightened Tides As a further extension of the previously outlined prin- ciples relating the positions and motions of the Moon to the amplitudes and durations of the tides, certain seasonal effects also are noteworthy. In summer, the rotational axis of the Earth is tilted toward the Sun. It is, therefore, also inclined toward the position of new moon, which must lie along the line of syzygies and between the Earth and the Sun. This fact implies that, close to the time of the summer solstice, in the Northern Hemisphere, tides experienced during the day should be higher, and those observed during the night should be lower because of the relative gravitational force components involved. These effects are independent of any other hydrographic, oceanographic, or meteorological influences. The inclination of the North Pole toward the Moon not only puts the Moon in the zenith at latitudes farther north, but renders the line of the Moon's gravitational force action shorter and more nearly perpendicular for Northern Hemisphere positions on the side of the Earth turned toward the Moon. The new moon, in line with the Sun, will cross any local meridian about noon, local ap- parent time, and, located centrally in the sky, will exercise its maximum influence in the Northern Hemisphere only during these midday hours. During the full phase of the Moon, just the opposite of the above situation is true, with nighttime tides higher, and daytime tides lower, in the Northern Hemisphere. Since the Earth's axis is inclined away from the Sun ( and toward the full moon on the opposite side of the Earth from the Sun) in winter, the same tide-raising force con- siderations indicated in the preceding paragraph hold but are now related to the full phase of the Moon. The full moon transits the local meridian about midnight, appar- ent time, and its maximum gravitational effects in the Northern Hemisphere are felt only during these late night- time hours. In spring and autumn, with the Earth's rotational axis inclined at right angles to the plane containing Earth and Moon, the tides produced at the two positions of lunar quadrature should be equally high as far as seasonal causes are concerned, but should occur in unequal periods of time. If the Moon is above the horizon at first-quarter phase, the floodtides should be smaller and of shorter duration than the ebbtides; if the Moon is below the horizon at this time, floodtides should be larger and last longer than ebbtides. At last-quarter phase, just the op- posite is true. In spring, also, the conditions at the two quadratures are the exact reverse of those encountered in the fall. Again, all of the above influences are astronomi- cal, and are not inclusive of local effects produced by other causes. Effects of the Phase Inequality and Diurnal Inequality The origin of the phenomenon of phase inequality lies in the synodic revolution of the Moon, which is responsible for the regular succession of lunar phases as seen from the Earth. This phenomenon is characterized by a variation of tidal forces associated with different geometric con- figurations and the resulting vector additions or subtrac- tions of the gravitational forces of the Sun and Moon. \:>2 Strategic Role of Perigean Spring Tides, 1635-1976 Such tidal force variations are caused by the alternating reinforcement of tidal forces created by the alignment of Sun, Earth, and Moon at the position of syzygy, and the opposition of these same forces at the times of lunar quad- rature. A wide range of relative force values exists for all positions in between. The basic concepts of lunar phase production are fully explained in the appendix (fig. 3) and will not be repeated further here. The diurnal inequality is caused by the position of the Moon ( and/or Sun ) over a latitude north or south of the Equator, and results in the two successive high waters and/or low waters being of unequal heights — or in a single low water. This phenomenon is also discussed in the appendix. Certain perturbations of the lunar orbit resulting from the gravitational attraction of the Sun will be described in the next chapter. The special conditions resulting from the combination of perigee with syzygy which constitute the main topic of this work will be reserved for substantive discussion in part II, chapter 4. The foregoing sections of part II, chapters 1 and 2, together with the appendix, provide a reasonably com- prehensive summary of the principal astronomical influ- ences affecting the tides. All of these effects must be con- sidered as acting upon, causing potential modifications in, or adding their contributions to, the particular factors causing perigean spring tides. It must further be empha- sized, strongly and repeatedly throughout this monograph, that the forces producing the tides are of harmonic nature and that none of these effects is totally independent of the other or may be so regarded. Although the isolation of the astronomical elements associated with the production of perigean spring tides of various degrees of intensity and the satisfactory confirma- tion of the special case of proxigean spring tides are ca- pable of direct analytic and empirical treatment, the estab- lishment of the relative tidal flooding potential of such tides, when taken in conjunction with various meteoro- logical factors, is not a simple, straightforward task. The following chapters represent an effort in this direction. Chapter 3. The Action of Various Perturbing Functions in Estab- lishing, Altering, and Controlling the Amplitudes of Perigean Spring Tides In chapters 1-2 of part II, certain standard astro- nomical principles and nomenclatural definitions have been introduced pro forma. These are valid without modification for all conditions in which the gravitational forces present are assumed to act in accordance with Newton's law of gravitation, upon unit or point masses, and in a closed two-body dynamic system, without the intervention of any disturbing functions exterior to the system. Such would be the case if the Moon were re- volving in an unperturbed Keplerian ellipse. However, the presence of the Sun in the system com- plicates matters to a considerable extent by exerting its own very major force influences. This action serves con- tinuously to disturb the motions of both the Earth and the Moon in their respective orbits. The result is to produce so-called perturbations in the orbits of both bodies. In the case of the Moon, the existence of these perturba- tions — through their accompanying changes in ( 1 ) the lunar longitudes, (2) the instantaneous distances (or parallaxes) of the Moon, (3) various of the lunar orbital elements, and (4) the times of occurrence of the phase aspects or configurations, in turn exercises an important influence on the tides. The Effects of Perturbations Upon Lunar Distances and Orbital Motions Lunar perturbations consist of dynamic disturbances in the instantaneous positions and orbital motions of the Moon, resulting principally from the individual gravita- tional attractions of the Sun and Earth, as well as their mutual interactions. The dynamic conditions present be- long ostensibly to the classic problem of three bodies in celestial mechanics. However, the comparative proximity of the Moon to the Earth, the unsymmetrical geodetic configuration and mass distribution of the terrestrial body, and the fact that the orbit of the Moon is in no sense a re-entrant one and permits only the establishment of an instantaneous osculating orbit, result in many nonperiodic variables which cannot be described by standard three- body methods. In lunar theory, the analytic solution of the Moon's orbit involves 36 differential equations, which cannot be treated rigorously. Nonetheless, an empirical knowledge of the orbital mo- tion of the Moon is well established by observations ex- tending over many centuries, and most of the irregular motions of this body resulting from perturbative influences are well known. Only those perturbations which relate to, and have a perceptible effect on, the Earth's ocean tides will be discussed in this work. The astronomical origins of these perturbations as they affect the instantaneous longi- tude and the differential motion of the Moon in this co- ordinate, as well as the eccentricity, major axis, and in- stantaneous shape of the Moon's orbit, the geocentric horizontal parallax, the variable motion of perigee, and the length of the lunar day all will be described in the present chapter. The corresponding influences of these astronomical variations upon tidal parameters will be re- served for chapters 5-6. The Lunar Evection The first and foremost, largest, and earliest discovered influence among the lunar perturbations is the lunar evec- tion. This is a perturbation producing a continuous altera- tion in the shape of the Moon's orbit, and is a function of 153 Ill Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR EVECTION EFFECT TO SUN | /PERIGEE i Nl PERIGEE-SYZYGY LINE OF APSIDES NEAR COINCIDENT WITH LINE OF SYZYGIES ECCENTRICITY OF ORBIT INCREASES; PER IGEE DISTANCE BECOMES LESS; LUNAR PARALLAX IS AUGMENTED ORBITAL VELOCITY INCREASES BETWEEN FM AND NM ORBITAL VELOCITY DECREASES BETWEEN NM AND FM ORBITAL ECCENTRICITY IS EXAGGERATED FOR CLARITY TO SUN PERIGEE-QUADRATURE LINE OF APSIDES NEAR- COINCIDENT WITH LINE OF QUADRATURES ECCENTRICITY OF ORBIT DECREASFS; PERIGEE DISTANCE BECOMES GREATER LUNAR PARALLAX IS REDUCED ORBITAL ECCENTRICITY IS EXAGGERATED FOR CLARITY ORBITAL VELOCITY AT PERIGEE-QUADRATURE S MUCH LESS THAN AT PERIGEE-SYZYGY. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 15!) the relative positions of the line of syzygies with respect to the line of apsides in the lunar orbit (see figs. 26A, B) . The effects of this disturbance upon the Moon's orbital motion are twofold: When the line of apsides and line of syzygies coincide, the Moon moves faster in celestial longitude between the phases of full moon and new moon and slower between new moon and full moon. In addition, when these same two axes come together, the eccentricity of the lunar orbit is increased, producing a redistribution of the Moon's velocity in orbit. Figures 26A, B. — Lunar evection consists of a periodic fluctuation in the eccentricity of the lunar orbit as a func- tion of the phase angle and true anomaly of the Moon (its instantaneous angular differences in longitude from the positions of conjunction and perigee, respectively) . This phenomenon results in changes in the eccentricity of the lunar orbit, produced by the combined interaction of the tangential and normal components of the Sun's gravitational force. To illustrate the effects of evection throughout a com- plete lunar revolution, a condition of perigee-syzygy alignment will initially be assumed. At perigee-syzygy, the tangential component of the solar gravitational force, here applied at right angles to the lunar orbit, is ineffec- tive in altering the eccentricity of the orbit ; however, the normal component of the Sun's force is negatively effec- tive and tends to increase the orbital eccentricity. As the Moon moves from the position of perigee-syzygy, the normal component decreases, while the now-negative tangential component acts to decrease the eccentricity. The superposition of these two forces results in an eventual balance and a condition of zero change in eccentricity somewhere between perigee-syzygy and a point approximately 54°44' along the orbit. Thereafter, the eccentricity decreases until the Moon reaches a posi- tion following apogee-syzygy. As the Moon passes through the vicinity of apogee- syzygy (a position never as well defined as perigee-syzygy) , the same process occurs in reverse as the eccentricity — after a brief interval similar to the preceding during which a balance is reached between the tangential and normal components of force — now steadily increases while the Moon approaches perigee-syzygy. The net result is that, following upon any given align- ment of perigee-syzygy, the effect of evection decreases the eccentricity of the lunar orbit during slightly more than half of a synodical revolution. The eccentricity of the orbit then increases during the succeeding half-revolution, plus a little more. The associated variable gravitational force factors are of greatest consequence in their contribution to tide- raising action in the period just prior to perigee-syzygy, when the influence of evection has collectively resulted in: a maximum increment in orbital eccentricity; the greatest reduction in perigee distance of the Moon; a significant augmentation in the lunar parallax; and a corresponding increase in orbital velocity to add to the Keplerian in- crease in velocity at times of perigee (see the necessary velocity catch-up effects discussed in chapter 6). However, exactly at the configuration of perigee-syzygy, the acceleration in lunar velocity due to this perturbation is zero and, close to the position of perigee-syzygy, it is nearly so. As a result of the previously mentioned increase in the eccentricity of the lunar orbit at perigee-syzygy, the main contribution of the lunar evection to the phenome- non of perigean spring tides therefore comes about through an accompanying marked increase in the geocentric hori- zontal parallax of the Moon. This reduction in the lunar distance at perigee-syzygy, with its corresponding increase in gravitational tide-raising forces, will be treated exten- sively in a later section of this chapter. The influence of this perturbative function will also be discussed later in connection with the differences between mean and true lunar parallax and mean and true lunar longitude. Finally, if a coincidence occurs between the line of apsides and the line of quadratures, the eccentricity of the lunar orbit decreases, and the Moon moves slower at this time. But this circumstance bears no direct relationship to the occurrence of perigee-syzygy responsible for peri- gean spring tides. The Lunar Variation The second important perturbative influence is the lunar variation. Lunar variation is a function completely dependent upon the particular longitudinal orientation of the Sun with respect to the orbit of the Moon. This phe- nomenon is responsible for a continuously changing shape of the lunar orbit. The change in orbital figure takes place through a lengthening of the orbit along an axis at right angles to a force vector extended from the Sun toward the lunar orbit. In its causal relationship, the Moon's variational effect is entirely independent of the angle between the line of apsides and the line of syzygies. However, as the result of the variation, the respective sections of the Moon's orbit on the same and opposite sides of the Earth from the Sun become less sharply curved. The corresponding lunar dis- tances from the Earth are reduced in these two sections by the Sun's perturbational influence. Significantly for the present discussion, if the Moon happens to be simultaneously along this force-axis con- necting Sun and Earth (i.e., the line of syzygies), its dis- tance from the Earth is slightly reduced, and its horizontal parallax is increased. This effect supplements the variable distances imposed by the revolution of the Moon in an elliptical orbit ( the elliptical variation ) and resulting from the opposite orientations of perigee and apogee. However, if the line of apsides and line of syzygies coincide, the 156 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR VARIATION EFFECT (ON VELOCITY) A. DECREASED ORBITAL VELOCITY FQ T v S'-*-" ^--~* INCREASED FIVl/ : G : \NM INCREASED ORBITAL VELOCITY t~ . E . ORBITAL VELOCITY ^^~-~~"~^^ M / T ^ : : S> JlL^-^^^' ^ LQ DECREASED ORBITAL VELOCITY DISTANCES ARE NOT TO SCALE Figure 27A. — The phenomenon of lunar variation results from the considerable range of distances of the Earth and Moon from the Sun (and the corresponding difference between the Sun's gravitational force upon these two bodies) at various lunar phases. At the quadratures, the solar gravitational force acting upon the Moon and the Earth is the same; at the syzygies, the greatest difference in solar gravitational force upon these two bodies exists. On the side of the Earth nearest the Sun, the Sun attracts the Moon away from the Earth with constantly increasing force as the distance of the Moon from the Sun diminishes between LQ and NM. This force is exerted with its predominant compo- nent S x contributing a significant accelerative action parellel to one of the two rectangular components of velocity subject to which the Moon is moving. (The gravitational or centripetal component is directed along MG; the tangential or centrifugal component is exerted along MT.) A velocity accelerating influence is applied cumulatively (the angle of effective force action, < MSE, decreasing while the magnitude of the force itself increases) between LQ and NM. Since, between NM and FQ, the solar force is exerted with its principal component opposite to the corresponding veloc- ity component of the Moon's tangential motion, a negative acceleration (deceleration) results. Thus the Moon's velocity is accelerated between LQ and NM and retarded between NM and FQ. On the opposite side of the Earth from the Sun, between FQ and LQ, the Moon is more distant from the Sun than the Earth is, and the latter body is pulled away from the Moon. The difference in the relative forces of the Sun on the Moon and the Earth increases steadily as the Moon approaches FM. In the gravitational action, the effect is exactly the same as would occur if an imaginary Sun were located at S', at the same distance as S from E, along the line of syzygies extended. For the same reasons above enumerated, between FQ and FM, the Moon's motion is accelerated, with a maximum veloc- ity attained at FM. Between FM and LQ, the Moon's motion is retarded, to a minimum at LQ. The lunar orbital velocity resulting from the effect of lunar variation is, therefore, greatest at the syzygies and least at the quadratures. As seen in figure 27B, correspondingly varying centrifugal forces result in a varying configuration of the lunar orbit. lunar evection can measurably increase the value of the parallax and reduce the lunar distance at the time of perigee-syzygy. The increased tidal forces produced by the diminished distance of the Moon are related to a com- posite of changes in several orbital parameters, as de- scribed below. 1. Alternating Acceleration and Deceleration of the Moon's Orbital Motion The first factor contributing to ultimate variations in the tide-raising forces involves the changing angle between the direction of the Sun from any given point in the Moon's orbit and a tangent line from this same point. The tangent line also represents the instantaneous vectorial di- rection of the Moon's motion in its orbit. At third-quarter phase (fig. 27 A) (except for the small angle subtended by the radius of the lunar orbit at the distance of the Sun) the tangent line from the Moon's orbit is oriented almost directly toward the Sun and the Sun's gravitational force is fully effective in accelerating the orbital velocity of the Moon. As the Moon moves toward conjunction, the angle between the force vector from the Sun to the Moon and the Moon's velocity vector increases from 0° to 90°. At new moon, the Sun's gravitational force vector is directed exactly at right angles to the Moon's orbital motion and exerts a zero influence in producing any change in orbital velocity. Between new moon and first quarter, and again between full moon and third quarter, the situation is just reversed, Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 157 as the angle between the Sun and the Moon's velocity vector decreases from 90° to 0°, and the orbital decelera- tion of the Moon varies from zero to a maximum. Like- wise, the changing angular relationship that exists be- tween third quarter and new moon prevails between first quarter and full moon, but with the Moon's velocity vector now oriented in the opposite direction in the sky. Between first quarter and full moon, the angle separating the two vectors increases from 0° to 90°. In recapitulation of the forces acting, at new moon and at full moon, since the gravitational attraction of the Sun acts at right angles to the Moon's orbital motion, no in- crease in acceleration is produced. However, in moving away from these two positions, the orbital acceleration of the Moon is altered by the Sun's gravitational force and attains maximum positive and negative values when the full force of the Sun is exerted directly along tangent lines to the lunar orbit at the positions of third quarter and first quarter, respectively. 2. Changing Lunar Orbital Velocity With Respect to the Earth A second important influence of the lunar variation results from the combination of the previously described effects and the fact that the Moon moves from a position inside the Earth's orbit around the Sun to a position out- side this orbit during each monthly revolution. If only the effect of the Sun's gravitational influence on the Moon during these revolutions were considered, the resulting lunar motion would be a relatively simple one. Consider, for example, the single effect of the Sun's gravitational in- fluence as the Moon moves from its position of conjunc- tion ( between the Earth and the Sun ) and revolves toward its position of opposition, 180° from conjunction, on the side of the Earth farthest from the Sun. In this outgoing portion of the Moon's motion with respect to the Sun, it would be moving against the Sun's gravitational attrac- tion (and its motion would, accordingly, be subject to a retardation ) . Conversely, on the return portion of its orbit, from opposition to conjunction, the Moon might be thought of as "falling" toward the Sun (and hence ac- celerating in its velocity of motion ) . Such a simplified assumption is not the true case, since the gravitational force of the Sun is also exerted on the planet Earth. This results in the condition actually pres- ent, in which a clear-cut distinction between the forces acting must be observed : When the Earth, Moon, and Sun are aligned at either new moon or full moon, the gravitational attractions of the Sun and Moon tend to reinforce each other in their actions on the Earth's tides. However, in considering the reciprocal forces exerted on the Moon, the gravitational force of the Earth is respectively reduced or increased by that of the Sun at the positions of new moon and full moon. The reasons for the latter circumstance will now be described. In moving from the position of new moon to a position very nearly that of first quarter, the Moon is at all times closer to the Sun than the Earth is, and hence is at all times being attracted more by the Sun, and in a direction slowing the Moon's orbital motion. As the Moon revolves from a path normal to the line connecting it and the Sun at new moon to a path nearly along this line at first- quarter position, the attraction of the Sun upon the Moon is exerted in a direction increasingly more opposed to the Moon's orbital motion. In addition, as the Moon nears first-quarter phase, a small sideward component of lunar deflection increases, directed toward the Earth, but caused by the Sun. This latter circumstance results from the fact that the Moon makes a small acute angle ( as seen from the Sun) with the line connecting the Sun and Earth. The Sun's gravitational attraction exerted along this line possesses a slight component impelling the Moon inward toward the Earth. Both this inward deflection and the fact that the gravitational attraction of the Sun on the Moon is exerted in a direction increasingly more opposed to the Moon's orbital motion (thereby effectively reduc- ing the latter) create the net result of diminishing the Moons orbital velocity with respect to the Earth. In revolving through the first-quarter phase and pass- ing on toward the far side of the Earth and the position of full moon, the Moon moves to a greater distance from the Sun than the Earth has. The attraction of the Sun for the Earth — both because of the Earth's larger mass compared with that of the Moon and the Earth's closer distance to the Sun — becomes greater than the Sun's at- traction for the Moon. Because a relative separation occurs between the Moon and the Earth, the effect of gravitational (centripetal) force in restraining the Moon to the Earth is reduced, and the satellite's own centrifugal force ( associated with revo- lution in orbit and tending to cause an outward deflec- tion of the Moon) is augmented. The radius of curvature of the Moon's orbit is increased, and along this straighter portion of the orbit, the motion of the Moon with respect to the Earth is speeded up. The relative motion between the Moon and Earth is continuously accelerated until the position of full moon is reached and the Moon's orbital r>8 Strategic Role of Perigean Spring Tides, 1635-1976 motion is precisely at right angles to the gravitational force vectors of the Earth and Sun. Conversely, between full moon and third quarter, the Earth is subject to the Sun's gravitational attraction acting in the same direction as that of the Moon's motion. Be- cause the Earth is closer to the Sun than the Moon is during this period, the Moon's velocity with respect to the Earth is effectively reduced. But as the Moon passes third-quarter phase, its distance from the Sun again be- comes less than that of the Earth's distance from the Sun. Responding to the consequent increase in gravitational force, the Moon's motion with respect to the Earth is accelerated as it moves toward the position of new moon. At new moon, this acceleration ceases, since the Moon's motion is here again completely at right angles to a line joining Moon and Sun. In summary, at the syzygies, the Sun decreases the gravitational attraction between the Earth and Moon by separating the one which is closest to it from the other. At the quadratures, the full gravitational force of the Earth on the Moon is effective, undiminished by that of the Sun, which in these cases is exerted at right angles to the force vector joining the Earth and Moon. The explanation of why the Moon, in consequence, travels faster in its orbit at the syzygies and slower at the quadratures is contained in the next section. 3. Changes in Curvature of the Lunar Orbit A subsidiary effect of the lunar variation is a flattening of the orbital curvature (i.e., an increase in the radius of curvature ) at the lunar syzygies, coupled with the creation of a more sharply curved orbit (smaller radius of curva- ture ) at the times of the lunar quadratures. Immediately, however, it must be emphasized that these dynamic ef- fects are small, are superimposed upon, and act as modi- fiers of, the larger and more meaningfully fluctuating orbital parameters of eccentricity, semimajor axis, and mean parallax. The lunar variation involves a small in- dividual difference between the lunar distances from Earth at the times of the syzygies and the quadratures, but only a secondary influence upon the lunar distances at perigee-syzygy. In this connection, the concept of a smaller radius of curvature in terms of a more sharply curved orbit but a slower orbital motion of the Moon should not be con- fused with ( 1 ) a greater orbital eccentricity, which indi- cates only a more elongated orbit, with the most sharply curved portions at the two apsides, or (2) a larger geo- centric parallax which, because of the inverse relationship in its definition, implies a closer distance of the Moon to the Earth, with the closest proximity thereto occurring at the time of extreme perigee-syzygy. At the position of perigee, which lies along the major axis as well as along the line of apsides of the lunar orbit (the former is but a portion of the latter), the curvature of the orbit, all factors considered, remains at maximum (i.e., the radius of curvature is the least). In accordance with dynamic principles, the centrifugal force of the Moon at any point in its orbit varies directly as the square of its velocity of revolution. It is this out- wardly directed force which must be just balanced by the inwardly directed gravitational force of the Earth at any point in order for the Moon to remain in a stable orbit. Since the centripetal or gravitational force of the Earth upon the Moon does not vary except with the Moon's changing distance from the Earth, any change in orbital velocity and in the resulting centrifugal force must be balanced by a corresponding change in the Moon's dis- tance from the Earth. As the Moon changes its distance from the Earth, the radius vector between the Moon and the Earth likewise changes in length. This radius vector also corresponds with the radius of curvature at any point in the Moon's orbit. Therefore, according to the above relationships, when the Moon slows down, the Earth-Moon distance becomes less and the curvature of the orbit becomes more pronounced. Whenever the Moon accelerates and the radius of curva- ture and corresponding circumference of the orbit become larger, the orbital curvature is reduced and the orbit it- self becomes more nearly a straight line. A comparison will now be made between the actual conditions existing in the disturbed (three-body) lunar orbit compared with those that would theoretically exist if only the gravita- tional effects of the Earth on the Moon (two-body prob- lem) were considered. At points 45°, 135°, 225°, and 315° around the orbit from the position of new moon (dividing the orbit into octants ) , the curvature of the disturbed orbit corresponds exactly with that of the undisturbed orbit. At these points, which separate the regions of least and greatest orbital curvatures, the curvature is the same as that in the two- body orbit. Combining these relationships with the previously de- rived conditions of acceleration and retardation of the Moon's motion at various points in its orbit, the following summary of conditions is obtained: between 315° and 45°, and between 135° and 225°, the orbital curvature is the least; between 45° and 135°, and between 225° and 315°, the orbital curvature is the greatest. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 159 Since the actual eccentricity of the lunar orbit is quite small (0.054900489), its undisturbed configuration may, for purpose of graphic representation, be regarded as a circle. The perturbed orbit resulting from the effect of lunar variation alone may then be comparatively repre- sented by the elliptical orbit shown in figure 27B. The Elliptic Variation The elliptic variation is, in actuality, not a true physical perturbation, but a variation of periodic nature in the Moon's motion which occurs as a result of the Moon's monthly revolution around the Earth in an elliptical orbit. As described in part II, chapter 2, this motion results in the Moon's alternating passage through the perigee and apogee positions in its orbit where it is respectively at its closest and farthest distances from the Earth in each monthly cycle. As in all of the other examples of physical perturba- tions, this effect is accompanied by a corresponding in- crease in, and reduction of, the gravitational force ex- erted by the Moon upon the tidal waters of the Earth. The amount of the distance variation, in the present case, can be represented completely by means of a simple quan- titative function, viz., the geocentric horizontal parallax of the Moon. The actual increase in the value of this term at the times of perigee -syzygy — and the augmented gravitational force resulting — will be discussed in several ensuing sections. The minimum parallax of the Moon is 3,235", cor- responding to a maximum possible distance from the Earth of approximately 406,154 km or 252,364 mi; the maximum lunar parallax is 3,692" which corresponds to a minimum Earth-Moon distance of about 355,880 km or 221,126 mi (fig. 41). From a tidal standpoint, the elliptic variation is equivalent to the lunar inequality. The Annual Variation This perturbation in the Moon's apparent position re- sults from the Earth's annual revolution around the Sun in an elliptical orbit, carrying the Moon with it. The origin of the analogous tide-related phenomenon of solar parallactic inequality has been discussed in part II, chap- ter 1. Its effect is that of bringing the Earth, revolving in an elliptical orbit, to a position of closest annual approach to the Sun (perihelion) around January 2-4 of each year, and causing the Earth to withdraw to its greatest distance from the Sun about July 3-6. Tied to the Earth by mutual gravitation, the Moon shares this same motion. The satellite body revolves around the Earth in an elliptical orbit which, subject to maximum perturbations, can cause an overall variation of about 50,274 km (31,238 mi) in distance from the Earth. At the same time, the Moon, along with the Earth, undergoes a larger variation in distance from the Sun caused by the Earth's annual motion in an elliptical orbit. The Sun-Earth dis- tance can vary from about 147,100,000 km (91,408,000 mi) to 152,100,000 km (94,515,000 mi). The Sun-Moon distance will fluctuate over a still greater range, depend- ing on which side of the Earth the Moon is at the time considered. The maximum effect of this variation in terms of re- inforcing the already augmented gravitational and tidal forces associated with perigean spring tides will be evident around the time of solar perigee — the time of closest an- nual approach of the Moon to the Sun — which must occur within one-half of a lunar month of perihelion. The particular consequence of the annual variation is discussed later in this same chapter. The Lunar Reduction One further orbit-refining procedure it is necessary to consider astronomically in the representation of the Moon's precise position is applicable as a positional trans- formation known as the lunar reduction. The necessary corrective factor results from the difference between the Moon's true longitude in orbit and its apparent longitude in the ecliptic as conventionally tabulated. However, any effect upon tide-raising forces resulting from this correc- tive term is so small as to be considered negligible in the present discussion. Differences Between the Mean and True Astronomical Positions of the Moon and Sun As a matter of ready verification (tables 10, 17, 20), because of the Moon's elliptical orbit and the respective perigee and apogee effects upon the orbital velocity as predicted by Kepler's Law, the lunar velocity varies con- siderably throughout both the synodic and anomalistic months. The Moon slows down appreciably between peri- gee and apogee, and speeds up in nearly the same pro- portion between apogee and perigee. For convenience in the prediction of tides, during an early period in which hand-computations were necessary, any permissible means of reducing the computational load 160 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR VARIATION EFFECT (ON ORBITAL CURVATURE) B. MAXIMUM ORBITAL CURVATURE FQ *jT^ ^^\ a //v y\\ i MINIMUM ORBITAL CURVATURE FM E /\ MINIMUM ORBITAL T0 NM CURVATURE SUN ' \ \y xv THE LUNAR ORBIT IS ELONGATED ALONG AN AXIS AT RIGHT ANGLES TO THE FORCE VECTOR BETWEEN THE SUN AND THE LUNAR ORBIT. IV cV ^y D E THIS PHENOMENON IS INDEPENDENT OF THE ORIENTATION OF THE LINE OF SYZYGIES WITH RESPECT TO THE LINE OF APSIDES. LQ AXIMUM ORBITAL CURVATUF (SHORTEST RADIUS OF CURVATURE) ' Figure 27B. — The phenomenon of lunar variation also results in changes in the shape of the lunar orbit. To demonstrate these changes more clearly, the Moon may initially be assumed to move in the circular orbit ABCD rather than in its true elliptical orbit of small eccentricity. As was seen in figure 27A, at FM, the Earth, being closer to the Sun than is the Moon, is pulled away from the Moon. The Earth's gravitational attraction on the Moon is thus decreased, and the centrifugal force generated by the Moon's revolution in orbit exceeds the centripetal force. The radius of curvature increases, the local curva- ture decreases, and this portion of the orbit becomes flattened. At NM, the Moon similarly is pulled from the Earth. Here also the Earth's gravitational attraction for the Moon is decreased, the centrifugal force exceeds the centripetal force, and the Moon's orbit is flattened. The greater is the orbital velocity of the Moon, the more the centrifugal force exceeds the centripetal, and the greater is the orbit-straightening action. As shown in figure 2 7 A, the greatest velocity increase produced by the effect of lunar variation is at the syzygies and the greatest decrease is at the quadratures. Accordingly, the lunar orbit will be flattened to the greatest extent at the syzygies and possess the greatest curvature at the quadratures. Approximately midway between these four positions, the orbital path must pass through points of inflection where the curvature remains unchanged. In the octants (at angles of 45°, 135°, 225°, and 315° from NM) , no alteration in the shape of the lunar orbit occurs from the effect of lunar variation. The unperturbed (cir- cular) and perturbed (elliptical) orbits here coincide. In the case of the Moon's actual elliptical orbit, the same extension of this ellipse along an axis perpendicular to the instaneous direction of the Sun takes place — together with a slight flattening in the orbital curvature close to the two posi- tions where a line from the Sun cuts the orbit. The orbit-distorting effects of lunar variation are simply superimposed upon the true elliptical configuration, adding to the total complexity in the shape of the perturbed orbit. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 161 resulting from the very numerous astronomical terms was highly desirable. The necessary and sufficient calculating procedure, involving minimum complexity, and capable of representing the lunar orbital velocity as well as other related functions, was sought after and instituted. Aver- age values were freely resorted to wherever possible, and are still tacitly utilized in tidal computations. Using basic formulae derived by Simon Newcomb in the late 19th century, the mean longitudes of the Moon and Sun, and various of their orbital parameters, were originally adopted for epochs corresponding to the first day of each year, and these values still appear in standard tidal reductions. In addition, mean values are employed for the daily angular motions (real and fictitious, respec- tively) of the Moon and Sun. The instantaneous mean positions of these two bodies are computed for any date subsequent to a standard epoch by adding their average (mean) daily motions to their positions at the time of the standard epoch. The Derivation of True and Mean Astronomical Positions The actual, observed position of the Moon or Sun at any time, reduced through the application of a correction for parallax to the Earth's center — and with other correc- tions for atmospheric refraction and diurnal aberration duly applied — becomes the true (apparent) astronomical position of the object. It is important to observe at this point that the distinc- tions between observed and apparent positions for the Moon and Sun are the same as those applied generally to the positions of all celestial objects. However, the meanings of true and mean positions as used in the present connection are not the same as those of the terms true place and mean place used astronomically in relation to star positions. For all celestial objects, the observed place is that deter- mined by direct instrumental means by an observer on the surface of the Earth (topocenter), corrected only for errors in the instrument and others dependent on the method of observation (instrument collimation, leveling errors, in- equality of the pivots and V's, index or circle errors, appar- ent semidiameter of the Moon or Sun, dip of the horizon, clock errors, etc.) . The apparent place is a geocentrically referred position (i.e., corrected by application of the geocentric horizontal parallax where necessary) . It also includes reductions for astronomical refraction and diurnal aberration. Thus, in ap- parent place, the observed position is not only referred to the center of the Earth, but is free of atmospheric effects and the light-velocity altering influence of the Earth's diurnal ro- tation. The coordinate system in which the celestial object is referenced still includes the coordinate-altering effects of astronomical precession and nutation. Here any further re- semblance ends between the position-referencing system for the Moon and Sun presently under discussion and an ap- parently similarly designated system for indicating the posi- tions of the stars and other distant celestial objects. By contrast, when the precise positions of the stars are considered, the origin of coordinates is the center-of-mass of the solar system (barycenter) which is very close to the center of the Sun (heliocenter) . Because the distance of the Earth from the Sun and the velocity of the Earth's revolution around the Sun are now additionally involved, corrections for annual parallax and annual aberration, re- spectively, must be applied to the apparent place to yield stellar true place. As in the case of apparent place, true place is still given in a coordinate system which contains the effects of, and is uncorrected for, precession and nuta- tion. The star position is referred to the true equator and equinox of the date of observation. Finally, if a reduction for nutation is applied to stellar true place, the position of the star is represented in mean place. In all other respects except that the stellar position is now referred to the mean equator and equinox of the date of observation, mean place is exactly similar to true place. Mean place also still contains the uncorrected effects of precession. The Assumption of Mean Positions However, for tidal prediction purposes, the average or mean position of the Moon or Sun, referenced to a con- venient zero-point in time by application of similarly aver- aged increments of mean daily motion, is used. The con- cept of mean position as used in tidal computations has been extended to include the mean longitudes of the Moon, the Sun, the position of lunar perigee, the position of solar perigee, the point of intersection between the celes- tial equator and the Moon's orbit (reckoned in the orbit plane), as well as the lunar ascending node. The mean positions and motions are referred to the origin of coordi- nates at an appropriate mean epoch, in each case. The mean positions of these lunar and solar elements together with their mean daily motions appropriate to the years A.D. 1800-2000 are available in table 4 of Manual of Harmonic Analysis and Prediction of Tides 1 (1940). Certain values among the total list also are contained in tables of the Mean Orbital Elements of the Moon and the Inner Planets in annual volumes of The American Ephemeris and Nautical Almanac. The value of the mean motion of the Moon in its own orbital plane is obtained from the relationship 202-509 0-78 lf.2 Strategic Role of Perigean Spring Tides, 1635-1976 "I 360° 360° M Bld ~27.3216Gl d = 13.176396°/ d The mean apparent motion of the Sun is similarly ob- tained from the mean angular velocity of the Earth in its orbit during a sidereal year H C) 360° ^ 360° F 8ld ^365.256360 d = 0.985647°/ d However, because of the elliptical orbits of both the Moon and Earth, the two values determined above in no way express the real (lunar) or apparent (solar) angular veloci- ties of these two bodies on any one day during an entire revolution. The real daily orbital motion of the Moon at perigee will be appreciably larger than the mean value, and the apparent daily motion of the Sun will be measurably faster at perihelion than the respective mean motion. As a secondary step in these computations, the mean value of the lunar longitude, obtained as indicated above, is converted to an approximate true value by the appli- cation of arbitrary reduction coefficients representative of the lunar perturbations previously discussed. In addition, the value of the true parallax of the Moon expressed as a function of the mean parallax for each specified date enters into the tidal computations. Higher powers in these reduction equations are neglected, and various other sim- plifying assumptions are made, under the rationalization that the difference between the true and mean longitude of the Moon never exceeds 7.8° (0.137 radian) and that this latter value differs very little from the sine function (0.136) by which it is subsequently replaced. The justification for this procedure in evaluating the true position of the Moon from its mean position may easily be supported, based on the fact that, for tidal com- putations of the order of accuracy heretofore required, the existing methods are adequate. The differences between the true and mean positions of the Moon are indeed quite small. For all ordinary predictions not subject to the com- putational refinements made necessary by increased knowledge of perigean spring tides, potential tidal flood- ing attendant thereon, and burgeoning coastal popula- tions now vastly more dependent upon these predictions, the approximation would suffice. Furthermore, the maxi- mum differences between mean and true positions in some significant cases (but, as will shortly be seen, not all) occur at times when the tide-raising forces are at their lowest possible values and, therefore, are not seriously affected by these differences. Conversely, at the times of perigee-syzygy, when the tide-raising forces are considerably augmented, that part of the lunar evection term which acts to produce an accelerated motion in longitude, and a corresponding dif- ference between true and mean longitude, completely disappears. However, in subsequent sections, it will be noted that other and equally important tide-producing factors, whose magnitude could vary sensibly with the difference between true and mean place, also occur at perigee-syzygy and are not self-compensating. Further comment on the previously accepted simplifi- cations and assumptions will, therefore, be reserved until certain lunar perturbations and resulting influences pe- culiar to the phenomenon of perigee-syzygy — and the production of perigean spring tides — have been discussed. The Special Perturbative Influences of Lunar Evection and Lunar Variation Hugh Godfray in An Elementary Treatise on the Lunar Theory- (1871) has provided an excellent exposition from which it is possible to derive the effects of the most significant individual perturbations. These establish the differences between true and mean position in the lunar orbit. The effects of these perturbational terms are regarded as corrections to the mean longitude necessary to obtain the true longitude in orbit. By transforming the symbols in Godfray's equations to a compromise of those more familiarly used in The American Ephemeris and Nautical Almanac and other modern sources, the individual anal- ysis of the several terms can proceed as below : Where: X£=the true longitude of the Moon n<£ = the mean daily angular motion of the Moon L'=n^t= the mean longitude of the Moon at any time t L'o=the mean longitude of the Moon &t t=0 e<[ = the eccentricity of the lunar orbit r' =the mean longitude of the lunar perigee at time t=0 r' = (l— c) n^t-\-T' = the mean longitude of the lunar perigee at any time t, assuming a uni- form rate of motion c=an arbitrary factor introduced by Clairaut to indicate that the lunar perigee is itself in motion b = a factor similar in purpose and usage to that of c 7V=the position of the lunar node when the lunar longitude is Xj s=tan N Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 163 & = the longitude of the mean ascending node of the lunar orbit on the ecliptic X = the true longitude of the Sun n Q = ihe mean apparent daily angular motion of the Sun p=— = the ratio of the mean daily angular 71 ([ velocity of the Sun to that of the Moon ( = 0.0748) Z =the mean longitude of the Sun at time t=0 L = n Q t+ L =nipt + L = the mean longitude of the Sun at any time t e ffi = the eccentricity of the Earth's orbit r =the mean longitude of the solar perigee at time t = T = the mean longitude of the solar perigee at any time t. The general equation which includes all of the principal perturbational terms is: X([ (true longitude of the Moon) = L' (mean longitude of the Moon) +2^ sin (cL' — T\)+-e< L 2 sin 2(cL'~ T' ) (elliptic inequality) -f^W sin [(2-2p-c)L'-2L +T' ] (evecticn) +yp 2 sin[(2-2p)Z/-2Z ] (variation) — 3pe Q sin (L— T ) (annual equation) -|s 2 sin2 (bL'—a) (reduction) In keeping with the purpose of this investigation, a de- tailed analysis will be made only of those actual perturba- tional functions which are capable of producing a mean- ingful change in some tide-related parameter at a time of perigee-syzygy. Somewhat simplifying the second additive term in the previous equation, the correction for lunar evection may be written as \ (L =L' + l ^pe (L sin [2(L'-L)-(L'-T')\ Because, at the syzygies, L=L', and since sin \—L' — r')] = — sin (L'—T'), this yields, at either con- junction or opposition \0°). The true lunar position is behind the mean position when the Moon at syzygy is between perigee and apogee (i.e., L'— r'<180°>90°). In the quadratures, the first equation above reduces to \ (L =L' + jpe (L sin [2(90°)-(Z/-r')] and, since sin [180°— (L' — r')]= + sin (L'—T'), 15 X C =L'+- sin (L'-T')' Because the corrective term is now additive, the true place of the Moon lies ahead of the mean place between perigee and apogee and behind the mean place between apogee and perigee. If the line of apsides coincides with either the line of syzygies or the line of quadratures (i.e., if one of the lunar apsides occurs simultaneously with the new, first quarter, full, or third quarter moon), the difference between the true and mean longitudes of the Moon becomes zero. The same zero correction applies also when the Sun is midway between the Moon and either apse. The foregoing analysis relates to the perturbative effect of the lunar evection term alone. It is seen that, at the position of perigee-syzygy, this perturbation function by itself plays no part in altering either the true longitude of the Moon or the difference between the true longitude and the mean longitude thereof. As will be noted later, this is not true, however, of either the eccentricity of the lunar orbit or the instantaneous parallax of the Moon. In actuality, the influence of the lunar evection produces a significant change in the lunar orbit, as discussed in a preceding section dealing with the astro- nomical cause of this perturbation. When the effect of the lunar evection is combined with that of the elliptic inequality, the quantitative result is to alter the eccentricity of the lunar orbit by an algebraic factor i 15 . equal to approximately -^ pe^. 164 Strategic Role of Perigean Spring Tides, 1635-1976 The corrective term, whose complete value is given by the expression — pe^ cos 2(T'—L) is addi- tive if the line of apsides coincides with the line of syzygies, and subtractive if the line of apsides coin- cides with the line of quadratures. Thus at a time of perigee-syzygy, considering the effect of lunar evec- tion alone, the increased eccentricity of the Moon's orbit e\ is related to the former, unperturbed ec- centricity eXZ + |Q-sin 2 <^(X 2 + Y 2 -2Z 2 )] (1) where a typographical correction has been made in the first Y 2 (from Y 3 in Harris' report) . The equations which represent the effects of lunar evec- tion are For semidiurnal tides: X 2 -Y 2 =j£ pe^u* cos (2 g a I -2 U I - c L'r+2 c L r - ■cT'r) (2) penu 4 cos (2 9 a I —2 g L , I i- c L'r—2cLr-\- c T / r) (3) For diurnal tides : XZ= — 77rpe —> 4, and p are constants, and e^, u, and v are small positive variables. Since the sum of the val- ues «* and v* will always be larger than the term — 4u 2 v 2 , all terms in the expression for the effect of lunar evection on the fortnightly type of tide thus contribute toward increasing this type of tide at times of perigee-syzygy. However, the fortnightly constituents of the tide are not of major consequence. 2. Lunar Variation Effects The analysis of the effects of lunar variation upon the heights of semidiurnal, diurnal, and fortnightly tides can proceed in exactly the same way from equa- tions (6)-(8) above. (a.) Within the parentheses of equation (6), the values of the terms 2 q a r and 2 L/ are exactly the same as in the case of semidiurnal tides which are subject to lunar evection. The difference between these terms is also negative as before, and increases numerically with approach to perigee-syzygy. In the present case, the terms —2 c L' r and +2 c r' T exactly cancel out at perigee-syzygy, leaving the cosine of 0° and whatever small negative difference is represented by 2 q a t — 2 Lj . Again, the cosine of this small negative angle (in the fourth quadrant) yields a result for the cosine function which is very nearly the maximum possible value. 23 Both the fraction — and the symbol p 2 are constants, and the coefficient u 4 is numerically very small. Accord- ingly, at a time of perigee-syzygy, all terms in this equation contribute to an increased value of the semidiurnal term X 2 ~Y 2 corresponding to the effects of lunar variation. (b.) As noted, the effect of lunar variation on the diurnal tides, represented by the term XZ, is zero. (c.) Finally, there remains the influence of the lunar variation upon the fortnightly tides, given by the expression k(X 2 + Y 2 —2Z 2 ). In this equation it is obvious that, at a time of perigee-syzygy, the terms + 2 C L T ' and — 2 c L r ' cancel out, leaving cos 0° as the cosine function, and the maximum possible value of unity for this part of the expression. Since the factors ~, 4, 3, and p are all constants, and since u* and v* are always positive and their sum > — Au 2 v 2 , this part of the total expression also is Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 173 always positive, and increasing as the value of either u or v increases. Thus, lunar variation also contributes toward increasing the fortnightly component of the tides at a time of perigee- syzygy. 3. Summary Analysis It now becomes important to see how these various tidal components, as affected by lunar evection and lunar variation, provide a sensible increase in water level to create perigean spring (and, upon certain occasions later to be discussed, proxigean spring) tides. For this, it is necessary to go back to the original, full-length equation ( 1 ) of which these three types of tides form a part. (a.) In a procedure opposite to that used for the separate components of each expression, analysis will begin with the last expression in the series and move toward the first. The expression in X 2 + Y 2 — 2Z 2 rep- resenting the fortnightly components already has been seen to be at its maximum value at perigee-syzygy as the result of both the lunar evection and lunar varia- tion. The constants ^ and ^ in this last expression will not decrease its maximum value. The remaining func- tion ( - — sin 2 J is a function of the latitude of the tide station. As the value of increases, the value of the term in parentheses decreases, so that the effect of the entire expression is to increase the tide heights at perigee-syzygy to a greater extent at low latitudes, with a maximum value at the Equator. (b.) Returning to the second expression in the series for AS 1 — that indicating the contribution of diurnal tides — it was found earlier that, in the case of lunar evection, the effect was to reduce the height of the diurnal com- ponent of the tides very slightly at a time of perigee- syzygy. The presence of the lunar variation exercises no influence at all upon the height of the diurnal tides. ( c. ) Contrastingly, and by no means last in importance, there is the contribution to the increased height of the tides at time of perigee-syzygy provided by the semidiurnal component. As will be revealed in subsequent tide-curve analyses, this component is actually that most significant to the technical concepts of this work. The function X 2 — Y 2 was seen, in connection with both the lunar evection and lunar variation effects, to exercise an influence in augmenting the height of the tides at times of perigee-syzygy. The immediately preceding factor, - cos 2 0, is a function of the geo- graphic latitude and, as in a similar case for the fortnightly tides, implies an increasing effect on tide levels with lower latitude, becoming maximum at the Equator. Finally, there remain common multipliers for all three expressions, involving the constants 3/2, m c , M @ , and p s , and the parameters a^ and e^, which are vari- able because of perturbational effects. Since all of the constants have positive values, providing additive influences, only some major variability in a^ or e^ could conceivably produce a downward adjustment in tide heights, or subtract from the enhanced tides produced by the other factors in the tidal equation. Both <2(j- and e^ increase at a time of perigee-syzygy. The magnitude of a^ becomes dynamically greater due to the perturbations introduced by changing tangential forces as the Moon attains a greater veloc- ity in orbit (its maximum is at perigee-syzygy) and as the value of a^_ itself increases. 2 Where : V([ = the velocity of the Moon in orbit & 2 =the universal (Gaussian) constant of grav- itation ili© = the Earth's mass m([ = the Moon's mass r = 45°, E. or W., and D= 135°, E. or W., and 180°, with the Moon also at perigee, the lunar parallax is either decreasing or increasing in accordance with whether the Moon is receding from or approaching syzygy. Between D = 45° and D = 90°, E. or W., and D = 90° and £=135°, E. or W., with the Moon at peri- gee, the same relationship holds as in the previous sen- tence, but with the parallax increasing with lunar recession from syzygy, and decreasing with approach thereto. For completeness, it must also be noted that when either new moon (D = 0°) or full moon (D=180°) occurs in- dependently of perigee, some increment is added to the parallax provided that M is not 90°. However, the paral- lax increases to a maximum value as M decreases toward 0° or increases toward 180°. The effect of evection on the lunar orbit is temporarily to increase its eccentricity about 20 percent.whenever the Sun crosses the line of apsides of the Moon's orbit (or approximately 40 percent at the times of near-coincidence of perigee and syzygy ) . Both the lunar perigee distance decreases (parallax becomes larger) and the apogee dis- tance increases (parallax becomes smaller) under these conditions. In a geometric relationship similar to that distinguishing between the manner of production of spring tides and neap tides (although enhanced perigean forces are also involved in the present case ) , at perigee-quadra- ture or apogee-quadrature the eccentricity of the lunar orbit and parallax of the Moon are correspondingly de- creased. (See figs. 26 A and 26B.) 3. Effect of the Lunar Variation The cosine term in D alone is known as the lunar varia- tion. It is a function entirely of the lunar elongation, or angular separation in longitude of the Moon from the Sun. Its presence in the above expression for parallax is to cause the Moon's parallax to increase by a maximum of 28" (and the Moon's distance from the Earth to become correspondingly less) at both new and full phase, with a minimum addition to the parallax at first or third quarter. The addition to the parallax from this cause therefore 176 Strategic Role of Perigean Spring Tides, 1635-1976 varies directly from 28" at new moon to 0" at first quarter, to 28" again at full moon, to 0" at third quarter; and to 28" once more at new moon. No further complexities are involved. 4. Summary Analysis It is seen that several different lunar parallactic factors can contribute toward reducing the distance of the Moon from the Earth at the time of a near-simultaneous align- ment of either the new moon or full moon with perigee in the condition known as perigee-syzygy. In general, an in- creasingly larger increment must be added to the base value of the lunar parallax the smaller is the elongation angle between Moon and Sun and/or the closer is the alignment (i.e., the smaller is the difference in time) be- tween perigee and syzygy. All of the preceding maximum increases in parallax result from the near-alignment of, and the reinforcing gravitational forces exerted by, the Earth and Sun upon the Moon's orbit at these times of perigee-syzygy. Such gravitational reinforcements are seen to be a function of the smallness of ( 1 ) the lunar anomaly and ( 2 ) the lunar elongation; and, especially, a very small difference be- tween the angles ( 1 ) and ( 2 ) . Practically speaking, the separation-angle between the line of force action joining the Sun, Earth, and Moon (line of syzygies) and the per- turbed major axis (line of apsides) of the Moon's orbit can attain a value as small as 6 minutes in time. This happened, for example, in the perigee-syzygy alignment of 1931 March 4 (G.c.t.). 4 The actual dynamic effect of the combined gravita- tional forces produced by such a near-alignment between perigee and syzygy is to increase the eccentricity of the Moon's orbit around the Earth. Since the perigee distance q of a celestial object moving in an elliptical orbit is re- lated to the eccentricity e of the orbit through the rela- tionship g=a(l — e), as e increases, q always decreases, for the reasons enumerated in the immediately preceding section. When perigee and syzygy occur at very nearly the same time, the eccentricity of the Moon's orbit increases, and the value of q decreases in proportion. The Moon's perigee distance from the Earth diminishes accordingly. This will later be seen to be the cause of the situation described in this volume as proxigee-syzygy. Two corollary factors are significant in relation to a circumstance to be reviewed quantitatively in chapter 5. At the time of perigee-syzygy, when the differences be- tween these various alignment-angles become zero, the corrective terms necessary to convert from mean parallax to true parallax simultaneously attain their maximum values. The practical consequence is that the differences between true parallax and mean parallax also reach their greatest values at times of perigee-syzygy. Furthermore, a second circumstance provides rein- forcement to a basic precept which appears variously throughout this treatise. The longer the period of time during which the angular differences between these re- spective orbital positions remain near zero, the greater will be the length of time in which the angular additions to the lunar parallax remain at their maximum values. The fact that the Moon, the perigee position in its orbit, and the Sun are all apparently moving in the same direc- tion acts to favor such an extension in time. The comparative rates of daily angular motion affect- ing the positions of the Moon, Sun, and lunar perigee are important in this regard. The mean daily motion of the Moon in longitude ( 13.176396°/ d ) is far greater than that of the Sun (0.985647°/ d ), and the mean daily mo- tion of the Moon is far greater than the mean daily mo- tion of perigee (+0.1114047 d ). Summarizing the preceding numbered subsections — at times of perigee-syzygy, two distinct contributions toward the amplification of the tides result from the particular influence of solar perturbations upon the lunar orbit. These are : ( 1 ) an increase in the lunar parallax, and a corresponding decrease in the lunar distance from the Earth, thus augmenting the gravitational forces acting on the tidal waters; and (2) a lengthening of the period of time within which these augmented tidal forces can act. The two concepts cited provide widespread practical support to a basic theory of tidal reinforcement. In a variety of forms, but always involving the combination of ( 1 ) increased magnitude and ( 2 ) increased duration of gravitational forces, they will find repeated mention throughout this volume in connection with the amplifica- tion of perigean spring tides. At this point in the discussion, while considering factors relevant to item 2, it is important to note the greater length of time within which the Moon will be close to alignment with the position of perigee if the respective true motions of the Moon and perigee, rather than their mean motions, are considered. Several of the effects resulting from the substitution of mean motions for true motions in tidal calculations will form the subject of the section immediately following. (Note carefully the distinction between mean motions and mean positions, since the latter may be more readily determined and adjusted.) The values adopted for vari- ous mean daily angular motions are given in part II, chapter 2. Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 177 The Concepts of Mean Motion vs. True Motion in Relation to the Earth, Moon, and Lunar Perigee The differences between true motion and mean motion as these affect various aspects of the gravitational inter- relationships between Earth, Moon, and Sun are clearly shown in four of the ensuing diagrams. Each diagram illustrates a particular phase of positional inaccuracy resulting from these assumed average motions. 1 . The True Motion of Lunar Perigee Figure 28A is a plot of the motion of the true position of lunar perigee in units of right ascension during a period of slightly more than 1 / 2 calendar years. These positions of perigee were obtained from the positions of the Moon itself in The American Ephemeris and Nautical Almanac. The lunar positions were chosen for the exact times of perigee as tabulated in this same ephemeris. Since, at the time of perigee, the Moon must necessarily occupy this exact position in orbit, the tabulated right ascension of the Moon corresponding to the tabulated time of perigee must also be the position of perigee. When these successive positions of perigee, one anom- alistic month apart, are plotted against the dates of oc- currence of perigee, and a smooth trace is made through the resulting data-points, the sinuous curve of figure 28A is obtained. This illustrates clearly that the position of perigee oscillates back and forth, fulfilling one complete cycle of curve undulation in each 6.25-7.5 month periods The curves thus traced consistently show a point of inflec- tion and an enhanced, average forward motion of perigee corresponding to each case of extremely small perigee- syzygy separation-interval. At these times, the position of the juxtaposed event (representing the Sun, Moon, and perigee aligned in very nearly the same right ascension) occurs exactly halfway along that portion of the curve having the least curvature and whose values are increas- ing in right ascension with increase in time. The period from one perigee-syzygy to the next is approximately the anomalistic month of 27.6 days, but is quite variable * The commensurability between the anomalistic and synodic months is such that, once a very close alignment of perigee-syzygy has occurred, the next comparably close (nonconsecutive) alignment will be either 6.25-6.50 or 7.25-7.50 synodic months later. The exact period depends upon the sequential arrangement and separa- tion-intervals of intervening cases of perigee-syzygy and the varying lengths of the interposed anomalistic and synodic months (see ch. 6, table 17). If the first extremely close alignment of perigee-syzygy occurs at full moon, the next will occur at new moon; thereafter, the phase will alternate in each succeeding set of such close align- ments. between those months which are respectively close to, and removed from, perigee-syzygy. (See fig. 28A.) At the same time that the intramonthly and inter- monthly positions of perigee are oscillating back and forth in right ascension, the average position of perigee as rep- resented by the curve as a whole is moving progressively forward (toward increasing values of right ascension) throughout the course of the year. It is from this net forward movement averaged over a long period of time that the adopted mean daily motion of perigee (amount- ing to +0.111404°/ d ) has been derived. However, the instantaneous, true angular velocity of the lunar perigee is extremely variable and attention al- ready has been drawn to the relationship between its changing velocity and the apparent position of the Sun. This is a perturbational effect, and comes about as a result of the dynamic influence of the Sun upon the Moon's orbit. 2. Short-Period and Long-Period (Averaged) Perturbational Motions of Perigee Figures 28A, 30, 32, and 33 — which are based on the average true motion of perigee during several successive anomalistic months — point to the necessity for applying a rigorous analytic solution to define the direction and amount of this motion at any one instant of time. The purpose is to isolate those perturbational effects of shorter period occurring during a single monthly revolution of the Moon. During such smaller intervals of time, the mo- tion of perigee may be either retrograde or direct as it is intermittently over longer intervals, but the predominant (and hence also the net) motion of perigee is direct over any extended period. The above-mentioned diagrams are plotted using the times of perigee (and either the corresponding right ascensions or celestial longitudes of the Moon and Sun) interpolated from The American Ephemeris and Nautical Almanac. In this process, the positions of the Moon and Sun expressed in either of these coordinates for the time of perigee are obtained directly from the tabulated time of perigee. By definition, the positions of the Moon and perigee at the time indicated for the Moon's passage through perigee must be one and the same. However, such a graphical delineation as here represented showing the ensuing motion of perigee based on successive monthly returns of the Moon to this position involves only an inter- polation by monthly intervals. Although this procedure is sufficiently accurate to indi- cate, as a composite picture, the alternating direct and retrograde motions of perigee during several successive months and throughout the course of the year, the number 202-509 O - 78 i?a Strategic Role of Perigean Spring Tides, 1635-1976 OSCILLATORY MOTION AND PROGRESSION OF MOON'S TRUE PERIGEE AS SHOWN BY RIGHT ASCENSION DATA 1961 1961-1963 ^^ JUL 28.38 AT P y^ AUG 25.76 A. 28 -3 8d J2.h ^^ 28.41 ^^ "\ SEP 23.17 ^^ PERIGEE-SYZYGY (-8h) Aug 25.96 28.12 y^ OCT 21.29 26.92 I NOV 17.21 24.79 """" DEC 12.00 1962 27.58 J JAN 8.58 28.34 \^ m ^„.^y^ FEB 5.92 UJ 2850 © ^^ 5 23.10h^^ pMAR 6.42 ^^x 2846 ^y \ PERIGEE-SYZYGY (-0.5h) wAPR 3.88 AT P ^y " ""Mar 6.43 5 UJ I 28.20 d ft MAY 2.08 UJ 27.46 | MAY 29.54 UJ O JUN 23.83 25.29 2659 JUL 20.42 27.91 AUG 1 7.33 28.34 SEP 14.67 28.46 13.20h^^ OCT 13.13 28.45/- \ PERIGEE-SYZYGY (-10h) NOV 10.58 /"^ 28.13 " "Oct 13.32 DEC 8.71 1963 V 26.62 JAN 4.33 IAN OQOQ 24.96 3 h .5 2 h 5 1 h .5 O h .5 23 h .5 22 h .5 APPARENT RIGHT ASCENSION OF PERIGEE 21 h Figure 28A. — (Discussed in text. Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 179 of data points available is not sufficiently large, nor closely enough spaced, to reveal the pattern of perigee movement over a few days at a time. Several different short-period and long-period motions of perigee must be separately distinguished : a. Analytic computations made possible from the re- duction formulae given in table 16B indicate a variable- speed, short-period retrograde motion of perigee on either side of, and including, the time of perigee-syzygy. This particular retrograde motion is the result of the perigee- syzygy alignment itself, and occurs only in those lunations containing such alignments. b. The much larger and longer lasting net retrograde motion of perigee accompanying certain lunations in the aforementioned diagrams is caused by the perturbational action of the Sun when it is at or nearly at right angles to the line of apsides, with the only opportunity for the Moon to pass through perigee being at quadrature. (See the further clarification under "a" in the explanatory notes in connection with figs. 28B, C, below. ) c. Finally, the year-by-year net forward motion of perigee — resulting from an excess of direct motion in the alternating forward and retrograde movements of perigee in those months containing situations of close perigee- syzygy or perigee-quadrature, respectively — is exemplified by the continuing progre.ssion of this lunar position toward greater right ascensions or celestial longitudes. The situation depicted by these four diagrams accords with the general concept of the motion of perigee during successive orbital revolutions of the Moon. This concept is represented i n classic reference sources ranging from Sir Isaac Newton's Principia, 1686 (proposition LXVI, theorem XXVI, corollary VII, and subsequent manu- scripts in the Portsmouth Collection) through Roger Long's Astronomy in five volumes, 1 764 (book 4, chap. 4, pp. 624-625) down to Forest Ray Moulton's Celestial Mechanics. 2d rev. ed., 1914 (pp. 352-356). More recent and comprehensive mathematical devel- opments of lunar theory have been made by George W. Hill and Ernest W. Brown (see Reference Sources and notes, pt. II, ch. 3), together with the publication of the Improved Lunar Ephemeris, 1952-59 (1954) by the U.S. Naval Observatory. These advances — plus the in- novation of the high-speed electronic computer — have made possible modern analyses such as those represented by the algorithmic expressions contained in the supple- ment to table 16 (table 16B — Refined Reduction For- mulae, para. 3 ) . The retrograde motion of perigee brack- eting the time of perigee-syzygy alignment is described in the immediately following section. 3. The Special Motion of Perigee Close to the Position of Perigee-Syzygy Alignment The Sun's apparent annual motion brings it recurrently to the same celestial longitude as the line of apsides of the lunar orbit, and at varying phases of the Moon. The result is an induced perturbation and angular displacement of the position of perigee. Since this perturbation is some- times in a direct sense of rotation and sometimes in a retro- grade sense, but with the greatest percentage of motion being in the forward direction, the net, long-term effect is the mean progression of perigee around the lunar orbit in a period of 8.849 tropical years. The average motion of perigee is thus +0.1 1 1404° /day or approximately + 3. 043 742° /month. This perturbational angular velocity is a mean value based on the composite forces produced at all possible positions, configurations, and alignments of the Moon and Sun. However, the perturbations of perigee are distinctively affected by the alignment of the Sun, Earth, and Moon at perigee-syzygy as the Moon moves to a position near the line of apsides at the same time the Sun is along this line. The orbital velocity of the Moon always exceeds the ap- parent velocity resulting from the annual motion of the Sun as well as that of perigee in any phase of its oscilla- tory motion. It is, therefore, the motion of the Moon bringing this body, upon occasion, nearly simultaneously to the position of perigee and into a syzygy configuration with the Earth and Sun which permits relatively short- period recurrences of perigee-syzygy alignment. This coincidence of events is responsible both for the phenome- non of perigee-syzygy and the associated special perturba- tions of the lunar orbit. The increases in the eccentricity and semimajor axis of the Moon's orbit due to perturbations by the Sun at the time of perigee-syzygy have been discussed previously. The value of e can then increase by a maximum of 0.023 to a value 40 percent above its mean value (0.05490). Conversely, if the Moon reaches perigee b while in a posi- tion of quadrature with the Sun, the value of e is mini- mized (i.e., if the Sun is at a position along the extended b It is noteworthy that although there are two orthogonal con- figurations involving perigee and either of the quarter phases of the Moon which are possible at the time of quadrature, only one of these represents true perigee-quadrature. The first (and true situa- tion) is the actual arrival of the Moon at perigee while in either of its quarter phases, the Sun then being at right angles to the line of apsides. The alternate, spurious relationship is the arrival of the Sun at the longitude of the Moon's perigee position in orbit, with the first- or third-quarter moon located at right angles to the line of apsides. It is the astronomically defined case, with the Moon physically occupying the position of perigee, which is considered here and is depicted in the top portion of fig. 28B. I HI) Strategic Role of Perigean Spring Tides, 1635-1976 minor axis of the Moon's orbit while the Moon is at peri- gee, the smallest possible eccentricity of the lunar orbit results). The motion of perigee is also affected in varying de- grees by solar perturbations. These perturbations are a function of the phase angle between Earth, Moon, and Sun, and the closeness of alignment between the line of syzygies and the line of apsides in the lunar orbit. The general expression for the angular rate of motion of perigee at any relative longitude with respect to the Sun and at any elongation of the Moon from the Sun is, very approximately: ffl=+0.11°/ d -3.05°/ d cos (I— 2D) + 0.96°/ d cos (1+2D) + 0.82°/ d cos (21-4D) -0.66°/ d cos t. . . . (many higher-order terms have been neglected; note that this motion is projected along the ecliptic rather than in the Moon's orbit plane) where cs=the angular rate of motion of perigee, in longitude, in degrees per day (a minus sign indicates retrograde motion, and a plus sign, direct motion) E=the angular distance, in longitude, of the Moon from perigee. (Note : This value is equivalent to the "average" mean anomaly L used in the computer printout of table 16 — see the introduction to table 16.) Z)=the lunar elongation, or angular separation of the Moon from the Sun, in longitude With the Moon at perigee, £=0°, and this equation reduces to: s> = _0.55°/ d -2.077 d cos 2D + 1.26°/ d cos4i)-0.267 d cos6Z). . . . At perigee-syzygy, the corresponding value for the rate of motion of perigee becomes approximately : At either new moon (£=0°, £>=0°.) or full moon (1=0°, £>=180°), a=-1.6°/ d . And (with t=0°, £=90°) for perigee at first or third quarter, a= + 3.0°/ d . Hence, with the Sun at right angles to the line of apsides, and the Moon at perigee and either first or third quarter (see fig. 28B), the motion of perigee is direct, with an angular velocity of approximately +3.0°/ d . In a situation possible only in a different lunation, as the Moon approaches perigee-syzygy at either new or full phase, an induced small retrograde motion increases steadily in magnitude, reaching a maximum velocity of — 1.6°/ d at the time of perigee- syzygy- (See also par. 1 under "Tidal Force Evaluat- ing . . ." in ch. 5.) Thereafter, the direction of mction remains retrograde, but the negative angular velocity diminishes toward zero and then turns positive. At apogee- syzygy, o=+3.3°/ d , approximately. The net result of this retrograde motion of perigee in the vicinity of perigee-syzygy is to prolong slightly the period of time in which perigee and syzygy are close to each other. Thus, immediately prior to a perigee-syzygy alignment, with the motion of the Moon and perigee being in opposite directions and their relative (head-on) velocities increased to a maximum, a tendency exists to hasten the time at which the Moon reaches the position of perigee-syzygy. Subse- quent to the perigee-syzygy alignment, with the motion of perigee in the same retrograde direction as before, but diminishing in velocity, the effect is to keep the position of perigee in the vicinity of syzygy for a slightly longer period. The greater duration of time in which perigee remains in the vicinity of syzygy, together with the dual reinforcement of gravitational forces resulting from this near-alignment, yields a correspondingly increased tide-raising potential. This phenomenon will be discussed further in chapter 6 along with other factors producing an extension of the in- terval during which enhanced gravitational forces act at the time of perigee-syzygy. Explanation of the Short-Period Motions of Perigee In figure 28B, the positions of an hypothetically unper- turbed lunar orbit and that of the actual perturbed orbit are shown. The latter orbit is a function (among other factors) of the changing value of e produced by the gravitational attraction of the Sun. As has been shown earlier in this chapter, the perigee dis- tance (q) of the Moon from the Earth is given by: q = a(l — e) where a and e represent the semimajor axis and eccentricity of the lunar orbit, respectively. a. It also has been noted previously that, at the time of perigee-quadrature, both the eccentricity and semimajor axis of the lunar orbit decrease (the former relatively faster than the latter), the value of the perigee distance increases, the curvature of this part of the lunar orbit becomes less, and the perturbed orbit lies outside the unperturbed orbit. This situation is illustrated in the top portion of figure 28B. ( For comparison, the phenomena of perigee-quadrature and perigee-syzygy have been plotted simultaneously on the same diagram, and the primed symbols corresponding to the position of perigee-syzygy alignment should, for the moment, be completely disregarded. These two phenomena do not, of course, occur together in any single lunation.) In the present analysis, the position A/ 7 corresponds to the position of the Moon at a time approximately 7 days prior to the alignment of the Moon with the Sun at con- junction. The assumption is here made that no perturbing effects on the lunar orbit due to the Sun are present. The position P 7 similarly indicates the original position of perigee toward which the Moon is moving in this undisturbed orbit. However, subject to the action of solar perturbations, the value of q increases and the perturbed orbit results. To con- Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 181 MOTION OF LUNAR PERIGEE 7 o B- AC ~o\:Z- o\o rrv\ -rv tf>\ PERTURBED ORBIT \M ^^: " ^ ^ PrA f^^ "pT~~ M 7 ~— ______^ UNPERTURBED ORBIT M 3 y^ \ // q °\ ^7 S'1- LINE OF A , ^ f j M'o \ a o ■ / p'o q'o ^^ E APSIDES u ^ p 3 SO b Figure 28B. — The positions of perigee -syzygy (P' M' ) and perigee-quadrature (P M ) are plotted on the same diagram to show the opposite motions of perigee — retrograde at perigee-syzygy and direct at perigee-quadrature. The location of the perturbed orbit outside the unperturbed orbit at quadrature, inside it at conjunction also is indicated. See the text discussion under "Explanation of the Short-Period Motions of Perigee." form with this change in the distance of the Moon, beyond the position M 7 the path of the Moon swings outward from the Earth, producing the new orbital arc M 7 P . Matching the Moon's motion in the same period of time, the position of perigee moves outward to establish an increased perigee distance q at position P , very close to M . It is readily apparent from the diagram that the arc distance M 7 M is longer than the original span of the Moon's motion M 7 P 7 necessary to reach perigee. The net effect is to displace the original perigee position P 7 along the arc P 7 P , which possesses a continuously in- creasing radius with respect to the Earth. This displace- ment is evidenced as a direct motion of the lunar perigee. The amount of the forward movement is a maximum in this case near perigee-quadrature. This motion represents a short-period displacement of perigee during only a portion of one lunation. As such, it provides only a partial contribution to the average perigee motion over the entire lunation and throughout successive lunations. These short-period motions of perigee near peri- gee-quadrature and perigee-syzygy are, as a seeming para- dox, exactly opposite to the average perigee-to-perigee mo- tions shown in figures 30 and 32. It must be remembered, however, that the angular velocity of the Moon is the great- est during the perigee portion of its orbit, and it covers this portion of the orbit in the least number of days. Hence, the cumulative effect of the motion of perigee in that half of the orbit containing perigee is the least and is overshadowed by the cumulative effect of perigee motion during the Moon's passage through the opposite half of its orbit, com- pleted over a greater number of days. b. It has further been demonstrated previously that, at the time of perigee-syzygy, the value of e increases in the lunar orbit due to the effect of solar perturbations, and at a faster rate than a increases. A retrograde velocity of perigee becomes quantitatively significant at M 3 , some few days prior to lunar conjunction with the Sun, and reaches its maximum value when the perigee-syzygy alignment (M ') is reached. In this approach interval, the value of q continu- ously decreases (i.e., the lunar parallax becomes steadily greater) . In figure 28C, the path of the Moon close to the time of perigee-syzygy has been enlarged from figure 28B in order better to show the relationships between the perturbed and unperturbed orbits of the Moon. In this figure, the posi- tion P 3 represents the original position of perigee toward which the Moon is moving in its undisturbed orbit, from its initial position M 3 . The distance q ' represents the corre- I ,'52 Strategic Role of Perigean Spring Tides, 1635-1976 Figure 28C. — Enlargement of the left portion of figure 28B, defining the retrograde motion of perigee at the time of perigee-syzygy. sponding perigee distance of the Moon from the Earth in this undisturbed orbit. In a period of 1 day the Sun, in its apparent annual motion eastward in the sky, has moved from Si' to S f . As the Moon also moves eastward toward the position of perigee-syzygy alignment (M n 'S ' or P '), the Sun's pertur- bational influence due to this alignment acts to increase the eccentricity of the lunar orbit, correspondingly reducing the value of q. The path of the Moon beyond M 3 in turn swings nearer to the Earth to accommodate this reduction in the perigee distance, thus producing the new orbital arc M 3 M '. It is obvious that the arc M 3 M ' necessary for the Moon to reach the new position of minimum distance {q ') from the Earth is shorter than the original arc M 3 P 3 . The physical result is to displace the original perigee posi- tion P 3 along the arc P 3 P ' possessing a continuously short- ening radius with respect to the Earth. This displacement action is evidenced as a retrograde motion of the lunar perigee. The amount of the retrograde displacement be- comes greater, the greater is the reduction of q (i.e., the closer the position of perigee is to alignment with syzygy). The maximum retrograde motion therefore occurs at the time of perigee-syzygy. After the Moon passes through this position (Po')j the retrograde motion of perigee decreases again. ***** 4. Comparison of True and Mean Motions Another way of representing the difference between the mean and true motions of perigee is by means of a graphic comparison of the relative motions of the Sun and Moon, plotted in the true and mean systems of reckoning. These comparative motions are illustrated in figures 29-30 and 31-32. In these diagrams, the angular position of the lunar line of apsides corresponding to a very close align- ment of perigee-syzygy (1962 Mar. 6.5), as well as the positions of the Sun during the course of this same year, are indicated as the Sun apparently revolves around the Earth in consequence of the Earth's actual annual revolu- tion around the Sun. The family of concentric ellipses shown represents the successive monthly cycles of revolution of the Moon. Dou- ble-shafted arrows indicate the corresponding monthly motions of perigee. Figures 29 and 3 1 portray the mean motions of perigee, as they are assumed, for convenience in computation, in tidal theory. Figures 30 and 32 repre- sent the true motions of perigee. As noted earlier, succes- sive lunar orbitings are in no sense re-entrant ones, but continuously fail to close on the same position as the result of perturbations encountered in any one revolution. Ac- cordingly — without loss in factual integrity — the Moon may, for greater ease in graphic presentation, be depicted as revolving, month by month, in the separate orbits in- dicated. These are drawn to successively smaller sizes to prevent overlapping and confusing crossovers between the adjoining elliptical paths. According to the assumption of a perturbationally in- duced, but constant, mean daily motion, the Moon's peri- gee is conceived to move in a counterclockwise direction in the orbital plane, with the previously stated mean angular velocity of +0.1 1 1404°/ d . The rather sizable differences between this value, adopted for computational convenience, and the constantly changing lunar velocity which actually prevails is revealed by a comparison of figures 29 and 31 with figures 30 and 32. When the true motion of perigee is plotted, over suc- cessive months, from the same data used to construct figures 30 and 32, the considerable differences between the true and mean motions is evident. The maximum true motion in orbit may be determined by taking the total angular distance through which the Moon revolves in orbit during an anomalistic month (a time period which is itself subject to a considerable variation in length — see table 17), and dividing this angle by the exact period between consecutive perigee-syzygies. By this means, the true average angular velocity of perigee in an anomalis- tic month containing a close perigee-syzygy alignment is found to be some 0.55 VS or approximately five times that assumed for its mean motion during this same interval. Selecting, as a starting point, and representative ex- ample, a date when the position of the Sun first comes within less than 30° of alignment of the line of apsides of the lunar orbit (on 1962 Jan. 8.5, in figure 30), the Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides !:>;;, SUN=0 JUN 24.0 O 92 MAY 29.5 O 67* APR 4.0 O LONGITUDES GIVEN ARE MEAN GEOMETRIC POSITIONS REFERRED TO THE MEAN EQUINOX OF DATE MEAN MOTION OF THE LUNAR LINE OF APSIDES 1962 JAN 8.5 - JUN 24.0 Figure 29. — (Discussed in text.) subsequent motion of lunar perigee can be closely ob- served. As the longitude of the Sun comes increasingly closer to that of the perigee position during the immedi- ately following months, it is obvious that a marked accel- eration occurs in the true motion of perigee. (The perigee attains an average angular velocity of some 16° in 28.5 days, or 0.56° / d between the perigee-syzygy alignments of Jan. 8.5 and Feb. 6.0 depicted in figure 30.) This forward motion of the line of apsides (and with it the Moon's perigee position ) continues for several suc- cessive anomalistic months ( at an average angular veloc- ity of between 0.54°/ a and 0.56° / d in the example shown). The largest forward angular motions of peri- gee are generally centered around that perigee-syzygy date (of several always occurring in a row) when the separation-time between perigee and syzygy is the least of the series. Such maximum values in the forward angu- lar motion of perigee usually do not occur during more than three successive months (or, at the absolute maxi- mum, during four successive months) in any one perigee- syzygy cycle. Following upon these maxima in perigee motion, the separation-time between perigee and syzygy becomes larger, and the forward motion of perigee diminishes. Some 4/ 2 to 5 months after the first considerable forward motion of perigee began, this motion reduces to 0°, and thereafter reverses in direction. Thereafter, the motion of perigee continues in a retro- grade direction, and again this motion accelerates (in the period of regression illustrated in fig. 32, for example, to an average angular velocity of 0.98° / d ). The retrograde motion is maximum at the time the Sun lies approximately at a right angle to the line of apsides. The motion dimin- ishes rapidly as the longitude angle between the Sun and perigee further increases. ( The latter angle is nearly that which, in the plane of the lunar orbit, separates the Moon L84 Strategic Role of Perigean Spring Tides, 1635-1976 SUN = Q MAY 20 2 LONGITUDES GIVEN ARE APPARENT GEOCENTRIC POSITIONS REFERRED TO THE TRUE EQUINOX OF DATE DEC 8 5 O TRUE MOTION OF THE LUNAR LINE OF APSIDES 1962 JAN 8.5-JUN 24.0 Figure 30. — (Discussed in text. from perigee and is known as the true anomaly.) By con- trast with the direct motion of the line of apsides, the retrograde motion usually lasts for only two or, at most, three months between the two forward-moving cycles of perigee which normally occur in any one calendar year. Since the forward (counterclockwise) motion of perigee takes place during approximately 4/ 2 months of each year, while the retrograde motion generally occupies only 2-3 months, the net result is an average, cumulative for- ward motion of the axis connecting perigee and apogee which is known as the progression of the lunar apsides. Both the averaged, long-range, forward motion of peri- gee and the intermittent retrograde movement may be further graphically illustrated by preparing, for the same close perigee-syzygy situation in each case, a comparative plot of the true and mean motions of perigee with respect to the time, as shown in figure 33. This diagram repre- sents, in a somewhat different form, the same astronomical event of this type depicted in figure 30, and which was associated with the great mid-Atlantic tidal flooding of 1962 March 6.5. In this diagram, the mean motion of perigee is de- rivable from its successive positions in mean longitude along the straight line a— z. The corresponding true motion of perigee may be obtained by taking differences in true longitude from the curve b-y. Forward motion occurs from b to n, retrograde from n to q. 5. The Minor Sinusoidal Variation Between True and Mean Longitude Finally, the effect of the previously discussed perturba- tions in causing a small but measurable difference be- tween the mean and true longitudinal positions of the Moon is shown in figure 34. The diagram represents a period of approximately 2 lunar months. It is immediately apparent that, in terms of the small incremental function in longitude it is necessary to apply Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 1 85 SUN=0 LONGITUDES GIVEN MEAN GEOMETRIC POSITIONS REFERRED TO THE MEAN EQUINOX OF DATE THE LUNAR LINE OF APSIDES 1962-63 MAY 29 5 -JAN 4.5 Figure 31. — (Discussed in text.) in order to convert mean positions of the Moon to true positions, the correction becomes 0°0' at times of both perigee and apogee. At these two positions in every luna- tion, the straight line representing mean longitudes of the Moon and the sinusoidal curve representing the deviation of positions in true longitude from those in mean longi- tude come together. Hence, any variation in lunar gravitational force or in tide-raising potential resulting from the difference in position of the Moon in these individual coordinate sys- tems is of no consequence at either of these two lunar apse positions, or at times of perigee -syzygy. Paradoxically, the effect is exactly the opposite to that encountered under the analogous requirement for apply- ing corrections to mean parallax to achieve true parallax. In this previously discussed case, the differences between true and mean parallax were found to reach a maximum at times of perigee-syzygy. Subordinate and Counterproductive Effects on Perigean Spring Tides Certain ancillary tidal influences are in no way as- signable as direct causal factors in the production of perigean spring tides. However, because of their general dynamic influence upon all types of tides, they may play a significant role in either increasing or decreasing the amplitude of perigean spring tides after these have been generated by their own causal factors. Other actions present among the broad range of gravitational forces mav be definitely counterproductive in connection with perigee springs, or any other tides. In this concept of providing a potential modification of existing forces and actions, these secondary influences will be included here. Other important astronomical, oceanographic, and hydrographic factors contributing to the maximization of perigean spring tides will be discussed in the next chapter, i;-;h Strategic Role of Perigean Spring Tides, 1635-1976 SUN^O O *S MAY 29.5 ^ O MAY 2 O MAR 6.5 O ;45 LONGITUDES GIVEN ARE APPARENT GEOCENTRIC POSITIONS REFERRED TO THE TRUE EQUINOX OF DATE TRUE MOTION OF THE LUNAR LINE OF APSIDES 1962-63 MAY 29.5 -JAN 4.5 Figure 32. — (Discussed in text. and both the additive and partial amplitude-negating effects of wind and atmospheric pressure will be covered in chapter 7. Effects of Declination on the Tide-Raising Forces In figure 35, a tidal force reference system is defined by the rectangular coordinate axes x, y, and z- In this reference system, the xz plane represents that of the Moon's orbit and xy (the plane of the paper) a plane at right angles thereto, containing the zenith of the observing station S, located on the surface of the Earth. The angle in the xy plane represents the angular distance of the zenith above the Moon's orbital plane, and therefore is also equal to the zenith distance of the Moon. The declination of the Moon is given by 5^, so that the geographic latitude of the observation station, =0-\-b^. The distance of the place of observation from the center of the Earth is designated by p. In the plane of the paper (i.e., with the Moon on the local meridian of the place ) , the total gravitational force of the Moon at S is indicated by the force vector F, which is resolvable into two components X, parallel to x, and Y, parallel to y. The angle H represents the angular altitude of the Moon above the horizon. D is the distance of the observing position from the center of the Moon, and R is the distance between the center of the Earth, O, and the center of the Moon, C. The respective tide-raising components of force in terms of X, Y and Z are : 2x -.'/. R 3 Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 187 Since the gravitational force potential is related to each of these components by the relationships x= dU. Y= dU. dx' dy' dU dz' the value of this potential can be derived by integra- tion as follows: TT _9U,SU,9U U ~dx + dy + dz mf 2xdx -hj ydy -^j' where f<£ = the zenith distance of the Moon =0, the angular distance of the zenith above the plane of the Moon's orbit 5([ = the lunar declination /*,(£ = the hour angle of the Moon <£=the geographic latitude of the observing position Substituting the trigonometric portion of the tidal force potential, (3 cos 2 0—1) from its previous deri- vation, and letting ^ = 6: 3 cos 2 0—1 = 3 [sin S^ sin + cos 5(i cos h] 2 = 3 [sin 2 5 + 2 (sin 5([ cos 8^ sin <£ cos 4> cos h^) + cos 2 8(i cos 2 h([_ cos 2 ] — 1. Since sin 8q_ cos 8^ = - sm ^C and sin cos <£=- sin 2, AS- i(s-:Xs)I 3 sin 2 8 d sin 2 + ^(sm 25(j; sin 2 cos h^) +3 cos 2 8$. cos 2 h(i cos 2 - 1 ;;;; Strategic Role of Perigean Spring Tides, 1635-1976 20Cf 200 ANNUAL PROGRESSION OF SYZYGIES AND APSIDES (IN TRUE LONGITUDE AND MEAN LONGITUDE) -1962- [ JAN I FEB I MAR I APR I MAY I JUN I JUL I AUG I SEP I OCT I NOV I DEC ] Figure 33. — (Discussed in text.) For a location at the Equator, 0=0, and in this Similarly, when the Moon is on the meridian, h^ = 0° position: which has a significance in tide-raising action de- scribed particularly in chapter 6. For h^_ = 0: AS =f(g)(|) 3 [ 3cos25 ccos^,-l]. AX s(s-:x§)w 8 c-i Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 189 COMPARISON BETWEEN TRUE AND MEAN LONGITUDES OF THE MOON WITH POSITION IN ORBIT 1962 True Mean Feb Long. Long. NM 5.00 315.60° 317.71° PS 5.46 322.54 323.75 P 5.92 329.49 329.79 FO 11.65 52.37 45.39 FM 19.55 150.37 149.48 A 20.88 166.09 166.49 L 2 7.66 248.59 256.28 1962 True Mean Mar Long. Long. P 642 345.1 345.31° PS 6.43 345.25 345.45 NM 6.44 345.40 345.60 FQ 13.19 82.07 74.62 A 19.88 163.06 162.65 FM 21.33 180.22 181.82 L 29.17 277.94 285.18 Figure 34. 4 6 8 10 12 (Discussed in text.) or the tidal height is a fixed function of the constants indicated, and varies directly only as cos 2 8^. Maximization of Declination in the 18.6- Year Period of the Lunar Nodical Cycle Another tide-modifying factor which has a direct con- nection with the lunar declinational effects above de- scribed is the lunar nodical cycle. This involves a periodic revolution of the Moon's line of nodes in a westerly or retrograde direction around the lunar orbit. (The line of nodes is the axis joining the two points, 180° apart, at which the orbit of the Moon crosses the ecliptic. ) The slow, retrograde motion of the nodes is the result of perturbations induced in the lunar orbit by the Sun's gravitational influence. Since the Moon's orbit is inclined to the ecliptic by some 5°9' (the actual value may range from 4°56' to 5° 20' due to other perturbations), the Sun continuously strives to pull the plane of the Moon's orbit into its own plane, that of the ecliptic. However, in accordance with the laws of precessional motion in rotating bodies, in- stead of this action being completed, an alternate motion is introduced at right angles to the applied force. This I'd) Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR DECLINATIONAL EFFECT ON THE TIDE-RAISING FORCE NOTE : FOR CLARITY IN GRAPHICAL REPRESENTATION, THE MOON IS SHOWN IN A POSITION CLOSER TO THE EARTH AND AT A GREATER DECLINATION THAN IT EVER ACTUALLY ATTAINS. Figure 35. — (Discussed in text. results in a revolution of the pole of the Moon's orbit around the pole of the ecliptic. At the same time, rather than any permanent change occurring in the inclination of the Moon's orbit, the nodes shift westward and complete one circuit of the lunar orbit in 18.6 years. This regression of the nodes along the ecliptic gradually alters the maximum angle which the orbit of the Moon can make with the celestial equator. The average angle of inclination of the Moon's orbit with the ecliptic is the aforementioned 5° 9', and the average angle between the celestial equator and the ecliptic (termed the obliquity of the ecliptic) is 23°27'. Because of the geometric rela- tionships involved (see fig. 36), the separation between the lunar orbit and the celestial equator may range, over one-half the nodical cycle, from the direct sum of these angles to the simple difference between them. Thus, when the Moon's ascending node coincides with the vernal equinox, the maximum declination (either pos- itive or negative) of the Moon is 23.5° +5°, or 28.5°. When the Moon's descending node coincides with the vernal equinox — and the ascending node coincides with the autumnal equinox — the value of the maximum decli- nation is only 23.5°— 5°, or 18.5°. The first condition re- sults in a corresponding range of 57° in lunar meridian altitude; the second produces a range in meridian altitude of only about 37°. The above-mentioned variations in lunar declination, involving a maximum semimonthly range of — 28.5° to + 28.5°, and a minimum semimonthly range of —18.5° to +18.5° occur, under the appropriate circumstances at times which are one-half of a nodical cycle, or 9.3 years apart. The effect of this variation in increasing or decreas- ing the Moon's orbital velocity at certain epochs in the Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 191 nodical cycle is shown at the end of the present chapter ( Case 2 ) . This readily verifiable phenomenon leads quite naturally to another related aspect of the lunar declina- tional influence on the tides which is of direct importance to the present discussion. Aside From a Lack of Onshore Winds, Why Does Coastal Flooding Not Occur With Every Perigean Spring Tide? The principles of scientific method require the applica- tion of a series of negative as well as positive tests for the adequacy of any scientific hypothesis. Specifically, this necessitates the fulfillment of both the negative and posi- tive premises in the classic set of syllogisms: "If p is true, q is true; if p is false, q is false," described as equivalent propositions in deductive logic. As space permits, an effort will be made throughout this work to include such a positive-negative balance of supporting checks. (A meaningful example is the inclu- sion, in table 27, of a realistic sampling of cases of ex- tremely high astronomical flooding potential, yet total absence of any tidal flooding, despite the extremely close perigee-syzygy alignments. These situations are clearly ex- plainable, however, by means of the accompanying weather maps as lacking the necessary contribution of on- shore winds.) The first of two examples entails an equally accountable reduction in the flooding potential of perigean spring tides under certain conditions. The accompanying analysis also helps to answer the very cogent question "Why does tidal flooding not occur at every close alignment of perigee and syzygy?" Each of the examples under discussion involves the ap- parent daily motion of the Moon on the celestial sphere. In both instances, actual daily changes in lunar right ascension have been obtained from The American Ephemeris and Nautical Almanac for the dates concerned. As an extension of the similar, although more general example in part II chapter 2, it is now possible to evaluate these two separate situations in which the combined ef- fects of the Earth's diurnal rotation and the Moon's orbital motion are incorporated. One definitely significant aspect shown by the results of the subsequent computations is the strong likelihood that a perigee-syzygy alignment occurring in the first of the two circumstances under consideration will have a rela- tively small tidal flooding potential. This is despite the simultaneous presence of other generally favorable tide- building forces and conditions. The foregoing statement, it is emphasized, defines an event of lesser statistical probability, but does not imply total exclusion. This assertion should in no way be inter- preted to mean that tidal flooding will not ensue when a situation of large lunar declination occurs at the same time as perigee-syzygy. An exception is particularly possible where the Sun is in an exactly opposite (or similar) declination and therefore in the same plane as the Moon, and the production of a large lunar parallax results from this circumstance (see table 13). Furthermore, conditions may exist where the additional tidal range induced by the phenomenon of diurnal inequality associated with a large lunar declination is locally important to the pro- duction of flooding. Finally, yet another exception to the previously stated example exists in the second case of the two which follow, illustrating the oppositely acting effects of an extreme lunar declination. It is necessary, at this point, to distinguish between these two different circumstances which arise from the 18.6-year nodical cycle and which involve, respectively, the association of a perigee-syzygy situation with : 1 . A path of extreme lunar declination, resulting in a corresponding very large inclination between the lunar orbit and the celestial equator — with the Moon being on or near the celestial equator at the time of perigee-syzygy. 2. A flattened peak of the declination curve, combined with an extreme maximum in lunar declination, thereby permitting a correspondingly large lunar motion in right ascension — the Moon being at this high declination at the time of perigee-syzygy. These two cases will be discussed from their contrasting points of view, first in an analytic fashion, and then by the application of actual numerical data. The first example selected for investigation occurred on 1950 April 2. In this case, the coincidence between the ascending node of the lunar orbit and the vernal equinox just prior thereto produced ( 1 ) an extreme declination of the Moon and, in consequence, (2) a maximum angle of inclination between the Moon's orbit and the celestial equator. The situation presented is one in which, near the celes- tial equator, the component of declinational movement of the Moon (see analogous curves of figs. 44, 152) is very large, while the movement in right ascension as a function of steep orbital inclination alone is small. As noted earlier, unless this factor is offset by a large parallax (e.g., at perigee-syzygy) it tends to reduce the possibility for a protracted tidal day. The declinational motion of the Moon likewise remains large throughout l92 Strategic Role of Perigean Spring Tides, 1635-1976 most of the lunation, producing relatively sharp-pointed peaks at the two declination maxima. This results in com- paratively short periods of time in which the corresponding motion of the Moon in right ascension remains at or near its own largest values (i.e., at the top of the crest and at the bottom of the trough of the curve, where the slope is zero, and where most of the Moon's motion is in right ascension ) . Combined Effect of Changing Parallax and Large Declination on the Moon's Hourly Motion in Right Ascension The major influence controlling the apparent hourly motion of the Moon in celestial longitude, AA^, is the Moon's instantaneous parallax, with but little contri- bution from celestial latitude because of its small value, even at maximum. By contrast, the Moon's motion in right ascension, Aa c , is strongly affected by its corre- sponding position and motion in declination. Although the Moon's movement in right ascension, as in celestial longitude, is duly influenced by its variation in orbital velocity between perigee and apogee, this is by no means the sole contributing factor in its apparent daily and hourly motions. There is no consistent, one-to-one correlation between the hourly motion of the Moon in right ascension and any single astronomical circumstance — because of the harmonic interrelationship between all parameters in- volved. However, the following general principles may be deduced covering the various major factors of influ- ence. All deal specifically with the Moon's relative motions in right ascension and declination, as a cofunction of its instantaneous position in declination: 1 . Exclusive of the effects of parallax, the two times at which the maximum hourly motions of the Moon in right ascension occur in any one month are usually less than a day from, but rarely exactly coincide with, the two times of maximum declination during this same lu- nation. (See also paragraph 3, below.) As the positions of the respective semimonthly peak and trough of the curve of Sj plotted against a(L or time (fig. 44) are reached, and the value of the slope A5 ff Ma c becomes equal to zero, all of the Moon's motion occurs in a. Accordingly, the maximum value of Aa^ also occurs very nearly at the time that AS € reaches its zero value. The value of Acxj is always positive, since the direction of the Moon's movement is continuously counterclockwise. 2. The two maximum values of Aa c which occur in each synodic month consist of a larger maximum and a smaller maximum. These may occur for either (+) or (— ) values of 6 C and without regard to the sign of A5<£. The two distinct maxima having dif- ferent amplitudes are a function of the Moon's varying velocity in its elliptical orbit. During the anomalistic month, the Moon moves the fastest in its orbit (and therefore in either celestial longitude or right ascension) — from the effect of parallax alone — in a period extending from approxi- mately 5 days before perigee to 5 days after perigee. Conversely, the Moon's apparent motion from this cause alone is the slowest from about 5 days after perigee to 5 days before perigee (bracketing the apo- gean portion of the orbit) . The relative angular veloc- ity of the Moon is also a function of the comparatively greater proximity (or the greater distance) of the Moon from the Earth, subject to the dynamic condi- tions creating such extremes at times of proxigee- syzygy and exogee-syzygy — or establishing moderate parallax distances at times in between. The Moon moves considerably faster than usual and the value of Aaj increases when the parallax is large, and the Moon's motion is slower when the parallax is rela- tively small — even though the latter parallax value may represent a maximum for that particular lunation. 3. The largest value of Aa^ does not necessarily occur coincidentally with the largest value of 5 C during the year; neither must it occur simultaneously with the closest separation-time between perigee and syzygy in the year. 4. The maximum value of Ad^, on the other hand, usually occurs very close to, but not necessarily simultaneously with, the two times each month when the Moon crosses the celestial equator. This cor- responds to the point of inflection in the curve of the Moon's motion in declination, when this is plotted against motion in right ascension. At such times, the maximum component of the Moon's total motion is in the coordinate of declination, and the least motion is in right ascension. The combination of a small lunar motion in right ascension and a limited period of maximum tidal force application establishes a somewhat less favorable situation for either enhancing or prolonging the tidal forces present. Therefore, despite the fact that very large parallax values may occur at such times through the coincidence of a close perigee-syzygy alignment, the situation remains an essentially negative one for the maximum development of perigean spring tides, and offers an excellent oppor- Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 193 tunity for verification of the "If not p, then not q" aspect of the hypothesis being tested. Effects of Extreme Lunar Declination on Motions in Right Ascension A subsequent frequently discussed aspect of the Moon's apparent daily and hourly motions in right ascension re- lates to the catch-up motion of the rotating Earth upon these lunar motions in a variable with different times and circumstances. When the Moon is observed in a position close to the celestial equator, the factor of chang- ing angle of inclination of the Moon's orbit with respect to the celestial equator becomes of considerable signifi- cance. As a seeming paradox, both at the minimum as well as the maximum lunar declinations, the conditions which determine the amount of motion of the Moon in right ascension are affected (but in an opposite manner) by the ultimate magnitude of the greatest northern and southern declinational excursions of the Moon. As will be shortly seen, the effect of observation of the Moon from the Earth's surface rather than from its center, to which all geocentric parallaxes are referred, is also an important factor in the present connection. The increased steepening of the angle of inclination be- tween the lunar orbit and the celestial equator at times of extreme lunar declination is demonstrated in the first of the following quantitative analyses. The especially notable increase in the angle between the Moon's orbit and the celestial equator is revealed as one proceeds toward the Earth's Equator. It is at this point that the angle of inclin- ation reaches a maximum and reduces the length of the lunar day (the period of time between successive lunar transits of the meridian) to its extreme minimum value. This shortening of the available time during which the increased gravitational forces created by a perigee-syzygy alignment can act partially offsets the greater amplitudes and flooding potential of perigean spring tides when they are associated with such conditions. As shown in figure 36, upon those occasions when the vernal equinox and the ascending node of the lunar orbit coincide, the geocentric angle of inclination (Jo) between the Moon's orbit and the celestial equator can attain its maximum value slightly in excess of 28.5°. However, the Moon's sizable parallax angle can add appreciably to this value as measured from the Earth's surface. Woolard and Clemence 5 have given appropriate equa- tions which permit a quantitative analysis of the differ- ences caused by the parallax effect. If / represents this same angle of inclination, but as measured topocentrically from a point on the surface of the Earth, its value is defined by: where tan (90°- y —v X = (1/t)'1£ cos 5^(Aa^y y' = (l/*)"(A8c)' € = p COS0' cos h' = ihe geocentric latitude of the place of observation As in the example of chapter 2, the Moon is as- sumed to be on the celestial equator, and to be transit- ing the meridian of the U.S. Naval Observatory in Washington, D.C. 0'=38°55'14.O" p cos 0' = 0.77906. 202-509 0-78-15 I'M Strategic Role of Perigean Spring Tides, 1635-1976 EFFECT OF MOON'S 18.6-YEAR NODICAL CYCLE UPON THE MAXIMUM LUNAR DECLINATION EARTH VIEWED FROM THE VERNAL EQUINOX ALONG THE MOONS LINE OF NODES PLANE OF PAPER IS THAT OF THE CELESTIAL MERIDIAN Figures 36A, B. — (Discussed in text. The Moon's parallax -k^ is also assumed for con- venience to be 60'(=3,600"). In the year 1950, a very good example of the coin- cidence of the lunar ascending node and the position of the vernal equinox occurred. 6 (With fl at T, A a =0°.) On September 19 at 0400 Oct., the Moon attained a maximum southerly declination of — 28°43'47.3" for this year. Approximately 6 months earlier, near 1200 Oct. on March 26, as the ascending node coincided with the position of the autumnal equi- nox (a 90° j the Moon reached a maximum northerly declination of + 28°42'19.1" for the year. The values of the astronomical latitude around these same times were C = — 5°16'55.9" on September 19.0, Oct., and j 8 I =+5 o 10 , 31.3 // on March 26.0, Oct. A relatively high value of each semimonthly maximum in lunar declination persisted during every lunation throughout the year. The probability that a simultaneous alignment between perigee and syzygy, as well as the lunar node, will occur at the exact time of either the vernal or autumnal equinox is, statistically, very remote. The period of revolution of the vernal equinox caused by the precession of the equinoxes is 25,800 years (one-half of this, or 12,900 years is, therefore, required for either of the two equinoxes to revolve to the position of the other). For all practical purposes in the present tidal discussion, the vernal equinox may be re- garded as essentially stationary, and only the motion of the lunar node with respect to it in a mean revolutionary period of 6,798.4 days (18.6 years) need be considered. A period of time equal approximately to the average of a synodic and an anomalistic month occurs between each Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 195 instance in the customary pairs of perigee-syzygy alignments possessing a separation-interval (P — S) of + 24 hours. (See table 16.) Following the smallest P — S value of any one close perigee-syzygy alignment, the mean interval to the next comparably close alignment will be either 191.95 days or 221.48 days, depending upon the controlling conditions enumerated in chapter 6, "Cycles of Alternation in Perigee- Syzygy Alignments." The possibility of securing a coincidence between the combined condition of perigee-syzygy and both the lunar node and one of the equinoxes is made further remote by the fact that, as perigee and syzygy come into alignment, the position of perigee moves rapidly forward, subject to solar perturbations. The opportunity for arriving at even a near-commensurability between these four elements is thus even further reduced. For the record only — recognizing that the periods covered by the tabulated data, and the data alone, do not cover all possible cases, with any rigorous interpretation thereof thus being rendered invalid — the following summation is made: 1. Only two among the 1,318 cases of perigee-syzygy with a separation-time of 24 hours or less occurring between 1600 and 1999 and listed in table 16, fall within even the same year as one of the 19 cases of extreme lunar declination listed in table 11, covering the 342-year period of the present study. 2. Among the 100 representative examples of major coastal flooding occurring at a time of perigee-syzygy, cata- loged in table 1, only three cases occur even in the same year as that in which an extreme value of the lunar declina- tion occurs. The three flooding cases involved (which are mutually inclusive of the two indicated in the first para- graph) are those of 1894 January 22 (perigee-syzygy sepa- ration-time, -24h), 1932 November 2 ( — 13h), and 1969 December 10-14 (4- 38h). 3. For several years in a row both before and after an extreme declination is attained, the lunar declination re- mains above-average in its monthly values throughout the entire year. However, the three cases mentioned of flooding which occurred in the same year as that of an extreme lunar declination were at least 8 months removed from the exact date of the extreme declination. It is tacitly obvious that no solar or lunar eclipses can occur on these exact dates of highest possible lunar declina- tion — but may occur on dates during the same year of high lunar declinations when the lunar node and the position of the Sun very nearly coincide. In the same manner, perigee- syzygy may occur on some other date of node-perigee- syzygy alignment throughout the year when the Moon may also be in a position of crossing the celestial equator. On the other hand, previously mentioned factors may apparently somewhat paradoxically support an increase in tidal flood- ing potential under certain conditions of high lunar decli- nation, as will be brought out in subsequent chapters. It is because of the various commensurate possibilities that an examination of the differences between the two cases in- cluded in the following discussion is important. Table 1 1 . — Approximate Dates on Which Maximum Lunar Declinations Occurred, According to the 6,798.4-Day Nodical Cycle (Based on Epoch 1932 January 12.1 ) 1634 Mar. 19.7 1652 Oct. 29.1 1671 June 10.5 1690 Jan. 19.9 1708 Sept. 1.3 1727 Apr. 13.7 1745 Nov. 23.1 1764 July 4.5 1783 Feb. 13.9 1801 Sept. 26.3 1820 May 7.7 1838 Dec. 18.1 1857 July 29.5 1876 Mar. 9.9 1894 Oct. 20.3 1913 June 1.7 1932 Jan. 12.1 1950 Aug. 23.0 1969 Apr. 3.4 (1987) Nov. 13.8 When the Moon crossed the celestial equator on April 2, during that particular cycle which contains the extreme maximum lunar declination, the relatively large hourly motion in declination necessary to accomplish this large excursion from the celestial equator was clearly evident. This position represented a point of inflection between the trough and peak of the curve, where the slope of the curve in the declination component reached a maximum. The hourly differences in right ascension and decli- nation of the Moon subject to this circumstance, occurring at approximately 0230 G.c.t. on April 2, were Aa c = 130.97 s and A5 C =- 1,075.6". The latter value indicates the greatest hourly change in declina- tion for the year. The corresponding hourly differences with the Moon on the celestial equator during the second cycle of maximum declination, at about 2130 G.c.t. on September 12, were Aa c = 125.40 s1 and A<5 C = — 1,030.8". (It should be pointed out that, for various reasons, the maximum value of A5(£ does not coincide precisely with the time at which the Moon crosses the Equator. In the first case, A5 C reaches a greater value of —1,078.6" at about 0930 G.c.t. on April 2, in the second case, Af^ reaches a value of -1,033.2" at about 0330 G.c.t. on September 13. The greatest value of Aa^ more nearly — but again not exactly — agrees with the time the Moon reaches its extreme declination for the year.) 1. Decrease of Motion in Right Ascension, and Shortening of the Tidal Day at Times of High Lunar Inclination to the Celestial Equator Selecting the April 2 example of the Moon's crossing of the celestial equator as representative of such a high-inclination situation, and using the I'll, Strategic Role of Perigean Spring Tides, 1635-1976 appropriate value of the lunar parallax (tt ( = 60'25.88") at this time: x' = l/3626"X15 cos 0°X 130.97 s = 0.00028X 15X 1 X 130.97 = 0.55007 y' = 1/3626" X 1075.6" = 0.00028X1075.6 = 0.30117 |' =0.77906 X cos 0°X 0.24956 radian = 0.19442 ,,' =0.77906 X sin 0°X sin 0°X0.24956 radian = 0.77906X0X0X0.24956 = 0.00000 tan (90°-J) = 0.55007-0.19442 : 0.30117-0.00000 0.35565 0.30117 1.18089 arc tan 1.18089=49.74° J=90.0°-49.74 o =40.26° Since the geocentric inclination of the lunar orbit to the celestial equator (J ) reaches a maximum value of about 28.5°, the topocentric inclination involves an angle which is approximately 1 1.8° greater than the geocentric. With this increased angle of inclination, and the maxi- mum component-motions in declination which result, the apparent movement of the Moon in right ascension is reduced proportionately. As noted in chapter 2, the tidal day is thereby shortened, and the tide-amplifying effects are reduced. 2. Increase of Motion in Right Ascension and Lengthening of the Tidal Day at Times When the Moon is at an Extreme Declination Contrastingly, in the perigee-syzygy situation which occurred with a mean epoch of 0500 G.c.t. on 1950 December 9, within 24 hours of an extreme lunar declination of — 28°25'41.9", the direct motion of the Moon in celestial longitude reached one of its largest possible values (AX C = 15°20'49.4", or 15.347°, between December 8.5 and 9.5). The hourly motion of the Moon in right ascension, Aa^= 173.01 s , likewise reached a maximum value for the entire year between 2130 and 2330 G.c.t. on December 9. (The exact repetition of the same maximum difference over a 3-hour period indicates a flattened peak on the dec- lination curve, yielding a protracted maximum.) The semimonthly maximum declination of — 28°25'41.9" occurred at about 0500 G.c.t. on December 10. The value of tt c on December 9.0 G.c.t. was 61'27.09". The latter figure may be compared with the only slightly smaller parallax of 61' 26.702" associated with the great mid-Atlantic tidal flooding of 1962 March 6.5, and the somewhat larger value of 61' 30.0009" which accompanied the west coast tidal flooding of 1974 Janu- ary 8.5 — both discussed extensively in chapter 7. However, the distinctive feature of the 1950 Decem- ber 9 event was the extraordinarily large daily motion of the Moon in longitude on this date. As indicated, this was 15°21' during the latter event compared with values of 15° 15' on the 1974 date and 15° 14' on the 1962 date. Since the Moon is never far from the ecliptic, the rapid motion in celestial longitude is directly corre- latable with the rapid motion of 173.01 s / meh in right ascension which occurred on 1950 December 9. This was associated with the relatively large declination of — 28°20'23.4", increasing, within some 7 hours, to an extreme declination of — 28 25'41.9" for the month. For comparison, the declination of the Moon on 1962 March 6.5 G.c.t. was -7°42'05.42", with a corresponding value of Aa^= 146.543 s . The maximum declination for this lunation was — 19°50' 19.35", having a corresponding Aa^_= 147.955 s . On 1974 Jan- uary 8.5 G.c.t., the declination was + 20°36'21.33", with a value of Aa c = 159.999 s . The maximum decli- nation for this lunation was +23°52'04.40", with Aa c = 163.965 s . The effect of an increased daily motion in longitude produced by the Moon's extremely close distance to the Earth in 1950, 1962, and 1974 thus was added to in 1950 by the effect of the relatively large declination at the time of perigee-syzygy, and a consequent increased motion in right ascension. The comparatively high declination at perigee-syzygy was, in turn, a function of the extreme dec- lination of — 28°25'41.9" during the same lunation, caused by the coincidence of the lunar ascending node with the vernal equinox in this year. The greater speed of movement in right ascension re- sults in an extension of the necessary catch-up time, an increase in the length of the tidal day, and an augmenta- tion of the tides. The synoptic weather map for this 1950 December 9 date has been included among those grouped in chapter 7 to indicate a logical reason for the lack of attendant tidal flooding. Although the tides predicted for December 9-10 were appropriately high, in the complete absence of any strong, persistent, onshore winds on either the east or west coasts of North America, no major tidal flooding occurred. Chapter 5. The Essential Conditions for Achieving Amplified Perigean Spring Tides As a direct follow-on to the theoretical discussions of the preceding chapter, it is noteworthy that certain other astronomical influences may act to produce both regular and irregular, but measurably significant increments in the positive and negative amplitudes of perigean spring tides — tending toward their ultimate maximization. In the present chapter, a brief summary of each such con- tributing influence will be followed by a quantitative anal- ysis of its individual effects. The General Concepts of Maximization of Perigean Spring Tides One immediate cause of the secondary enhancement of tide-raising potential is a purely statistical one estab- lishing, in varying degrees — over both quasi-periodic and aperiodic intervals of time — more exactly commen- surable relationships between the synodic and anomalistic months. This close commensurability results, in turn, in an accompanying more precise spatial orientation between the line of syzygies and the line of apsides in the lunar orbit. Increased dynamic factors acting upon the Moon's orbit because of the near-coincidence in the lines of gravi- tational force action connecting Earth, Moon, and Sun are responsible for an increased eccentricity and parallax, and hence a considerably closer proximity of the Moon to the Earth at perigee. This condition may also be ac- companied, on occasion, by an independently originating, close alignment of the Moon and Sun in declination — whose influence is most effective when the two bodies are simultaneously at perigee-syzygy. Accordingly, for reasons involving both decreased lunar distance from the Earth and a mutually reinforcing combination of lunisolar forces, the tide-raising potential is augmented. In accordance with Kepler's third law, these same cir- cumstances also cause a temporarily increased apparent daily motion of the Moon in both longitude and right ascension. An appropriate catch-up motion by the rotat- ing Earth becomes necessary in order to bring any given meridian on the Earth's surface into alignment with the axis of enhanced gravitational attraction of the Moon (and Sun) . As will be seen, this required catch-up motion in turn increases the period of maximum tide-raising force application during the course of the tidal day. The total tide-raising potential present is thus a func- tion of two separate categories of influence : ( 1 ) those factors which, causing a very close alignment and a rein- forcement of lunisolar gravitational attractions, coupled with an extreme proximity of the Moon (and Sun) to the Earth, increase the tide-raising forces exerted upon the Earth's waters; and (2) those factors which lengthen the tidal day — the interval within which these or other aug- mented tidal forces can act — and by this means likewise cause an increase in both the positive and negative ampli- tudes of the tides. In dealing with the influences which act to generate increased high and low waters at time of perigee-syzygy, it is necessary to consider both of the above categories. Those factors involving purely force influences will be discussed in the present chapter; those associated with various astronomical influences producing changes in the length of the tidal day, often accompanied by other time- related effects, will be covered in chapter 6. Factors Increasing the Intensities of the Tidal Forces Acting (a) Unquestionably, one of the most important con- ditions — next to the positions of the Moon and Sun at perigee and perihelion, respectively — which serves 197 1MX Strategic Role of Perigean Spring Tides, 1635-1976 strongly to increase the tidal forces acting is the pres- ence of either or both of these two bodies near to, or di- rectly in the local zenith (i.e., at an altitude of 90°). From a point of view related solely to the tide-raising potential, a greater vertical gravitational force exists under these conditions because the shortest distance be- tween either the Moon or the Sun and the Earth's surface is at all times along a perpendicular to the surface. For reasons given in the preceding chapter, nowhere north or south of a declination of ±28.5°, respectively, can the Moon be perpendicular in altitude to the Earth's surface. Similarly, the Sun cannot reach the zenith if the latitude of the location is greater than ±23.5°. Since tidal forces vary inversely as the cube of the distance of the attracting body, this perpendicular distance to the Moon and its position in the local zenith are very important elements in establishing the greatest tide-raising potential. a In considering relative tidal heights at any station, the location of the Moon directly over the Equator b is of fur- ther importance in another connection — that of diurnal inequality. In the equilibrium theory of the tides de- scribed in the appendix, it is seen that the tractive or horizontal force of the Moon tends to draw the waters of the Earth to a point where the line of gravitational at- traction between Moon and Earth is perpendicular to the surface of the Earth. The maximum peak of the tidal bulge is produced in the vicinity of this sublunar point (together with an almost identical tidal bulge on the diametrically opposite side of the Earth). Because of several accelerating and retarding factors to be discussed in chapters 6 and 8, the Earth's two tidal bulges do not usually lie directly beneath, or in a position exactly 180° around the Earth in longitude from, the Moon. However, when the Moon is directly over the Equator twice each lunar month, the two crests of the hypothetical tidal force envelope (see fig. 5, appendix), do tend to be centered precisely in the equatorial plane. The Earth's diurnal rotation occurs in a manner to carry any point on its surface in a direction which is always parallel to the Equator. When the tidal bulges lie on the Equator, therefore, any point on the Earth's surface in high-middle to low latitude rotates (between high and low water) into and out of the tidal bulges and a It is important to note in this same respect, however, that the maximum horizontal or tractive tide-raising force is exerted upon the Earth's surface by the Moon along a small circle everywhere 45° from the current instantaneous position of the Moon. (See fig. 35 and the accompanying discussion.) b As will be seen in chapter 6, the apparent westward (rising and setting) motion of the Moon caused by the Earth's rotation is the greatest when it is on the celestial equator, but the Moon's apparent eastward motion in right ascension due to its real mo- tion in orbit is then the least — factors of importance in connection with relative catch-up times. through uniformly high tides on both sides of the Earth. There is no diurnal inequality. (See fig. 5 in the appen- dix. ) Since the effect of increased tidal range is influen- tial at certain locations in adding to the heights of perigean spring tides, this lack of a higher high water in equatorial type tides can, in some cases, be partially counterproductive to the increased lunar gravitational in- fluence present with the Moon on the Equator. (b) A second very important influence upon the avail- able tide-raising force is the alignment of the Sun and Moon in the same (or exactly opposite) declination at the same time they are aligned in celestial longitude (at times of syzygy). The coincidence of perigee-syzygy with a common alignment of the Sun and Moon in declination adds appreciably to the tide-reinforcing effect caused by lunar proximity to the Earth. The possibility of both the Moon (in its orbit) and the Sun (in the ecliptic) being exactly aligned also in the plane of the celestial equator (8 = 0°) at the same time they are aligned at perigee- syzygy is definitely less common. Such a situation is pos- sible only when a lunar node coincides with one of the equinoxes — this action taking place (when within the angular limits defined in the footnote ( c ) on page 7 ) at the same time as a total lunar or solar eclipse. However, the likelihood of the Sun and Moon becom- ing aligned at some declinational angle other than 0°, either on the same side of the Earth (at new moon) or on the opposite side (full moon), is not uncommon, con- sidering that the Moon goes through its complete range of declination once in each tropical month of 27.321582 mean solar days (from vernal equinox to vernal equinox again). (c) Seasonal factors also enter into the frequency of occurrence of various reinforcing combinations of gravi- tational force. As will be seen in table 13, the most favor- able situation for increasing the forces acting at time of syzygy — thereby decreasing the distance of the Moon from the Earth — exists during the winter months. This is because the Earth is then closest to perihelion, per- mitting the Sun's gravitational force to be exerted to its fullest extent upon the tides. The Sun is, during the winter season of the Northern Hemisphere, at its maximum negative declinations. In order for the Moon to achieve a direct or opposite alignment in the Sun's declinational plane, it is necessary for the new moon to reach the same comparatively large negative declination as the Sun, or the full moon to attain an equal positive declination. These declinational alignments will act to enhance the already greater tide-raising forces produced as the gravi- tational forces of Moon and Sun are combined at syzygy. Should the calendar year begin with the declinational Essential Conditions for Achieving Amplified Perigean Spring Tides 10fi plane of the Moon close to that of the Sun, while the Sun itself is near perigee with the Earth, (i.e., at peri- helion) an additional amount of tide-raising force is produced. A Quantitative Evaluation of the Various Tide-Maximizing Factors Table 12 illustrates the effect upon the proximity of the Moon to the Earth resulting from the astronomical condition of perigee-syzygy when this geometrical align- ment is combined with the location of both the Moon and the Sun on or near the celestial equator. The Sun, in its apparent annual motion along the ecliptic, crosses the celestial equator around March 21 and September 23 of each year — at the vernal and autumnal equinoxes, respectively. Since the Moon is never more than 5°9' from the ecliptic, the time at which the Moon, while at perigee- syzygy, can be simultaneously near the celestial equator will always be close to one of these dates, a fact confirmed in table 12. This table lists 45 cases of perigee-syzygy in which the separation between the two components is < 24 hours and the declination of the Moon is <_ + l° (one case of 1.1° is included). The additional solar gravita- tional and perturbational forces acting on the Moon when the Sun is in, or very nearly in, the same plane as the Moon around the times of the equinoxes — as shown by the relatively larger lunar parallaxes resulting under these conditions — are clearly revealed by these data. However, a comparison is also desirable between this table and table 1 3 — which shows the effects of the addi- tional gravitational force of the Sun on the lunar orbit caused by the occurrence of perigee-syzygy close to the time of perihelion. Such a comparison reveals that the latter situation is far more effective, in increasing the lunar parallax, if the Sun and Moon are coplanar in declination. As examples of this, in table 13, note especially the large value of the parallax for the date 1912 January 4, despite the very high lunar declination of +27.6°, and again for 1930 January 14, with a lunar declination of + 26.0°. Both dates are, of course, very close to that of perihelion, when the Sun's gravitational effect reaches its maximum. Finally, a comparison can be made between the data of table 13 and those of table 14, which show the effect upon the lunar parallax of a situation in which the Moon is at one of the two nodes of its orbit (i.e., crossing the ecliptic) at the time of both perihelion and perigee- syzygy. The circumstance under which the Moon is simul- taneously in the plane of the ecliptic, and either pre- cisely or very nearly aligned in celestial longitude with the Sun is that of a total solar or total lunar eclipse. The type of eclipse which occurs depends upon whether the Moon lies between the Earth and the Sun, (at new moon) or on the opposite side of the Earth from the Sun (at full moon) , respectively. The combination of the gravitational forces of the Earth and Sun, exerted along nearly the same axes in A and /J, creates an additional perturbing force upon the lunar orbit. However, as will be seen in table 14, the effect upon an increase in the lunar parallax is not as pronounced as in either of the two preceding examples. This is due in some degree to the fact that, in the case of a total solar eclipse, the gravitational forces of the very massive but vastly more distant Sun and the less massive but closer Earth — exerted in opposite directions on the Moon's orbit — are partially compensating. On the other hand, the production of a maximum lunar parallax is the result of undiminished, maximized solar forces and perturbations. Consider, for example, the large but not extreme lunar parallaxes at the times of the solar eclipses of 1967 No- vember 2 and 1985 November 12 in table 14; also the comparatively large parallax values in the following cases chosen from table 1, associated with coastal flooding. Date and Time Maximum (G.c.t.) of Duration Conjunction in of Eclipse Longitude Totality 1901 April 18 2200 b 6.5 m . . . . 1949 October 21 2100b (Partial). Sepa- ration- Interval P-S All four cases have a perigee-syzygy alignment within 6 h or less. The first two cases also are approaching the time of perihelion. However, the further coincidence of lunar opposition and very close proximity in time to perihelion necessary to achieve either an extreme or a maximum proxigee-syzygy (table 13) is lacking. Summary of Relative Gravitational Force Influences Assuming a common limiting condition in which the separation between perigee and syzygy is <24 h : A situation in which the Moon (passing through one of the two lunar nodes at times of solar or lunar eclipse) crosses the ecliptic at the same time the Earth is near perihelion (between November 2 and February 26 in table 14) is, in general, not as effective in increasing the lunar parallax as either — 200 Strategic Role of Perigean Spring Tides, 1635-1976 Table 12. — Selected Cases of Perigee-Syzygy, Showing the Relationship Between the Equinoctial (Near-Equatorial) Position of the Moon and the Lunar Parallax Over the 400-Year Period 1600-1999 Primary Limiting Range for Perigee-Syzygy Separation: P — S < ±24 h Secondary Limiting Range for Proximity of Moon to Celestial Equator: 5(£ < ± 1° Resulting Bracketing Ranges for Proximity of Perigee-Syzygy to Vernal or Autumnal Equinoxes: Spring dates 3/8-4/2 Autumn dates 9/9-10/6 Time (G.c.t.) of syzygy Lunar ph£ Horizon tal parallax at : syzygy 61 19.0 61 18.3 61 20.3 61 25. 1 61 8. 1 61 10. 8 61 1'). 8 61 26.3 61 20.0 61 27.8 61 25.4 61 26.0 61 14. a 61 27. 8 61 5.3 61 23.2 61 23.0 61 20. 9 61 4.2 61 6. 8 61 12.3 61 22. 1 1)1 9.5 61 1'). 7 61 22.9 61 23. 1 6,1 24. ') 61 l a. a 61 7.0 61 23.5 hi 7.4 61 a. i, 61 21.2 61 14.4 61 18.4 61 7. 6 61 24.0 61 24.5 61 27. 1 61 9.4 61 21.2 61 18.2 61 26.7 i.l 30.0 (.1 24.7 at syzygy Perigee - syzygy 1617 Sept. 15 4 1621 Mar. 8 2 1626 Mar. 27 1') 1635 Mar. 18 16 1649 Mar. 28 11 1662 Mar. 20 2 1675 Mar. 11 ia 1679 Mar. 12 9 1679 Sept. 20 2 1684 Mar. 31 2 1696 Sept. 11 9 1701 Oct. 2 2 1705 Oct. 2 17 1710 Mar. 15 9 1718 Sept. 24 9 1745 Sept. 25 17 1750 Mar. 8 8 1759 Oct. 6 9 1780 Sept. 28 7 1789 Mar. 11 14 1794 Mar. 31 7 1820 Sept. 22 7 1825 Sept. 12 15 1830 Mar. 24 15 1834 Oct. 2 23 1847 Mar. 16 21 1860 Sept. 15 6 1864 Sept. 15 21 1869 Mar. 27 22 1869 Oct. 5 14 1874 Sept. 25 22 1883 Mar. 9 4 1892 Mar. 28 13 1895 Sept. 18 21 1900 Sept. 9 5 1905 Sept. 28 22 1922 Sept. 21 5 1927 Apr. 2 4 1935 Sept. 12 20 1939 Sept. 13 1 l 1944 Oct. 2 4 1953 Mar. 15 1 1 1967 Mar. 26 3 1993 Mar. 8 ID 1998 Mar. 28 3 -0.6 +0.3 +0.3 +0.6 + 0.8 -0.3 -0.7 -0.4 +0.6 +0. 1 -0. 1 + 0.3 +0.3 + 0.3 +0.8 -1.0 -0.5 + 0.5 + 0.7 -0.9 +0.9 +0.2 -0.4 + 0. 2 +0.7 +0.2 -0.7 +0.8 +0.8 -0.6 -1.0 -0.8 +0.3 + 0.6 -1.0 + 0.7 + 0.8 0.0 -0. 3 + 1.0 -0.9 + 1. 1 + 0.6 + 0. 2 +0.7 h + 13 -16 -10 + 1 + 19 4-17 + 13 - 2 + 12 + 4 - 6 - 1 -16 - 3 - 20 - 5 + 8 + 13 - 20 -22 -16 - 9 r-18 + 10 + 9 - 8 + 3 -12 -21 - 7 +20 + 19 + 9 -13 6 14 + 19 + 1 - 6 - 2 -17 -11 -13 + 5 - 2 4- 4 Essential Conditions for Achieving Amplified Perigean Spring Tides 201 Table 13. — Compilation of All Cases of Extreme Proxigee-Syzygy Occurring Over the 400-Year Period 1600-1999, Showing the Combined Influence of Perihelion, Lunar Opposition, and Approximately Coplanar Lunisolar Declinations in Reducing the Perigee-Syzygy Separa- tion and Increasing the Lunar Parallax (see text explanation). Selected Lower Limit f sr Lunar Parallax: ,r>61'29. 0" Resulting Limiting Rar ge for Perigee-Syzygy Separation : P-S<±5h Resulting Bracketing Range for Proximity of Perigee-Syzygy to Perihelion : 10/31-3/8 Date Phase Parallax at syzygy Declination Perigee minus Parallax at perigee Declination syzygy (G.c.t.) , ,/ o h , // o 1603 Jan. 27 FM 61 29.9 + 14. 1 + 5 61 30.2 + 13.3 1609 Nov. 11 FM 61 30.4 + 13.3 -1 61 30.4 + 13.2 1627 Nov. 22 I'M 61 30.6 + 15.9 + 2 61 30.7 + 16.2 1629 Jan. 9 FM 61 29.8 + 22.8 -1 61 29.8 + 22.8 1630 Feb. 27 FM 61 29.7 + 12.9 -3 61 29.9 + 13.7 1645 Dec. 3 FM 61 30.3 + 17.8 +4 61 30.6 + 18.2 1647 Jan. 20 FM 61 29.6 +20.8 + 1 61 29.6 + 20.7 1671 Nov. 16 FM 61 30.3 +23.2 -2 61 30.4 + 22.8 1673 Jan. 3 FM 61 29.9 + 26.3 -5 61 30.2 + 26.7 1689 Nov. 26 FM 61 30.9 + 25.6 61 30.9 + 25.6 1691 Jan. 14 FM 61 30.5 + 24.7 -2 61 30.6 +25. 1 1707 Dec. 9 FM 61 31.0 + 27. 1 + 3 61 31. 1 + 27.3 1709 Jan. 25 FM 61 30.5 + 22.3 61 30.5 + 22.4 1725 Dec. 19 FM 61 30.4 +27.8 +4 61 30. 7 + 27.9 1727 Feb. 6 FM 61 30.0 + 19.2 +2 61 30.0 + 18.8 1751 Dec. 2 FM 61 29.4 +21.4 -2 61 29.5 + 21.3 1753 Jan. 19 FM 61 30.8 + 15.4 -4 61 31.0 + 15.9 1769 Dec. 13 FM 61 29.7 + 22.5 1 61 29.7 + 22.5 1771 Jan. 30 FM 61 31. 1 + 12.8 -2 61 31.2 + 13. 1 1787 Dec. 24 FM 61 29.4 +22.8 + 3 61 29.6 + 22.6 1789 Feb. 10 FM 61 30.9 + 9.5 + 1 61 30.9 + 9.5 1807 Feb. 22 FM 61 30. 1 + 5.8 +2 61 30.2 + 5.2 1813 Dec. 7 FM 61 30.3 + 18.9 -2 61 30.4 + 18.6 1830 Oct. 31 FM 61 29.7 + 10.0 +2 61 29.8 + 10.3 1831 Dec. 19 FM 61 30.8 + 19.6 () 61 30.8 + 19.6 1849 Dec. 29 FM 61 30.8 + 19.4 +2 61 30.8 + 19.4 1868 Jan. 9 FM 61 30. 1 + 18.4 + 3 61 30. 3 + 18.2 1875 Dec. 12 FM 61 30.5 + 27.9 -4 61 30. 8 + 27.6 1893 Dec. 23 FM 61 31.4 +28.2 -2 61 31.4 +28.2 1912 Jan. 4 FM 61 31.6 + 27.6 + 1 61 31.6 + 27.6 1930 Jan. 14 FM 61 31.3 +26.0 + 2 61 31.4 + 25.8 1948 Jan. 26 FM 61 30.4 + 23.6 +4 61 30.8 + 23.0 1954 Nov. 10 FM 61 29.7 +20.8 -1 61 29.7 + 20.7 1972 Nov. 20 FM 61 30. 1 + 23.6 + 1 61 30. 1 + 23.8 1974 Jan. 8 FM 61 30.0 + 20.5 -2 61 30.0 + 20.7 1975 Feb. 26 FM 61 30.0 + 4.4 -3 61 30.2 + 5.2 1990 Dec. 2 FM 61 30.0 + 25.7 + 3 61 30. 1 +25.9 1992 Jan. 19 FM 61 29.9 + 18.6 + 1 61 30.0 + 18.5 1993 Mar. 8 FM 61 30.0 + 0.2 -2 61 30. 1 + 0.6 A situation of perigee-syzygy with the Moon simulta- neously in or near the plane of the celestial equator (5^ < 1 °) and close to the position of one of the two equinoxes (be- tween March 8 and April 2, or September 9 and October 6 in table 12), or— A situation in which the alignment of perigee-syzygy occurs concurrently with the Earth at or near perihelion, the Moon at opposition, and the Sun in the same declina- tional plane as the Moon (see table 13). The influence of such combined perigee-syzygy, lunar opposition, and lunisolar declinational alignments occurring in the period near perihelion — producing the largest geocentric horizontal parallaxes of the Moon over the entire 400-year period between 1600 and 1999 — will be discussed further in the following section. o, y> Strategic Role of Perigean Spring Tides, 1635-1976 Table 14. — Selected Cases of Perigee-Syzygy Occurring Simultaneously at a Lunar Node ( Total Solar Eclipse) and Near Perihelion, Showing the Combined Effect of These Factors Upon the Lunar Parallax Over the 100-Year Period 1900-1999 Limiting Range for Perigee-Syzygy Separation: P— S< ±24 h Limiting Range for Celestial Latitude of Moon at Conjunction (Total Solar Eclipse Certain): /3(£=the latus rectum of the Moon's elliptical orbit, equivalent to the radius vector (p) for j/=90° <7=the perigee distance, or least monthly distance be- tween the Moon and the Earth ?=the eccentricity of the lunar orbit p=the radius vector, or distance of the Moon from the Earth at any instantaneous position in orbit Then: p=q(l+e) = p( a tv=90°) q=a(l-e) = p (atv=0°) In a perturbed orbit, each of these equations is theo- retically valid only for the moment of arbitrarily selected zero-disturbance in the osculating orbit — equivalent in this case to the instant of perigee-syzygy as above described. However, as noted several paragraphs earlier, the values of both the celestial longitude (A) and the radius vector (p) of the Moon tabulated in The American Ephemeris and Nautical Almanac contain the effects of perturbations and are, therefore, representative of the perturbed orbit. By definition, the value of p — the only quantity not evaluated for the time of perigee-syzygy — is equal to the tabulated value of p for the position where y = 90°. Hence, the time corresponding to this position in the lunar orbit 90° from perigee can be obtained by reverse interpolation in the tables for the instant where y = 90°. The true anomaly is the angular distance of the Moon, expressed as a difference in longitude, from perigee. The true longitude of perigee is, in turn, equal to its instanta- neous angular distance from the vernal equinox. At a close perigee-syzygy, the Moon itself must also be at very nearly this same longitude. The true longitude of perigee may thus be obtained, to a close approximation, by extracting the apparent longitude of the Moon from The American Ephemeris and Nautical Almanac for the exact time of perigee, also tabulated. An alternate procedure is to inter- polate the value of the mean longitude of perigee from various available tables. (At the time of perigee-syzygy, the mean longitude and true longitude of the Moon are theoretically the same.) However, because the instant of the Moon's passing through perigee is being considered, the accelerated motion of perigee at the time of perigee-syzygy is not taken into account in the mean motion of the line of apsides, and hence in the mean longitude of perigee. The resulting differences are shown among the following com- putations. If 90° is added to the derived true longitude of perigee, the true longitude of the Moon at the position p is obtained. This longitude of the Moon as it reaches the latus rectum of the orbit (subject to the perturbed motion imposed in the interim since perigee) can then be used — again by a process of reverse interpolation in the ephemeris — to find the time at which the Moon reaches this position. Proceeding next to the table of true geocentric distance of the Moon published in the ephemeris, this interpolated time can be used to find the actual value of p, the radius vector of the Moon, at this position in orbit. This value corre- sponds to the dimension of p. The value for q for the instant of perigee-syzygy also can be obtained from this same table. Then since: 1, and substituting the appropriate values and following the pro- cedure outlined above, a comparison can be made between the results obtained for a condition of close perigee-syzygy and the adopted mean values for e and a which represent an average of all conditions encountered in the lunar orbit. For the close perigee- (proxigee-) syzygy alignment of 1974 Jan. 8.5 (G.c.t.): (a) The value of the apparent (true) longitude of the Moon interpolated from The American Ephemeris and Nautical Almanac for a time corresponding to that of perigee, and therefore very nearly equiva- lent to the true longitude of perigee is : 106.828765° By comparison, a derivation of the approximate mean longitudes of the Moon and perigee from tables 4—5 in Harmonic Analysis and Prediction of Tides gives : Mean longitude of the Moon 106.95° Mean longitude of perigee 106.23° (b) The apparent longitude of the Moon's position at pointy is then: 106.828765°+90.000000°= 196.828765° Whence, using inverse interpolation in the ephemeris to obtain the time at which the Moon reaches p : i p =Jan. 14.6866 (c) The value of p, and hence the corresponding value of p at this time, obtained by the use of polynomial coefficients in the table of true geo- centric distances of the Moon is: p =p = 60. 1 60203 Earth-radii (d) Similarly obtained, the value of q at the perigee of 1974 Jan. 8.4583 is: p=? =55.9010709 Earth-radii Then: 1=0.076005 (e) Comparing this with the mean value of the eccen- tricity of the lunar orbit: 6=0.05490 the value of the eccentricity at the time of a very close perigee-syzygy alignment thus represents an increase of 38.4 percent above the mean value of the eccentricity. (In the classic work, Astronomy- 218 Strategic Role of Perigean Spring Tides, 1635-1976 Vol. I, by Russell, Dugan, and Stewart, the authors specify that when the Sun crosses the line of apsides of the lunar orbit, the resulting increase in eccen- tricity is about 20 percent. This value, however, refers to the average of all cases, including both wide separations between perigee and syzygy at the time of solar coincidence with the line of apsides, and the special case of a close perigee-syzygy, as here exemplified. (f) Also: 60.509753 Earth-radii By comparison, at the Earth's mean distance and eccentricity, the mean semidiameter of the lunar orbit is : _ 239,000 mi ftA „,„, „ ., ,.. a = o J.O o — ^ = 60.304804 Earth-radii 3,963.2 mi The lengthening of the semimajor axis of the Moon's orbit at the time of such a close perigee- syzygy alignment thus represents an increase of only 0.3 percent with respect to its mean value. This comparatively small increase in the semimajor axis over its mean value, when compared with the much larger increase in the eccentricity of the orbit at this same time, accounts for the fact that the distance of the Moon from the Earth at perigee as given by the equation q—a(l — e) also consistently decreases at the time of a close perigee-syzygy alignment. The Effect of Solar Perigee In table 13, a very noticeable consistency appears in the fact that, over a 400-year period, the largest values of lunar parallax tabulated all occur in the winter months of the year, between October 31 and March 8. This cir- cumstance immediately suggests the effect of the Sun's additional gravitational force (the solar inequality) on the Moon at the closer distance of solar perigee, a phe- nomenon which occurs near to the Earth's perihelion position. Because of the proximity of the Sun to the Moon during this circumstance, the extra solar force acting adds its effects to those noted above. By further increasing the instantaneous eccentricity more than the semimajor axis of the lunar orbit in accordance with the previously described conditions, this supplemental force also in- creases the lunar parallax. At the same time, as will be seen in chapter 6, it slightly diminishes the orbital velocity of the Moon at perigee-syzygy by reducing the Earth's pull on the Moon. The Effect of Coplanar Lunisolar Declinations Another significant relationship evident from table 13 is the fact that, in each of these closest approaches of the Moon to the Earth, the lunar declination has a positive sign. Combined with the circumstance that all of these cases of maximum lunar parallax occur ( near perihelion ) in the winter months when the Sun is south of the Equator and, therefore, always at a minus declination, the con- clusion is obvious. At these times of close proxigee-syzygy alignment and large values of parallax, not only are the Sun, Earth, and Moon at full phase aligned nearly exactly in celestial longitude (or right ascension) at a time near perihelion, but they also lie along a straight line passing from the negative declination of the Sun through the center of mass of the Earth to the positive declination of the Moon. The combined gravitational force compo- nents of the Sun and Earth, exerted in or very nearly in the declinational plane, greatly enhance the total force potential acting upon the Moon's orbit, serve to increase the eccentricity of this orbit, and aid in augmenting the Moon's parallax at proxigee-syzygy to a near-maximum value. For a further consideration of all elements con- tributing to the above-cited winter phenomenon of the Northern Hemisphere, see also page 151, "Seasonal Fac- tors Influencing the Production of Heightened Tides." The three-dimensional alignment of Sun, Earth, and Moon in a common or near-common plane of declination as well as celestial longitude (or right ascension) during these winter months is thus an additional direct cause for the preferential grouping of these tabulated maximum values of v. Significantly, the comparatively high fre- quency of severe coastal storms accompanied by strong, persistent, onshore winds in these winter months adds a further potential factor for tidal flooding at such times. The Effect of Nodal Alignment The alignment of Sun, Earth, and Moon in celestial latitude is of further importance in the same connection. A significant reinforcement in the magnitude of the lunar parallax can occur when the Moon at perigee-syzygy is simultaneously at one of its two lunar nodes (j8=0°), while the positions of perigee-syzygy and the lunar node are also in the same celestial longitude. This condition can come about as the result of a com- mensurable relationship between the rotation period of the Moon's line of nodes and that of the lunar line of apsides. The former perturbed motion (taking place in a direct, or counterclockwise sense as viewed from the north pole of the Moon's orbit) requires about 18.612 Essential Conditions for Achieving Amplified. Perigean Spring Tides 2\<) years to complete one rotation; the latter, retrograding in a clockwise sense, requires approximately 8.849 years. (The units specified are tropical years of 365.24219878 mean solar days. ) However, for the effect of nodal alignment to occur simultaneously with both the Moon and the Sun being at their closest distances from the Earth, as well as in mutual alignment in longitude — to yield the ultimate require- ment for coincidence of node, apse, and perihelion — is a very rare astronomical circumstance. This is indicated from the fact that, as previously specified, the last pre- vious occurrence was in A.D. 1340. Summary Evaluation of Extreme Lunar Parallaxes The two principal astronomical perturbing effects re- sponsible for significant changes in the values of the lunar parallax upon different occasions of perigee-syzygy are (a) lunar evection and (b) lunar variation. The phe- nomenon of evection acts to increase the eccentricity of the lunar orbit and thereby effectively to bring the Moon closer to the Earth at the position of perigee (see fig. 26A). The lunar variation has a similar result, but in- volves a different cause in decreasing the Moon's perigee distance from the Earth at times of perigee-syzygy align- ment (see fig. 27B). Because the Sun is closest to the Earth during the Northern Hemisphere winter season, these two influences on the Moon's orbit occur most prominently in the winter months. The closest possible approaches of the Moon to the Earth (with .resulting increased tidal forces) occur early in the month of January when the Earth is near its perihelion position (closest annual approach to the Sun), usually around January 2-4. The generally accepted absolute maximum value of the lunar parallax (derived from Brown's lunar equations as the highest value theoretically possible) is s max. — 61 '3 2" (fig. 41) The corresponding absolute minimum value is ffimi„. = 53'55". Table 16 represents a computer printout of all perigee- syzygy alignments in which the separation-interval be- tween components is < 24 h , occurring over the 400-year period between 1600 and 1999. From the special con- solidation of these data in table 13, it has been determined that the closest approach g of the Moon to the Earth at a time of proxigee-syzygy during this 4-century period oc- curred on 1912 January 4, at 1300 h G.c.t. (perigee-syzygy separation-interval +6.5 minutes). At this time, the full moon approached the Earth within a center-to-center distance of 356,374 km or 221,441 mi. However, this distance can be considerably less for a point on the Earth's surface and directly beneath the Moon (i.e., with the Moon on the meridian of the place and directly in the zenith ) . For the purpose of determination of any local tides, the effect of the lunar tide-raising action must be considered in terms of the Moon's distance from the Earth's surface at the latitude where the tides under evaluation occur. In a similar connection, as a result of the lunar aug- mentation effect (fig. 25A), the Moon is some 4,000 miles (a distance equal to the Earth's semidiameter) closer to the surface of the Earth when the satellite is in the zenith than when it is just rising or setting on the hori- zon. The Moon's actual distance from the Earth's surface is, accordingly, a function of the latitude of the place, the vertical angular distance (altitude) of the Moon above the horizon, and the lunar declination (or vertical angular distance north or south of the celestial equator) . Because of the lunar nodical cycle, the latter value reaches a maxi- mum value every 18.6 years. In the latitude of Atlantic City, N.J., as an example, the theoretically closest possi- ble approach of the Moon to the Earth's surface at this largest possible declination angle of the Moon ( ±28°47'") and with the Moon transiting the meridian, is 350,008 km or 2 17,485 mi. s Note: The parallaxes listed in this table are expressed for the times of perigee and syzygy, which may be uncertain by several hours. Because of the difference between topocentric and equatorial geocentric horizontal parallax, on some occasions the lunar distance from a position on the surface of the Earth located at high latitudes and with the Moon at a large meridian altitude may be even less than at the precise time of perigee- or proxigee-syzygy, as was the case for 1974 January 8.5 (G.c.t.). See footnote (c) in this same chapter for a further discussion of the 1912 January 4 instance of proxigee-syzygy in terms of the lack of associated tidal flooding. 220 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR PARALLACTIC INEQUALITY (MAX IMUM EFFECT) gee (Exogee) Which Next Follows® Pr ox I gee-Syzygy R A L L AX V ' \ PROXIGEE- 3692 " \ \ SYZVOY \\ Ni«or Full M Moon In Near- .err; - '•- • - '•-' ■ - ■-•■■>"© Coincidence® Moon T / with Perigee, 355.880 / Reducing It* 221,126 / Distance (Proxi- es' gee) from E e r t h HANGING DISTANCE f FROM EARTH '^ EFFICH <» "o«-* o» < Figure 41. — A graphic representation showing that the geocentric equatorial horizontal parallax is equal to the angle subtended by the equatorial semidiameter of the Earth's figure as seen from the instantaneous distance of the Moon. The maximum value of the lunar parallax here indicated (61'32" ±1") is that derived in a computerized evaluation of this term at the U.S. Naval Observatory in 1976. Table 16 Cases of Perigee- (Proxigee-) Syzygy P-S = <24 h 1600-1999 Introduction to Table 16 The computer printout of table 16 was provided by Dr. Thomas C. Van Flandern, of the Nautical Almanac Office, U.S. Naval Observatory. The mathematical expressions used in deriving the quantities given in this table are listed below. It should be observed that several of these evaluating equations involve two different sets of series expansions. Certain of the original approximate solutions (whose constituent terms are indicated in table 16 A) were found to show minor but unacceptable differences when compared with corresponding data appearing in The American Ephemeris and Nautical Almanac over the more than 120 years of its publication. The small residuals (ephemeris value minus computer printout value) appeared especially when the separation-interval between perigee and syzygy was 2 hours or less (i.e., at a time of maximum perturbation of the lunar orbit in the parameters represented by the formulae) . Table 16 Z=the "average" mean anomaly of the Moon (the angular distance, in longitude, of the Moon from its perigee) Z/=the mean anomaly of the Sun (the angular distance, in longitude, of the Sun from the solar perigee) F=the mean argument of latitude of the Moon (the angular distance, in longitude, of the Moon from its ascending node) D=the mean elongation of the Moon from the Sun (the angular distance, in longitude, between the Moon and Sun) Af=the mean longitude of the Moon=F+ Q, S= the mean longitude of the Sun T=the period of time, in centuries, from 1900 Other Equivalents the mean longitude of the Moon's node the mean longitude of the lunar perigee the mean longitude of the solar perigee the mean anomaly of the Moon the mean anomaly of the Sun The values of the Julian Dates corresponding to syzygy given in column 1 of table 16 are printed out from pro- grammed 6 magnetic tape compilations in the U.S. Naval Observatory, and are determined for the "mean instants" of syzygy. (See main Explanatory Comments for table 16.) A considerably more refined approach, more than doubling the number of terms defining the quantities most affected, was adopted in the preparation of the final printout. These more precise calculating expressions are given in table 16B. All tables in the text (except No. 24 — see footnote in connection therewith) are now based on these more definitive values. The symbols and terminology used throughout tables 16 A, B are given below. The corresponding symbols of E. W. Brown's theory, employed in the Improved Lunar Ephemeris, as well as the notation used in the Explanatory Supplement to the American Ephemeris and Nautical Almanac, adopted throughout most of the present work, are also included: 5 ILE l=L-u> l'=L'-a' F=L-a D=L-L' L V I ESAE M=C— r' (not the M of the first column) g=L-T D=a~L V r M g The values may differ in tenths of a day from the values given in hours in column 2. These Julian Dates form a direct part of an evaluative procedure only in table 24, where an accuracy to a few tenths of a day is completely adequate. Table 16A Approximate Reduction Procedure 1. Column 2 gives the time of syzygy rounded off to the nearest hour . Syzygy is defined as the instant the celestial longitudes (or, alternatively, the right ascensions) of the Moon and Sun are the same, and hence the lunar elongation is equal to zero. Initially, the following approximate equation was used for the determination of the times of syzygy. The desired values were obtained by setting this expression representing the difference in longitude between that of the Moon and Sun equal to zero : X C -A =Z)+ 22,640 sin Z-4,586 sin (L— 2D) + 2,370 sin 2D4-769 sin 2L — 668 sin L' . . . (All coefficients are in arc seconds.) The results from this approximate formula were utilized finally only in table 24, where the least accuracy required is in tenths of a day. All other tables contain data derived from the refined formulae (table 16B). 223 224 Strategic Role of Perigean Spring Tides, 1635-1976 2. The equation originally used for obtaining the geo- included in table 16B after the 17th term in the series. Data centric equatorial horizontal parallax of the Moon at the based upon the more fully expanded series of table 16Bhave instants of syzygy and perigee (cols. 4, 10) is given below. been recomputed for all tables included in the text. It represents a truncation of the more definitive expression *•"(£= 3,422.608+ 186.540 cos L + 34.312 cos (L-2D) + 28.233 cos 2D + 10.166 cos 2L+ 3.086 cos (L+2D) + 1.918 cos (L'-2Z))+ 1.444 cos (L+Z/-2Z)) + 1.153 cos (L-L') -0.978 cos D -0.949 cos (L+Z/)-0.714 cos (L-2F) +0.622 cos 31+0.601 cos (L-4Z>) -0.400 cos Z/+0.372 cos (2L-4D) -0.304 cos (2L-2D)- 0.300 cos (L'+2D) . . . (All coefficients are in arc seconds.) 3. Perigee (or proxigee) is that position in the orbit of mate expression for r £ was used in the initial computation the Moon where it reaches its closest approach to the Earth. for the time of perigee (and hence that of the separation- At this point, the parallax (which varies inversely as the interval P— S) in column 9 of table 16. The results cal- distance) attains its maximum value. Immediately prior to culated to this first degree of approximation have been the position of perigee, the values of the parallax which incorporated only in table 24, where less stringent accuracies have been increasing steadily (cf., figs. 37-38) begin to to the order of tenths of a day are involved. The corres- increase less rapidly, pass through a point of zero change at ponding series expansion given below represents a truncation perigee, and then begin a steady decrease. At the instant of of the more exact equation represented in table 16B perigee, the rate of change in parallax denoted by tt^ is, following the sixth term. therefore, zero. 7r c = -42.54 sin L+6.78 sin (L — 2D) By differentiating the expression for n^ given in (2) and — 12.01 sin 2D— 4.64 sin 2L setting the resulting -k^ equal to zero at the maximum —2.02 sin (L+2Z>)+0.78 sin (L'—2D) . . . value of 7T<£, the time of perigee is obtained. This approxi- (All coefficients are in arc seconds.) Table 16B f° r determining the difference in longitude between the r> c j n j • -r> i Moon and Sun. The instant at which this expression, Refined Reduction Formulae equated to 0°, shows that the lunar elongation is zero, 1. The time of syzygy to the nearest hour (col. 2) is corresponds to the time of syzygy. obtained by the use of the following improved equation X (I -X G =Z)+ 18,222 sin L-7,751 sin V -471 sin 2F+ 470 sin 2L -321 sin (L+L')+ 190 sin (L-L') . . . (All coefficients are in arc seconds.) 2. A more exact expression used to derive the geocentric equatorial horizontal parallax (cols. 4, 10) of the Moon at times of syzygy and perigee (applicable also at any position in its orbit) is: 7r" (5: = 3,422.608+ 186.540 cos L + 34.312 cos (L-2Z>) + 28.233 cos 2D + 10.166 cos 2L+3.086 cos (L+2D) + 1.918 cos {L'-2D)+ 1.444 cos (L+L'-2D) + 1.153 cos (L-Z/)-0\978 cos D -0.949 cos (L+Z/)- 0.7 14 C os (L-2F) +0.622 cos 3L+0.601 cos (L-4D) -0.400 cos Z/+0.372 cos {2L-AD) -0.304 cos (2L-2Z))-0.300 cos (Z/+2D) +0.283 cos (2L+2Z>)+0.261 cos 4D +0.230 cos (L-L'+2Z))-0.226 cos (L-L'-2D) +0.149 cos (L'+Z>) + 0.125 cos (2L-L') -0.1 19 cos (3L-2Z))-0.109 cos {L+D) -0.105 cos (2F- 2D) -0.103 cos (2L+Z/) + 0.092 cos (2Z/-2Z)) -0.083 cos (L+2F-2D) +0.067 cos (L+Z/-4Z>)+0.048 cos (L+2Z/-2D) -0.048 cos (L+Z/+2D)-0.048 cos (L-2F+2D) +0.044 cos (L+4D) + 0.040 cos \L -0.038 cos (I-3Z)) + 0.035 cos (Z/-4D) . . . (All coefficients are in arc seconds.) Essential Conditions for Achieving Amplified Perigean Spring Tides 225 3. The reduction for the rate of orbital motion of the Moon with respect to the perigee is represented by the values given in degrees per day in cols. 5 and 1 1 . These values result from the fact that the angular distance along the plane of the lunar orbit between the Moon and perigee is equal to the true anomaly v^. Accordingly, it is only necessary to differentiate the appropriate algorithmic expression for the true anomaly to obtain (in radians per day) the rate of motion of the Moon, in true anomaly. When the constant term 13.06499°/ d expressing the mean daily lunar velocity in the anomalistic month (360°/ 27.554551 d ) is added to this derivative of the true anomaly i>(T_ (converted to °/ d ), the result is equivalent to the Moon's daily angular velocity with respect to perigee. The computer printout shows that even 169 terms are insufficient to reduce the numerical coefficient to zero in the fifth decimal place. The first 136 of these terms which were truncated after reaching a nearly integral digit 3 in the fifth decimal place and employed in the computation of cols. 5 and 1 1 are given below. £ c = + 13.064997 d H-0.05715 cos (L— 2D) +0.03578 cos L-0.01624 (L+2D) -0.01350 cos (2L-4D) +0.00943 cos 2D -0.00718 cos (3L-4Z>)+0.00558 cos 2L -0.00510 cos (2Z,-2Z>)+0.00333 cos 3L +0.00328 cos (4L-6Z>)+0.00313 cos (L+Z/-2Z)) +0.00290 cos (31- 6D)- 0.00232 cos (2L+2Z>) -0.00222 cos (3L-2D)- 0.00 154 cos (2L+L'-4£>) -0.00112 cos (4L-2D) -0.00 102 cos (5L-8D) +0.00093 cos (4Z,-4Z>)- 0.00085 cos {L-V+2D) +0.00081 cos (5L-6D) -0.00080 cos (3L+2D) +0.00077 cos (2L+4Z>)- 0.00068 cos (4L+2D) +0.00065 cos {V— 2Z))-0.00064 cos (L+4D) +0.00062 cos 4L-0.00060 cos (4L-8D) -0.00060 cos (3L+Z/-4Z)) +0.00059 cos (6L-8D) -0.00054 cos (5L-2D) +0.00049 cos (3L+Z/-6D) + 0.00048 cos (4L+Z/— 6Z>) + 0.00048 cos (5L-4Z>) +0.00048 cos {L-L') -0.00040 cos (L-L'-2D) -0.00035 cos {L-6D)- 0.00034 cos (3L-V+2D) +0.00029 cos (6L-10D) -0.00028 cos (2L+L'-2D) + 0.00024 cos (6L— 4Z))+0.00024 cos (7L-10D) -0.00023 cos (5L+Z/-8Z))-0.00022 cos (L'+2Z>) + 0.00022 cos (2L+Z/) + 0.00021 cos (L'-4Z>) +0.00021 cos (2I-L'-4 J D) + 0.00019 cos (3L-2F-2D) + 0.00019 cos (2L- 3D) -0.000 19 cos V + 0.00018 cos 4Z)+0.00018 cos (Z-Z/+4Z)) + 0.00017 cos (2L-Z/)- 0.000 16 cos (6L-6D) + 0.00015 cos (3L-L')-0.00015 cos (2L+V+D) -0.00015 cos (3L+Z/-2D)-0.00015 cos (2L-L'+2D) -0.00015 cos (4L+L'-8D)+0.00015 cos (3L+Z/) + 0.00014 cos (2L+2F+2Z))+ 0.000 13 cos (L+V) +0.00013 cos (L+2Z/-2£>) + 0.000 13 cos (L+L'+2D) +0.00013 cos (5L-10£>) + 0.000 12 cos (L-2F) -0.00012 cos (2L+Z/+2£>)-0.00012 cos (2L+2Z/-4Z)) + 0.00012 cos (3L+4D)— 0.00011 cos D + 0.00011 cos 5L-0.00011 cos (4L+L'-2D) + 0.00011 cos (2Z/+2Z))- 0.000 10 cos (6L-2D) + 0.00010 cos (3L+2F-2Z))- 0.000 10 cos (6L+L'-8D) + 0.00010 cos (2L-8Z>)+ 0.000 10 cos (5L+Z/-6Z)) -0.00009 cos (2Z,+£>) + 0.00009 cos (4Z.+Z/-4Z)) -0.00009 cos (7L—6D) — 0.00009 cos (7L-8D) -0.00008 cos (2Z,— 2F—2D)- 0.00008 cos (5L+2D) + 0.00008 cos (L-2F+2D) + 0.00008 cos (8L-10£>) +0.00008 cos (7L—4D) -0.00008 cos (3L-5D) -0.00008 cos (2L-2Z/) + 0.00008 cos (2L+2F-2D) + 0.00007 cos (L-D) -0.00007 cos (4L-2F-4D) + 0.00007 cos 6L-0.00007 cos (8L-12Z>) -0.00007 cos (31- Z/-6Z))- 0.00007 cos (L+6D) + 0.00007 cos (6Z.+Z/-10Z))- 0.00006 cos (3L-L'-2D) 202-509 0-78 22( : Strategic Role of Perigean Spring Tides, 1635-1976 (Continued) -0.00006 cos (31- 2F+ 2D) +0.00006 cos (21— Z)) +0.00006 cos (Z,+Z/+4D)+ 0.00006 cos (31— Z/-4D) +0.00006 cos (Z-— Z/— 4D) +0.00006 cos (\L—V) -0.00006 cos (4L— Z/+2D)+0.00005 cos (4L+Z/) — 0.00005 cos (4L— 5D) + 0.00005 cos (5L+L'— 4D) +0.00005 cos (L'+D) +0.00005 cos (3L+2Z/-6D) +0.00005 cos (3L-8D)- 0.00005 cos (4L-Z/-6D) + 0.00005 cos (7L+Z/-10D) -0.00004 cos (Z/-6D) +0.00004 cos (Z/+4D)- 0.00004 cos (5Z-2F-4D) -0.00004 cos (2Z,+2F) + 0.00004 cos (2F+2D) + 0.00004 cos (5L—L')- 0.00004 cos (2F— 4D) -0.00004 cos (3L- 3D) -0.00004 cos (2Z-Z/-3D) -0.00004 cos (9L—12D)- 0.00004 cos 6D + 0.00004 cos (L-4D)- 0.00004 cos (5Z+Z/-2D) +0.00004 cos (L+3D)- 0.00003 cos (3Z+2Z/-4D) +0.00003 cos (4Z,+2Z/— 6D) + 0.00003 cos (3L—D) + 0.00003 cos (L+2F-2D)- 0.00003 cos (4Z.-Z/-2D) -0.00003 cos (7Z.-1 2D) -0.00003 cos (L-2Z/+2D) -0.00003 cos (2L-2Z/+ 2D) +0.00003 cos (2L-2F+2D) -0.00003 cos (L+2F) . . . .] radian/day. (All coefficients are in radians.) 4. The following expression is used in computing the Moon's daily rate of angular motion in right ascension, o;j (cols. 6, 12), determined for the instants of true syzygy and true perigee, respectively. This value represents lunar motion as it is projected into the plane of the celestial equator. As such, it more exactly represents the portion of the diurnal motion of the Earth (occurring in a plane either coincident with, or parallel to the Equator) through which it is necessary for any given meridian of the Earth to rotate in order to catch up on the Moon. However, cyclically, over long periods, the calculated motions in right ascension show deviations from values consistent with the existing parallax. These deviations are the result of the effects of the 18.6-year nodical (draconitic) cycle which causes — in addition to a 5° increase in the range of the maximum declination of the Moon (fig. 36) — a much smaller but gravitationally effective variation in the extremes of lunar latitude. Such latitude excursions are responsible for periodic quantitative deviations in a<£ from values to be expected from the existing parallax. These are approximately equal in magnitude to similar deviations caused by the solar parallactic inequality. With these latter factors properly considered, a value obtained from this equation is useful in determining the additional angular motion necessary for a given terrestrial meridian to catch up with the Moon and occasion a lunar transit, subject to the Earth's rotation in, or parallel to, the same equatorial plane. a (C =13.17640 o [+5,162 cos L-4,067 cos 2M -1,756 cos (F+M)+ 1,008 cos 2D + 906 cos (L- 2D) -668 cos (L+2M) + 351 cos 2L-288 cos (L+M+F) + 227 cos (L-2M)-191 cos 2F + 176 cos 4M+149 cos (3M+F) + 127 cos (Z+2D)-121 cos (L-2M-2D) -107 cos (2M+2D) + 97 cos (L-M-F) -80 cos (2L+2M)-75 cos (3M-F) + 68 cos (Z/-2D) + 53 cos (L+2M-2D) -53 cos (L-M-F-2D) + 51 cos (2M+2F) +48 cos (L+4A0-46 cos (M+2D-F) -44 cos (M+F+2D)+41 cos (L+3M+F) + 37 cos (L+Z/-2D)-34 cos (2L+M+F) -33 cos (L+2F) + 3l cos (L-L') -29 cos (L-4M)-27 cos (Z+Z/) -27 cosD+26cos3L -25 cos (L-3M-F)-24 cos (L+2M+2D) + 23 cos (L-4D) + 23 cos (L+M+F-2D) + 15 cos (2L+2M-2D)+14 cos (2L+2D) + 14 cos (2Z-4D)+14 cos (Z/+2M) -13 cos (Z/-2A0-13 cos (L+3M-F) -12 cos V- 11 cos (Z/+2D) Essential Conditions for Achieving Amplified Perigean Spring Tides 227 (Continued) +10 cos 4D+10 cos (Z--Z/+2D) -10 cos (L-2F)-\0 cos (L+M-F+2D) +8 cos (Z+2M+2F)-7 cos (5M+F) + 7 cos (M+3F)]/3,600". (All coefficients are in arc seconds.) 5. The expression used in obtaining the apparent declina- true perigee (col. 13), which is also applicable at any time on of the Moon at the time of true syzygy (col. 7) and in the lunar orbit, is: 81 = [83,523 sin M+] 17,662 sin F +4,599 sin (L-M)+4,570 sin (L+M) + 964 sin (L+F)+954 sin (L-F) -952 sin (L+M-2Z>)-903 sin (L-M-2D) -594 sin (>-2Z>)-578 sin 3M +517 sin (M+2Z>)-434 sin (M-2D) + 374 sin (2M-F)-366 sin (2M+F) +274 sin (2L+M)-183 sin (L-F-2D) -153 sin (L+F-2D)-\33 sin (L'+M) -133 sin (Z/-M)+108 sin (F4-2D) -101 sin (2F-M)-93 sin (2L+M-2D) -88 sin (L-3M)-87 sin (I+3M) + 67 sin (L+M+2Z>)-65 sin (M+2F) + 57 sin (2L+F)-54 sin (L-F-2M) -54 sin (L+F+2M)-47 T sin M -41 sin (L+ L'+M -2D) -41 sin (L+L'-M-2D) -33 sin (L'+M-2D)-33 sin (L'-M-2D) + 31 sin (L-F+2D) + 30 sin (2L-M) + 29 sin (L-L'+M) + 29 sin (L-L'-M) +29 sin (2L-F)-27 sin (Z/+F-2Z)) -25 sin (M+D) + 25 sin (M-D) -22 sin (L+L'+Af)-22 sin (L+L'-M) + 19 sin (L+3M-2Z))+18 sin (L-2M+F) + 18 sin (L+2M-F)+17 sin (L-3M-2D) + 14 sin (2M+F-2D)-14 sin (2L+F-2D) + 14 sin (L+F+2D)+13 sin (L-M-2F) + 13 sin (L+M+2F)]/3,600". (All coefficients are in arc seconds.) 6. The corresponding declination of the Sun at the any other time in the apparent annual motion of the istant of true syzygy (col. 8) and true perigee (col. 14)— or Sun — is given by: 5° = [83,797 sin S+ 1,404 sin (L'-S) + 1,403 sin (Z/+£)-594 sin 3S -46 T sin S-30 sin (L'-3S) -30 sin (L'+3S) +26 sin (2L'+S)]/3,600". (All coefficients are in arc seconds.) 7. The expression used to obtain the time of perigee and low. Because of the mathematical assumptions used, this ex- hence the separation-interval P—S (col. 9) by differentiating pression is the most accurate near the alignment of perigee expression (2) and setting x^ (the rate of change in par- and syzygy. aLax) equal to zero at the maximum value of ir^ is given be- ^=-42.54 sin L+6.78 sin (L-2D) -12.01 sin 2£>-4.64 sin 2L -2.02 sin (L+2Z))+0.78 sin (L'-2D) +0.26 sin (L+L' -2D) -0.24 sin (L-L') +0.23 sin (I+L')-0.17 s in (L-2F) +0.37 sin (L-4D)-0.43 sin (L+2L) —0.25 sin (2L+2Z))-0.22 sin 4D L'lifi Strategic Role of Perigean Spring Tides, 1635-1976 (Continued) + 0.21 sin D— 0.15 sin (L— Z/+2D) +0.15 sin (2L-4D) + 0.13 sin (Z/+2D) -0.06 sin (2L—L') . . . (All coefficients are in arc seconds.) In considering the computer printout of table 16, two important characteristics common to such close perigee- syzygy alignments are readily discernible : 1. This table is based upon a maximum separation- interval of ±24 h between perigee and syzygy. Accepting this arbitrary 24-hour interval between the two astronomical configurations as defining the upper limit of a typical close alignment of perigee-syzygy, it is obvious that such close alignments almost invariably occur in pairs, averaging 29.5 days apart. These occurrences are followed and preceded, in the average case, by another such pair, one component of which is separated by approximately 6.5 or 7.5 periods of 29.5 days from its matching component in the first pair having the smallest interval between perigee and syzygy. (Sometimes, however, as the result of the limiting 24-hour perigee-syzygy separation-interval, one component of either pair may be eliminated.) Either of the components in each pair may have the smaller separation-interval between perigee and syzygy. This results in the corresponding vari- able length of time (i.e., 6.5 or 7.5 periods of 29.5 days) between it and the component having the smallest separa- tion-interval in the preceding or following pair. 2. Since lunar months rather than calendar months are involved in the succession of perigee-syzygy events, one or both components of any pair may also overlap 2 con- secutive calendar years. The tropical or calendar year, usually (but not always) containing four ordinary perigee- syzygy alignments with a separation-interval <24 h , consists of 12.37 synodic months. Thus, the successive pairs belonging to a perigee-syzygy cycle of 6.5 or 7.5 periods of 29.5 days can easily lie in different calendar years, and due care must be exercised in relating these cycles over long periods of time. Table 16 Designation of Columns Table 16 is reproduced by electronic composition directly from a computer printout of lunar and solar data provided by the Nautical Almanac Office, U.S. Naval Observatory. This table contains data pertinent to all cases between the years 1600 and 1999 in which lunar perigee and syzygy occur within ±24 mean solar hours of each other. The arrangement of this table is as follows : Col. 1 gives the Julian Date to the nearest 0.1 day, corre- sponding to the time of mean syzygy. This position is based upon the mean apparent motions of the Moon (13.176396°/ d ) and Sun (0.985647°/ d ) and represents the average time at which these two bodies reach syzygy align- ment. The apparent discrepancy between the decimal por- tion of the Julian Day and the time (in hours) given for syzygy in column 2 is due to the fact that the latter time cor- responds to true rather than mean syzygy. For any date in history, the Julian Day also starts at noon (Greenwich mean time) , whereas all of the times given in column 2 are in Greenwich civil time (or more exactly, ephemeris time) which begins at midnight. The inclusion of these Julian Dates makes more conven- ient the subtraction of differences in time, and the estab- lishment of related periodicities between individual occur- rences of perigee-syzygy. It is also possible by means of this artifice to determine the day of the week for any instance of tidal flooding, making possible the cross checking of early documentary sources of such flooding. For all practical purposes, one-half of the difference in hours (col. 9) between true perigee and true syzygy may be algebraically added (as a decimal part of a day) to the Julian Date of mean syzygy to obtain the approximate mean date of perigee-syzygy. Proper allowance must also be made to convert from ephemeris time at Greenwich to local stand- ard time at the location of the flooding by subtraction of the appropriate number of hours which the station is west of Greenwich. For example, in establishing the corresponding day of the week in eastern standard time, 5 hours (0.2 d ) is subtracted from the Julian Date. The date and decimal portion are then rounded off to the nearest unit. Any result- ing decimal value of 0.5 d is rounded off, in practice, to the nearest even unit, either higher or lower, as the case may be. The appropriate day of the week is obtained by dividing the entire rounded-off Julian Date by 7. If the remainder is 0, the day is Monday, if 1, Tuesday, etc., through a remain- der of 6 for Sunday. Column 2 contains the year, month, date, and 24-hour time of true syzygy (rounded off to the nearest hour) for each case of syzygy associated with a perigee-syzygy align- ment in which the two components occur within the pre- scribed separation-interval of ± 24 hours or less. All dates, regardless of year, are given in the Gregorian (New Style) Calendar. Prior to 1752, if Old Style dates are desired for comparison purposes, the tabulated dates must be corrected according to the procedure outlined at the close of part I, chapter 1. In the data processing procedure, the necessary reductions have been made, and all times given are in ephemeris time, which corresponds very closely with Greenwich civil time. Using data referred consistently to Greenwich civil time throughout this and subsequent columns of the table, no ad- justment is needed for the fact that, after January 1, 1925, the beginning of the astronomical day changed from noon (Greenwich mean time) to the preceding midnight (Green- wich civil time) . To convert to eastern standard time, 5 hours should be subtracted; Pacific standard time similarly is 8 hours earlier. Because of rounding-off and data-truncating procedures used in the computer processing, the times given in this col- umn will not, in all cases, agree exactly with those contained in The American Ephemeris and Nautical Almanac and other ephemerides, or as reproduced in various governmental tide tables. Where rounding-off errors combine in the same direction, the differences may amount to as much as an hour. The more accurate ephemeris values have been used in all cases throughout the text where times to the accuracy of minutes are involved; however, the present tabular values will suffice for all instances in which values accurate to the nearest hour are required. Column 3 indicates the phase of syzygy as either new moon (N) or full moon (F). Column 4 lists the geocentric horizontal parallax in min- utes, seconds, and tenths of seconds of arc, corresponding to the time of true syzygy. Column 5 contains a series of angular values expressing the rate of orbital motion of the Moon with respect to the perturbed motion of perigee, determined, for the instant of syzygy, in °/ d . The procedure by which this value is calcu- lated from the time rate of change of the Moon's true anom- aly is explained in the Introduction to table 16. The method of using this angle, and that from column 6, to obtain the special value designated in this monograph as the "Aw-syzygy coefficient" is described in chapter 8. This coefficient represents the astronomical portion of a total quantifier indicating the potential for tidal flooding associ- ated with the simultaneous occurrence of perigean spring- tides and strong, persistent, onshore winds. 229 2:»n Strategic Role of Perigean Spring Tides, 1635-1976 Column 6 tabulates the orbital motion of the Moon in right ascension (expressed likewise, for comparative pur- poses, in °/ d ) at the instant of true syzygy. Column 7 is a tabulation of the apparent declination of the Moon (to the nearest degree) at the time of true syzygy. Column 8 notes the apparent declination of the Sun (to the nearest degree) at the time of true syzygy. Column 9 indicates the increment or decrement (in hours) which, according to algebraic sign, it is necessary to add to, or subtract from, the time of true syzygy in column 2 in order to find the corresponding time of true perigee. This difference in time is consistently taken in the sense perigee minus syzygy, and represents the perigee-syzygy "separation-interval" frequently referred to throughout the volume. With the exception of a few cases caused by the combination of rounding-off errors, no value in column 9 exceeds ±24 hours. The mean epoch of perigee syzygy (see column 8 of table 1 ) is obtained by dividing the figure in column 9 by 2 and adding the result algebraically to the time of syzygy in column 2. Column 10 designates the geocentric horizontal parallax of the Moon (in minutes and seconds of arc), in the same manner as column 4, but now as it applies to the slightly different time and position of true perigee. Column 1 1 repeats the instantaneous value of the rate of the Moon's motion with respect to perigee (in °/ d ) de- scribed under column 5, but now referred to the time of true perigee. Column 12 gives the orbital motion of the Moon in right ascension (expressed also in °/ d ) for the instant of true perigee. Column 13 reproduces column 7, but gives the apparent declination of the Moon (in degrees) at the time of true perigee. Column 14 provides the corresponding apparent declina- tion of the Sun (in degrees.) at the time of true perigee. Essential Conditions for Achieving Amplified Perigean Spring Tides 231 — co oo 10 ff> 01 m ^ o m co *a- o oo cvj in n oi i — otflOimTt o eg in co ^t cn — en in ^i c\i eg po ^ 06 oi to rv ^ oi d ^h in iri csi r— cm CD ro — i co co csi iri — . — — CM CM CM CM CM —I — < — — CM — CM CM CM CM CM — « CM — i in CO Cn I — — ' ID 0"> id iDintn O) micieoo — r— oo id o eg id ro o> ro en •— » o r— o r— co oo r — co 10 r— cn o nicnrxin cm 10 ^- oo eo in cn ** r— ^- ^ ^ t rooo tfincvi m-n cm m 10 oo f cm rx oo o o i — cn o r— i — in ^ in cm in oo ^ cm o o ioio cm o 10 o ^ m tn ^ m m en oo ro 1010 ooo < — i ct> oix id «f cn cn m m «* cm cm in co 01 ^f to i-j cn pn n -q- in id id id iDic'ib in in ^- ^- *cf *a- ^^^a-^a-in inintDiniD inioininin ^a- ^a- *cr *cr ^r' *a- *a- **' *3- *3- in in id id id IDCJl CMOO ^H CO OO OJ O) <-ilDOOIX(D CM oocm oiONOin cooicorxco oo — i «a- r-» id en oo oo o-> in cnoioooi O) «ooo en ooicooio cnoiocnoi oo oo r-.oo oo o o r^. en oi ->qcoq en en oo oq o en oioi q -a- r-. oq iq co — — ; in — r-- cm r-. «» o r-~ cq oq eq en "tqcgin^ ir> oo — oo in to ^ oo in cn i ^h ix! en id cn i oen -.i — — . rt id^- idoi — « t cnoo >» a- n m n — icmi — cor- >jcoenoi >» cnoocomin id ooi — ooo m en oo i — i — r— ^t- *a- cm ~^ oinegcoco ro cn r— in id r— cq o ^ cq oq cq o ^3; — iDomoo^ in ^^co^ *=r cm r— o en cncoeoioi — «j ^- in ^ in in'iniDiniD in id in in in ^ in^r ^- ^ *a- *a- *cr ^a- «=j- in in co in id it «7 en ^- in cmoocm i — coencsi^j-i — id ^h en r* cm o< oorvrtffien io«t enenco or-, r— i — ■«3- cm i — oo — oo cm> en en co co oo en «— < co oo en •— i en oo en co en en co en en oo i — ID — ID en — co id id co r— co id i — oq wqqrven en — o oq o en cn en en o cqencneq co — * cd i — eo in ^ en en oq en cq in o eq q q ^ oo in oor^oino cmco o ^ en ens cm co en « — i m rgen ^ incocnm^ biriinrtoi —r^i— ^r^— I dindt' cd d cm ^ oo in ids'idoid r-1 — dd t' in « ob — i s! i< cm id id d ob en cm o cn •— » CM CM CM CM CM •— « CM CM — »— I CM CM rH CM in N rt CM CM Cg CM ID CM CM — CM CM" — " CO — — .— ■ CM ID ID CO ID ID ID ID ID ID ID ID ID ID ID ID ID CD CD ID ID ID ID ID ID ID ID ID ID ID ID CD CD ID ID ID ID ID ID ID ID ID ID ID ID ID ■a-cgininn ooomoco en •«a- cm — < coeoincM encMCMCMcn co m co cm eo cm — en oo en 2 r-- m r— CM CM m m ■** CO ~-i CM CM ro -" eo eo cm co — ■ — < CM CM en en r— -iCMCM en i — ID ID ID CM CM CO -3- CO 2 z: — I CM CM 1 CO CO co ro co •"* eo — < in in cm — ID r ~" — < CM oo en co •a- en eo *a- m ID -CM in ID r— cm — > r— oo en CM OO OO cn co -a- in CO - cm in ID -H CM CO eo o CO — co co eo eo co CO CO ID ID CM CM CO CO CD CD o CO CO CO CO CD CD CD CO ■*»• co eo CD CD CO CO CD CD o eo ID ID m CO ID m CO ID m in id cd eo co eo co ID ID ID ID IDIOS eo co eo CO ID ID eo co ID ID CO ID CO ID oo CO ID CO ID CO ID co en CO CO CD CD CO CO cn CO cn co CO — CO CO CO CO CD ro o» « ro oo ro csi co ir> r-* r-* cn cn *-* ^ co lO lO UO LT> U"5 j-O to *-£> <_o CD lO «— * cn cn '^ ^ co cvj uS *sr r--' co co co cn to cn oo ^^ r^. CD co cn CD CD cn u-> co r-*. oo OO CD CD ^ < en cn cn cn cn cn en Table 16 232 Strategic Role of Perigean Spring Tides, 1635-1976 PO ^ IT) Tf CSJ tO CNJ O) ^h CD CT> LO 0*» CNJ •— " CO ^ IT) ^t r-» «— i CO ^ O OO CM tO O uO O OHD -I n d csl ob cm cb o in ^ 06 co c\l oi ro 06 d lo lo ro csi cb c\1 CSJ^-*CSI^h«— 1 — I —• CM CM CM CM CxiCMCM~^^ .— . ^ ^ fsg ^ CM ~^ CM CM CM CM CM ^ ~^ ^ ^ m ro t ^ ^ oorooors *}■ _, 00 ^a- cni ^a- to co •— • o to to ct> 00 co ro ^-« co to -^ ^s- m^mooo ooirs^^ to o m cm 00 cm to 00 o 00 -q- 1^ 00 c\hd cm -^ OO tn O r^ O O rv OO C\J OO Cn CO O tO O •— < O to CM *=T <— 1 in m CO m O O O ^t ID I — ^ ID CO CO CO m <£> _« ^ csj ^a- ooyjinoo^ to n, 00 cm co -^ C) ^ en ct> ^ooin^in o ^ en 1 — 00 u: in 00 ^ in °9 t£ ? tb to to in ^ rorororo^t «t intbrN rs rN to to ^ ■**- ^- f) CO *3- *3" ^r in" in to to to to to uSuS rv cm co o> 1*^ ^h to — • 00 to to 00 •— < 00 1 — to cm co to 00 cm cd 00 in ro co en m in n co to co en co cm 0010 ocn 0100 o o en o^ o o 00 00 en •- < o-> 00 en o o 00 en ocnen 1 — o o coenco ^- o cooioo o 01 00 o> 01 o IT) CM Cfl IN CO 0)CMN«f^ CO If) in cn m co cm cm co no m en 00 o o 01 cno o o o cn cn o o 00 00 en <— ^-i ^ CM CM -— • ^ CM CM CO ^ ^-r CM ^ ^ CNJ CM ^ ^h CM CM CM ^_, ^ ^ CM -" CO CM CM ^_ ^ ^ •— « cm 00 en co ^t o --h ^ in cvj cmid pv cm ^h cm cn 00 cm co ^ en o co ^- m ^ cMin to n cm - — 1 to n, 00 cm co co oi o ^r o en 'i- en ^-coco cnto oocMoocorN cm in cm n. < — ■ 1 — ^ to «— no ^-h m o to o m en m o i ^trr ibifirs NO) O) oo>h d cb cm cm ^r ^r to to uo ob rs. o en en -^ ^ co cb cm in *t to to to 00 rNOO) cmco r-i i-s. o to o coo) cm m ph - m 00 ^f cn o 10 id in 00 en o .— >CNjcocom into r*. r^o) cn ^ ^ <— • co co m in in n, in o» o> O) ^ ^coco'S-in ^? 5? 5? <=> OOOOO O OO O ph ^_, ^ ^ ^ ^ ^_< ^ ^ ^ ^ rn CM CM C\ CM CMCMCMCMCM CMCMCMCMCO COCOCOCOCO I CO CO CO COCOCOCOCO COCOCOCOCO COCOCOCOCO COCOCOCOCO COCOCOCOCO ICMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CM CM CM CM CM CMCMCMCMCM Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 2l:\ CO OO <= to oo ^ CO oo to oo CO <=• to oo oo oo CO oo CO CO LO oo oo CO oo OO oo oo Csl oo -3- CO OO Csl CO oo Cs oo oo Csl LO CO oo oo >o CO CO Csl CO to Csl oo Csl <^> 1 1 Csl 1 1 Csl 1 1 1 1 1 Csl Csl Csl Csl Csl Csl 1 Csl 1 1 1 1 1 Csl CM Csl Csl LSJ 1 1 UO ^ uo CO „ oo Cs LO to ( oo oo CM Csl oo ^ oo CM oo OO oo _ LO to ^ to OO OO OO OO oo ' ' 1 1 1 1 1 Csl Csl Csl Csl Csl C-sl CS! 1 oo CO oo oo to oo to oo LO CO CO OO OO oo LO Csl CO oo uo CO CO OO oo Csl CO Csl OO oo oo CO oo CO to OO a to to LO LO o- oo CO CO LO CO to oo OO Csl to Csl ^ 2 LO to LO to to LO LO LO LO 2 a 2 2 T 2 ■=r -3- to to to to to to •*T ■LT OO CO OO 2 to to to oo oo OO oo Csl Csl OO CO oo oo oo LO OO oo oo LO to CO « c: tc OO Cs o- or OC tr. CO LO i.O OO oo oo Csj Osl CO CO OO CO CO OO oo oo oo CO CO oo oo CO OO oo OO <=: CO OO CO Ol OO CO CO OO OO CO <=> to to to to to to to to 2 s to - to to to ^ CO <=> to „ Csl oo LO oo rt oo oo _ _ CO Csl OO LO OO LO p^ to CO CO oo OO Csl ! o OO UO _ „ oo ** «9 oo oo to ^ o-i CO *» to *3- to oo oo to Csl to Csl uo oo oo to uo to " ■"■ "~" LSI "* ■* H — < LSJ LSI LSI ""■ Csl LSI Csl ""* Csl Csl "" OO ~- — ' —' Csl — ' Csl Csl Csl Csl Csl Csl Csl Csl Csl ~~ LSI LSI - H LO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to O") LO to to LO oo LO Csl oo e> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Csl lo „ to _ rt ■«■ „ LO „ Csl _ LO to oo oo CO oo ! oo OO ^ Csl rt CO CO <=> to oo oo ^ m LO oo oo oo LO oo 1 1 Csl Csl Csl Csl Csl 1 1 1 1 Csl Csl 1 Csl Csl Csl Csl 1 Csl 1 1 1 Csl 1 Csl 1 1 ^ oo CO to oo ^ „ oo LO oo LO Csl oo oo to ^ CO oo oo CO Csl _ oo oo oo p^ oo oo oo oo oo oo OO ^ cs, oo OO Csl oo in LO to oo to oo oo Csl oo CO CO CO LO LO m oo Csl uo LO CO ' 1 1 1 1 1 1 1 1 1 1 1 1 1 Csl Csl Csl Csl Csl Csl 1 1 Csl Csl Csl Csl Csl csj 1 Csl 1 UO oo LO oo oo Csl oo -3- -3- oo oo oo -3- oo OO to LO oo Csl CO CO oo Csl CO oo UO OO uo LO oo CO CO •t* ■"3- oo ■«3- •3- to oo -3- Csl oo to Csl to oo CO to to uo o oo Csl ■=3- LO s to to to LO •cj- ■=3- 2 LO LO to LO to to to to UO LO 2 s oo oo oo 2 LO 2 to to to uo OO oo LO oo oo OO oo Csl LO LO oo to CO to oo oo oo to to oo to OO CO to oo LO oo OO LO oo Csl uo CO oo m Csl u-j oo o-> oo oo oo co CO oo OO oo CO CO OO OO CO OO oo OO CO CO OO CO OO CO <=l CO oo oo CO oo CO CO oo U, oo OO oo ^ Csl oo ■=3- •9 CO oo CO oo Csl oo oo Csl CO «* rt Csl Csl ~~" "-* Csl LsJ "" "" LSI ""• ~ LSI LSI — ' ~ "-' oo - H - , Csl •"• ""■ r-H Csl Csl ~ — ' Csl Csl *"■ — ' Csl Csl rt — ' Csl LSI — ' « to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to LO to - - -. CO to CM OO oo oo cr> Cs. Csl I- Csl -. oo oo Csl - CO -3- OO OO CO -3- -. CM OO OO -H oo to ~ oo oo oo - LO LO Csl CO oo -3- o Csl to r; „! oil _i (J, ,J, pi CO J, OO pi Csl oo Csl Csl Csl Csl Csl Csl Csl Csl csj «* CO " LO to zz a to f- rt Csl oo oo Csl OO CO 3 •3- UO CO ~ a to r - a - 1 Csl r- oo — Csj oo CO oo -3- CO z: LO to Csl — to r - *-' Csl rsi OsJ OO" oo' oo oo «-f „f uo LO LO LO to to to to oo oo oo oo CD oo oo CO CO CO CO ^_' z^ Z5 „" Csl Csl Csl oo OO oo »3- "3- to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO oo OO «3- oo CO oo CM oo Csl CM ^ CO to LO CO LO CO LO oo uo OO T „ oo OO oo oo oo C oo Csl r ^ ,^ Csl oo OO ■>=r to oo OO CO CO Csl oo to LO oo oo oo CO CO Csl Csl to LO oo CO Csl 'S- x-> *n ZJ> :sj » -o ro CO ^o Csl -3- oo -o -3- «3- oo to oo •"3- to en LO oo oo CO oo m ■"3- •"3- "=>■ "* -3" LO LO LO LO LO LO LO LO LO LO LO to to to to to to to CO co oo OO Csl oo Csl oo Csl OO oo oo oo oo oo oo oo OO Csl OO OO Csl CO Csl OO Csl OO OO oo Csl oo oo Csl oo oo oo OO OO Csl OO oo OO 00 Csl oo Csl oo Csl oo Csl oo Csl oo Csl oo Csl oo Csj OO CO CSI Table 16 234 Strategic Role of Perigean Spring Tides, 1635-1976 oo CO UO CXI oo CO CXI en ■<3 UO CO OO CO ^ UO oo oo UO CXI oo CO CXJ CO T CXI CO CO CO UO CO UO CD CO CXI CO •>» to co CXI to oo OO CO OO CO oo UO UO CO en UO CD OO OO OO CXI OO CXI UO CO en UO CD oo 1 1 1 CXI 1 CXI CXI CXI 1 1 ' 1 1 1 1 1 CXI 1 CXI exj CXI exj 1 CXI CXI 1 1 1 1 1 CXI ^ CO csj oo CXI o-> oo oo CO to UO CO UO oo CXI en OO ! ^ oo oo CD OO UO ^ r ^__ CO CO oo OO OO UO ^. UO UO r __ ^ oo en CO UO _ «3- _ C-» oo oc oo to to en UO UO UO UO OO CO CD CD CD oo to OO oo CD UO oo UO UO 1 1 CXI CXI CXI ' 1 1 1 1 1 1 1 1 1 1 1 1 1 • 1 1 1 CXI oo CSl oo to UO oo OO CXI UO CO oo Psi •<3- oo oo tc tr. Ox UO in CO CO en cx UO OO oo oo CO CO OO CD UO UO UO CD a-> oo oo oo oo UO to to to UO UO UO UO UO 2 2 2 CO 2 2 2 UO UO UO UO UO UO UO ■"3" *3- 2 •"3- 2 "3- "3- -3- UO oo UO "3- •«3- en OO CXI CXI en oo UO oo oo OO CXJ OO UO CO oo oo oo CO OO en oo CO o-> oo CO en CO CD CD oo CD oo CO CO OO OO CO co en CO CO CO CO CO CD en CO to to to to to to UO UO UO to UO UO UO to UO UO UO UO to UO UO UO to UO o-> co CXJ „ „ CO ^ ^ CO OO CXI oo CO en OO r oo en ^ en en oo CXI UO oo en UO T ^ CD UO UO ,, CXI UO OO CO CO CO CO UO CXI CO oo oo oo to CXI oo UO UO UO OO CO oo en UO CD UO oo m OO U) CD CD oo UO OD CXI m — ~ IsJ "* H tg **■ tsi N CM "- ""■ —' "" CXI CM " "" tsj CM — ' *"* CM CXI ~* CXJ CXJ CXJ -" CXI tO to to to to to to to to to to to UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO CO to to oo OO oo oo OO OO oo CXI CO CXI oo OO UO to UO o» 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (XI CO oo OO CXI CXI UO OO oe — to CO CO ~ 7 to to CXI oo oo CO OO CO OO 7 CXJ UO UO 7 CO en • CXI UO to OO oo CXI CO CXI CO CXI CXI CXI CXJ CXI CXI UO CO CXI 7 en " ' CD 1 oo OO CXI oo to to oo (^ ^J. OO _ oo ^ ^ oo UO CO to UO CO UO ^ UO CO _ oo -3- OO „ CXI UO CO -3- CD CXI CO to ^ UO UO UO _ CXJ CO tO oo oo — co CXI CXI CXI CXI CXI UO CXI CO CXI oo UO CXJ CXI <«r UO 1 7 CO ^ ^ oo CO CD cn OO oo ^ 1 UO OO ~ 1 UO OO CD UO CO to oo oo UO to oo to s OO oo 2 OO ■"3 s s to UO UO UO - UO 2 oo 2 2 2 2 UO 2 UO 2 UO UO UO UO UO UO UO UO UO 2 «3- 2 2 2 ■"3- UO — UO in oo CXI oo oo oo CXI UO OO OO CO CXI UO UO UO a CO UO OO UO in oo co CO UO en OO CXI CXI UO OO en oo to OO UO "3- CD oo CD OO CO UO CO oo m oo co CO en OO CO oo oo en oo CO o^ CO CO CO CO CO CD en ° to 2 to to to to to UO UO UO UO UO UO UO UO UO UO UO uo UO UO UO UO UO UO to CO to ^ CXI 1=1 OO CO en „ ^ CO OO oo CO „ ^ OO CXI CXI _ UO en CXI UO CXJ oo oo CO CM OO to CD UO UO o CD OO UO to oo -3" •*r CXI CXI ~"* IxJ k J U.J I J ' ■ ' 1 ' ■ ' to to -O to to to to to to to UO UO to to UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO UO m - z oo cr> ■CT OO OX, OO CXI CO CD oo cx, CD „ ^ CO oo _ OO oo CO UO UO CO en oo oo CO —J* Cxi CXI — * CXI 7 — p 7 7 7 7 7 7 7 7 7 — ■ " — * 7 7 7 7 CXJ 7 en ^ 2 S3 Ox! UO CXI UO UO OO CXI CXI CXI CXI CXI oo o-> £ oo OO oo OO OO CM UO UO UO 2 OO OO "3- CXI OO CXI - Oxl CO CO OO en CXI oo ^ 2 •"3- UO CXJ oo CD oo ■w OO CO «* to CXI OO oo OO oo oo oo oo ~ ~ 5 c ~ " 3 " <=i 5 " =r to to to to to to to to UO UO UO to UO UO UO UO to UO to to CO to co UO co UO CO "3" en UO en ^ OO en OO oo oo OO oo ^ oo r ^_ CXI oo CXI ^ „ ^ UO _ UO _ CO UO CO UO to CO •a- en OO oo oo UO UO UO oo CO OO oo UO UO UO CD oo CO CO CXI CXJ oo UO CD oo i.r> UO r-D CD CD OO UO m to CD CO oo oo OO OO OO 2 oo oo oo OO 2 en en en en en en en en en CD CD CD CO CXJ to CO CO CXI CO CO CXI CO CM CXI CXJ Oxl CXI J5 CXI CM CXI cm CM CXI CXI CXI CXI CXI CXI CXI CXI CXI CXI CXI CXI CXI Cxi CXI CXI CXI CXI CXI CXI CXI CXI CXI CXI Oxl CXJ CXI CXI CXI CXI Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 235 cm o cm cd O to CO to CSI Cn CT) „ tO oo o r-~ csi CSI CSI CD ^j- cn o-> CO tO CSI CO Cn to OO oo oo CSI CM OO cr> ^ to u-> CO CT) cn CO CO ~* u-> csj cr> CO CSI CO o-> CSI oo o-> «* •*3- CSI OO CO to cn CO CO CM OO -=r CM CM CM CM CSI 1 1 CM CSI -^ 1 1 1 — • CM ~H CSI CSI CSI CM ~ CSJ 1 1 1 1 CM CM CSI 1 CSI CSI 1 1 M rt M -H CT> P~ OO to cn cd "3" cd to CT> CO cn <=> CSI —I CSI us m «t rt ■«3- CD CO CSJ CSI „ CD CD CSI to „ OO CM f ^_ CO CD LO CO cd cn CO to r- moid CO oo r-~ CD CD CO to CO Cn to CD OO — 1 CM CM CSI CM CSI « ' ~ CSI 1 1 CSI CM CSI 1 I 1 1 1 1 ' 1 ' ' cm r~ co ^r «er -«3- «3- ■*»• cm co iors rt isoi m -h to cm -> r-~ 3 «3- - CD cd o-> en *3- cn CO cd CD o r~« rs m oo to to — t to oo to CO CD CSI OO CT) CO cn CO CD to CO o-> «3- CD —< COOIs (nooo cn cd » i — tO tO >■— r-~. to to to to r~ to to r- to ISIOIS i — r«- CD ~^ to to co ro ^- cn co cm r— cn co cn — t ^a- oo cn to OllsOOrs OIOOOOIOO I—.' to to CO CO ^^ i oioqo' UJlDNI to cn to o cn en r-J to to CM CM rt CSJ CM CM -H CSJ CM CM — CM CSI rt <— i CM CSI — I ~ CM CM -H CM CM to to to to to to to to to to to to to to to to to to ^ «0)COW V -HrtPli CM CM •-« CM CM co cm cn cn cm "a- — -^ cn esj »»■ oo «3- cn cm T us io oi cm •«3- CO r— to cn «3- oo cm cn cm cn ^ o ro cm cm i csicsico«co cd ~^ ob cn > CMCMCMCMCM CM « — • •h cm cm oo >h co ro o co x 't oo o — < cn to cn to oomoinoo cm co to *3- cn cni — *3- ro to csicn'co co — i to csi cn co -^ ro cri co ob oo *3- co csi -i co ^t in ui oS ro d ro cm r-^^^esj^ -HCM -H CM rt CM CM CM — « CM — I —> — ■ —I — i — ■ CM CM CM CM rt CM rt -H oo« cnoiin ooro«D; isdoid- ci^ci -H(M-HCM3 : to ^co^-co'co ^ tri ^ to to tcuj r^ujrs to cb *3- cb *a- cb cb *3-' rb to ro ro -^ -^ to oo tr> — < to to co -h cn cm ro cm 5 o r» o> «t cm lONromcM co to to «3- ro oo -^ r- — i oo cm uj o Tt ™ -^ to g -^ cd oo en cd — ;siO)cno ocooiqcn encoq ^ oo cn i— . — • o co cn oo j*- p^ r-^I to to r-~ r-~ to to to r-~ r^i to to r-~ to to to r*-* r-^ to to" to r—. r~- to to to tors cnoiM o o »» m cm CO tO CM CM ••S- CD CM Cn f-~ CM cn oq CD »— < cn cn ^^ cd cn cn —■ CM ~-l CM CM -^ CSI CM tO CM CM CM tO CM — ■ CM U1 CM — I CM CM — " CSJ CM — I CM CM to to to to ooen-HMO — i oo cn cm C3 CD oo ro z: — cn co CO CD CD ro CD CO CO CO oism« CD oo ro ~^ CD to CM 22 r - oo 22 CM CD r- CM CD CO — CO CM CM -^ — CSJ O O) -h o cm *-* en ro cn cn ^ to oo — ■> CM CM CM *3- •«*■ tr> "3- " CO -^ CM CM CO ~ CD cn CD CO — i en 15 cn i — CM CM to 2 CM £ ro CM ~ CD 1 CD CM OO CM — to r— CM 2 m zz ^ £2 *^ 2 ZZ Z^ ^ no to to to to »3- »a- «3- •«3- ■«■ to to to to to «» *a- T »* to to to to to oo "3- to to oo to oo cn to to cn cn to to cn cn to to CD to to CD to to CD to CD — i to to to to to to -c-HCMN to to to to to to to to CM to to to to ro ro to to to to ro ro to to to to ■«3- to to to •"3- to to to to to to to to to to to to to to to to to CMCMCMCM CM (M CM CM CM CO CMCMCMCMCM CMCMCMCMCM ro co co ro ro ro ro ro ro ro CMCMCMCMCM CM CM CM CM CM «3- i — co to ro CM CM CM CM CM *~! ^P •"! co csi to (ooimcoxj ■>3- *3- to to OO «3- to to oo *3" oo ro ro tototototo tototototo CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM Table 16 236 Strategic Role of Perigean Spring Tides, 1635-1976 m ..o ro on LO ro ro CD CD CD CD cn cn cn CD cn oo CD CD cn oo cn CD CD cn CD CD cn CD CD cn cn CD oo cn oo o-> cn cn CD ■XI to to to to to to to to to to to to to to to to to to to iri to CO rn CD rn rn CO rsj to to CO ro to Csj ro cn to ro cn ■cr oo CD UO oo oo ££ C-SJ IN Csj ""■ CSJ csj CNl ~"" rsj rsj 1-1 tsj tsj tsj *"* Csj tsj rsi F " H IN tsj tsj ~* tsj ro tsl rt •"" " rt " — ' "- 1 ""' t j ■XI CO to to " ■ to uo to ^ * - " ~ " - ^ m m m oo uo tn to CD m ro oo uo uo m rsi m UO oo rsj csj on o cn CD OC) to ■cr rsj 00 OO to oo rsj m en CD CD en CD cn oo CD CD cn oo cn CD CD cn CD CD cn cn o^ cn CO to to to to to to to to to to to to to to to to to to to to to to to to Csl ro uo ro ,, CD CD rsj to ^ CO oo cn ro CD rsi OO cn uo ro cn CD uo OO cn ^ CD oo OO OO oo UO _ _ ro UO OO o-> oo rn ro cn to rsj cn CD to CD Csl cn to CO CD OO CD ro CD ■cr rsj UO ro oo ro ■* tsj *"■ rsj CO CO CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to „ ■z. Z - o-> oo -; - cn ro ro ro ro ro CD CN CN ro CD r- ■cr CD oo ro rsj -. UO uo csj cn r-. ■cr en rsi to to Osl CO oo oo Csl - ro m ro ro rs m ro oo en - J, 5 ^ UD s rsj J, -i s rsj CD rsj CsI CD CD ro ^ oo oo CD rsj OO CN UO uo s ro S3 ro ro ~ ~ en OO C-D rsj cn oo rsi rsj oo 00 to S3 B to Csl rsi Csj ro CO ~ "* UO CD ~ rsj to ^ 2 - rsj r - OO — ro cn 2 ro "* CD 3 UO to 2 ~ to p "" ~- ro OO cn Csj ro "* cn CD ' T uo to zz rsi UO oo OO OO oo to tn to to tn tn tn to to tn tn tn to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CN _ to _ to CD UO „ UO CD „ cn UO cn ■cr ro cn ro oo OO oo ^ ro rsj ^^ CSJ r ^ to rsj to UO to CD uo CD UO CD ^ CD ^ uo to en oo CD CD rsj UO UO m oo CO csj ■cr to OO ro rs/ to tn oo OO CD CO cr: CM OO to in od ui I CM CM ~-i .—I } oo -a- to oo I cn en oo i r- ^j- to cm i cm 'S- ■*a- oo I CMOO MO '< ciciin -i i m CM -H (M 1 to to to to i to to to in oo r-~ oo to i cm .— i -^ cr> I CM CNJ .—I ^-i to ' cn ~=f o I CM CM -< CM i ocd inco » U3 en co oo I OO I — < CO I OO i — i oo -a- oo i oo -a- oo o CD O ~-i tb ■ CM CM •— ■ — I • to to to to ' oo cnj en oo OO •>* CNJ CNJ 1" rocorct i -■ o rocn I CNJ CNJ CNJ CNJ I CNJ CNJ CNJ CNJ Table 16 ^f OCOrt to CD CM 1 — CM «* -a- o oo cd cn OO CO "3- in OO to CO ,, ^ „ to OO oo cn cr. LO ^ LT> oo oo to ^ ^ p^ LO ^. oo CM CO OO oo CM CM cn CD oo OO cn CO CNI CM OO cn CD CO CNJ CNJ CNJ — i CM ' 1 ' CM CM CM 1 1 1 1 ' 1 1 1 ' 1 ' oo to om«t oo oo o cn oo to cn oo ^ cn CM oo LO oo cn CM to oo oo ,__ oo LO ^ en oo CNI ^ oo to <=> ^ CO _ CO cn to CM oo to CD CD LO cn cn CD oo CO CD CD to CD CNJ CNJ CNJ CNJ 1 1 1 1 CM ' I , 1 1 CM CM CM CM CM CM 1 ' ' 1 ' 1 ' 1 ' 1 1 ' ' ' ' 1 1 ' »3- r~~ CM m to O 1 — u-> in CD CNI oo OO o-> cn CM oo CD oo ^ O CO O) CM o CM cm — m cn CM cn oo oo cn oo CM CM oo r~- to to to to •>* ■"» OO 22 OO -=r S into to to 2 2 2 2 2 OO ^ " to to to to LO LO LO to o oo en cn cm r-~ o cn ~-> oo cn CM to CD CD cn cn CNI CNI CD cn CM cn oo m en oo o o cn woo oo O CD o cn cn co en cn OO O cn cn CD CD cn cn CD cn CD a cn cn oo cn cn CD OO to to i — r-~ to to to i — r— to 1— . to to to i — to to to to to to to to to to to to to to to to 00 i — «m ^ ^ m o r-~ to O CM to oo to «3- o to to CM oo CM CO ^ „ r ^ cn CM to oo oo LO *3- C=> oo ! CM oo _ ^ ^ oo to m to o CNI LO on CNI m — "" CM ~i CM ~-< *"* CM —• CM — ' co ~^ CM CM OO CM ~ H CM CM CM rt CM CM IN ""' IM CM CNI 1-1 ~* IM "" CM " INI CM ~ CM to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to lO Osl on CD CM m CO CM m O at CM •— I ~^ 1 1 CM CM — < ' ' 1 ' 1 1 1 1 CM ' CNI CM ' CM 1 CM "t cn coo OO O to ** O O oo CM OO cn oo oo OO CM CM «=r cn O CO CM oo cn CM OO cn CO oo OO CM ~-l CM rt ' 1 ' 1 ' ' ' ' IM ' 1 ' 1 1 ' 1 1 ' 1 oo oo cn oo to to CM tO OO to OO CM o cd CM CM CM cn CM CO cn to to to ^ to CM oo oo ^ CD LO ^ CM oo oo oo CM to ^ ^ cn OO «» — i -H lO cn CO CM OO OO to to ro LO m <— > CM CM CM CM 1 1 1 1 CM 1 1 1 1 1 CM CM CM CM CM CM CM 1 1 ' ' CM 1 1 CM CM CM CM 1 1 1 1 ' 1 ' cn wro -h — i cn CM CM to CD tr OO CO O to oo CM to to «=r to to CD LO OO cn CM to O CM ~^ r» CM l — to r~ to to in oo •«3- OO oo OO «3- OO OO to to to to «» to to to LO to LO " LO " ^ 3 2 to -a- oo oo CD CD CM O to to in cn CM cn en CM OO OO OO CD cn OO cn to on in ? cnooqq to to r-i r-~! cn cn o o oo o cn cd cn cn O cn cn oo CO CO CD CD cn oo cn cn to CD o-> to cn co lo cm -=T ^ cn oo to oo O r- cn OO CM cn cn OO en _ to ^ oo CM oo CM CM LO co cn CO oo to ■* CM CM CM CM CM ~^ CM INI rt oo CM "" r* IN CM •- 1 "~* IN ISl "■ ■""■ tsj "" ^ LSI tsj — , CNJ CM — CM to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CD to co ^ 2: - m to osl m to to CO OO oo Osl cn LO OO •"J" -J* •"j 1 <~f •"]" *f "f -""■ "-j 1 ■"J 1 — ' —* '"V . es — ' ,J, oo oo m oo oo to to to lO w» OO .^ CM CM CD „ cn _ CD oo pi oo r^ LO oo LO ^ ^J. CNI __, CM „ ,—, CM CM OO ~ ~-i CM CM OO CM CM C CJ ^ CM CM z^ c; tsi l -ii 1i ~ d ^ " ^ CM c c; CM CM CM z? 1 ' CD o ^ ZZ ^ iil y " M ^ OO OO OO cn cn CD CO CO o CO CO r „' ^ rt ^ CM CM CM oo OO OO ■cr ^ ■"3- *^- to to LO LO to to to rir r^ r^' rC CO OO oo m m to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to cn^cn-* oo oo cn oo oo CM oo oo ^ OO CM 1— . CM ^ „ to to „ to „ CD to CD LO CD ,, cn cn ^ oo oo oo oo oo OICJ) rH r< oo CM tO -3" to to oo oo CD O CD oo to to cn oo CD CM CM oo LO in o-> O O CM CM OO «* to to oo cn CD OO oo «=r m m oooo O CD o ^ ~-i CM CM CM CM CNI OO OO OO oo oo OO oo oo OO oo oo oo OO OO OO OO OO oo OO oo oo OO OO OO oo oo oo oo CM CM CM CM CM CM CM CM CM CM CM 238 Strategic Role of Perigean Spring Tides, 1635-1976 a-> CD LO CO ^ ^ -3- ^ ^ CO cn LO LO ^ LO ^ *» CNJ •"3- ^ ■o- CNJ ^ LO cn CD LO ^ LO ^ ^ OO CNI ^ oo ^ ^ CNJ LO ^ CNI CO CO CD CO CO cn CO CO CNJ CO CD CD CO CD cn CO CO CNI Cn CO cn CNJ CM 1 1 1 1 1 CNI CNJ CNJ CNJ CNI 1 1 1 1 1 CNI CNI CnI CNI CNI CNJ CD CO CO CM cn en CO en CD CO CO oo CO CO CO oo CO CD CO ^ CO CD LO CD „ CNJ CO CNJ CO ^J. ^ ^ ^J. CD CNJ to CD CNJ CD r ^_ rt _ CO CO LO to to CNJ -3 LO «3 CD LO cn CD CO CO CO LO oo oo oo LO CD 1 1 1 1 1 1 1 1 1 m LO CNJ to CO oo CD oo LO cn CNJ « cn or cn ■=!• lO rr. CO CO CO -3- CD •* oo CD en cn CO CO CO CD CO cn CD cn »3- LO CD -3- "3 ^3 LO LO CO CO to LO LO LO *3" s 2 2 2 2 T LO CD s CO s CO LO 2 CO co CO CO - ** CO CD CO LO »3- CD oo CO to CO oo CO CO LO to LO en LO CD CO CO CO oo CO oo CO « Cn cn CD CD CO CO CO lO tn CO CNI CO CNI CD CO CD CD OO a^ CNI CO cn oo CD cn oo CD CD en cn CD CD CD CD cn CD 2 CO CD CD CO CO CO CD CO CO CO CO CD CD CD CO a CD UD to CD CJD CD CO CO m cni co ^ CO CD CD CD CO CD en CNJ CO CD „ LO CD CD ^ LO oo oo cn ,, oo CD cn cn •el 1 •* CO oo CNJ CO CJD CO CO CO en CO CO oo -=r en CD ■a- CO CO CO CNJ CD CNI — ~ "" IN ""* ~" ~* ■"■ -" tM —' — ' — ' 1-1 CM tNl INJ —* tNl "" CO ""' CNI ~* CO — CO CO CO CO CD CD CO CO CD CD CO CD CD CO CD CO CO CD CO CD CD CD CD CD CD CO CD CD CD CO CO CO CO CO CO us CO to CO CO CO CO CO CO CD o» - CNI CD 1 cd co CD 3 en CO ^ "7 en CO CO 3 oo CO -3 oo 3 «3 CO en CO - CO oo CO cn CO oo 3 3 CNI CD cn CO CO CD CNI cn CNJ CD CNI CD 7 „ ^_ cni CO ^ CD CO cd ■* •"=r CD CNI en CO CO en CNI CO CNJ CD CO CO cn CO CO CNJ CO CD CD to CO cn CO CNI CNI 1 ' 7 1 ' 1 1 1 1 CNJ 1 CNJ 1 1 1 1 1 1 CNI CNJ CNI CNJ CNJ 1 CNJ CO lo CD _ oo ^ CD «* CD oo «a- CO CO cn ! CO 1 _ 1 CO oo CD _ _ oo ^ CO CO ^. CO _ cn LO cn _ ^ CD CO "* 3 C-4 CO CD CNJ -" '** oo CNJ CO oo cn CO «3 CD zz LO CD 3 CNJ r> * oo 1-1 CNJ oo cn CO CO CD 3 ** LO CD zz 2 CO f*" CM ~ r - oo CD S no oo oo CO oo oo oo OO oo or. oo oo oo ori OO oo oo oo oo oo oo oo oo oo CO oo oo on co 1 CO CO CO CO CD CO CO CD CD CD CO CO CO to CD CD CO to to CO CO CO CO CO ^ og CD c-j CD CD CO LO LO CD CD LO a-> ^ ^ cn CO en oo CO oo CO CNI oo CM r _^ ^ CNJ CO _ „ to CD CD CD LO LO CD CD cn -3- CO to oo in CD CO CO LO CO CO CD en CO CO LO CO oo oo CD CD CNI CO LO LO oi CD CNI CO to oo oo CD CD CNI CNI CD to LO LO LO CD to cn to CD CD CD CO CD ro ro CO ro CO CO CO CO ro CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CM CM CNI cni CnI CNJ CM CNJ CNI CNJ CNJ CNJ CNJ CNJ CM CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNI CNJ CNI CNJ CNJ Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 2 ,.,, lo to CO ^ oo CSJ ^ OO »3 Csl CO LO LO to CO CO cn oo to oo «3 oo CO LO LO CSI CO CSI cn Csl LO •"3 oo ^ ^ OO to (C »3 to CO CSI CO CO en to to cn CO CO oo CSJ en CO CO cn to -3 cn CO CO oo CO cn 1 1 1 ' 1 1 1 1 1 CSJ 1 Csl CSI Csl Csl 1 CSI 1 1 1 1 1 cn cr> co- CD Csl Csl UT> __ OO CSJ N en _ oo LO CSI to LO „ M oo ^ cn Csl ^ cn CO CSJ CO ^ ^ T _ co «* to to LO ! CO CO „ CO Cs, ir o-> en co cs CO CO LO in LO LO CO LO 1 1 1 1 1 1 1 1 Csl Csl 1 1 1 1 1 1 1 1 CM CSJ CO LO LO LO LO lO Csl to tc CT cr CO OO en Cs cr. CSJ cs CO cn to CO CO CO co CO cr »3- CO Cs "3- to to CO LO CO cn CO CT> LO LO CSI oo -3- CO CO CO ^3 CO CO *3 «3 to to to to LO LO "3- •«3 2 - 2 2 2 2 LO LO LO to LO to LO to LO LO LO LO LO 2 2 2 2 2 2 "3 •"3- LO to co CD CD o-> to OO LO CSI Csl LO LO LO LO en LO CO Csl CO to CO oo "3 CO oo LO -3 cn CO S s co o-> en en CD en en CD OO en CO cn oo cn cn oo cn CO cn oo CO oo en OO CO CO oo en cn cn CO CO en en OO en * to to to to to to to to to to to to to to to to to to to to to to to to to to CSJ oo to to _ CO CSI LO _ LO CO to *3- CSI r ^ -3 oo ^ ^ ^ to Csl to CO en to to cn to OO ^ ^ CO LO CO oo ^ CSI „ CSJ to to LO s Csl CSJ CSJ Csl CSI CSI CSJ Csl CSI —' •" ' Csl CSJ CSI Csl Csl Csl Csl CSI Csl Csl Csl ■"■* Csl to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to ' - - oo CSJ T to to 1 - 7 2 to LO 7 to to 1 CSI co LO to Csl - Csl «3- oo CsJ - Csl Csl en a CO T cn CSI a CO CSI oo -3 a - CO "7 to LO 7 CO CSJ ^ io ^. en en oo ^ CO eo to to f to CD CO Csl CO CO to to Csl CO o oo Csl cn Csl CO CO •>3 oo CO cn 1 1 1 1 1 i 1 ' 1 1 CSI 1 CSI CSI 7^ Csl 1 CSI 1 1 1 ' CO to lo CO CD LO rt -3- CD CO CO •"3- to ^ cn oo ^ _ cn cn to CO CO Csl CS! LO r __ LO CO CO LO Csl cn CO _ „ .^ to oo CO ^ CO CO oo "3 LO to oo »3 CO OO to cn CO LO CO CSJ CO oo LO oo LO OO oo LO OO CO oo CO LO CO er> CO cn *3 CO LO LO 1 1 1 1 ' ' ' 1 1 1 1 1 1 1 1 ' CO LO 3 to m in O-l LO CO to CO LO to ^ CO CO 2 CO "3- LO to LO to to LO to LO ~ 2 2 2 ~ 2 «a- »3 LO •«3 LO LO LO 2 LO s to LO "■3 ■*3 "3- 2 2 «3 -3 "3 "3 CT> cn ■"=* CO CO CSI CO CO to CD CO to CO CO to CO oo LO oo CO Csl CO Csl cS LO CO to s to CO LO CSI LO s CD CD Cn CT) en en CD CO OO en o oo en CO cn oo en cn CO oo cn CO cn cn oo CO CO oo cn OO CO CO oo CO co cn cn CO cn en to to to to to to to to to to to to to to to to to to to to to to to to to to to 00 uo Csl CO CO oo „ en LO to LO to to CO CD "3- CO , LO «3- to CSJ r ^_ oo CSI CO to CO cn Csl ^ ^ oo LO ^ CO CO cn o OO cn lO LO ■=a- CSI CSJ " rt Csl Csl "■* Csl Csl ■"* Csl CSI Csl Csl ™ Csl CSJ CSJ CSJ Csl Csl CSI CSJ LO _ CSI Csl "- to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO to tn z= z - - oo CO oo CO •"j" -j* ' .' 1 ~y 1 . •-j 1 T? 7 1 •"J 1 ■ .' 7 ~f "j 1 . "T 1 - .' ' .' ' .' . "f ,-, r^_ LO , _ Csl 1 rn r-_ r^. r-^ LO CI Csl _ CSI _ i cn Csl Csl d CSI Csl C! Csl Csl Csl CO Csl d " CSI Csl Csl Csl Csl CO " d CJ IM a a zz !^ M « i-2 !=! !=< M — . CO LO LO LO to to to oo oo oo cn cn cn CO CO CO CSI Csl CSI Csl en en en en en en en en en cn en en oo en cn cn en cn cn en en en cn cn cn CO CO CO CO CO CO to to to to to to to to to to to to o-> CO o-> CO CO OO CO ^ Csl Csl r ^_ „ to „ to „ LO CO to CO LO cn LO CO -3- CO "*3 cn ■>3 oo *» oo CO cn CO oo Csl oo CO ^ CSJ f^ Csl LO en en cn CO LO en Csl CO LO LO CSI •>3- CD CO CO ~D Csl LO CO CO Csl LO oo CO to cn LO oo CO to cn Csl o-> oo LO en en no CO LO LO oo cn en CO CO LO LO OO cn CO Csl CO •» LO to On 3» OO oo cr> en co OO CSI CSJ Csl CSI CO CO PO m ~o CO ro CO CO CO CO CO CO CO CO CO CO CO Csl CSJ CSJ CSJ Csl CSI Csl CSI CSI CSJ CSJ CSJ CSI Csl CSI Csl Csl Csl CSJ CSJ Csl Csl Csl CSJ CSI CSI Csl CSJ Csl CSJ CSI Csl CSI Csl Csl Csl Table 16 240 Strategic Role of Perigean Spring Tides, 1635-1976 co oo to cm csjoocouo^r ro n oq ^r ro oo oq in ^a- cm rooooooo m cnro o oo^r ro cn oo csj t co oo *=r oo cn co to o ^r co cm cm ~^ ^t ob oi rv cr> csi od d o> uS .— « cm cm co .— • rri 06 oi to rv csi c\i 10 in r*! csj co co 00 csi 02 cn cm o o in 00 csj o <7) tp cn cn o r»- cm (X) ^r ro rs. m cn co co co 00 -«d- ■*=}- 00 *3- ^ ro o o r^. o *=r o lo o ^ m oi csj x un to cm oi <- • in in to to cnj i — cd t ro to >- 1 cm ld cd ro cm cm *=r cm ^r r^. ^ rs. x ooro rs *tN cn o r-- cn co r-. to co r-- co 00 o m co O U3 Ot co <* ^ o cm a? 1 — o> tn 00 rs co ** r-. in cjo 1^. en ^ to m to o 00 o o ^ cm cm 00 to rs ld m 00 to in to cm o- co cm 00 n 00 ro m *j 00 co o ^ cm cd to to to to to lo ■*$■ ^j- co ro co ^- *cj- lo to 1 — r-» r — to to lo ^t ^f co co co co ^* ^j- lo to to" to to to lo in *zr ■*& •*& *zr *zr ^j- 1 00 ^ o ^ cm id -h m t tj o cn .— • to cn -«t o un o ro o ^ ro o co moo cm to o woco cmin. «^ ^h o lo cd 00 *^r cn cn ^3- roootorocM oomro«jrs cm cn 00 m r-» cnjph^ooo 00 cm tn co o co to 00 cm co ro^-001 — ro rotOLoroto co •? ai cn o cn oq co •— < cn oq o o cn cn q cj) o q en cn ^ cn oo cn cn ■— > cn cn o o o cn o cn en o o oo 01 ^-i o oo a^ o en co cd o cd to to r-» n to tor — r-. to to rs to rs n .'to to n to to to to'r> to tON r-i r-i to" n to to n p-^ to to n n to to n to to to r--* to cn 00 lo —h -— * cm co to to co in m m o *^ ^ m m rn to comco cm ph ^ 00 lo .— • cn ^ 't en o cm -h en 00 ro r^ r--.LOior-.r-- CO tO I — P— ■ ^3" OO •— < tO tO CTi co cm r — 00 00 co «— i r — cn co ^ co cm 00 co lo r—- ■— • co to r*» lo cm lo *3r to cn *3r lo r^-i p** r-i r-- *3- CM CM ^h ^h CM CM pHCMCMCM m CM C\ CM ph ^h CM CO ^h ^h CM ^ co ^ ^ CM i- h CM CM CM »—< CM CM CM ph CM CM ^h ^h CM CM ph ph CM CM ^1 encoocMO CMCOcocMco cn n ro r>s iri co oon tors. in con to ■- 1 00 00 t t -- < co 00 in cn **■ cm cm cm co •— 1 co^oo^*fl- co to in n o o cn <— < ^ co cm cm - 1 ^ a> cri rv ro cm 00 cn lo ph cm cm co ^ co co'eri to n co cm d ^ uS to r-! cm co co co" 06 cm" to co cm coco CMCMCMCMCM -^ -h ^^^h^^CMCMCMCMCMCM— 4 — • i-H ^-. __^CMCMCMCM^CM^^ ^-" co cq co cn o coq^t ^hco cm q ^ in <* r ?'~^ c ? r ? r ^: — < co to co co oocon^cnj ^tooNO cm q q ^ in to cm *— ; cm cm 01 ro ^ co ^ ooco^rcMCO to n o - 1 to Lor-.r-.0010 00 cm o cn r-- co cm in cn co > •— • to co m co to o co 00 cm to «* w to «— iCMCMCMCM ^CM- < -^ rH CM -- iCMCMCMCMCMCMCM'— < — < ^ ^-, CMCMCMCMCMCM^^CM'— < «— I to to co lo ^j- 00 r-» co cm cn ■**■ co >-o to co to r — lo *3- co co cr> r-— lo •— < co in r-. co 00 co to cm *s- co to 00 lo to cm 1 — cocMco o ^ n. cm r — cnin incMco lo -«a- - — 1 n o cm «t co co cm to o cm in r»- cn to in in ph n oicn n r-.^rcor-.tq co cm to co in to n q m_ in ^fq qcMin ^ 1 — ■ n q to .— < in in 10 00 ^rooencooo ^rcnoor-. in to to to to in to •>* ^t co co co co in* ^- d rs (O rs ^j- 00 •*&■ cm — 1 cn cn 1 — 1 lo co co co co ■— * ^r r-— co cm to 00 co cm cm to co -. r^ cn cn ^ - — 'cocotoin CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CM CM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 211 z to CN CSJ ^ CD CO Csi to CD Csj to CD 1 — . to OO CD CD LO LiS OO to CSJ LO oo to rs." rs! csi cd > «♦ 1DP)0«« oo CD to is rs CD en CD LO LO 3S332 to CO CD «=>; rs. csi o csi r-. to co en csi lo lo" 52 csj CD en — h to csi to rs' oi co to CO Csj OO CD CO is! tri tri csi CD 1 — IS CSJ IS en «* ^ cb cd 1 1 1 1 T T tO —i CD CD CD rs! CD CD Csi Csi "-H CSI CSI CSI CSI 1 1 1 1 1 coco-hoi ^ Csi CD rs' to rt 1 1 T 1 1 oo oo ^t o in to co csi en lo o «* ro en co — i csi lo is' rs' ro m en oo vj S 7DAY 5.010 5.589 5.941 6.048 6.095 6.147 5.898 5.476 5.605 5.181 4.867 4.512 4.582 4.459 4.308 4.510 4.663 4.749 5.156 5.015 5.705 6.040 6.218 6.430 6.496 6.474 5.989 5.266 5.122 4.447 3.922 3.726 3.651 3.992 4.641 5.572 5.749 6.678 7.333 7.027 6.987 6.243 5.988 5.021 3.975 c 70AY 6.984 7.118 6.971 6.837 7.054 7.094 6.911 6.868 7.080 7.077 6.997 6.974 7.078 6.977 6.857 7.038 6.973 6.947 6.871 6.918 7.099 6.999 6.919 6.905 7.048 7.134 6.918 6.919 7.028 7.029 6.951 7.010 6.991 6.994 7.092 7.083 6.949 6.930 7.112 7.009 6.858 6.921 6.956 7.110 6.963 2 . coistorstD ■ OO Is' Csi — i CO rt CSJ CSJ — H CSJ «<;rorsrt csi rt ^ csi rs! rs. lo cd to to OO CD Csi CD ^ CSI rt CSI -( -H LO ~- CD tO CD s!ro -H cos! Csi CSI CSJ ~-i CSI O-UDSrt to csi rs! csi rs! Csi CSI — 1 CSJ CSJ en oo csj rs oo CD LO rt CD CD CSJ rt CSJ OO CSI en csi en cd i-h td Csi CD CD td « (SI rH CO -H to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to -= 1 — LO OO CD ^cf co rooiCMO i "7 ""' T CSJ _4 « CSJ csj —i en csi csj -i^f coroo oo en csj to to oo co lo to rs sa^a ^cr to lo csj cd |~« CSI CSJ oo ° ^ssss CSJ to tO CD OO CO csi to c=> Csj CNJ CSJ ^ Csj —1 to •>a; oo to I—. CD CD LO LO CO rs' rs! csi CD ^ to CSI O 't >J — i CO CO csi CO CSI CSJ CSJ CSJ Csj is — < st CD to cd en cd to to tO CD OO to LO rs rt cd »=); to CSI . — i CSJ CSJ CSI 1 1 1 csi en «=f co oo CSI — CSI —i - csj to oo ■— ; cd cd rs! csi to d lo oo to rs. to CD CD td Csi LO en to oo rs. lo cri csi rs! to en tO CSJ Csj CD CD rs! « cd csj csi — I CSJ CSJ CSJ CSJ ^ oo to en csj Csj ^ •sf CD CD (SJ CSI -. rt rt 1 1 1 1 1 CD lo en co oo od i «a- •— < cd co rs, «a- lo oo *3; CSJ ~-i CSI CSJ CSJ 28.1 23.4 27.2 19.2 6.5 CO 7DAY 4.682 5.690 5.906 6.000 5.946 6.087 5.927 5.102 5.769 4.999 4.903 4.373 4.662 4.471 4.380 4.499 4.972 4.607 5.410 4.517 5.714 6.193 6.052 6.400 6.251 6.428 6.199 4.873 5.624 4.321 4.042 3.784 3.608 4.138 4.415 6.137 5.117 6.865 7.292 6.458 7.202 5.960 6.774 5.095 3.462 „ 7DAY 6.988 7.119 6.970 6.835 7.073 7.096 6.912 6.869 7.084 7.086 6.998 6.958 7.083 6.977 6.899 7.040 6.990 6.948 6.886 6.953 7.100 7.042 6.913 6.907 7.065 7.133 6.927 6.910 7.051 7.032 6.954 7.023 6.979 7.003 7.091 7.089 6.942 6.929 7.115 7.031 6.864 6.921 6.990 7.109 6.986 - 14.3 27.1 22.5 5.7 20.2 co co co co st comtdm^ CSJ CSJ Csj CSJ CO CO CD CO tO tO CO to CD CO to to CO OO t* Csi CSJ ~-t rs. rs. csi oo to OO i—l •— < to oo CSJ CSJ — I ■sr oo csj rs to rs! ^-i oo cd to Csj Csi ~-i ~-i Csi 24.9 18.9 13.6 22.0 26.4 rs. —i »a- »g- en to csi d d ■» — < « CSJ CO — i co «* — ; cp csj to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to - CSI 12-18 11- 4 21-10 19-17 29- 7 28-17 8-17 7- 16-19 15- 6 26- 24- 9 6- 8 4-17 14- 1 13-10 11-20 22-18 22- 1 31-12 29-22 29- 9 10- 2 9- 9 19- 17-11 28- 9 26-16 5-14 7- 14-17 14- 1 25- 1 23- 9 1- 3 30-14 12-10 10-18 19-16 18- 3 29-18 29- 7-18 6- 5 7-15 O^mcD^ cs,rsoo~ cnj oo CD oo ^ en cd ^ «a- LO CD — i csi to rs csi .—il — CO CSJ CO °> 2 m "* S -LO tO CSJ _ to rs. — i csi oo LO LO to to to to i — rsxco 22222 en en cd cd cd -i -i CSI (SJ CSI CSJ CSI CSJ Csi CSJ CSJ CSJ CSJ CO CO CSI csi csj CSJ csj Csi csi Csi csi est *3- LO LO LO tO to to rs i — i — CSJ CSI CSJ Csi CSJ - 2347735.3 2347764.8 2347956.8 2347986.3 2348148.7 2348178.3 2348370.2 2348399.8 2348562.2 2348591.7 2348783.6 2348813.2 2348975.6 2349005.1 2349167.5 2349197.1 2349226.6 2349389.0 2349418.6 2349581.0 2349610.5 2349640.0 2349802.5 2349832.0 2349994.4 2350023.9 2350215.9 2350245.4 2350407.8 2350437.4 2350629.3 2350658.8 2350821.3 2350850.8 2351042.7 072.3 234.7 264.2 456.2 485.7 648.1 677.6 840.1 869.6 899.1 LO LO LO LO LO LO LO LO LO LO CSI CSI CSI CSI CSJ Table 16 -509 0-78-18 242 Strategic Role of Perigean Spring Tides, 1635-1976 to CO CO OO to to OO CO CO CNJ OO CO CO to OO to to to CO CNI CO CNJ OO LO CNI cn to ■«3 OO CO ^ CO CO _ •*■ oo en cn CNI CNI "» -3- Ol OO CO CO oo. CNI CD CNI to CO OO OO cn CNJ to "3- cn OO CO OO CO ro OO OO to cn CO to 1 1 1 CNJ CNJ CNJ CNI CNJ CNI 1 CNI ' 1 ' 1 1 CNI 1 1 1 1 ' 1 1 CM CO co o-> OO CNI ^ CO CO r ^ OO en cn <=> OO CO CO CNI to ro ,, OO OO OO CNI OO OO „ _ cn to CNI _ cn to ^ CO ro u-i to CNI CNI «a- CO CO T OO OO CO 1 1 CNI 1 CNI CNI CNI CNJ CNI CNI CNI 1 1 1 1 1 1 1 1 1 1 to m OO CNJ CO OO cn CO OO CNI to CO to o-> IO to LO CO CNI to •>3 OO OO OO o-> co to OO to OO OO cn OO ro cn CO CO CO OO CO to CNI oo oo OO OO OO 2 2 to CO to 2 2 2 "3 = oo 2 2 «3 -a- 2 to LO to to to CO to to to to -3 *3- to to LO OO Osl CNJ CT> OO CO OO on to CNJ CO CNI CNI CNJ CNI CO CO ro cn cn to CNI CO cn ro OO ro cn £ CT> co OO OO CO OO o-> CO CO OO en OO CO en OO CO 00 OO CO CT> CO cn cn o-> OO CO CO cn en CO to to to to to to to to to to to to to to to to to to to to to 2 CO to CO ^ <=> to LO OO CNI CNI CO CO en OO to to CO CO r __ OO cn OO to OO OO oo ^ CO to OO to to to ^ cn to LO „ OO _ ^ cn cn OO OO CNI to cni iO IO CNJ LO CNI oo to CO ro s "" ' CNI * H Osl "" CNI CNI CNI CNJ CNJ ■"■ CNI CNI CNJ ■"■' CNI ~~" CNI ""* CNI ""■ CNI "^ CNI CNJ CNJ OO CNI "* CNJ CNI CNI '" INI l-J ™ CO to CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO to to CO CO to CO CO to to to to to - «* to CM co a 2 OO on: - ro a - a - ro "7 cn OO a ° ^ - IS CO - »3 to 7 cn OO « to £5 to to E5 s OO LO s CNI en OO cn - s ^ CNJ OO CD S oo CO en CNI 1 1 1 CNI CNJ 1 CNI CNJ ' 1 CNI ' 1 ' ' CNI CNJ CNI CNJ 1 1 1 ' 1 ' 1 _ CNJ OO CO ^ CO _ OO „ OO «* to ^ OO en CNI CO cn cn cn CO CO en cn CO CO CO en CO cn CO CO oo ' CO to to to to to to to to to to to to to to to to to to to to to to OO _ cnj to CO _ CO o-> CO ^ en OO to to CO to _ to en rt to OO OO to ^ to CNJ _ CO OO ^ CO „ CNI OO _ to LO O-J oo -«r ■"■ CM LSI " to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO to to to to to to to to to to co « - - OO - - r-^ LO in to ,3- ro _ ro OO ,_!, CO CO _ CO en OO to CT) fi to to to ^f -a- CNJ ^. OO OO _ _ _ c-, cn CO OO OO to LO ,-,. to to ro cni ,-,. CNI N 2 5 ~ 52 ~ 2 2 1 CNI OO OO oo on en en m oo CO CO ON OO OO to to to CNI CNI CNJ CNI CNI CNI OO OO OO OO OO CO OO oo OO oo OO OO OO OO ro OO ro OO OO ro oo ro ro OO OO OO lO _ to CO to CO to en to CO ,, en en ^ OO ^ OO oo OO OO OO CNI ^^ OO ^ CNI to CNJ _ to _ to uo _ to CO eo to cn LO „ cn OO cn OO -3 in m to to en CNI OO OO a OO CO on on ON, to a to ON tr- to rr m to tu OO on CO OO to to or- rr cn OO LO LO or en iO io ir to to io LO LO LO tr LO to OO ro CNI " CNI CNI CNJ CNI CNI CNI CNI CNJ CNI CNI CNJ CNI CNJ ONI CNI CNI CNI CNJ CNI CNI CNI CNI ONI CNJ Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 243 CO OCM «» CO — 1 CM cd — ■ to oo CO r- oo CO CO r- ^S- CM OO oo <=> „ CO LO CD oo ^ ,, CO ^ CM ^ ^ OO _ ^ j^ CO — ■ to to OO CO CO OO OO Osl to Csl on CO to oo oo CO oo Csl OO to <=> Osl oo CD « CM (VJ CM CM 1 1 1 CM rt 1 1 1 1 1 ' Csl CM CM Csl 1 CM 1 1 ' ' ' Osl Osl CSI ' 1 vomox in to CO '—• ^ «3- to CO to ~-i CD lo r-~ OO CM CO OO LO to LO ^. 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J, "3" CM J, CO CM J, CD <=> CO to pi. pi LO to LO "3- OO LO 4- Osl CM J_ _!, en pi ^ ^ -^ £i £i CO CM Si ^ t^ si ~ zt Zt ^ E^ " r^ l -il ^1 ^ OO tr c Osl .-. cm — « to r~ £-1 ""* 2 "* M t-i ™ !=; " !£j !£i CD CO CO CO o Csl Osl oo oo OO LO LO LO LO to to to to CO -3- "3- "3- ■>=r ■=r "3- "3- »=t- -3- «t -3- -3- ■"3- -3- -3- «=r •"3- CO CO ^ CO CO r-~ co CO CM r ^_ CM ! to CM tO „ _ to CO LO LO CO ■=r c=> CD •"3- CD ^ oo CD oo oo CM oo OO CO Osl CM to CM CD CD CO ~^ CO OO CM 4- to to OO CO CD oo •"3- to to oo CO en rH -1CM CO t to CO oo CD CO Osl CM «3- to to OO CO CO en CO co CO CD _ cn CO CX ,, CM CO en CO CO CD OO cn ^ CXJ cn un „ _ CD cn CD CO r ^_ co CO cn CO CO r __ CO CD cn cn cn CO m CO CXI OO CO cn CO CO 1 1 1 ' ' ' ' 1 1 1 ' ' ' ' 1 ' ' CX cn cr> CO o on CO cn CO CX cn CO cn CO OO CX cn CO cn CX CX cn cn cO cn cx cn CO en OO cn CX a-> cro CO CO CTD CD en CD 2 cO CO CO co «d- - " ^ " ~ ~ s un CD CO CO s 2 3 s - " co ~ = 2 CO CO CO OO OO en cn oo m CXI CO ran on co co en oc CM en oc cn CO CO m co CO cn cn OO CO CO cn CO CO CD CO cn CO CO CO CO CO OO cn CTD cn cn cn CO CD cn cn OO CO CO CO CD CD CO CO CD CO CD CO CO CD CD CD CD CD CD CD CO CO CD CD LO CM en CXJ en CD CO CO CO OO ^ _ _ CO CO CO OO CO ^ „ r ^ OO OO OO co CD co ^ OO ^ CxJ _ ^ CO _ ^ CD _ on on CD CX CO cn cn CO CZ: cn CXI OO CO CXI en ifl on — CXJ CXJ ■"* CX " H CXI ~' ■"■■ ex "" ' LCI " " CO CX *"' CX CXI CXI "— CXJ CXI ~* CXI CXI CXI CXJ Cxi cx CXJ ™ CX CX CX CXI co CO to co CO CD CD CD CD CD CO CO CO CO CO CD CO CD CD CO CO CD CD CO CO CD CO CO CD CO CD CD CO CD CD CD CD CD CO CO CO CO CO CO CD o, - OO a a - a OO s Cx, CX S OO 2 cn CO OO - CO s CO a - cx* 2 - s - CX 2 OO CO - CO - - cn CO OO co _ CM OO CD en CO CX ^ , n CM ^ OO CO CO 1 1 1 ' 1 ' 1 1 1 ' 1 1 1 1 1 1 1 CXI CXJ CX 1 un ^_ OO r ^__ J^ CXI CD •CD ^ cn OO OO OO ^. CO OO CO CO CO CD __ CO ^ CXJ CD ^ CO _ _ CO . CO ! ^ CO CM CO ^ CO en CO cn CD CD cn CO cn ..o CXI CXI CX CX 1 1 1 ' 1 1 ' 1 CXJ 1 CXJ ' 1 ' CX Cxi on CO co cn on OO CXI OO CO CX CO OO cn OO CXJ on en OO cn cn cn C 3 *=r CD OO CO cn OO CD CO CO o-> CTD CO CXI co OO OO OO ex CXI CO co 2 2 CD ^r - " ^ " CO " CO CD CO cn co cn 00 ran co cn CO CO CO CD cn OO cn c— 1 CO in ° CT> CO OO CO CO CO en cn on CO cn OO CO CO cn en CO CD CO CD CD CO CO OO OO CTD OO cn CD cn CO cn CD cn CD on CD <=> OO CD CO CO OO cn OO CD CO cO CM CM cO en ^ «=r CO CO CO CO OO cn CX ^ _ CO on CO CX ^ CO CD ^ ^ „ cn CO CX OO on ^ CXJ ^ CO CD CX cn cn Cxi cn en co O CO CO CO CO co in ■"3- ex CM " CO CO CD co CO co CO CO CD CD CD co CO CD CD CO CD CD CO CO CO CD CD CD CD CD CO CO CO CO CD CD 10 CO CD CD CD CO CD CO CO CD o CD 3 CO „ z z. OO CO - cr. en - - - CXI OO to °, iC S3 'f\ co cn cj s Jh g g cn CO CO CO CX s CO CO CD OO CX CD S § g § g cn OO cn cn g CX CXI CXI CD "* !—! CXJ g CO cO CD CD CO CO CO ran OO OO cn cn cn cn cn CO CO CO CO CO CO CO CO CD CO CO CO _ CO „ CO CO co CO LO CO ^_ CO cn cn OO CO CO OO CX OO CO r ^ CX _ ^ _ CD CO CD _ un _ CO CO CO CO CO on „ CO „ cn CO o en en cn e > S _o :n CO CO cn CO BO CO co 00 cn ■n -71 m m cn CO c^ ': CD L. CO CO o ■ ■ CO CD CO CO CO co CD CO CD CD CO CO CO co CD CO CO CD CD CD CD CO CD CD CO CD CO CO c^ CO CD CD CD co 1 c£ c£ co co 1 cS CO X cx CXI CX Cxi Cxi CX CXI CX CX Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 2-1. r > O *«■ CO CO CSJ CM OO CO co in in ^t o cm o rorstoorN to ^t Tf m m r— *a- m cm oo ^3- co co to o oo cm cd cm co co -m' cd cm r— oo in in cd cd cm cd ui c\i ob ro ^ co ed cvi r— ' ob •— < — H CM CM CM CM CM CN ^ •- I «— I — I CM -H CM -^ CM CM CM CM CM M CM CM CM CM CM CSJ i— t — - t ■«3- CO — I LO CD O -M in -M I — O CM CM O CM CD *» tO — > CO -imiooi *3- o co to — c co oo co -a- cm oo »» — i p— ^ co •>» to — i o to in to to cm o i — co — i o> i^ « co r— cmi co co in o co oo — < co <=> "a- — ■ — < to o tors, co r^. co Oi oo ^ co in eg o o cm —* cm cm to in id m co in . — i otom rn in to r— to to in in *a- co co co* coco '^ in in ioin!isi — .'to in n »* co co to co '^ in in to to to to to id in iri in r>. oi <* cjiocim ^ oiDCj com i — 10 o ■ — i -^ >-i — co -^ co cm omcni — i — o id ^ idi — ooocj co ■-< < COOICOOO COOIOOOOI OlOOOOOl OOlMOrt CO CO CD CD CO CO CD CO CD O OlOlOlrtO OlfflOOM (Jl Ol oo o mcocotq i d r^ *3- in -^ ^ to co cm cm co r>-! cd ob -^ cd *a- cb co to — < — * d d rs! r^. ^ I »-H - — i CM CNJ ' — I — * CM CM - — itMCM CM ^H CM CM CM < — I CM CM CM —- ■ w— * i — It — I M i — I i — I - — I rH CO ^H CM CM ^H CM CM to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to i rt CMCOCOCO rt rt COCD cm m p— 00 co>j rvm to «a- i — coco rt CO CO — H CD CO CM ■«3- O rt CO CO ' co cq •— i co oo in p— cm coco'-! ^ CD CM CMCM -HCM « CM —I CO -M CO co co™ cm in *3; CD -m oq co in r— co in dd cm dcMcoco'^ dc\j r-lr-i to to tq in r — tnmcMCMi — «* cm o m cd in in in co in d d cm d to cm ob cb -m* co d co '^ rv in in ^ o — I -M CM -1CM-H CMCM CM CM CM - ' — • — ' il;Ttr>.coin co-;qin« CO CD CM CD CO m r— ^ — H CM CMCMCMCM -H CM —H — I ■ CM CM eq i— ; -HCOCMCOC7I MOO • in cm co in in r— p— r— *a-' cm -m t — -I CM ' — I CMCMCMCMCM Oi r-H • cmx O cm to m CD co CD p— co m ocot j— > m w o O in in in co CD in - — i «* oors co co co rN co > — i *a- m r— . i — co co ^co ^ oocoi — tor — — • cm ^h t o co com mco cm id ^ co ^t co co ^ cm co m cm — * CO CO mr^cM coin ^ ro o (^ M co in p— co CD q qooq cm *3; cq "3; CD ■>* in m q iv cm ■«; CD cq — « -a; p~.eqcqr-.r-~. oooco-hco r— in oo in in CMnoiq-H co co in ^; m corsiniDin to ^- co *a- co co co '^ in* ^ d in! d rv d m '^- ^- co co ^-co ^r in d d d in d in d m' m in co ■ — i o toco m cd m in to «a- *a- i — locm co o ^t cocm oco^mcM cofl)N- j cq oq cq cq cd cq cq cq cq cq cd q co co o < — i co co ^h o co co ocooo co coco - — i o co co cd cd co co co o o q d ddr-!iv to to to r-' to to p~! p~! to P-! p-i to to p~! p~! id d in r-! id id r-! id r-i ps' to to to r— I p—' to to p-~' r-~ to to to r-~' r— ' p~! co in cm q «t o» CMin-Hin Tfe-^qq cq cq cq cq to tqeqcococM cd cd r— cm cd inr-.CMr-.co oo co — < -m cm co co q q q cm'cm di- r-i ■*/ ^ ob r-~ in in •» in cm -< r-! in cm d d cb m i-~! cm to cocdedoi— ^ r-! desj dd d r- d -i cm 06 ob cm r- d CMinCMCM CMinCMrt CM CM -H rt CM CM -H rt CM CM -H rt CM CM rH CM CM CM - < -M — I CM — I -M CO -H — I rt CM CM to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to ZZZU.U. 2EZZU-U- ZZU.U.Z 2E U- U- Z Z u_ u_ Z Z u_ U- z Z U- U- Z Z U- Li- U- z Z L-. U- u- Z Z U- u_ z — icomoo oomcocMoo to -^ co r— co cmi-o in- 1 cd p— ^j- •^a- oo to to cd co -a- -^ oo cd to r— co to co cd to to co -^ t~~ cd com mo co > — icoi — i — co r — i — to in m coco co cm- — • cm o oco co in co i- m j-^-inin inmininin mmin_ co co m I — , I — oo oo oo oo oo CMCMCMCMCM -MCMCMCMCM Table 16 246 Strategic Role of Perigean Spring Tides, 1635-1976 LO m ^ LO CNI CNJ ^ cn CO OO „ CNI CO cn cn oo CO ^ « CNI -a- CO cn CO OO ^ CNI oo cn cn oo CO CO LO CNI CO CO OO «» •*■ CN cn OO CO oo CO cn cn OO CNI LO cn ' 1 1 ' CNJ ' 1 1 1 ' 1 CNI ' ' 1 ' 1 CNJ on -a- _ ^. CD CD LO ^ CNJ cn ^ CO CO CO CNI CD CO ^ CNI CO CO CNI CNI _ LO CO OO oo CNI CO CO cn CO "3- •» „ ^_ OO OO T CO CO n Cn cn co LO OO oc CNI oo CO CO OO LO CO LO ' 1 ' 1 ' ' 1 1 ' ' ' 1 1 ' 1 1 CNI CNI CNI CNI CNI CNI CNI ' 1 ' CNI CNI CNI CNI CNI CNI CO cn CO CO CNJ e <—> cn CO cn < CO CN CO cn CNI m CO LO LO LO CNI cn CD LO CO CO CNI CO CO cn OO CD CO OO CO CO CO CO CO CO oo OO en CO CO cn T UO LO CO «=f 2 S " 2 CO CO CO CD CD CD CD CD LO LO 2 2 CO CO CO - 2 CO LO CO CO oo cni CO co CO CD m LO cn cn m CO cr O uo CC C5 m m oo oo CO oo cn cn oo CO cn cn OO cn c=> OO cn oo CO OO cn oo CO CO en en CO en oo CO CO on oo on <=> oo OO CO CD cn CD CD CD CD CD 3 - CO CD CO CO CO CD CD CD CD CD CD CO CD CD CD CD CD CD oo ^ ^ CNI co LO ^ cn r __ cn „ r ^_ rt _ CNI o CO on CO CO LO CO ^ cn CD ^ CNI CNI oo , CO CO CD CM CO LO CO co CD co CD CNJ LO oo LO CD oo CO CNI oo CNI cn CO CD CD CNI CO CO oo CO on CO on m cn OO — " tM ~* ~" — ' 1-1 "" ""■ CNJ INI IM "" CNI CNI CNI ~' INJ IN CNJ INJ "- ~ CM INJ "* — CO 80 *° CO CD CO CO CO CO CD CO CD CD CD CD CO CD CD CD CO CO CO CD CD CD CD CO CD CO CD CD CD CD CD CD CD CD CO CO CD CO CO CD CD CD CM oo LO CO cn CO CNI CO CO cn CO CO CO CNI CO CO CNI CNI 1 1 ' 1 1 1 1 ' ' 1 ' ' 1 1 CNI CNI 1 CNI CNI ' CNI 1 1 _ <=> _ „ CNJ CO „ cn CO cn CO CO cn CO CNI CNI cn CNI CO oo ^ CO cn CO OO OO CO <=> cn CO on LO oo ^ ^ CO oo CO ^ CM in oo CO CNJ ' 1 ' 1 1 CNI 1 1 1 ' 1 1 1 ' ' 1 1 1 CNJ CNI CNI 1 un co oo LO CNJ CNJ CO oo ^ cn oo CD ^ CO CO CO CO CO CO cn cn CO CO OO CO _ CO „ ! oo CO ^ CO CNI CO CO CNI cn CNI ^ on CNI CO „ 7 co 7 *t oo 7 CO oo oo T oo 7 CNI CO 7 CNJ oo CNI CNI -3- cn on CO ™ Si CM CM on T " H CM CO CO CD en *? 7 LO OO CD OO CNI CD OO r-> CM CO CO CO CNI CO oo CO oo LO CO CO CO cn on cn co cn CO tn ^ CD CD CO CD 2 ^ «=r - 2 " - ~ - CO CO CO CO 2 CD 2 CD CO oo CNI CNI CD CO CO CNI Cn cn cn oo CO CO CO CNI oo cn oo OO CNI cn oo CD LO co On 00 co CO oo oo co oo cn cn cn CO cn cn OO on CO OO on oo OO cn oo CO CO oo cn CT> CO cn cn CO CO cn oo CO CO OO CO OO CD CO CNI CO CD oo CO CO CO CNI _ CNI oo CD CD CO cn cn LO CO ^ oo CO CO CO cn CO cn CO oo CNI oo , cn cn CNJ CNJ CO CO CO _ CO to oo CO CD OO OO oo CNI CO CO CO on T oo CO CO CO cn CO in ■«»• — ' CM CM -* CNJ CNJ co cn CO LD CD CD CD CD CD CD CD CD CD CD CD CO CO CO CO CO CO CO CO CO CO CO CO CO CD CD CO CO CO CD CO CD CD CO CO CO CO CD CD CO CD CO z - CO ro oo CO LO CO OO CO cn CO LO CD en CD CO on LO CD CO r __ r ^ CD CO cn cn ^ CO cn CO — ' 7 7 7 *N 7 7 7 7 7 . 7 7 7 7 7 . 7 1 7 7 7 7 CNI l-O r - CO 2 co LO a CNJ c^ CO S cn cn cn cn: cn oo '-" CD LO Em CO CNI "3- CNI -3- CO — CM CO c^ on CNI OO CNI CO oo oo - s Em Em £ s CNJ '" s ;__, — !=! zz U y z* zn M ii OJ CD CD CD CO oo oo OO OO on cn On cn CO oo CO oo CO oo CO oo oo oo oo § oo oo CNI OO OO OO CO CO OO CO in CO CD LO CO cn cn ^ oo OO CD CO oo CNJ oo CO ! CNI r _^ CNI ! „ , _ CO „ CD _ LO CO CD CO CO on lO ■o- cn ■«3- cn m CO CNI CD CD OO OO CO CO cn «=1- CO CO CO cn oo CO CO LO CO CO C 5 C 3 c J> o CO CNI CNJ CNI CNI " OJ CM CNI CNI CNI CNI CNI CNI CNI CNI CNI CNI CNI CNI CNJ CNJ CNI CNJ CNI CNI CNI CNI CNI CNI CNI CNI CNI CNI Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 247 en eg oo ■«» ur> o — < — ; co ^3; co ^- rs oooom co *» ed — i er> *& *t to Csi en co co en eg is ^ eg .— 1 eg m 00 icooniN rNTtio<»)-H eg is, •»» to is. on >f inq to rs cq — < rs lorv^-mrt usin »j « io en ~^ en to in >finin(D<» ro 06 eg o (*) rod-" i in! -h ** co ^* eg en en m *a- en *3- -"a- o ~^ id o en cd cd id 00 1^ 00 00 00 to id *3- «3- ■— ! 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Is" cjd to to Is to to td to is td is is to to to Is is td to to I — - Is to to to Is to to is to „ en eg is m m eg co 10 ^*- eg eg ^h o t£> o rs ■— 1 ~^ en m eg 01 *a- m *^ m o *3- m m eg m co en rs rsto rn ^ is eg cx> rs *a- en " is! i»j 00 00 »t td^oSeooS 01s 6 en is id — < cd cd ^ en csi ** is en doi ro'iri 00 in^^in'od to cd cd m rs m to m 00 ^ eg eg « -* eg eg eg « eg eg eg — 1 eg eg — 1 -~ eg ~ co — 1 ^ eg -h eg eg eg ~h eg eg eg ~^ eg eg eg -1 eg eg — « — 1 eg csi £ ^ co^ mi — is m < is to rsfooomoi -^- co co ■—< csj rooO'H'H «t m en en eg «* ^t eg en ^h n co m o eg *3- m id en eg ^ 00010 eg ™ — 1 eg — 1 eg eg co rsq «t eg is csi oi 00 «» — * « CSJ — 1 —I to co to < •— • in to co eg co to is m m egeg ^ eg en »h en co in cy> co co en cr> m oco 1 — im en eg ooo^f m-cooono roicegio ^ eg is eg to co m (O^cn m 1 — 1 — cgN m en o o en q q q q 00 en in co in en 00 co to egoocomto en ^^ to mm troio «a- eg m to eg cni — rooooi en to ~^ eg r — to CO CO CO ■^ co -a; 00 nqatvri is cvi in ^- ^t tnistdegod m' W 00 en i_ csi eg — . — 1 eg Nrt-i egeg — 1 — * .— 1 eg — 1 — 1 eg co — 1 csi m en »a- in o o en ^ s . — 1 00 o - — ' tocoooegin cdcsicjoincri in rs id m cd «* csi en co ^ egeg csjin eg ~^ eg m eg —• egeg ID tjD ID tO tO ID tO tO tO tO tO tO tO tO tO to tO to tO tO to tO tO tO to to to CO to to CO tO tO tO tO m co co co en to m csj to in o eg -h ocn o 00 co 00 to m ^ co co ■— < *— < co ■— < o en i-h eg eg ^ rn -h eg -h co to co 00 to «— • CO CO CSI CO CJ> CO CO ^3" ■— < »t ^j •«»■ ^j- ■«» *3- »3- *» • co 00 csi mom en m en st en «i en m 00 ^ < co i co eg ^t *t id id in 00 is d en en ~- « — « cd cd csi m t is id co oeiio eg m ~ ^-i — cotoeoinoo moo^so tocnincors encnen ^ ^fo com mini — 1 — rs en en ^h -h eg cocoinmrs ^- ^ ^- in m m in m in m m in in in in to to to to to to to to eg eg eg eg eg eg cgcg eg eg egeg egegeg egegegegeg eg egeg eg eg eg eg eg eg Table 16 248 Strategic Role of Perigean Spring Tides, 1635-1976 lo m co r^. oo CO u-> OO o-> en I— 1 OO CM to CO CO co ^ CO «t oo ^ cn ^ oo to en «=r CM CO CO to ^ ^ oo ^ to to CO •«r cm cn cn CM to CO CO CM CO oo cn CO oo to CD CO OO — • — « CM CM CM CM CM — I 1 1 1 1 1 1 ' CM 1 1 1 1 1 1 CM 1 CM 1 1 ' — < — i to cr> vo muJio CO 1 OO CM to OO CM CO cn CO en ^ -3- _ ^ to oo to CM oo CM CM cro ^. OO ^ CM to cn CM ^ CO co W MIC OCM to oo to to to to CD CO — i — i — i CM CM CM CM CM 1 1 CM CM ' 1 CM 1 CM 1 1 1 1 cm ~ co r^ o CD OO cn cn CO CO en cn OO s m unooi -i CD CO CM tO CD oo r- CM CO to CO CM CM CO CM to to oo ° «TTf mioic ^ 2 ^ T co CO CO CO 2 to to to to to 2 - 2 2 2 2 2 to to to to to to LO " 2 2 2 LO to cn cn to < CO CO ■«3- cn to cm r- OO cm r-- m LO cn cn oo CO to oo co oo OO O") -— ' CO oo O-HO) OO CO CD en cn CD cn CO CO cn oo cn CO cn OO oo CO cn cn CO CO cn CO cn cn CO CO cn CO oo cn CO cn oo to to s -H«norxco OO « -«3- — CM co o-> en en r- CO to CM ^ ^ to ^ en cn CM „ CO CO to „ to CO ! cn to ^ oo <=> CO to ^ to CMI _ CO •*»■ LO CO CM in cn CM LO to to CO oo CM cn cn og CO — -< -HCMCM « CM CM CM ~ ^ CM CM - 1 CM CM CM CM LM ""■ CM CM CM ~* CM CM CM ""■ LM CM CM ~< CM CM CM "" CM LM ~* "* CO rt — ' CX-COCOCOCO «=^«> to to to to to to to to to to to to to to to uo to to to to to to to to to co to to to to to to to to to to to O) - i^ i-~ l<-> ^a- oo uo r-~ •«a- OO CM en •«a- oo 33 CO CO CO 3 CM CO S3 CO CM CO 7 CO CM oo - cn CM to - - 2 to LO to E5 to LO CM oo to IO-ioi^oo co ^ oo CO OO — i CM CM CO ~-> CO to CO — CO CM OO CO cn CM to CO "CO CM cn CO OJ to CO CO oo — > — < CM CM CM 1 1 1 ' ' 1 1 1 CM ' 1 1 1 1 1 1 1 1 1 1 1 ^ ,,. m ,,. <-, in co CO CD co tO CM to CD — H CM to CO to OO en CO CO cn _ CO _ CO CO oo <=) _ to „ ^ oo CO to CM CO CO to i— c — . 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OO OO CO CO CM CO to to en cn CO oo CM oo — i o CM — i ^r oo tr> CM oo «=r to cn oo CO cn cn CM oo CJ cn to 1 — OO CD r~~ oo OO oo oo OO oo OO to oo oo oo oo CO CO cn CM cn cn cn en to en to en oo en oo cn to CO oo CO CO CM CO oo CO CO CO oo to CO CO CO en CO r~- r^ i~^ r~^ r^ rS rC r^ CO CO CO oo oo oo oo OO CO oo oo oo CM C-J CM CM CM CM Cm cm CM CNj CM CM CM CMI CM CXI CM CM CM CM CM CM Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 2V) CT1 OO CM ^ m — ■ CD to "3- to r- "* -«3- to CM OO CNJ CO CT> ., cnj in CO ~^ CD to CO to ■«3" CO CM ~^ CO „ oo LO ro CD CD oo to CO ^ OO ■9 CO 1 — CO CNJ CNJ CO CO CO OD "3- CD 1 — oo CO CO to CM CO 1 1 1 rtrtCNCMCM CM CM CM ~i — I 1 ' 1 1 ' CNJ —i CM CNJ 1 1 1 1 1 1 1 mCDOOCDCD CM CO tO CM OO co-rnco ■»NCMI — OO CO CM CO CO CNJ cm to in en ^ to CO CNJ CD _ CO CO CD ^J. r ^ ^_ CD ^ CD - mmo^m rvlooOOl OO OOOOtD^^- 77 , ; 7 to CO —i m m co — i CM CNJ CM CM CD lO s CD co 1 1 7 7 CM CM to CM ooiofom to to CO — I CO OMIN CD OO 1 — CO oo CM lO CM CM CM LO c^ CO CO OO CNJ CM MOOOrt 00>rvco«» OlOII — «3 •*a- oo to oo oo CM CD CD CD ^J- *3 »3 in in in m to to to tO U"> LT> LT) IT) -a- "3" ■«3- "3" 3 *a- "3- «3" "3- 'S- in in inc. to to to 22 ^3 2 CO 2 2 to lanmooo m to to in ■«3- CO CO — < to CD CNJ OO OO en CO CM en to CD « cx> ■•a- CD to m co cd m in in 1 — in CM -a- on «3" CNJ CO en CO en CD 00)0000 — ■ CO CD 1 — CO OrsOOOOO O CO CD CD CO CD OO CO CD CD r- to r~ to r- in to to to r^ r- to to to to to i — to to to to to to to to to to MBOKf o co r-^ co co cd CM W-ITf r-. 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CM CNJ CM oro >t in o -H^mujN -H(OINOO-i CNJ OO CD CO oo "3- CD CO « ^3 in —i cnj to '-- a — CO OD CM CO OD CO ** LO ~ a LO to CM CO CO CO CO —i CM LO m in co co co co co CO CO CO CO CO CO CO CO CO CO OO CO oo oo oo oo oo oo oo oo oo oo oo oo oo oo CO OO oo oo oo oo ^ cororero co cm r^ co i — CM tO CM 1 — rt to — i to — i to — 1 m OlOO m od ■■a- «3 CD CO CD OO -3" oo CO oo CM to CM to CO OO 1 — CO CO CO CO tO CM m OO "3- IN OlD oimoorN 1 — CD CD CD ~-i o-> CD ~- ^^ CNJ CO CNJ CNJ CNJ CNJ CNJ CO CO CO OO CO CO OO OO OO OO OO OO oo OO OO oo oo oo oo oo oo oo oo oo CM CNJ CNJ CM CNJ CM CNJ CM CM " CNJ CM CNJ CM CM CNJ CN, CM CNJ CM CM CM CM CM CM CM CM CM CM CM CNJ CM CM Table 16 250 Strategic Role of Perigean Spring Tides, 1635-1976 -■ ID -• O f OO -H LO CM CD CD — H OO — ■ co CO CD to co ■» CO CSJ CD CD CO «* CD to "3" CO CO CO CSI CM oo CM to _ OO »-H ••a- r-. to cm CO CSI CSI CO CD to "3- CO CM CO "3- CO CD to to CO CM CO "S- 1 1 ' CM CM CM CSI CSI CSI 1 ' 1 1 ' 1 1 1 1 ' «3- •O- CD CS1 LO OO tO to LO ^ •o- ■^ to ■>» to ^ CD co csi CD ">* CD to to CD CO CSJ to to CO CO CO CD CD „ to to _ to CM CSI oo CD CO (0«>(VJN(D o-> cd cm co to to to lO CO CO CD OO to CO CO CM CSI to to CO 1 1 1 1 CM CM CM CSJ CSI 1 1 1 1 1 1 CM 1 1 1 1 1 1 1 1 «WI — — ■ CO CO to co cd co moi«rs CD CD 5 CO to CM CO CD to to oo to CM CO •» to CO CM to CM CO CO CO CD CD to ■"3- a) toi^in^ CO CO CO CO to r~ i — to to to to to CO to to s to to to to to to to r— ID O CO O OO CD tO to CM co OO ^ CO CO _ to CD CM to CO OO OO _ to _ „ CD _ _ CO CO CSI _ to CD OO _ ^J. CD CSI tn CM — OO CD CO CO CM to to to to to to to to to — — I CM CM ~^ CM MM« tM CM CM ~ CM CSI CSI — " CM CM CSI *"* CM CM "■' CM CSI *"" ~ l CM CSJ ~* CSJ CM CSI """' CSI CSJ CSJ ~" CSI CM — 1 CM CO CO CO tO CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to o> - o ro co cm ^ cy — . ( cm ( CO cm cd co CM to CM O CD CO CD 7 CD CO - to CD ~ to to oo CO - s - * OO oo 2 " - 7 - CO -3- 7 CO 7 a« cd CO CO CM ••s- ^. oo CM to to to i— I CM — 1 CM — < ' 1 1 CM CSJ CSI CSI CM CM 1 ' CSJ CM CM CSJ CSJ CM 1 r~. 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CSI rt CD •—• , oo CD OO to ^. to ■rr *rf CO CM _ CSI _ , CD CD oo oo r^ to lO csi N CM — « .— I ~ CM CM CSI CM s CM 2 - s 1 2 CM CM $ CO ^r rt rt ^ CM CM CM CM OO oo x» ^ ^r *3- to to to to to to to to r^' r^ r^" oo OO en en CD CD c~> CM CM CM CM CM CM CSI CM CSI CSJ CSI CSI CSJ CM CO CO CO OO OO OO OO OO OO OO OO OO OO oo oo oo oo oo OO OO oo oo oo co -h to o in _ to CO ->3- to tO CD •»»• CD CD oo OO oo OO ! oo CM r ^_ _, , to CM to _ „ to CO tO to <=> ^. CO CD ^ CD OO CO r» CD CD — ■ to to to oo OO CO CD CM CO CO uo to to CD OO CO c— 1 CSI CSJ oo to CO to CM oo -«3- r— . -«3- to CD OO CO to CD CD oo t ■> oo CD ■CT O oo oo to CSI T CM tO oo on oo oo OO oo on OO oo oo CD en OO OO OO OO OO OO OO OO OO OO oo oo oo oo OO OO OO oo oo oo on on on OO OO oo oo oo OO OO OO on OCT OO OO oo on CO OO CO CO OO OO OO oo oo OO OO oo OO OO CO oo oo CO oo oo OO OO oo CM CSJ tM CSJ CM CM CSI CSJ CM CM CM CSI Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 251 «» CO CT> CO <«3 Ol»)<«)«t-H OO OO UO CO oo CMOors«j- OO CO — co oo UO CO oo OO — « CO cm r-. CO OO CO OO ^3 ^3- CO oo co ^r —• oe CM CT> CO —1 CO OO CM CO — I CO CO rt 0)00 — « oo UO rt CO CM CM CO — ' CM -^ 1 CM — ' CM CM CM — 1 CM — < 1 1 1 1 1 1 1 1 CM CM CM 1 1 1 * 1 1 ' CM CM CM CM CM CM 1 ' cm uo co uo to CM CO CM oo ^a- ^ CO CM CM UO OO uo co r~. uo UO oo ^ oo oo X* CO oo oo UO CO UO 1 — oo — . 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O CM CM OO CO 7 7 CO OO OO ^- «3- — -1 1 — CM OO CO CO CO OO CM CO « ro CO CO OO CM CO — CO CO CO 00*3 00 oo co oo ~ r- i~» r- co cm co rt UO CO OO UO co r-» CO CO CM -* oo •>3 CM -^ CM ^- ^- oo co r-~ CO CM CM OO CO 7 ,777 1 1 1 1 1 1 CM CM —• f— i UO CO CO UO UO CO UO — CM OO -^ s CO -h OO — 1 CM CO CO — i CM CO oo oo uo cr> UO CO UO CO UO UO »3- *3 ^- CO 22222 co r-~ UO CO - «3 CO CO CO CO CO UO •«3- CO UO CO CO r-. co 2£ •*3 UO CO i—l CM CO CO CM CO CM CO r-~ CM uo «a- i — — • oo r— cm uo CO CO ^3 oo « co s CO OO OO OO — I CO OO OO -^ CO oo oo CO CO oo OO CO oo OO CO oo co oo CO CO oo oo oo CO — « oo oo r-. co CO CO 1 — i — co co r-~ r- . co co r-. i — co r-. co co r— r- CO CO r- co CO P- CO CO CO 1^ CO 2 CO CO CO CO 1BNN CO CO OO OO oo CO UO CO oo r- r __ CO oo OO CO CO CO CO oo CM "3- r-~. uo V CM — • CO rt —i •— 1 CM CM rt rHMN>H — CM "" —* CM CM ""* IM UO CM — c CM CM CM CM CM ..... ..... ..... CD CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO r— oo uo i-. ^r CM OO «3 —f -NN CM — 1 — • CM « CM — 1 CM •— 1 CM ~r — I CM *"? —t —f . "T °V 7 i CO CM CO oo oo tvOOl — CO «3- UO CO CO UO CM rttoNOO) co oo 1 UO l"i to ^- UO -a- CO UO CO CO CM — 1 CM •^ oo oo r-~ oo oo CO CO UO '" jj "* CO -^ CM OO Oi CM CO C-> ~ CM r- CM CO CO *3 UO co r- OO ~ CM CO CO CO CO CO CO CO CO CO CO CO «3 'l- oo oo oo oo OO OO OO OO OO oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo OO oo oo OO oo oo oo oo oo OO CO OO CM OO co r— . cm r-» cm -r-.^icii) - 31 OO CO CO CO CO CO oooo« Cvl CM CM CM CM CM CM CM CM CM CM CO CO CO CO CO OO OO OO oo oo oo oo oo OO oo OO oo oo oo OO oo oo OO oo oo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM Table 16 252 Strategic Role of Perigean Spring Tides, 1635-1976 uo — < co cn •— i ^f c\j rs. 10 co m on *a- co cm to m •— i tfloo t cnj oo to m en m ^- x csj m co m co co oo cm un ro 01 co m cn m co to r^ m ^h oS o <-< en in ^ r-J csl co .— < co cxi to r^i csi ^h co ^ in* in" r--! csidro ^ ro ■— I ^-t^^CM^CMCsJCMCM'— <<— • ~^ .— • »h --h CSJ C\ CNJ CM CM ootri to -* q - o to cn r*. - to ^ ^ oo en oo en ro r^ -h cm ^ co in co r — co «— • co cm m *=r r-s. o cm ^t ^t CMcoCMuor-^ ^-« co cn co co — <-— ttoco~^ a^ co co n en oo to ^ m oo enen o en co cq cn cn co q ■"-; cr> oo q o ai ai q o o o 001 o o o - ) co o ^ ocnen o^h coenencnen en o en en to to to r-«. to to r — to to to r-» r — to to r — r-. to to r-- r-. r-— r-! i — .' to i — ■ r-" to" to to r-*-" r-^ to to r** r**o to" to to to to to i — " to to •HCMCM ^-< CM CM ^ ^i CMCM -^ rn CM CM -i CM CM CM — i ^ CM CM ^ ^ CM ^ CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to cm rs m — < ^ -^ co m cn eo to m to m tom ^- co to rs cmoit oo cm ai -q- cm •-( ro o ^h ^ co cm cn en cm ^^coeocn t t oo in -«j «j to to en cn to to m r-. cm to d cm ^ c> d in in r-ir-^CMcd^ CM ^ CM ^ ^ ^-«CM CM -• cn ^- cm m co to ^j- co ■— i r-. to m co co to mcM to ^ in m to en en »t co r^ to to co rv ^j- - o co *t m cMcocMtor-. co o o to cm ^r-— CXI co cn CD "* " E CNJ LO CD •— < CVI -* r ~~ CO ~* CNJ 00 CO cn co "* CD ZZ "* in ~ CO OJ CNI CO l 00 OO 00 00 CO CO 00 eo 00 00 l eo eo eo 00 00 l l CO CO CO CO CO CO OO OO CO OO OO er> 00 CD CO CD CO 00 CO 00 CO CO CSJ CO Csj CO CO 00 00 CO eo CO .— . in co in cn in en ^r ^3- en co en 00 co 00 co cm co cm r— r-» cm to •— < to •— • to co to co in co m eo ^ en en ^3- 00 «* co lo r^ n I — cn oo to ooo o m 10 cm ^ CM ^h CO (X) *=t- CO CO < f-i T to ** co cn -Hooroin CO r-^ to .— i ^ uS cxjr-vir-^^ ^ CM CM CM CM CM CM CM «BS* O) cm ro ^ o CM CM CM CM oo *3- ^ to cr> r-^ cm co co cn r-^ cm r^ ^ co co co co to co t I — U3CMCMCD m WCOOCM O I — CO- CO to co *a- ««=r to cm co ^^ co cm cm cm i co co t co m co r*- r-* r — co lo ^j- ^j- ■ O^tCDN CO CO CO CO CO LO UO — i CO CO csi^a-^s-coto 0)00cmloo co cn co oo cn r^csj^-r-co oo ^ en cm ^ en m ro ^ lo cm to ^ ^ ^t oo o ^r ^ n ocM^cncM O) LD -h OO O) O ^ IN LO CM I — O LO CD OO .-h ^ ■— < CO CO •— i CO 0"> LO CD ^ LO tO ■- 1 LO O O ^t (^ O CO CM N O CO CM -^a" CO CO o oo O) o O) oocn o O) 01 o o 00 o> o o 00 o ^h en en ^ o en en en cnoo o o en en o - • en cn 00 co co cn cn co co co co CM ^ CM CM ■ cn co co co 00 co encoco cm O) «^ en ro en^ phcoo o) cmco ^h ^h cn (^ CO CO CO CM CM CM CM ^^ CM cm lo co co cn ooocm<3- OO T CO T — i COCO > cnLOiotooo co co to 1-— g oq^rcntoiN to T r-^ ^ *3; r^^i— jr^oo cm to cT~ CO CO CO CO T CO t CO CO CO CO T CO T CO J"""* CO i o LOtococMi-o 00 cn ro to cm cn o w 00 ^ to co cnoo- — 1 00 cn co cn cm *a- cn tocnooooco cmoocmcoco to co cn co r — cMcnr — 10 ^ co to «— 1 too t co •— 1 o o lDOO-h CO lO CO CO - cor-^r-^cn co'ed^cd CM ^-« CM CM CM CM ' lo cn cn lo cm i — cn to 00 to en 00 00 00 cm cn to csicM^fN Tco'cbr^-* ^-<' co ^ r-^ cn ^ r^." ^ CM CM CM CM CM CM CM ^ CM LO CM <— < ^ «— 1 CM CM *— < ^ I co to to to to to co to to to to CO co to to CO CO to CO CO CO CO CO CO CO CO CO CO CO CO CO co to to to CO CO CO to CO CO CO CO CO CO CO 00 LO CO <=> CO C= m rt rt 00 co CT> CVJ 2 co •0- 00 CNJ ~ —1 O cn S CVI 1 LO TJ- co •*»• ■«3- CNJ Cvj CVJ Csl CO CVI CVJ Cvj ~-i -* cr> CO cr> r "- s s CVJ CVI ** CO cvj co r- — <* *- 00 co «a- o-> <=> ■ CVI CO ~ HI 00 00 OO lo lo lo 00 00 00 CD OO LO LO 00 00 OO LO OO OO LO LO 00 00 00 cr> CO CO 00 o-> <=> LO CO CO CO <=><=> Hi CO OO OO CO CO CO CO CO CO CO 00 00 CO CO 00 CO 00 CO 00 00 oc CO 00 00 cn evi ^ CT> CO CO CO CO rt CO <=> O CO OO CO CO CO CO c*j c*j cj> CJ» OJ CVJCVICVJCVICVI CVJCVICVJCVJCVI vt vt U>lO U3IVOOCT1 I — — . CO CO — • ci co cvj ^ ^ <=> o co CVJCVICVJCVJCVJ CVJCVICVJ CVJ CVJCVICVJCVICVI CVICVICVJCVICVJ Table 16 254 Strategic Role of Perigean Spring Tides, 1635-1976 on to CNI ■^J- CM , to CO to LO CNJ OO CO CO to CD CNI OO OO _ _ „ ^J. to _ ON LO OO CNJ OO ON CO ■«3- CNJ OO OO LO o ON CO CO oo CNI CO CNJ CO OO CNJ to o CO OO CNJ CD to CNJ OO OO CNJ CO CO OO UD CM On! CSI CNJ CNJ 1 CNJ 1 1 1 1 1 1 1 1 1 CNJ 1 CNI CNJ CNJ CNJ _ lo LO H „ LO CNJ _ o-> CD „. _ CO CNJ CO CO CNJ ^ OO ^ , LO OO OO p^ ^ CNJ ^ CNJ _ ■"3- LO ON _ o _ CD CO OO -3- to to CNJ to CD ■«3- to oo OO OO OO to to *» "3- <=> to CD LO CO CO LO to CNJ CO ■«3- «* to to CO OO LO CNJ 1 1 1 1 1 1 l T 1 1 1 1 1 1 CNJ CNJ CNJ CNJ OO OO LO o-> o-> CO LO to LO cm « CNJ CO OO OO OO LO CO OO OO LO OO CO LO LO LO CD OO oo to to to to LO LO LO LO "3- «• T to to to to to LO LO 2 2 "3- CO - OO 2 2 LO i£ to - - CO CO to CNJ r ^ ^ p>> OO o-> to to LO CNJ CNI CO LO CD OO CNJ ON LO S CO CO OO CO CNJ CNJ LO ON OO CO ON ON ON CD ON CO <=s ON ON ON ON OO c= to to to to to to to to to to to to to to to to to to to to to to to to to to to ~ to to «*• CNI to CNI OO _ CO OO CNJ CD OO r ^_ _ CD ^ „ CNJ _ OO CNJ p^ OO OO to to CNJ ^ ON to CNJ OO ON LO ON CO ON CNJ ,, CO OO CO OO CNJ Ol CNI to CNJ LO CD OO OO CO OO OnI LO OO LO hi CSI cni tN •"" tNJ CO •"■ ~~" tNJ ■"■ tNJ — ' "" tNJ *"■ CNJ ~* CNJ CNJ ""■ tNJ CNI tNJ —" CNJ CNJ CNJ CNJ CNJ ~ CNJ CNJ CNJ — ' CNJ CO LO to to CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to s 3 to to CO LO to LO CO en LO to "=T CD CNI OO OO CO to LO <=• LO LO o> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 ^ ^ ^ CNJ on OO CO m CNJ CO 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 CNI 1 CNJ ONI CNJ CNJ 1 CO 00 en CM ^ ^ OO CNJ CD LO "3- OO CO to OO OO ^ OO CO ■"3- to OO OO ■«3 CO CNJ ««t LO ON OO to CO "3- CO LO «» to to OO ON LO IT) OO CO OO CO CD CD CD CD LO •«3- CNI CO OO CNJ •"3- •er CNJ CNJ CO ONI ON CNJ OO to 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 CNJ CNI CNJ CNJ CNI LO CNJ CO CNJ OO CO CO to CD OO ON «• CD ^3- CO OO CO to ON to "3- ON CO lo <=3 CD ' — LO LO to LO to to LO •<3- «=r 2 2 2 2 2 2 2 to "3- to "3- 2 •"3- 2 to - to ~ CO CO CO CD LO OO CO CO to CO CO CNI OO to CO CNJ ON ON ON ON on cr> CD OO on o OO ON CD CO CO CD CO CO OO CO CO OO co OO ON ON CD ON ON CO ON ON OO CD ON OO CO to 2 " - to to to to to to to to to to to to to to to to to to to to to s to 2 2 - •W CD OO CO CD « OO _ CD LO LO CNJ CNJ CO CD OO CNJ OO to OO ^ ^ ^ (=> CD CO CNJ OO oo ,, OO ON CD to LO o "»■ — ' og CNI to uo to to to to to to to to to to to to to to to CO to UD to to to to to to to to to to to to to to to to to to to to CO to to to to „ - - - - - — i — 1 cm •f CNJ CNJ CNJ iO Jr r\l J_ pi en LO 1 LO IO «tt CO "3- OO CNJ CNJ CO _ CD OO OO 1 — OO to to OO to LO LO CO LO en OO CNJ „ _ CO rr ~? 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M M s p.; ji oo" OO OO OO CO en ON CO CO CO <^> CD CD CD Z-T — 1 _ r_ CNJ CNJ CNJ CNJ OO OO OO OO CO «sr -3- ■cr *t ^3- LO LO LO LO to to to OO OO OO OO CO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO CO CD to on LO cr> en CO OO ^ OO CO ^ OO OO CNJ ^ CNJ p^ CNJ to CNJ to _ r ^_ _ to CD to _ LO CD LO CD ON LO ON ■"3- ^ ON CO LO CO to OO OO CD CO OO CO LO LO to ON OO OO CO CD CNI OO LO LO to ON CO LO LO en OO ON ON c : or «3- tr: to OO CO CO CO On ON ■"3- to -«3^ -=t ■«3- ■a- LO to to tc tc tc a- c=> CD CD CZD <=2 CD CD CD o a CD CD CD •=> co <^> u C_3 CD C-D CD tj> CNI ° J CNJ CNI CNJ CNJ CNJ CNJ CNJ CNJ CM CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ Osl Osl CNJ Oni Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 255 Cn OO CO en CO 00 !____ en ^ CO 00 en „ ^ en CM CO CM CO ~^ ^ « CO 00 00 CO CO ,, 1 — cn to CO CO CM CO CM LO CO CO en •^- to CO CO CO CM CO CO CXI CO 00 en ■ct- to CXI en 00 CO CO to ' 1 1 1 CM 1 CM CM CM CM 1 CM CXI 1 1 ' 1 1 1 CM CXI Cxi CXI CXI 1 1 1 1 OO OO in r~ -o- CO cn CO CM tO o-> CO to oo CO to ^ to V, en to en CXI ~-> ^ CM 00 CO CXI -3- «* to 00 ^ to 00 ^ ^ ^ ^ ■>3 •«3 00 en cn f~ o to CM on cm CO 00 LO OO OO OO 1 — LO LO CO 1 1 1 1 ' CM 1 1 1 1 1 ' 1 1 1 1 1 oo cn CO to CO — I to to CO CM CO to en CO CM en 00 1 — CO OO LO on 00 to ~^ CO co en 00 on r— r- 00 to to «3 CM to CM ■>3 •«3- 00 CM CO co to CO 00 CO CO CO en 1 — cxi en LO CM to CO CO IT) *3- CO CO CO CO - to to to to to to to LO LO 2 s s 2 2 ~ ™ to to to 22 «=r "3- 2 " S 3 " oo oo Cn to CO ■*3- oo to *3" CO LO en en CO to CO CM CO CXI ~-> CO CO to LO •"3- tO to 00 CO "3" CO LO to p^ r~- en — 1 o-> cn CO CO CO en o-> o-> co CO o-> en en en 00 en CO CO 00 en en en co CO CO en 00 CO CO 00 en ^ CO 00 CO CO en cn CO 00 ° 1 — to to to to to 1 — to to to to to to - to to to to r»» to to 1 — to to c~ to r— to to to to to to oo lo to to cn CO ^ ^J- oo to OO CO CO CM en 00 CO ^ CXI CM to to CO 00 CO ^ 00 to en CO -3- OO -3" en ! CO CXI 10 —1 .—1 OO -h "3- CM to CO LO CO en oo CM CO CM 00 en CO ^J- «*■ CO CO 00 «3- CO co en CO CM CM to to to cn a •"" tM " tM ~* tM tM tM —' tM CM ~" tM tM Cxi rt ^ LM CM ■""' LM tM tM ~ ""■ to tO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to o> - r-» to to co en to - CM cneo o-> 3 CO a - *Y CXI CO a - -3- 3 co en •=)- CO "T 00 ^ OO CO 1 — co to to OO >=3- ^ 1 " cn 3 to a CO COLO oo OO cn cr> r-~. CO .. -a- « ! r __ . ^ to . . ! _ P~ LO CO T "" ~ CO ' CM to to oo CO CO CO CM CO -7 CM LO CO -7 CO en ' ts- to 00 00 "7 CO CM CM CM CXI CXI CO Cxi Cxi 1 -p 00 cn ' cn 1 rt CM •— 1 1 CSJ oo «3- •-< CO CO „ CO — 1 CO to en LO oo CM CO «s± CO to CO _ 00 00 to to CO to OO CO CM CO ^3- „ 00 CM „ ^. CO ^ CO 00 cn cn " LO oo en to to LO CO 00 en to CM 00 00 to en cm — i 1 1 1 1 CM CM 1 1 CM CM CM CM CS1 1 1 1 1 1 ' 1 LO en to LO CI 00 — < 00 i~- on CO to CO en LO O-l CO 00 OO *3- en en o> en ^3- 00 to cn to CO 1 — CO LO LO «3- CO «3 CO CO 2 «3- ss s to to to to 2 LO 2 LO - ~ S «3" LO to to «3- ^ ^ 2 2 2 222 en 1 — to CX] CM I.O Ox| CO CO CO to CO CO 00 CO en ^r on to •* LO — « CT> en O co CO cn cn en co CO en en •=> CO en en GS en en en co 01 en to O OO en — 1 cz> 00 CO CO o-> en CO cn en 00 co ~^ CO CM CO 1 — t CO CO o-> to ^ LO to ^ CO LO ^ _ _ to en „ CXI to «3- to ^ en r ^ Cxi OO 1 — en uo to — 1 to CO to ^ -a- CO CXI =3- CM CM — ' ~-> CM CM ' ' ' ' ' ' UJ L J ' ' ' ' ' ' tD CO to to to to to to to to to to to ..o to to to to to to to to to to to to to to to to to to to to to to to to — ■ "? °V ■"J" CM CM rJ. Jl CI J!, J_ 00 en OO ^ en 1 — to ^J. to .— r CM ~^ CXI CM CO 00 ~- 00 en 00 r^. to 1 tOLO^ .— • OO o-> CM CO cn CO "* LO .— • t^ LO to t^i 3 *"■ '~- 00 " CM CO 00 cn co 13- <=> 3 «3- u ' CXI r-~ ~^ tM c j "* U. 00 ■«3 to — « oo en cn o-> o-> CM txi CXI 00 CO CO CO ■cr «* to to to 00 OO OO oo OO oo oo oo oo oo oo oo oo oo oo oo 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 OO OO 00 00 OO 00 00 00 00 CO CO 00 00 OO OO OO OO CO r~.eo CM ^ CM 1 — to CM to _ LO to CO to CO LO CO •3- CO ■■3- en en "«t 00 ^. CO 00 CO 00 r-~ OO r- cxi CXI ! „ to „ to — - to en in oo LO oo in o-> CM 00 r— . co en CM Oi CXI •«3- CO CO CM to to Oxi LO OO ^f •=3- to to oo on en CO CM 0-1 LO to 00 en CO cxi r-~ en on 00 LO LO 1 — 1 — cn CO c > CO CO to a co C^ to CO CO CO CO C.J CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CXI CXI CM CXI CXI CM CXI CXI CM Cxi CXI CM CM CM Table 16 256 Strategic Role of Perigean Spring Tides, 1635-1976 cm cm cm O *a- 001 -h cnrs id rooO't rs rs rs cm cm csj rN. ^j- o oi •— • r — cocoon i — .uor-.r-.oq CNjr-.^ruocr> rs u=> p-^ co cm en r-.uouoen rs co to n n r — to ^ o en to to cm rr to n ^ o -— < — h co ph co in to en co to in oo rs rs. co en co p— i enen en ^ ^t m o co o o r>. en oo n pn co en ^r cm mm' to to to to to to n n *a- ^j-" ed ed ro coco^ruo'uo to to r^ to to to uo^rcoco co co -st- -st n to to to to to n' -st- ^ -st- -st- cm co cm co to oo r— . to co oo uo «— i en •— • m cm en -st — * to -st- en co to < — i m co en cm to lo o co co co o -st- to •— i o co r-. <— « cm co^a-uoco o co cm to to en to co to co to o o ^ fn oo oo o co en o co ^ co o n cm p-^ p— ■ co •—< oo to en co "*a- o rs co rs ooenoo— « •— • r«. en co o en r^ en en o co en -^ o en oo co ^ co oo en o -h en o o o o o en en o o co en ph o oo en en r^ oo ^ to o o to n m co to o rs to to tocouoenoo m to ^ co t oo rs co oo to oouooorooo rr n ^ ^- r>. rv o o to en to rsi Tt cm cm uo'r^uo-^^-' ro d r-i ^ c\i co — I ob cm o" rs' to .—^ — * *-^ r^ en en d rsi en to "^ o o lo I n co co cm rs" uo en *^ cd CM CM •— • CM CM CM ph CM CM p-H CM — • CM •— • <-■ CM <-h CM ^h rH CO — • CM p— < p— i CM CM p-^ -h CM CM CM CM CM CM ^-^ — h CM CM -• ^ CM ph to t cm en co en n co o o cm ^r cm o en co co o cm oo co o cm 't * cm en cm en ^ en o «-" o oo •— i n ococo en co rs co p— i co m 't co o o w to ^ n en to to en to cm to ^- n en ^ ro cm cm 1 od co «— < co co co oo cn rr «t cm cm en co co tri in cm en co d co en co oo I ^ ^t cm ph r>. co in in d en d co cm cm •— < ^j- d CMphCMCM CM p-^ CM p-^ p— < p-^ p-^ p-^ CsJ p-^ CM CM CM ^ CM p^ CM ph ph r— i p-h — t CM CM CM CM CM •— 'CM encMuotocM co n rs to cm to ^ cm rv co — < co p-^ cm *a- nen cm^- en en co -^ oo to ^- oocm nto pho) woocm oo •— i o cm to co — i o n en o -si- p^ r — co to cm cm p— i co cm oo en co co -st p-^ en cm oocnoop-^ p— < co en co o o n en en o enen ph o en co co p— i en co en o ph enen o o o o co en o o oo en ^ o co en d to to r> r-^tdtdtdi — ■ i — to to to rs to to r^ r^.' to tdr-!r-^totd to in, rs to to r-^i — rs' r — to td i n rs to to r-^r-!tdtdi en 't Tf co ^ n cm ^t ro en «t en r>. rs cm oo en n oo n n rs. -sT n co en co en rs ■**■ n en en to cm to p-h n en oo n to to rs in od tt to en co oo tri oo" cm «— i d n r^ ^ uocm co t en ^-cn •- « « — ■ o ^ *t oo d ^t n n co to rs' •*& r^. en *zr ^-< rv co in co CMinCM *— I CMlOCM CM CM CM CM p-^ CM i-H «-H CO CM r— < ^ CM p— I *-H p-^ CM CM p— ' p— < CM CM p-^ p-h CM CM p— 'CM to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to rs *-r p-^ co o-^Tp-^locm cm ph in ^- co cm to to cm co tocoinuoto cm rs rs co p— « on cm coto *sr en o -sT p-^ co en cm n p-^ , — i CM , — . H CM ph CM ,-_, ,_h CM p— * CM «— ' p-^ (— ( p— • p-^ CM CM CM f-H CMp-*CMCM CM incocMCM ph cm , — i o en oenoor—co to to ^t- ^f m ih •— i ro cm t t to n co rs d en in 00 n co p-^ rs cotoencsjoo -— < rs co co en cm en cm in p— < -cf o to cm n p-^^rcotoco ton oo 7 to m co r-» co 00 cm cn r-^ co in o> cnj r*. <* .— iro roup r->! co" in in co co cn cm co r^-! cm cxi co •— • co 6 oj r^! r^! ^h ^h r^ CN ^h Csl CM CM CM CM CM ^ — < co O) o m r*^ cm CM CO CM CD *— « ^" CD r-. CO en cm r^ o CM LO CM ^ ~-« CO tO ^3" _> r-. CO O "*T CO CO CO CO ■*3- ■*}■ cd r-^ ^ co ^ cd oo to ^ cm oo oo «) ro m in ^a- in uS m" in od U7 uj in m' in uS in ^t ^ ^r ^ ^ CM ^ CMCMCMCMCM CM ^h >-h CO •— 'CO CD CD tO tO CM ^ CD C7) CM r- 1 CO CO CM CO cn oo co rv tD ^ ro en to to r--. cooo-Hcnco ■«=*- ^r co cd m ^ cm rn cm in cd in -*a- ■— i co ^j-tocDtoco ^_ ^_, ^_ ^_ CM CM tococooo co co cn to m i^. t co en m cd ^j- to csi oo ■>* en ^ o o rs, loco en ^ co cd en m to rs. cn cm co »» corvoooo LO^-inmcM entoencooo cMrN^co^ to cm ^ to to co n CTNJ r-» co to ^j- in r-^ in m cn > co csi csi r--! ^ in cn co co csi ro r>i ai od *t ^_; csi csi co "^ oi o r^ ob rn r-! ^ cn ^r ^ ^-« to csi cn co •— I co cn csi r--i od i co* < CslCMCM^CM^^*— • •— ■^CMCMCSlCMCsl — • •— < ^ ^CsJ^CNJ^CNIOJCNJ^CSI^H ~~, csi o cn co cnj ^t oo lo cnj pn co co m oi -*r r-* co m co x ^ <* oo oo r*. co un en o com oo n rv co co ^h r-« co id t co^j-csicsicn o U3COCO m en to •— • cn in co m to m r-^ rs ro i — co n *— n£>o rocsj cm in in ^ r-. cr> o n r-. co cn ^j- cn cm noooNps cn cm ^3- r-. in oro o<- < csi lo c\i m cnj csi o to ^ co o cm ^ cm r--. co o oo inai cm to co cn co co csi co ^ ^ csi cnj un ro rooo ifl ion r-^ ^ cn r-»- .—< ^foro oo cm oj co n m en tj> ro o cn cn o to ^ ■— i r-» co m ** m is r-^ to to m m- • ~^ *it in co m o co o m ^ ro r>- o ^t oo -h in n co m ~^ to ^ cm -^ rs. rx r-i rs. « o to to co co O rs « • m co cm ^ o id en cm ^ ^ co cn •— < co co to ■^r cooiomeo en cr> t -h o s. ^ co is -^ cm rs r — fs cm o co ro ro ro cn cn .— ; en co cn o i— « cn o o o o o co en q o co en ph o co en o co co o cn o co o ■ — icocn co o o i — cn en o o co o to to is to to to is r — to r — rs rs is rs to to rs rs to to fs rs' to to rs to to rs to" rs to rs rs to to to is rs to to to i — ' is to i — ' ~^ CM ^ CM ^ CM ^ CM CM CM — • CM CM CM *— < CSI CM ^ ^H CM CM i— i^-*CSI CSI •— I CSI CSI CSI ^H CM CNJ CSI -— ' CSI CSI CSI ^ o en cm o ^ co -t en cm rs in co m rs in --^j- rs rs ^j- csi entD (D csi cm co ts . — 1 in m ^r to to 1 — comcoco co- — 1 o ^ cm "t co -=r — • CSI — 1 — c O S22^S 00 inin CSI LO UO co •— i m — 1 csi ^-. <=> cn ~-> c=> oioorvooio 2SS UO CO CSI CSI CO CSI — c io csi — ■ csi i~~ 00 — 1 csi 00 cn ""SH^ uo csi — c UO 1 — • csi co cn co ir cn co «3- LO •— * CNi UO UO r-~ csi — 1 r— 00 cn csi co 00 cn sssss s^ £££ sssss cJ^cnS ££ sssss cn^SScn _ _ ^_ Csj CSI CSI CSI CSI CSI CSI cn cn sssss ^ ^- en en t co cocococmco i — . cm r*- cm > — 1 rs ^ to o to ■ — iincoinco mcnincn^r o to CNI 00 CO CO CNI CO to •XT to to en CO Cxi CO cn to to 1 1 CNI CM CNI 1 CNI CNJ 1 1 1 1 1 Cxi Cxi 1 CNI Cxi 1 ' 1 ' ' ' ' 1 CO o-> -3- ■xT o-> ^ CO CO en UO en CO CO CO CO CNI CO ^ CNI cn CO CNI CNI Cxi _ CO _ CO CO CO _ CO cr ^ OO UO CO CO Cxi o LO to to UO Cx to cn Cx CN cn 00 1 1 ' 1 1 1 Cxi Cxi CNI Cxi Cxi Cxi 1 1 ' 1 ' ' 1 1 1 1 J CO CT> CO CO cn <— ) UO m Cxi to 00 «=r CO CO CO <^> to CO ■xj- OO co OO OO CNI 00 CO uo en cr CN 0- o-> CO CO CO " uo to UO UO UO s to " •xT ■xT CO CO 2 ■xT to CO to to s 2 CO CO CO CO CO to to to CO ■xf CO CO to CNI to m 10 Cxi CO CO CO OO CO «J to tc CNI CN CO to UO CC CO oc CO on cn OO 00 CO OO to CO 01 00 CO 00 cn cn CO OO cn CO 01 cn CO cn CO to CO 00 cn CO CO to CO to to to to to to to to to to to to to to to to to to to to to - to ^ o-> OO CO „ UO 00 CO to UO to CO UO to ^^ en CO CO •xT en ^ 01 to _ ^ 00 ^ CO CO CO CO CO to CO CO ,, ^ to CO ,, CNI 00 CO ^ CO CO 00 CO UO CO CNI 00 CO CO UO cn 00 — '"' CNI CXJ *"■ CXJ ""* IS! I'M —' CNI CNI "" 1-1 CNI Cxi CNI Cxi CNI CNI "" Cxi 1-1 CNI CO " H — ' Cxi "* Cxi ~ CNI Cxi CNI — ' CNJ Cxi CO CO CO to to to to to to CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO to OO ■xi- CO CO CO CO cn 1 1 ' 1 1 1 1 1 1 1 1 1 ' 1 1 1 1 1 1 ' CNJ CO ^ CO ,, to to „ CO ■«xf ^ CO ■xT 00 to 00 CO UO UO . ^ CO CO ^ ^ CO UO ^ -3- 00 ! CO to CO ^ ^ cr> UO Cxi ,, CO CO CN, so CO to to *? 7 7 7 1 — 7 1 "7 — - 1 7 — CNJ Cxi °l CXJ CO 00 uo CO ^ 00 O CO CO OO en CNJ _ en CNI CO CO CO 00 CO CO UO CO CO 00 CO CO UO CO CNI Cxi to CO CO „ UO CxJ _ „ to Cxi UO OO cn CO CO CO to CO CxJ CO CO 00 to UO to co 00 cn CO to 1 1 1 1 1 ' 1 CNI 1 ' 1 1 ' 1 1 Cxi Cxi CNJ CNI CNI Cxi 1 1 1 1 Cxi 1 CNI CNI CNI Cxi Cxi CNI UO UO m CO to CNI en CO UO 00 Cxi cn en UO 00 CNI OO 00 00 Cxi CO CO UO to Cxi co cn CM CO cn CO UO cn CO * •«*■ " = 2 uo uo - - ~ CO CO CO CNI Cxi 00 CNI OI to CO CNI cn cn co CO CO to cn CO CO CO CNI CO OO co CD o-> CO 00 CO OO OO CO en en CO en CO CO 00 00 CO cn 01 cn CO cn CO CO cn en CO cn CO CO CO CO CO i2 - co to to to to to to to to to to to to to to to to to to to to to s " CO _ Ol o-> OO CO CM ^ to ^ 0. 00 uo uo ^ CO ^. OO co 00 uo CO CO to 00 00 CO UO CO CNI _ CO ^ Cxi 00 CNI cn OO in CO UO Cxi to CO to CO to ■•a- en 00 CO 0-1 CO CO m UO •» — ' CNI to to <-o to to to CO to to to to to to to to to to to CO to to to to to to to to to to to to to to to to to to to to to to to to to to „ - z - - UO 00 UO CO en CO Cxi cn CO <-f "T 1 •*[• ,_, 00 r-x en o-> 00 00 00 Cn CO en Cn 00 00 00 OO OO en en 00 00 00 00 00 cn cn cn OI en cn cn CO cn cn cn cn en cn Ol cx> cn «a- 00 CO 00 CO 00 CSJ 00 CNI r _^ Cxi to „ _ to CO to uo CO UO CO 00 UO cn ^ ^. cn CO oo CO CO CO CO co r ^ CNJ CO CNI ! ^ 01 to UO en cn cn 00 to 00 UO no CO to cn no Cxi 00 CO cn Cxi CO m 00 UO CO rn CO CNI uo CO ro ■>xt- «=T to to to to to to CO CO to co CO cni NJ NJ M CNI CM Cxi CNI M Cxi Cxl rxi CNJ Cni Cxi Cxi CNJ CNI CNI Cxi Cxi CNJ CNI CNJ Cxi Cxi CNI Cxi CNI CXJ CXJ Cxi CXI CNI «=T •a- «a- ■>3- ^3- CNI Cxi Cxi CNI CxJ CNI CNJ Table 16 260 Strategic Role of Perigean Spring Tides, 1635-1976 to to 1 — CO CO to oo CO "3- CO to to US co CD CO CO ^ to 1 — 1 — co «* P~. CO is to UO CM CO OS CO to oo to ^ CSI OS CD CO oo rs co OS CO — I CO CM CM to — i -3- OO CD OO CD CM 1 ' ' CM CM — . 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""* CSI CSI ** H ~- csj CM ■"* " CM CM —I CSJ CM CM " CM CM CM "" CM CM CM — CM CM — CM CM CM —• IM OJ CM 1-1 CM CM to tO to to to to to to to to to to to to •° *° <£> tO CO to UO to to to to to to to to to to to to to to to to to to to to to to UO CO o CM en uo OO CO to oo UO oo CD CO OO -i « in CM CO OS —i — . — I CO CD oo o> ' CXI ' 1 CSI 1 1 1 1 1 ' 1 1 ' 1 — ^-i CM CM — CSJ 1 CM « « CM 1 1 1 CO in ^ to CO CO CD CD CO is CD CM „ CO^sO to ,, CO CM CM CM CO "3- OO CO CO ■<3- rs co to to CM CO- OS ^ to ^ _ UO ro CD to to ' ' 1 ' ' ' 1 1 ' ' 1 ' ' 1 1 1 1 1 1 „ ,, UO CSI CNJ CO ^ oo CM LOI oo to to CO OO CO ^ OS CD _ to to oo rsoio OO «3" rs OS OO CM co rs os Cm CD CD CO CO to CM CO Cnj 1 os 7 7 CSI " ~ to ^ ^ CD CM CO CM csi co "3- oo CSJ •— < — ■ •-' OS 1 1 ^ u^rs 2 oo to oo T77 p- OS T os «a- oo CM 7 CD " CO oo ^r co to to to CO OO CD -i«lO OS OO CO 1 LO OS OS to CO « oo uo CD OS CD CM CD CD •* t inoo OS CO «3- CD OS oo to to I CO •cr co CM OS CO 1 CO to to to CSI CO CO oo ° to tO " 22 2 CO 2 - "- ' - - - ~" — — - - - - - - ITS P~ oo CSI CD CO CO OS CO en CM CO p- to "3- — ■ CO rom« UO CSJ CD — CM CSJ oo OO _ CO oo CD CO CD os <=> OS OS CO OS oo CO CO OS OS CO CO CO CO CO OS OS CD CO oo oo OS « CD OS OS CO CO CO to tO to to to to to to r-- to to Ps. to to rs to to to 1 — to to P- to to UO to C3 CO UO cr. uo to to CO to r» Csj CD OO CO COOlrs CO „ ^ OS to oo UO OO CO OS CO P- _ CM OS CM UO <—> UO rj — 1 CO CM OO — < oo CO OO CO CD CO •«3- OO CO CO oo OO IS — OS to oo ■"• CM to CS| _ CSJ to to CO to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to tO UXO.O to to to to UO UO - " - - - to — to CO OO OS OO CO CO CO CM -LOI CO CO tO CM CM CO CD CM CO LO CM CD ■"j" •— ' CSI ■■j 1 CM CM CM CM . 7 1 7 ~p —i CSJ — i CM ~* r^ UO ■rr m uo ^j. rsi fll OS _ CO o CO CO OO r^. r^ i m ^r to CO CO CO 1— < CO ~ ~ CO OS OO CO oo oo to to rs to to ^J. CSJ CSJ ■cr CSI _ CSI CM ^ to ""- oo CSJ CO oo CD CO CO "* OS CO ^ to s a to rs - CM oo OS CM CO CO CD 5 to S s CMUO to CM —1 CSJ rs oo — i CM CD CO CO ■* CD s- to to oo OO OS CD OS OS CO CO CO CO — • CM CM CO CO CO CO CO CO CO CO CO CO OO cr. OS en CD CD CD cr. CD OS US _^ uo CO to CO to CO to CD ^ CD CD ^ OO ^ CO OS CO OO ^ CO ! CM CM -rs- to — to — to CO to O LO OS UO ■er OS ^ OS oo rs to m to <— > 1 — OS OS OS OO is OU CD OS 00 — CD OS CM OC ion CM to — CSi oo oo C 3 n CO in OO OO CO — I CM co 1 — OS CO — CM OS OS — oo OO oo OO oo 00 OO OO OO OS OS OS CD CO CO CO CO CO CO CSI OJ CM CM CM CM CM CM CSJ CM CSI CM CM CM CM CM CM CM CSJ CM CM CNJ CSJ CSJ CM CM Table 16 Essential Conditions for Achieving Amplified Perigean Spring Tides 261 «3- CM en cr> OO CO CM OO CM OO CD LO oo to CO ,, ^ ^ oo CM LO „ r ^ CM ^ to OO LO OO oo m«rt r-. cm CO CO oo CNJ to r—. oo CM to CO LO CNj CO CXI to CO ^h ^h CN CM CSI CM CM — < ~-l ' ~H CM CM CM CNJ 1 1 ' 1 ' ' ' ' 1 1 -tocDooto CM CD CO CO CO oo -*3- cr> en rt CM CM ••a- co ^ CNJ CM to CO CNJ -a- -a- r ___ to to CO to to _ ^ ^ to CD to OO OO ^ OO CXI CD CNJ CM o to co CNJ CNJ oo 1 ' — i ■— . CM ' 1 CM CNJ CNJ 1 ' 1 ' ' LO CO CO Cn .— 1 CD oo cn — i o-> oo oiomoi to en en oo CO CO oo cn CO CO CD CD OO CO CO OO CO to to to to to to to to to to to r-» mrvio — id — i —< OO OO CO to cm "a- to to cm en to en ^ to oo OO 1 — CO cr> CD to CD ^ ^ CM _ CO CM to r- OO CO T — I OO — i *a- cm CD en to co oo «»■ to rf to CO to CM -a- CD «a- -a- oo CD CD to — " CM —i CM CM CM -icNn-H-i NCNrt rt CM CM ~^ CM CXI "-* LM ""• CM CM CM ,-. LM CM ""* LM —' CM -* — ' ""■ LM "* ~ LM ■"" ' ^ CO CO CO CD to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to o> - 2J5--S r— to «a- oo to tO CM CO tO to CM CM «a- oo a CD CO a CO a rt CO CD 2 a - s oo s ^ ~ "7 - s CD 1 to -a- to moootvm oo 1 — M WO CO tO LO — i CO CM CO oo to r- CM c— i LO <— > to — 1 rtrHNNN 1 1 1 CM CM ^ — 1 1 1 1 ' — I CM 1 ' CM CNJ CM 1 CNJ ' ' 1 1 ' CM CM CM CNJ CXI CXI 1 CXI ^^^^^ to CM tO — OO ^ orv00 OO -a- co -a- to r- ^ CM . LO CD to to to _ _ ! CD ! oo oo , OO LO -a- CNJ ^_ LO oo ^^ ininn^rt to oo to CO r- •=a- CO CM OO OO CD CD CO «a- CM OO CM CD CM tO —I — I CM CM CM NNCM-HtN ' 1 1 1 1 1 ' ' 1 CM CM in in ^ in cd o tO to to •«3- to 2 "~ to to LO to ~~ ^ oo 2 s s to to to to to «a- to CD •— < CO CO oo oo to oo —• to to m OO CD CD oo CD -H LO O Ol CT) ^-i o CD CO CO oo oo oo CO CD OO CO CD CD CD CD CO CO CD CD CO CD OO CO r~ co co r~ r— to to r^ to to to to to to to to to to to to to to to to to I-- jiMrtoom IC U)"t "» i-~ cm en r^ CO OO r ___ r-~ co to CM CD CD OO LO to LO CO oo CNJ CD c=> ~^ r-~ r— "* CM ~H CM CM —I CM CO —i -^ CM CM — ■ CM CM "" ' LM CM "* CNJ CNJ " _ co to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to CO to to to to to z Z u- "7 ~~t *y T ' ,' ■ .' 1 - .' 'V ^J 1 I ~T "7 ~r "J ~-p rj < ~-" —■ "-' o-> — • O OO 1 — OO OO tO "* tO co -a- co cm ^_ CM CM — O-l CD _ CT> oo oo to r-^. to -a- ^T- LO ,-j oo ONI ro CNJ CM „ rt CO CNJ CM CM CNJ CNJ o, P-l to LO CM — I 2 zz ~ 2 2 2 z: 2 zz CnI OO " en CO CO CD CO CO CM CM CM CM ■"* ■"3- •"* «* LO tO to LO LO LO CD CD CD CD CD CD CD CD CD CD CD CD CD CD en cn «3- OO CO CO OO cm r— r-~ cm to c M _ to OlO-H LO CO ^ LO CD LO CD -a- cd -a- CD oo OO ^ oo CO ^ OO CNJ CM to cm to to •«r to to oo OO CD CD CM «3- CO CO LO LO CO oo oo CO CO CD i — -a- i — to en 1 — CO CO CT> CM oo Ci oo CO ONI to i — cr> cn — i — i I^C7lO-H co ->a- -a- oc> oo CO CO CNJ CNJ CM to «a^ oo oo oo OO CO oo OO OO oo oo oo oo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CXI CNJ CM CM CM CNJ CM CM CM CM ONI ^ CM CM CM CNJ CNJ CM CM CM CM CXI CM CM CM Table 16 262 Strategic Role of Perigean Spring Tides, 1635-1976 CD 1 — CD OO -3- CM to CO CD "3- v- OO CD CD tO CD OO to CDlO CM LO tO CO CD OO CM CD to OO OO ^ ,, CD LO CM LO CO CD CO CD CD LO LO LO CD ^a- — I OO CO CO CO CO CD CD OO OO CM CM vT OO CO i 7~ ' 1 1 , ' CM — ■ CM ~-> CM CM CM CM 1 1 ' ' — CM •«3- en cm ^ ■«3- COOllO ^ CO ^ ^ m ^ ^. 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CO O i^cMCO CO CM ^CM-r^ oo - CM CD O CO T 2~^ CO CM " CO r~~ — h cm oo CD CM CO Tj- OO OO O) O) CO co co co co r-~ O) O) O) O) CD O CO O O) O) CD O) CM CD CM CD CM CD CM CM CO CO CO CD CD HI ■=3- CD CD CD CD CD CO CO O) O) lOiorN O) O) OO CD OO CD SS" CD CD CD O O O r~ oo oo oo CD CD CD CD COCM COCMI — r-~ CM lOCMlC^lO CM ~i "3" CO CO i CD OO ~H CO ••a- i — coco CMCMCMCMCM CO CO CO CO (O COCO ■S3- •«3- "3" ^r CMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM CMCMCMCMCM Table 16 264 Strategic Role of Perigean Spring Tides, 1635-1976 2 o> (£) ro oi ^ i — . q iv *t oq — * co cnj — ; rs cn ^t x oi to ro o 't co o i — *s- o-> - — i csi . — i 'T cm oo o oo ro ^d- co co r-. o ^ csi ^ CD ~ uo csj r-«! oo cd co cd co ob csj td co csi .—< cri cd ~^ cd td 06 r-^ co cd oo — < co csi cd cd csi oo cd ^ cd ob rv! oo o csj ro ro csj — i — i CSI - i Csi Csi CSJ CSJ CSI — , CSJ — , ^_ rt _ __ c CSJ CSJ CNI CSJ CSJ CSJ — . CSI - 1 rt ~- CSI CSI CSJ CSJ CSJ 5 toooincoco tn csj csi csi rs. id csi co oi rs . — 1^*3-, — i to in ^h co ^- ro *cr • — > in ^h co i — co en o en co oo r— co *3- csi en o csi ro cd uo to ~^ uo to oS cd csi csi ob csi csi oo uo uo en cri oo ro uo csi csi 06 cb ^t rs i — ! ob co csi ~^ uo cri ~^ d fs ro en d ^r uo d in ro i — ii — i i— » . — ICSJCSJCSJ CSJ CSI CSJ .— I ~^ . — I . — li — li — (CSJ CSICSJCSICSJCSJ CSI CNI ~* ~^^CSI CSICSICSICSICSI Csi 7DAY 4.352 4.526 4.372 4.853 5.212 5.284 5.920 5.872 6.422 6.426 6.679 6.344 6.245 5.737 4.875 4.838 4.120 3.979 3.736 3.609 3.740 4.172 4.079 5.046 5.926 6.277 6.984 7.042 7.352 6.736 5.732 5.556 4.516 3.761 3.401 3.425 3.684 4.351 5.239 5.460 6.383 6.988 6.903 6.783 6.293 = 70AY 16.937 17.033 16.907 16.959 16.815 17.021 17.116 16.868 16.962 16.860 17.128 17.094 16.829 16.945 16.873 17.067 16.975 16.816 17.004 16.967 17.027 16.931 16.949 17.110 16.982 16.948 16.844 17.006 17.091 16.885 16.880 17.051 17.094 16.972 16.986 17.061 17.004 17.021 17.004 16.946 16.916 17.108 17.054 16.927 16.945 s . fN rN oo q •-; CNiLOoocnoo rN un a» ^ o phn ^toN to en .— i to o cnj ^3- to *— * 00 co ^h csj cn to cnj csi *3- cz> r-. .— n to co ^ O pn crtin ^3-r-^r-^*— 1( — ld m rN oo « rri uS cri un 00 csi <£> 06 «^ 06 pn en ^t 06 to ^ 00 en ro 00 cd cz> ^" cd r^.* r--! 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CN J^ p ^;^ < -P co .'~1 u ? c:: ? ^ "? ^ ^ "^ o ^t cn cn ^-< r— » co cd csi m *t «* to to co co d cn csj ^ ro ro in in rs co od od co cd csj ^ od rH ^- rs co us csj m co ** rs oo co to oo in co r^ o to cn co •-• rs o o oo cn cm •— < tOtOCOOOOO OOOCM CM *t ^t ID CD CO CO O 'H CM CM -^ UO tO rs CX> Ol O rn CO cn cn cn cn cn cn cn cn cn cn cn co co co co co co co co co co <— i < — < t— i •— • •*=f *zt ^t- ^j- ■**■ ^a - uo m m oo in to m in uo m m m in in CMCMCMCMCM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM Table 16 Tidal Force Evaluating Significance of the Data Contained in Table 16 1. Lunar Motion in True Anomaly It has been seen in part II, chapter 4, that solar pertur- bations produce a retrograde motion of the lunar perigee at times of close perigee-syzygy alignment. This motion of perigee is in a directly opposite sense to that of the of the Moon will add vectorially to the daily motion of the Moon in true anomaly tabulated in columns 5 and 1 1 of table 16 is measured with respect to perigee, any mo- tion of this orbital position in an opposite direction to that of the Moon will add vectorially to the daily motion of the Moon relative to perigee. The result will be a value of the daily rate of lunar motion which is in excess of the motion in celestial longi- tude obtained by taking daily differences in The Ameri- can Ephemeris and Nautical Almanac. This accounts for angular velocities in columns 5 and 1 1 which are consist- ently 1.3° to 1.7° greater than even the maximum daily velocity of the Moon ( 15.4° ) at perigee-syzygy, measured in celestial longitude and with respect to the vernal equi- nox. The difference is due to the relative angular motion of perigee. (See ch. 4 — "The Special Motion of Perigee Close to the Position of Perigee-Syzygy Alignment.") A further advantage of these two columns of the table is that they indicate the velocity of the Moon in its orbit rather than as geometrically projected along either the celestial equator (in right ascension) or the ecliptic (in celestial longitude ) . Summarily presented, the use in columns 5 and 1 1 of the Moon's rate of angular motion in true anomaly at the instants of syzygy and perigee serves as an excellent single- parameter indicator of the combined tide-raising forces of the Moon and Sun at these times for the following reasons : a. REPRESENTATION OF THE SOLAR INFLUENCE It has been shown previously that variable solar forces determined by the Moon's changing distance from the Sun and relative angle of alignment therewith are re- sponsible for perturbations in the lunar orbit and an oscil- latory motion of perigee. It is these same solar forces which combine with lunar gravitational forces at times of perigee-syzygy to produce amplified tides on Earth. Thus, any variance in the solar force upon the lunar orbit caused by the changing distance of the Earth from the Sun in consequence of the Earth's own elliptical orbit will be reflected in the rate of motion of the lunar perigee. As noted in the introductory section above, any such motion of perigee will, in turn, affect the velocity of the Moon with respect to this selected reference point. A distinct advantage derives from the later use of this particular velocity component as one astronomical con- stituent of a coefficient of tidal flooding potential. This is because any diminished distance between Moon and Sun appears directly as a small additive function to the rate of lunar motion in true anomaly. The circumstance may be confirmed by calculating the interval (in days) separating each of the tabulated instances of perigee-syz- ygy from the nearest date of perihelion (solar perigee). This will involve a maximum of 182.5 days' separation from perihelion to the next succeeding or following aphe- lion, beyond which the time interval to perihelion again decreases. It is obvious from such an analysis that those values of the lunar motion in true anomaly which are seemingly too large in comparison with the corresponding parallax are the result of a particular closeness in time to solar perigee. Similarly, velocity values which are apparently too low to accord with the indicated parallax contain the effects of a relatively large separation from solar perigee. The principal factor establishing the value of the lunar paral- lax is the separation-interval between perigee and syzygy as described below — added to whose effects the variation of the Moon's distance from the Sun acts as a modulating influence. b. REPRESENTATION OF THE SEPARATION- INTERVAL A second practical advantage in the use of velocity in true anomaly is that it possesses a definite relationship to the separation in time between perigee and syzygy. In this respect it takes into account increasing values of the paral- 2f»l, Essential Conditions for Achieving Amplified Perigean Spring Tides 267 lax (and a corresponding lessening of the perigee distance) as a function of closer proximity in the peri- gee-syzygy alignment. Exceptions from a nearly one-to- one correspondence between the velocity in true anomaly and the lunar parallax are imposed by any circumstance of a particularly close approach of perigee-syzygy to solar perigee as previously noted. However, these and other modifying factors are applied in strictly incremental or decremental fashion. The highest values of the rate of lunar motion in true anomaly are most commonly found at close perigee-syzygy alignments (1-2 hours' separation) occurring within at least a few months of perihelion. c. INDICATION OF INCREASED LUNAR VE- LOCITY IN ORBIT IN ACCORDANCE WITH KEPLER'S THIRD LAW That part of the Moon's indicated angular velocity in true anomaly which remains after the retrograde velocity of perigee is subtracted, constitutes by far the greater por- tion of the resultant of the vectorially combined velocities tabulated in columns 5 and 1 1 . Since the velocity repre- sented is the true one occurring in the plane of the lunar orbit, it is not affected by the Moon's excursions in decli- nation as are the values in columns 6 and 12. However, the velocity in true anomaly is directly influ- enced by the relative proximity of perigee to the Earth in any one lunation as the Moon revolves in its elliptical orbit. Any diminished distance of the Moon from the Earth becomes a direct function of ( 1 ) the increase in orbital eccentricity at the time of perigee-syzygy align- ment, as determined by (2) the increased magnitude of the perturbational forces acting at this time, which are, in turn, dependent upon (3) the closeness of the perigee- syzygy alignment and the commensurability of the lunar periodic relationships making possible these alignments. The greater orbital velocities of the Moon at such times of decreased distance from the Earth, as demanded by Kepler's Third Law — with the accounted-for exceptions previously noted — are quite logically found among the values given in columns 5 and 1 1 . The value of the lunar parallax, on the other hand, is implicitly related (through the chain of events above enumerated ) to the perigee-syzygy separation-interval of column 9, and possesses a close degree of correlation there- with. It is important to note that, although a one-to-one relationship between increased parallax and increased velocity in true anomaly does not exist, the variations caus- ing this lack of direct correlation have, for the most part, been introduced by the changing conditions of solar gravi- tational force described in paragraph 1. Thus, for exam- ple, where a very high value of lunar parallax exists and is not matched by a correspondingly high value of lunar velocity in true anomaly, this lunar velocity has almost inevitably been reduced by the occurrence of the perigee- syzygy alignment at a time considerably removed from solar perigee — perhaps even at solar apogee. In consider- ing the enhanced tide-raising action produced by the com- bined gravitational forces of the Moon and Sun at perigee-syzygy, it is necessary to have the effects of both of these forces represented in any index-quantifier pro- posed for potential tidal flooding. 2. Representation of Increased Lunisolar Tidal Forces in Those Cases Where the Sun Is Simul- taneously in the Moon's Orbital Plane It is further possible by means of table 1 6 to include an evaluation of the additional small component of lunar motion in true anomaly provided by the presence of the Sun in the Moon's orbital plane, should the Moon be crossing the ecliptic at the same time it reaches perigee- syzygy. This situation can be at least approximately assessed by taking the algebraic difference between the declina- tions of the Moon and Sun at the time of syzygy as tabu- lated in columns 7 and 8. Should this difference be less than 0.2°, a solar or lunar eclipse is very apt to have accompanied this syzygy alignment, although — as pre- cisely determined — the exact position of the Moon's nodes along the ecliptic must be considered. (See footnote on p. 7.) At the same time, the gravitational force on the Earth is enhanced by the combination of the solar and lunar forces along two nearly superimposed axes. It is obvious from an analysis of columns 7-8 and 13-14 that, in those cases in which the differences between the declinations of the Moon and Sun are very small (with due consideration to algebraic sign) the lunar velocities given in columns 5 and 1 1 are at least slightly above the average value which would be indicated by the corre- sponding parallax. This increment in velocity represents the combined gravitational influence of the Moon and Sun exerted simultaneously in dual, orthogonally inter- secting planes. In addition to the increased solar force on the Moon at perigee-syzygy associated with solar perigee as described in paragraph la, therefore, an additional component of solar force is provided by the Sun being in or near the Moon's orbital plane. Such a coplanar alignment in celestial latitude (or declination) is evidenced by a slight 268 Strategic Role of Perigean Spring Tides, 1635-1976 increase in lunar velocity with respect to a proportionately accelerated, but oppositely directed motion of perigee at this time. 3. Representation of Increased Lunar Motion in Right Ascension at High Values of Lunar Declination Columns 6 and 1 2 represent the orbital motion of the Moon as projected from the plane of its orbit on to the celestial equator. Since the latter plane is that in which or parallel to which the apparent diurnal motions of the celestial bodies occur as the result of the Earth's rota- tion, these columns are especially advantageous in de- termining the relative catch-up motion required for the rotating Earth to bring the Moon to transit of the meridian. In chapter 8, this joint indication of necessary catch- up times and lengthening of the tidal day at times of perigee-syzygy will be incorporated as a secondary astro- nomical term in establishing a coefficient of potential tidal flooding. The apparent motion of the Moon in right ascension, as earlier explained, bears a direct relationship to its declination at the moment. It is obvious from a com- parison of columns 6 and 12 with columns 7 and 13 that such increased velocities in right ascension occur when the Moon is near its highest declination angles. In summary, it is seen that all of the principal factors which make for an increased gravitational attraction of the Moon and Sun on the Earth's tidal waters at times of perigee-syzygy are represented by the corresponding pairs of values tabulated in columns 4, 10; 5, 11; 6, 12; 7, 13; 8, 14; and in column 9. The single terms con- tained in columns 5 and 1 1 likewise very effectively con- solidate the conditions expressed by seven of the remain- ing terms and incorporate the Sun's gravitational in- fluence as well. A separate advantage exists in the use of the data given in columns 6 and 12 as a measure of the daily angular velocity of the Moon in a plane parallel to the celestial equator. The role of this term in establishing the catch-up motion necessary for the rotating Earth to bring the Moon to the local meridian of a place will be extensively discussed in chapter 6. Chapter 6 Conditions Extending the Duration of Augmented Tide- Raising Forces at the Times of Perigee-Syzygy As had been seen in the preceding chapters, by far the greatest portion of the increase in amplitude (or range) of the tides accompanying situations of perigee-syzygy is the result of a vector combination of the augmented gravitational forces of the Moon and Sun — together with a reduction in the distance of the Moon from the Earth at such times. These gravitational reinforcements and enhancements are responsible for a corresponding am- plification of the tide-raising potential, and — when a co- existing strong onshore wind prevails — add proportion- ately to the possibility for tidal flooding. Yet there is another category of dynamic influences contributing to the increased rise of the tides associated with the near-coincidence of perigee and syzygy. On such occasions, the effectiveness of the tide-raising forces dis- cussed in chapter 5 is further enhanced by an increase in the total period of time during which such forces act at magnitudes close to their maximum values. One of the factors conducive to such force-protracting influences is an extra "catch-up" motion required of any position on the Earth's surface in accomplishing a meridian transit of the Moon (and a very nearly coincident transit of the Sun) at the time of perigee-syzygy. The General Principles of "Stern Chase" Motion The most important dynamic element involved in this necessity for catch-up motion is a temporary acceleration in the orbital angular velocity of the Moon at perigee, which the rotating Earth must overcome for any surface point to achieve a lunar transit. Secondly, the declinations of both the Moon and the Sun just prior to, and while passing through the position of perigee-syzygy, play a contributing role in the amount of catch-up motion re- quired. The position of maximum declination determines the time at which the apparent motion of either of these two bodies will be predominantly in the coordinate of right ascension, and hence within a plane parallel to the celestial equator. Their apparent motions in the direction of the Earth's rotation will then be the greatest, and the necessary catch-up motion by the rotating Earth to achieve a meridian transit of these bodies will reach a maximum. Factors Increasing the Length of the Tidal Day Each of the above-mentioned influences acts to in- crease the length of the tidal day (and, in similar fashion, that of the lunar day). These two slightly different chronological concepts are distinguished, in terms of their immediate application, later in this same chapter. The circumstances yielding a contribution to tidal amplifica- tion as the result of such catch-up motions at perigee- syzygy are outlined below and are amplified in subse- quent sections. 1. Lunar Parallactic Inequality The force-prolonging influence associated with this phenomenon originates from the necessity for the rotating Earth to catch up with a temporarily induced, more rapid motion of the Moon, revolving in its orbit around the Earth in the same relative direction as the Earth rotates on its axis. This catch-up motion is imposed at perigee- syzygy by an increase in the Moon's orbital velocity produced, in response to Kepler's third law, by a closer proximity to the Earth. The greater proximity of the Moon to the Earth is in consequence of: (a) the elliptical shape of the lunar orbit; (b) the location of the Moon at the lower apse of the orbit at time of perigee-syzygy; and (c) a further incremental increase in parallax at this time resulting from a corresponding increase in eccentricity of the lunar orbit. 269 270 Strategic Role of Perigean Spring Tides, 1635-1976 It must be clearly emphasized that this catch-up motion, taken by itself, is of a magnitude having only a comparatively small influence upon the production of extreme perigean spring tides. Its principal significance lies in providing support to other tide-raising and tide-prolonging factors. The maximum catch-up effect extending the length of the tidal day because of the con- siderably greater lunar velocity in orbit at perigee-syzygy compared with apogee-syzygy (see table 10) is some 10-13 minutes, depending upon declinational circum- stances. The effect of this extended duration of the tidal day is added to by another influence resulting from dynamic conditions at the time of perigee-syzygy. As mentioned on page 179, section 3, a perturbed rotation of the posi- tion of perigee itself occurs in a retrograde sense as the Moon's apparent motion brings it simultaneously to syzygy and perigee. Again, only when combined with other tide- raising influences does this small perigee motion achieve a quantitatively significant meaning. However, for the sake of documentary completeness, the particular con- tribution of this perturbed motion of perigee in the im- mediate vicinity of perigee-syzygy will be described later in this chapter. 2. Declination Effects It has been shown that, in direct contrast to the re- flected (diurnal) motion caused by the Earth's rotation, the greatest actual positional change of the Moon or the Sun in right ascension (resulting from their respective monthly and apparent annual motions) occurs when either of the two bodies is at its maximum declination. Under the same conditions, the angular velocities of these celestial objects also attain their maximum components in right ascension (a), with little or no constituent veloc- ity in declination (S). Both the Moon and the Sun in their corresponding real and apparent revolutions on the celestial sphere move eastward toward increasing values of a. The Earth also rotates in this same direction. Accordingly, any increase in the motion of the Sun or Moon will necessitate an additional catch-up motion by the rotating Earth to se- cure the meridian transit of these two bodies. The result- ing possibilities for the occurrence of such prolonged catch-up motions are : (a) Twice each tropical month, the Moon reaches positions of maximum declination, alternatively north and south of the celestial equator. In each of these two positions, the Moon's orbital path reaches a minimum of declination change, and then recurves equatorward. In these same two positions, the Moon's apparent angular velocity in right ascension also acquires its maximum value. In matching to this increased velocity, the requirement exists for a longer period of catch-up motion in order for the rotating Earth to achieve nearly coincident meridian transits of the Moon and Sun at perigee-syzygy. The Earth must complete an additional portion of a full axial rotation to accomplish each such meridian passage. Be- cause of the increased motion in right ascension evidenced as the Moon approaches either position of maximum dec- lination, the greatest influence of this particular modi- fication of the catch-up interval in extending the tidal day occurs at these two times. (b) Twice each tropical year, at the summer and winter solstices, respectively, the Sun similarly moves to declinations farthest north and south of the celestial equa- tor. At these times, the apparent solar motion in right ascension also reaches its greatest values ( although variable within the draconitic or nodical cycle ) . Since syzygy involves the common alignment of the Moon with the Earth and Sun, the attainment of this syzygy position is dependent upon the Moon catching up with any such accelerated motion of the Sun over an appropriate interval of time. Likewise, to feel the addi- tional tidal effect of the alignment of those two bodies at perigee-syzygy, the Earth must rotate a little farther to catch up with the nearly common Sun-Moon axis and achieve a meridian transit thereof. The tidal day is engthened proportionately. 3. The Counterproductive Influences of Solar Perigee (Perihelion) The effect of a combination of a large (coplanar) dec- lination and proximity to perihelion in increasing the value of the lunar parallax and hence the tidal forces act- ing, has been clearly demonstrated in the discussion accompanying table 1 3 of chapter 5. The influences of the comparatively close agreement in time between the occur- rence of perihelion and the winter solstice as these phe- nomena individually augment (a) the tide-raising forces and (b) the length of the tidal day also have been de- scribed. Finally, as will be noted in a subsequent section, the proximity of the Sun to the Earth and Moon at time of perihelion adds to the solar gravitational force which, at perigee-syzygy, swings the line of apsides through a retrograde angle and, in so doing, slightly extends the duration of the tidal maximum attained. By contrast, arising out of an astronomical quantity known as the annual equation, 1 a counterproductive fac- Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 271 tor exists which causes a decrease in the orbital velocity of the Moon at times of perihelion and hence acts as a direct modifying influence upon the catch-up motion described in ( 1 ) above. The apparent motion of the Moon in either celestial longitude or right ascension is correspondingly reduced. Should perigee and perihelion occur together, this factor subtracts from the tendency for an increase in the length of the tidal day at perigee-syzygy. The motions of the Sun or the Moon in declination are not strongly affected, either by the Sun's passage through perihelion, or by the Moon's passage through perigee, respectively. However, if perigee-syzygy and perihelion nearly coincide in time, together with a coplanar align- ment of the Sun and Moon in declination (see table 13), the influence of the combined action both in increased tide-raising force and extension of the duration of this force by necessary catch-up motions usually is quite no- ticeable in terms of the heightened tides produced. As an additional relevant circumstance, the dates of perihelion (usually about January 2-4) and the winter solstice (averaging about December 23) occur quite close to each other. This circumstance, which unites two influ- ences (the one due to perihelion, yielding an increased gravitational force, the other a maximum solar declina- tion, resulting in an increased apparent motion of the Sun and a lengthened tidal day) acts to offset 3 (the slowing action in the Moon's orbital motion produced near peri- helion). The net influence of such a combination thus still serves to reinforce the augmented tide induced by a perigee-syzygy alignment at this time. 4. Summary Significantly, in each of the cases described above, the lengthened periods of lunisolar tidal force action occur at times during which the magnitudes of these forces also have been increased — partially by the reduced distances of the Moon and Sun from the Earth, and partially by their combined, reinforcing, gravitational attractions. Each extended tidal day in which enhanced tide-rais- ing forces are active contains ( with some few exceptions ) the occurrence of a higher high water. The resulting quantitative effects thereon are illustrated by graphs for various tide stations in figs. 153-163 of chapter 8. It is noteworthy that, compared with the tide-heightening effects produced by force amplification, this extended period of force action can provide only a supplementary and considerably less sizable role in the production of augmented high waters. However, such a small but observationally detectable lengthening of the tidal day accompanies each near-co- incidence between perigee and syzygy, as will be shown in succeeding sections of the present chapter. The incremen- tal amplification of the tides which results when these particular catch-up induced extensions of the tidal day ( as opposed to extensions which occur also at each quadra- ture, for example ) coincide with periods of increased tidal force action will be discussed both in this chapter and in chapter 8. It should be observed that a similar bracketing of the times of low water by such a prolongation of the period of increased gravitational force application does not in any way interfere with, nor compensate for, the increased rise in water level at high tides. Reintroduction of the Concepts of the Lunar and Tidal Day Various introductory concepts relative to the lunar and tidal davs, citing the precise differences between them, have been discussed in part II, chapter 2, and it will not be necessary to repeat these. At this juncture, it is important to point out certain practical variations in the length of the lunar day which result from changing catch-up motions of the rotating Earth. These are respon- sible for similar variations in the length of the tidal day, and in this respect introduce new complications in the immediate problem at hand. The following brief review will, therefore, cover appro- priate aspects of the lunar day which relate to : ( 1 ) its origin in the respective revolutionary and rotational mo- tions of the Moon and Earth; (2) fluctuations in the length of this day resulting from the necessity for the Earth's rotational catch-up motion ; and ( 3 ) the produc- tion of corresponding variations in the length of the tidal day. Specific astronomical factors which alter the length of the lunar day, such as changes in the daily lunar retarda- tion time, also will come under consideration. In the asso- ciated quantitative analysis, an alternate method for determining the length of the mean lunar day, using a dif- ferent approach but realizing the same results as those in chapter 2, provides an independent confirmation thereof. Fluctuations in the Lunar and Tidal Days The lunar day is longer than the conventional mean solar day of 24 h m because the Moon revolves around the Earth in the same direction as the Earth rotates on its axis. If the period of time between two successive meri- dian transits of the Moon is defined as the lunar day in the same way that the solar day represents the period between two successive meridian transits of the Sun, a 171 Strategic Role of Perigean Spring Tides, 1635-1976 very obvious connection exists between these two periods of time as a function of the relative motions of the two bodies. 1. Derivation of the Length of the Mean Lunar Day The Moon orbits once around the Earth from position of new moon to new moon again (i.e., from one conjunc- tion of the Moon and Sun to the next) in a synodic month of 29.530589 mean solar days. As seen from the Earth, during this period the Moon describes an average 389° circuit of the celestial sphere (i.e., its sidereal revolution, plus a catch-up motion on the apparent motion of the mean sun in the same interval ) . The Earth rotates through approximately 361° on its axis (allowing for the Sun's own apparent mean daily motion) in 24 mean solar hours, to complete two successive meridian transits of the mean sun and accomplish the mean solar day. Both of these cases involve catch-up intervals caused by the orbital and rotational motions of the Earth in the same direction. Similarly, the Moon revolves in its orbit in the same direction that the Earth rotates on its axis. The rotating Earth must, therefore, in a like fashion catch up with the position of the Moon in order for the Moon to transit the local meridian of a place and complete a lunar day. In so doing, the Earth must fulfill an additional portion of its rotation equal to the angular distance through which the Moon has moved ahead of the meridian of the place during that same day (i.e., a distance equal to 1 /29.530589th part of the Moon's monthly revolution). In a period of 29.530589 days, the Earth falls back, in equivalence of time, one full rotation with respect to the Sun. The corresponding period of time for the Moon to complete one synodic revolution, expressed in lunar days, is a full day less, and 29.530589 mean solar days exactly equals 28.530589 lunar days. The mean lunar day is, ac- cordingly, established in relation to the mean solar day by the proportion : 1 lunar day = 29.530589/28.530589 = 1 .035050 mean solar days Or, expressed in terms of hours and minutes 1 mean lunar day = 24''0' n X 1.035050 = 24.841 200" = 24 h 50.472'" 2. Variations in the Lunar Day Therefore the lunar day is, on the average, 50.472 m longer than the mean solar day, but — of special signifi- cance in relation to tides — the actual instantaneous value may range from approximately 38 m to 66 m . a The figure 50.472" 1 , representing the average difference between the lengths of the lunar and solar day, may also be thought of as representing the increment in time which, added to 24 mean solar hours, gives the period of elapsed time between two successive transits of the mean moon across the meridian of the place. It is thus equivalent to the delay in transit times caused by the eastward orbital motion of the Moon, and is known as the mean daily lunar retarda- tion. Because of the dependence of this factor upon the actual observed transit times of the Moon, and the pos- sible large variations in the rate of motion of the Moon in right ascension, the instantaneous value thereof ranges widely between the limits noted. The differences between the instantaneous and mean values of the daily lunar retardation are due largely to the elliptical shape of the Moon's orbit (including its changing eccentricity, caused by long-term perturba- tions — as well as the effects of variation and evection described at length in chapter 4). To these dynamic effects are added the changing inclination of the Moon's orbit with respect to the celestial equator at different latitudes on the Earth (which, as seen on pp. 193-196, further modifies the continuously changing declination angle of the Moon associated with its motion in orbit). In addition to these astronomically produced, worldwide influences, the local meridian transit of the Moon is af- fected both by the latitude of the observer and the difference in longitude of the place of observation from Greenwich, England — for the transit of whose prime meridian the various astronomical data appearing in The American Ephemeris and Nautical Almanac are published. A combination of these astronomical and geographic influences results in a continuously changing daily lunar retardation which, if plotted against the time, follows a pattern closely analogous to that of the Sun's annual equation of time. However, other factors resulting from the geographic location of the observer on the surface of the Earth — including the local azimuth and altitude (or zenith distance) of the Moon, its topocentric distance from the surface of the Earth (affected both by geo- graphic latitude and, to a limited extent, by the elevation of the observer above mean sea level) — additionally in- fluence the lunar retardation and the times of moonrise and moonset on the local horizon. a Most of this maximum increase in the length of the lunar day is due to the increased velocity of the Moon at perigee-syzygy and the required catch-up motion by the rotating Earth. Thus l. r ).4 o/ ' , -f-360 o/,, = 0.0428"xl,440 n "" , =61.6 m . The remaining dif- ference is principally clue to declinational effects. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy -m 3. Variations in the Tidal Day It is now desirable to consider the effects of these vari- ations in the length of the lunar day and in the amount of the daily lunar retardation as they influence the length of the tidal day and the maximum daily height of the tides. The tides are implicitly related to the changing positions of the Moon — especially its distance, meridian altitude, and time of meridian transit. Additional and often larger variations are introduced in the corresponding daily re- tardation of high and low waters by hydrographic, hy- drological, climatological, meteorological, and other fac- tors. The hydrographic influences pertain principally to the depth of the water and the local lunitidal interval at the place ; further local variations in the times of arrival of the tides are introduced by the lunar phase age and parallax age for that locality. (See the correspondingly titled section at the end the present chapter. ) Thus, all factors considered, the length of the mean lunar day (the period between two consecutive upper transits of the mean moon across the local meridian of a place) and the mean tidal day (the average period of time between two successive higher high waters or other tides of the same phase at the same location) are not synony- mous, although closely related. The deviation of the instantaneous value of the tidal day from the average value of 24 h 50.47 m — which is gen- erally accepted for the length of the mean lunar day — has a particular significance in terms of any near-coincidence between perigee and syzygy. In this regard, a very useful quantitative indicator for tidal flooding potential results if the time intervals between successive higher high waters are systematically tabulated. The special importance and manner of application of such a series of daily tidal re- tardation times, computed from the tide tables, become appropriate topics for discussion in chapter 8. However, with due consideration to the complex nature of the vari- ous forces involved, before the distinctive patterns revealed by these differences at times of perigee-syzygy are analyzed in terms of their possible value for prediction in connec- tion with tidal flooding, the respective astronomical causes for the consistency of these patterns will be examined. Causes of Systematic Variations in the Length of the Tidal Day Two principal dynamic causes have previously been given for the difference between the lengths of the tidal day and the mean solar day. These are ( 1 ) the Moon's varying velocity of revolution in orbit, and ( 2 ) the rota- tional velocity of the Earth upon its axis. The Earth's rotational velocity is constant over centuries of time within very narrow limits. It is obvious, therefore, that any purely physical variations in the length of the tidal day — and hence in the values of the daily tidal retardations — derived from tide tables must be due, in one way or another, to factors relating to the changing positions, motions, and velocities of the Moon, together with its phase relation- ships with respect to the Sun. However, other causes for such observed variations exist which are individually attributable to astronomical, geographical, and computational factors. a. Astronomical causes for changes in the Moon's orbi- tal velocity are associated with : ( 1 ) the elliptical shape of the lunar orbit which results in continually changing dis- tances of the Moon from the Earth, and correspondingly altered lunar orbital velocities; and (2) both periodic and irregular disturbing influences (perturbations) of an external nature, which likewise act to alter the instanta- neous positions and velocities of the Moon. These various astronomically induced tide-raising effects are felt world- wide over the Earth's surface. b. At any one position on the Earth, further sensible changes in the times of local meridian transits, and in the lengths of the tidal day and the daily lunar retardation, are introduced by the particular geographic longitude and latitude of the place, the Greenwich hour angle of the Moon, and its azimuth and altitude ( or zenith distance ) at the time of upper transit. The use of arbitrary corrections for the times of high and low water at a subordinate tide station, based upon values determined empirically for certain standard sta- tions, is another approximation which may be responsi- ble for computational inexactness in the length of the tidal day. c. Finally, other less marked variations are introduced as a function of averaged, or approximate rather than actual, lunar positions. In the computational assumption thereof, these can affect both the calculated length of the tidal day and the value determined for the daily tidal re- tardation. Significantly, in this regard, the corrections for certain velocity-related parameters are the result of ad- justments to the average (mean ) , rather than real motions of the Moon. Such approximations are subjective ones generally utilized as a matter of calculating convenience which, in this arbitrary computational procedure : ( 1 ) incorrectly represent the true positions and velocities of the Moon (such as by the customary representation of the lunar motion in celestial longitude in lieu of its own orbital plane or, in dealing with catch-up effects, in the plane 274 Strategic Role of Perigean Spring Tides, 1635-1976 of the Earth's Equator); (2) make use of averaged (mean) lunar positions and motions rather than instan- taneous, actual (true) positions. This results in a need for a successively adjusted series of computational cor- rections to accommodate the approximations involved. The Role of the Increased Tidal Day Viewed in Perspective According to the thesis advanced in this study, the potential for tidal flooding is dependent variously upon : ( 1 ) the presence of increased gravitational forces; (2) a greater length of time for these increased gravitational forces to act ; ( 3 ) a very rapidly accelerating growth rate as represented by the curves indicating the rate of tide rise; and (4) a more readily achievable velocity coupling between the comparatively more rapidly moving surface current produced by perigean spring tides and any accom- panying wind movement over the sea. The first premise was adequately demonstrated in chapter 5; the second will receive special attention in the present chapter; and the third and fourth will be illustrated by examples in chapters 7-8. The ensuing sections of this present chapter will be devoted to an explanation of the condi- tions under which the total duration of the tidal day varies, and the nature of the factors which act to modify its length, together with a quantitative interpretation of these variations. At the outset, it should be duly emphasized that various astronomical factors may interact to alter the length of the lunar day. Thus, apparently contradicting what has been said concerning the special significance of the syzy- gies, it must be clearly recognized that both the lunar and tidal days may, in fact, attain a maximum length around either of the quadrature phases of the Moon, due primarily to declination effects (see figs. 44-45) . However, with due regard to accompanying gravita- tional reinforcements, the lengthened tidal day is most effective in producing unusually high waters when the Moon is in a position of closest monthly approach to the Earth and the tide-raising forces have been increased both by this diminished distance and by the simultaneous longitudinal alignment between the gravitational forces of the Moon and Sun at new moon or full moon. It is the in- variable increase in the lengths of both the lunar and tidal days (not necessarily to a maximum) coincidentally or nearly so with the augmented gravitational forces re- sulting from the concurrence of perigee and syzygy that adds its influence to the production of tides of increased daily amplitude and range. Effect of Increased Lunar Orbital Velocity Upon the Length of the Tidal Day Several cogent points of distinction are now necessary. At the time of perigee-syzygy, because of the increased gravitational force caused by the Moon's closer proximity to the Earth, the lunar velocity in orbit is increased. The Sun's alignment with the Moon at either position of syzygy of itself also has a slight velocity-increasing effect on the Moon, induced by the lunar variation. By contrast, a small, net counterproductive influence in slowing the Moon's orbital velocity is provided when the Earth reaches its annual perihelion position, about January 2-4. The Sun's retardation of the Moon's orbital velocity is, in fact, quantitatively dwarfed by the far greater average value of the Moon's angular velocity in orbit, and es- pecially by the increase in velocity produced at perigee- syzygy. Thus the occurrence of perigee-syzygy results at all times in a very considerable net gain in lunar velocity. However, the above synopsis points amply to the fact that any catch-up requirements applied to the Moon's orbital motions must be separately evaluated in terms of their relationship to ordinary syzygy, or to perigee- syzygy — the influences which lengthen the tidal day work- ing generally in the same direction, but in different de- grees, at these two times. (Cf., tables 21-22.) The greatest increase in the Moon's orbital motion is from about 11.8°/day at apogee- (exogee-) syzygy to about 15. 4° /day at perigee- (proxigee-) syzygy, a dif- ference of 3.6°/day. This stated maximum value also indicates an angular velocity at proxigee-syzygy which is 2.2°/day greater than the mean lunar orbital velocity (sidereal) of 13.2°/day. It is the total gain in velocity of 3.6°/day, acquired steadily between exogee-syzygy and proxigee-syzygy, with which the rotating Earth must catch up during the 24-hour period bracketing proxigee- syzygy. It should be reiterated that the effect of the daily catch-up motion by the rotating Earth resulting from the more rapid orbital motion of the Moon at perigee-syzygy compared with that at apogee-syzygy is small in units of time. The maximum lengthening of the tidal day due to 3 6°/ d this cause alone amounts to ' ' X l d = 0.01 X 24"/ d = 0.24 1 ', or about 14.4 minutes. However, this effect is additive to, and in support of, other influences. Further, and of greater importance to the present discussion, the force-protracting influence of a perigee-syxygy alignment upon the tides is greater than that which exists at ordi- nary spring tides, as described in chapter 7. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 275 Quantitative Evaluation of Changing Periods in the Moon's Monthly Revo- lution A quantitative evaluation of the influence of perigee- syzygy alignments on the lengths of successive synodic and anomalistic months during a 209 synodic-month period from January 1959 through December 1975 is provided in table 17. The discussion to follow will reveal a maximum lengthening of the synodic month above its mean value amounting to +0.2992 day, and a maximum lengthening of the anomalistic month above its own mean by 1.02 days, both at a time of perigee-syzygy. A corre- sponding lengthening of the individual lunar and tidal days contained within these months readily can be shown to be associated with perigee-syzygy. As the result of a frequent contiguous usage of these words in the text, several apparently related, but actually quite different concepts involving the length of the lunar day and the length of the synodic month should be clarified at this point. The lunar day is measured by the time between con- secutive transits of the Moon across the local meridian of a place. Since, at perigee-syzygy, the Moon is moving faster in the same direction that the Earth is rotating, an additional catch-up time is required for transit of the Moon, and the length of the lunar day is increased. The length of the synodic month, on the other hand, is determined by the number of mean solar days between two successive conjunctions of the Moon and Sun, as seen from the Earth. Since the Earth's period of rotation, for the pur- pose of the present discussion, may be assumed to be con- stant, the synodic month varies only with the relative orbital motion of the Earth (hence also the apparent motion of the Sun) and that of the Moon as a function of its changing orbital configuration, subject to perturbations. As the orbital velocities of the Earth and/or the Moon are increased, the necessary catch-up time to achieve the align- ment of Earth, Moon, and Sun at syzygy is likewise increased and, coincidentally, the length of the synodic month is in- creased — as shown in column 8 of table 17. Thus, the synodic month is composed of mean solar days, and may be related also to a given number of tidal days, but the two concepts are not directly connected. A further distinction for the purpose of clarity should here be made between the concepts of period of revolution, in days, and both angular velocity in orbit and mean daily motion — each of the last usually expressed in °/day. In the common physical case of uniform circular motion with con- stant angular velocity, as the period of rotation P increases, the value of the unit angular velocity n decreases, and vice versa. In an elliptical astronomical orbit, although P still varies inversely as the mean angular velocity ft throughout the entire revolution of the orbit, and may be computed approximately therefrom, its exact value for any one revo- lution depends upon a presumably fixed and unperturbed length of the semimajor axis a. (More precisely, P 2 varies directly as a 3 .) Any time in a lunar revolution that a varies, P varies accordingly. Therefore, as the instantaneous value of n increases at perigee (-syzygy) and decreases at apogee (-syzygy) the period is not directly affected thereby. Rather, its value is changed by corresponding alterations in the shape of the lunar orbit at these times. In the case of those months which contain a close align- ment of perigee-syzygy, both the NM-NM and FM-FM synodic months become longer when computed between the times of successive apogee-syzygies (see table 17), and the apparent daily motion of the Moon becomes faster in that portion of the orbit bracketing the time of perigee-syzygy. In the apogee-syzygy portion of the orbit, however, a much slower apparent motion of the Moon occurs, and the lengths of the synodic months calculated from perigee-syzygy to perigee-syzygy and containing the time of apogee-syzygy centrally located are considerably shorter than those com- puted from apogee-syzygy to apogee-syzygy, having the time of perigee-syzygy midway in the period. It might thus be readily assumed that the relatively high lunar velocity at perigee-syzygy would be compensated for by the comparatively low angular velocity at apogee-syzygy, and that the length of the month would average out un- changed. According to the specific time-referenced positions in orbit from which the data of table 17 are compiled, such is not the case. Finally, and worthy of special note in the light of ulti- mately more refined tidal predictions at these times of maxi- mized amplitudes, it will be observed by reference to table 20 that the actual daily angular velocity of the Moon in celestial longitude at proxigee-syzygy (15.2585°/ d ) is considerably in excess of the assumed mean value (13.l764°/ d ) presently used in tidal calculations; again, at apogee following even the ordinary syzygy alignment (with perigee at quadrature) given in table 21, the actual daily motion of the Moon ( 1 1.8491 °/ d ) is much less than this assumed mean value. Such an average value is far from representative at times of proxigee-syzygy and exogee-syzygy. Conditions Lengthening the Synodic and Anomalistic Months To illustrate these relationships clearly, the pertinent lunar data have been tabulated (for double-verification purposes) over a period of time equal to two complete rotations of the line of apsides in the anomalistic cycle of 8.849 tropical years (table 17) . In this table, columns 1-2 contain the exact dates of full moons, and columns 5-6 the exact dates of new moons, throughout this period. The changing lengths of the "synodic months" (see the second following paragraph), determined alternatively by the differences between the times of two consecutive full 276 Table 17. — Increase in Strategic Role of Perigean Spring Tides, 1635-1976 the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments Intervals between S1U'( CSS1VC Intervals between successive perigees W.ii Date FM Synodic Synodic month month FM-FM NM-NM Anomalistic Year month P-P Jan. 24. 8139 29. 5569 29. 5750 Jan. 9.2319 Feb. 23. 3708 29. 4639 29.6451 Feb. 7. 8069 Mar. 24. 8347 29. 3827 29. 6931 Mar 9.4521 Apr. 23. 2174 29. 3215 29. 6958 Apr. 8. 1451 May 22. 5389 29. 2944 29. 6542 May 7. 8410 June 20. 8333 29. 3146 29. 5882 June 6.4951 July 20. 1479 29. 3868 29. 5236 July 6. 0833 Aug. 18. 5347 29. 5007 29. 4729 Aug. 4. 6069 Sept. 17.0354 29. 6299 29.4417 Sept. 3. 0799 Oct. 16. 6653 29. 7389 29. 4236 Oct. 2. 5215 Nov. 15.4042 29. 7965 29.4201 Oct. 31. 9451 Dec. 15.2007 29. 7931 29. 4326 Nov. 30. 3653 Jan. 13.9938 29. 7312 29. 4632 Dec. 29. 7979 Feb. 12. 7250 29. 6264 29. 5056 Jan. 28. 2611 Mar. 13. 3514 29. 5014 29. 5514 Feb. 26. 7667 Apr. 11. 8528 29. 3854 29. 5882 Mar. 27. 3181 May 11.2382 29. 3049 29. 6095 Apr. 25. 9063 June 9. 5431 29. 2743 29. 6250 May 25.5188 July 8.8174 29. 2944 29. 6277 June 24. 1438 Aug. 7. 1118 29. 3597 29. 6146 July 23. 7715 Sept 5.4715 29. 4570 29.5813 Aug. 22. 3861 ( )■ i 4. 9285 29. 5701 29. 5347 Sept. 20. 9674 Nov. 3. 4986 29. 6854 29. 4889 Oct. 20.5021 Dei . 3. 1840 29. 7785 29. 4583 Nov. 18. 9910 fan. 1. 9625 29. 8201 29. 4465 I)r, . 18.4493 J.m 31. 7826 Jan. 16.8958 Jan. 5.833 25.42 Jan. 31.250 26. 17 Feb. 26.417 27. 96" Mar 26. 375 28. 38 Apr. 23. 750 28. 46 • May 22. 208 28. 33 June 19. 542 28. 04_ July 17.583 27.08 Aug. 13.667 25.04 Sept 7.708 27. 17 Oct. 4.875 28. 17" Nov. 2.042 28.46 Nov. 30. 500 28. 54 < > Dec. 29. 042 28. 38 Jan. 26.417 27.71 Feb. 23. 125 25. 17 Mar. 19.292 26.50 Apr. 14. 792 27.96 May 12. 750 28. 33 June 10. 083 28.38 4 ► July 8.458 28. 38 Aug. 5. 833 28. 04_ Sept. 2. 875 27.04 Sept. 29.917 24.92 Oct. 24. 833 27.33 Nov. 21. 167 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 277 Table 17. — Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic month month FM-FM NM-NM Anomalistic Year month P-P Year Mar 2. 5660 Apr. 1.2417 Apr. 30. 7785 May 30. 1931 June 28. 5264 July 27.8271 Aug. 26. 1347 Sept 24.4819 Oct. 23. 8965 Nov. 22. 4056 Dec. 22. 0292 Jan. 20. 7618 Feb. 19. 5542 Mar 21. 3306 Apr. 20. 0236 May 19. 6056 June 18.0854 July 17.4868 Aug. 15.8403 Sept 14. 1750 Oct. 13. 5229 Nov. 11. 9194 Dec. 11.3944 Jan. 9. 9646 Feb. 8.6194 Mar 10. 3257 29. 7834 29. 4452 Feb. 15. 3410 29. 6756 29. 4440 Mar. 16. 7854 29. 5368 29. 4493 Apr. 15. 2347 29.4146 29. 4702 May 14. 7049 29. 3333 29.5152 June 13. 2201 29. 3007 29. 5799 July 12. 8000 29. 3076 29.6417 Aug. 11.4417 29. 3472 29. 6764 Sept. 10. 1181 29.4146 29. 6687 Oct. 9. 7868 29. 5091 29. 6292 Nov. 8.4160 29. 6236 29. 5784 Dec. 7. 9944 29. 7326 29. 5306 Jan. 6. 5250 29. 7924 29.4819 Feb. 5. 0069 29. 7764 29.4312 Mar. 6. 4382 29. 6930 29. 3847 Apr. 4. 8229 29. 5820 29. 3611 May 4. 1840 29. 4798 29. 3764 June 2. 5604 29. 4014 29. 4347 July 1. 9951 29. 3535 29.5215 July 31. 5167 29. 3347 29.6146 Aug. 30. 1312 29. 3479 29. 6882 Sept. 28.8194 29. 3965 29. 7257 Oct. 28. 5451 29. 4750 29. 7257 Nov. 27. 2708 29. 5702 29. 6868 Dec. 26. 9576 29. 6548 29.6132 Jan. 25. 5708 29. 7063 29.5167 Feb. 24. 0875 29.7139 29.4194 28. 29" Dec. 19.458 28. 50 • Jan. 16. 958 P-S 28.50 Feb. 14. 458 1961 28.29 Mar. 14. 750 27. 58_ Apr. 11.333 25. 17 May 6.500 26.62 June 2. 125 27. 92" June 30. 042 28.33 July 28. 375 28. 42 ( > Aug. 25. 792 I'-S 28. 38 Sept. 23. 167 28. 12_ Oct. 21.292 26. 92 Nov. 17. 208 24. 79 Dec. 12.000 27. 58" Jan. 8. 583 1962 28. 33 Feb. 5.917 28. 50 ( 1 Mar. 6.417 P-S 28.46 Apr. 3.875 28. 21_ May 2.083 27.46 May 29. 542 25.29 June 23. 833 26.58 July 20.417 27. 92" Aug. 17. 333 28. 33 Sept. 14. 667 28.46 < » Oct. 13. 125 l'-S 28.46 Nov. 10. 583 28. 12_ 278 Stri tegic Role of Perigean Spring Tides, 1635- -1976 Table 17.— In crease in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date month month Date NM Year month Date P Year FM-FM NM-NM P-P Apr. 9. 0396 29. 6854 29. 3465 Mar. 25. 5069 26.62 Dec. 8. 708 May 8. 7250 29. 6299 29. 3132 Apr. 23. 8535 P-S 24.96 Jan. 4. 333 June 7. 3549 29. 5590 29. 3236 May 23. 1667 27. 71" Jan. 29. 292 1963 July 6. 9139 29. 4826 29. 3729 June 21.4903 28. 33 Feb. 26.000 Aug. 5. 3965 July 20. 8632 Mar. 26. 333 29. 4188 29. 4528 28. 46 < ► Sept. 3.8153 29. 3819 29. 5528 Aug. 19.3160 28. 38 Apr. 23. 792 P-S Oct. 3. 1972 29. 3834 29.6611 Sept. 1 7. 8688 28. 17_ May 22. 167 Nov. 1. 5806 29.4159 29. 7556 Oct. 17.5299 27.42 June 19. 333 P-S Nov. Dec. 30. 9965 30.4611 29. 4646 29.5132 29. 8028 29. 7757 Nov. 16. 2854 Dec. 16.0882 25.25 26.67 July 16. 750 Aug. 11.000 1964 Jan. Feb. Mar. 28. 9743 27. 5278 28. 1 1 74 29. 5535 29. 5896 29. 6792 29. 5500 Jan. 14. 8639 Feb. 13.5431 Mar. 14.0931 1964 27. 96" 28. 38 Sept. 6. 667 Oct. 4. 625 Nov. 2. 000 29. 6257 29. 4333 28. 54 < > Apr. 26. 7431 29. 6520 29. 3500 Apr. 12.5264 28.46 Nov. 30. 542 P-S May 26. 3951 May 11. 8764 Dec. 29.000 29. 6528 29. 3062 28. 04_ June 25. 0479 29.6174 29. 2973 June 10. 1826 P-S 26.29 Jan. 26.042 1 964 July 24. 6653 29. 5611 29. 3236 July 9. 4799 25.33 Feb. 21.333 Aug. 23. 2264 29. 5035 29. 3875 Aug. 7. 8035 27. 75" Mar. 1 7. 667 Sept 21. 7299 29. 4687 29. 4896 Sept. 6. 1910 28.25 Apr. 14.417 Oct. 21. 1986 29. 4563 29. 6229 Oct. 5. 6806 28. 42 i May 12.667 No\ 19.6549 29. 4576 29. 7514 Nov. 4. 3035 28.38 June 10.083 P-S P-S Dec. 19. 1125 29. 4556 29. 8250 Dec. 4. 0549 28. 17_ July 8. 458 I'm", Jan. Feb. Mar 17. 5681 16.0188 17.4750 29. 4507 29. 4562 29. 4854 29.8118 29. 7222 29. 6007 Jan. 2. 8799 Feb. 1.6917 Mar. 3.4139 1965 27.46 25. 12 26.71 Aug. 5. 625 Sept. 2. 083 Sept. 27. 208 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 27 ( ) Table 17. — Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic month month FM-FM NM-NM Anomalistic Year month P-P Apr. 15. 9604 May 15.4951 June 14. 0833 July 13. 7097 Aug. 12. 3556 Sept. 10. 9806 Oct. 10. 5931 Nov. 9. 1778 Dec. 8. 7236 1966 Jan. 7. 2201 P-S Feb. 5. 6653 Mar. 7. 0736 Apr. 5. 4681 May 4. 8757 June 3. 3201 July 2.8174 Aug. 1. 3792 Aug. 31.0097 Sept. 29. 7000 Oct. 29.4174 Nov. 28. 1118 Dec. 27. 7389 1£67 Jan. 26. 2785 Feb. 24. 7389 F-S Mar 26. 1396 Apr. 24. 5028 May 23. 8493 Apr. 2. 0146 29. 5347 29. 4826 May 1.4972 29. 5882 29. 3868 May 30. 8840 29. 6264 29. 3195 June 29. 2035 29. 6477 29. 2861 July 28. 4896 29. 6250 29. 2958 Aug. 26. 7854 29. 6125 29. 3521 Sept. 25. 1375 29. 5847 29. 4542 Oct. 24. 5917 29. 5458 29.5819 Nov. 23. 1736 29. 4965 29. 7035 Dec. 22.8771 29. 4452 29. 7805 Jan. 21.6576 29. 4083 29. 7938 Feb. 20.4514 29. 3945 29. 7479 Mar. 22. 1993 29. 4076 29. 6590 Apr. 20. 8583 29. 4444 29. 5466 May 20. 4049 29. 4973 29. 4347 June 18. 8396 29.5618 29. 3486 July 18. 1882 29. 6305 29. 3035 Aug. 16.4917 29. 6903 29. 3097 Sept. 14. 8014 29. 7174 29. 3597 Oct. 14. 1611 29. 6944 29. 4410 Nov. 12.6021 29.6271 29. 5326 Dec. 12. 1347 29. 5396 29. 6195 Jan. 10. 7542 29. 4604 29. 6930 Feb. 9. 4472 29. 4007 29. 7403 Mar 11. 1875 29. 3632 29. 7438 Apr. 9. 9313 29. 3465 29. 6909 May 9. 6222 29. 3570 29. 5959 28.08 28.46 28.58 28.42 27. 92. 26.08 25.58 27.71" 28.25 28.38 28.42 28. 17_ 27.50 24.88 26.92 28. 17' 28.50 28.54 28. 33 27. 79. 26.00 25. 75 27.71" 28.25 28.42 28.42 28.25 Oct. 23.917 Nov. 21.000 Dec. 19.458 Jan. 17.042 Feb. 14.458 Mar. 14. 375 Apr. 9. 458 May 5. 042 June 1.750 June 30. 000 July 28. 375 Aug. 25. 792 Sept. 22. 958 Oct. 20.458 Nov. 14. 333 Dec. 11.250 Jan. 8.417 Feb. 5.917 Mar. 6.458 Apr. 3. 792 May 1. 583 May 27. 583 June 22. 333 July 20.042 Aug. 17. 292 Sept. 14. 708 Oct. 13. 125 P-S 1965 P-S 280 Table 17. — Increase in Strategic Role of Perigean Spring Tides, 1635-1976 the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies tween successive perigees Synodic Synodic month month FM-FM NM-NM Date NM Anomalistic Year month P-P Date P Year P-S June 22. 2063 July 21.6111 Aug. 20. 1021 Sept. 18. 7083 Oct. 18.4243 Nov. 17. 2035 Dec. 16. 9736 Jan. 15. 6750 Feb. 14. 2799 Mar. 14. 7868 Apr. 13.2028 May 12.5451 June 10.8431 July 10. 1375 Aug. 8.4813 Sept. 6. 9222 ( >ct. 6.4910 Nov. 5. 1840 !)<•< 4. 9639 Jan. 3. 7694 Feb. 2. 5389 Mar 4. 2208 \pi. 2. 7819 May 2. 2181 May 31. 5549 June 8. 2181 29. 4048 29. 4909 July 7. 7090 27. 38 29. 4910 29. 4084 Aug. 6. 1174 24.67 29. 6062 29. 3673 Sept. 4.4847 27.21 29. 7160 29. 3653 Oct. 3. 8500 28. 25" 29. 7792 29. 3924 Nov. 2. 2424 I'-S 28.46 29. 7701 29. 4312 Dec. 1. 6736 28.46 29. 7014 29. 4785 Dec. 31. 1521 28. 29 29. 6049 29. 5354 Jan. 29.6875 27. 75 29. 5069 29. 6014 Feb. 28. 2889 1968 26.00 29.4160 29.6618 Mar. 28. 9507 25.79 29. 3423 29. 6896 Apr. 27.6403 27. 71 29. 2980 29. 6722 May 27. 3125 28. 25 29. 2944 29.6215 June 25. 9340 28. 50 29. 3438 29. 5591 July 25.4931 28.50 29. 4409 29. 5048 Aug. 23. 9979 28.21 29. 5688 29. 4667 Sept. 22. 4646 27.21 29. 6930 29.4417 Oct. 21. 9063 24.67 29. 7799 29. 4284 Nov. 20. 3347 27.40 29. 8055 29. 4285 Dec. 19. 7632 P-S 28.23 29. 7695 29. 4444 Jan. 18. 2076 L969 28.42 29.6819 29.4771 Feb. 16.6847 28.42 29.5611 29.5181 Mar. 18. 2028 28.25 29. 4362 29. 5583 Apr. 16. 7611 27. 75. 29. 3368 29. 5910 May 16. 3521 25.96 29.2812 29. 6125 25. 75 Nov. 10. 375 Dec. 7. 750 Jan. 1.417 Jan. 28. 625 Feb. 25. 875 Mar. 26. 333 Apr. 23. 792 May 22. 083 June 18. 833 July 14. 833 Aug. 9. 625 Sept. 6. 333 Oct. 4. 583 Nov. 2. 083 Nov. 30. 583 Dec. 28. 792 Jan. 25.000 Feb. 18. 667 Mar. 1 7. 063 Apr. 14. 292 May 12. 708 June 10. 125 July 8. 375 Aug. 5. 125 Aug. 31.083 1967 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 2ol Table 17. — Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing z-Syzygy Alignments — Continued Intervals between successive syzygie Intervals between successive perigees Synodic Synodic Anomalistic Year Date month month Date ] Year month Date P Year FM-FM NM-NM P-P P-S June July Aug 29. 8361 29. 1153 27. 4396 29. 2792 29. 3243 29. 4090 29.6271 29. 6284 29. 6105 June July Aug. 14. 9646 14.5917 13. 2201 27. 79" 28. 38 28.50 Sept. 25. 833 Oct. 23.625 Nov. 21.000 Sept 25. 8486 Sept 11.8306 • Dec. 19. 500 l'-S 29.5160 29. 5722 28.50 Oct. 25. 3646 29. 6312 29. 5222 Oct. 11.4028 28. 17_ Jan. 17.000 I'll,') Nov. 23. 9958 29. 7375 29. 4799 Nov. 9. 9250 26.92 Feb. 14. 167 Dec. 23. 7333 29. 8056 29. 4534 Dec. 9. 4049 24. 92 Mar. 13. 083 1970 .Jan. 22. 5389 29. 8076 29.4431 Jan. 7. 8583 1970 27.46 Apr. 7. 000 Feb. 21. 3465 29. 7320 29. 4368 Feb. 6. 3014 P-S 28. 17" May 4. 458 Mar 23. 0785 29. 6034 29. 4354 Mar 7. 7382 28.38 June 1.625 Apr. 21.6819 Apr. 6. 1 736 • June 30. 000 P-S 29. 4695 29. 4458 28. 38 May 21. 1514 May- 5.6194 July 28. 375 29. 3680 29. 4792 28. 25 June 19.5194 29. 3132 29. 5389 June 4. 0986 27. 83^ Aug. 25. 625 July 18. 8326 29. 3035 29.6118 July 3. 6375 25.71 Sept. 22. 458 P-S Aug. Sept. Oct. 17. 1361 15.4653 14. 8486 29. 3292 29. 3833 29. 4632 29. 6688 29. 6875 29. 6645 Aug. Aug. Sept. 2. 2493 31.9181 30. 6056 25.92 27. 92" 28.42 Oct. 18. 167 Nov. 13.083 Dec. 11.000 Nov. 13. 3118 29. 5660 29.6153 Oct. 30. 2701 28. 54 , Jan. 8.417 1970 Dec. 12. 8778 29. 6785 29.5611 Nov. 28. 8854 28.46 Feb. 5. 958 P-S 1971 Jan. 11.5563 29. 7645 29. 5091 Dec. 28. 4465 28. 04_ Mar. 6.417 Feb. 10. 3208 29. 7861 29. 4534 Jan. 26. 9556 1971 26. 71 Apr. 3. 458 Mar. 12. 1069 29. 7341 29. 3993 Feb. 25. 4090 P-S 25. 17 Apr. 30. 167 Apr. 10.8410 29. 6340 29. 3598 Mar. 26. 8083 27.42 May 25. 333 May 10.4750 29. 5278 29. 3541 Apr. 25. 1681 28. 17" June 21. 750 June 9. 0028 May 24. 5222 July 19.917 29. 4396 29. 3931 28. 38 July 8. 4424 29. 3791 29. 4708 June 22.9153 28. 42 < Aug. 1 7. 292 P-S Aug. 6.8215 29. 3473 29. 5681 July 22. 3861 28. 33 Sept. 14. 708 Sept 5. 1688 29. 3451 29. 6590 Aug. 20. 9542 27. 79_ Oct. 13.042 282 Table 17. — Increase in Strategic Role of Perigean Spring Tides, 1635-1976 the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic month month Date I FM-FM NM-NM Sept. 19.6132 29. 3750 29. 7201 Oct. 19. 3333 29. 4368 29. 7403 Nov. 18.0736 29. 5215 29. 7202 Dec. 17. 7938 29. 6097 29. 6590 Jan. 16.4528 29. 6764 29. 5673 Feb. 15.0201 29. 7035 29. 4625 Mar. 15.4826 29. 6938 29. 3723 Apr. 13.8549 29. 6555 29. 3173 May 13. 1722 29. 5958 29. 3070 June 11.4792 29. 5264 29. 3396 July 10.8188 29. 4570 29. 4076 Aug. 9. 2264 29. 4062 29. 5014 Sept. 7. 7278 29. 3875 29.6111 Oct. 7. 3389 29. 4042 29. 7174 Nov. 6. 0563 29.4431 29. 7937 I)e< . 5. 8500 29. 4881 29. 8042 Jan. 4. 6542 29. 5271 29. 7368 Feb. 3. 3910 29. 5598 29.6139 Mar. 5. 0049 29. 5958 29. 4847 Apr. 3. 4896 29. 6298 29. 3820 Mav 2.8715 29. 6507 29. 3188 June 1. 1903 29. 6396 29. 2951 June 30. 4854 29. 5979 29. 3056 July 29. 7910 29. 5410 29.3514 Aug. 28. 1424 29. 4952 29. 4368 Anomalistic Year month Date P P-P l'-S Oct. 4. 5139 Nov. 2. 8889 Dec. 2. 3257 Dec. 31.8472 Jan. 30. 4569 Feb. 29. 1333 Mar 29. 8368 Apr. 28. 5306 \ 1 ay 28. 1861 June 26. 7819 July 26. 3083 Aug. 24. 7653 Sept. 23. 1715 ( )ct. 22. 5590 Nov. 20. 9632 Dec. 20. 4063 Jan. 18.8944 Feb. 17.4215 Mar. 18.9813 Apr. 17.5771 May 1 7. 2069 June 15.8576 July 15.4972 Aug. 14. 0951 Sept 12.6361 l'-S 1-173 Nov. 9. 833 25.42 Dec. 5. 250 26. 17 Dec. 31.417 28. 00" Jan. 28.417 1-171 28.46 Feb. 25. 875 P-S 28. 50 < > Mar. 26. 375 28. 38 Apr. 23. 750 27. 96_ May 21. 708 26. 71 June 17.417 25. 21 July 12. 625 27.42 Aug. 9. 042 28. 1 7" Sept. 6. 208 28.42 Oct. 4. 625 F-S 28. 46 < > Nov. 2. 083 28.25 Nov. 30. 458 27. 87_ Dec. 28. 208 25.00 Jan. 22. 208 1972 26.58 Feb. 17.792 28. 08" Mar. 16.875 28.38 Apr. 14. 250 P-S 28. 46 < May 12. 708 28.29 June 10. 000 27. 96_ July 7. 958 26.67 Aug. 3. 625 25.21 Aug. 28. 833 27.46 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 2i','\ Table 17. — Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic month month FM-FM NM-NM Anomalistic Year month P-P Year Oct. 12. 1313 Nov. 10. 6021 Dec. 10. 0653 P-S Jan. 8. 5250 974 Feb. 6. 9750 Mar 8.4188 Apr. 6. 8750 May 6.3715 June 4. 9236 July 4. 5278 Aug. 3. 1646 Sept. 1.8090 Oct. 1.4431 Oct. 31.0549 Nov. 29. 6319 Dec. 29. 1604 975 Jan. 27.6313 P-S Feb. 26. 0521 Mar 27.4417 Apr. 25. 8299 May 25. 2438 June 23. 7042 July 23. 2278 Aug. 21. 8250 Sept. 20. 4931 Oct. 20. 2125 Nov. 18. 9361 Sept. 26. 5792 29. 4708 29. 5576 Oct. 26. 1368 29. 4632 29. 6930 Nov. 24. 8299 29. 4597 29. 8000 Dec. 24. 6299 29. 4500 29. 8298 Jan. 23. 4597 29. 4438 29. 7722 Feb. 22. 2319 29. 4562 29. 6597 Mar. 23.8917 29. 4965 29. 5368 Apr. 22. 4285 29. 5521 29. 4285 May 21.8569 29. 6042 29. 3486 June 20. 2056 29. 6368 29. 2993 July 19. 5049 29. 6444 29. 2882 Aug. 17. 7931 29. 6341 29. 3215 Sept. 16. 1146 29.6118 29. 4028 Oct. 15.5174 29. 5770 29. 5194 Nov. 14. 0369 29. 5285 29. 6472 Dec. 13.6840 29. 4709 29. 7466 Jan. 12.4306 29. 4208 29. 7895 Feb. 11. 2201 29. 3896 29. 7709 Mar. 12.9910 29. 3882 29. 7028 Apr. 11.6938 29. 4139 29. 6013 May 11. 2951 29. 4604 29. 4889 June 9. 7840 29. 5236 29. 3896 July 9. 1736 29. 5972 29. 3243 Aug. 7. 4979 29. 6681 29. 3070 Sept. 5. 8049 29. 7194 29. 3361 Oct. 5. 1410 29. 7236 29. 4041 Nov. 3. 5451 29. 6750 29. 4896 1975 P-S Sept. 25. 292 28.21" Oct. 23. 500 28.50 Nov. 21.000 P-S 28. 54« Dec. 19.542 28.33 Jan. 16.875 1973 27. 58_ Feb. 13.458 24. 88 Mar. 10. 333 26.83 Apr. 6. 167 28. 08" May 4. 250 28.33 June 1. 583 P-S 28. 42 < » June 30. 000 28.29 July 28.292 28. 00_ Aug. 25. 292 26.62 Sept. 20.917 25. 12 Oct. 16.042 27. 58" Nov. 12.625 28.29 Dec. 10. 917 28.54 • Jan. 8. 458 P-S 28.54 Feb. 6. 000 1974 28. 25_ Mar. 6. 250 27.42 Apr. 2. 667 25.00 Apr. 27. 667 26.88 May 24. 542 28. 04" June 21. 583 28. 33 July 19.917 P-S 28. 38 1 » Aug. 17.292 28.38 Sept. 14.667 28. 00_ LW Strategic Role of Perigean Spring Tides, 1635-1976 Table 17. — Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments — Continued Intervals between successive syzygies Intervals between successive Synodic month FM-FM Synodic month NM-NM Anomalistic Year month P-P Dec. 18.6111 Dec. 3. 0347 26.50 25. 12 27. 71" 28. 38 Oct. 12.667 Nov. 8. 167 Dec. 3. 292 Dec. 31.000 Jan. 28.375 1975 28. 54 • Feb. 25.917 P-S 28.46 Mar. 26. 375 28. 17_ Apr. 23. 542 27.29 25.08 26.92 28. 00" 28. 33 May 20.833 June 14.917 July 11.833 Aug. 8. 833 Sept. 6. 167 I'-S 28. 46 • Oct. 4. 625 28.42 Nov. 2. 042 28. OoJ Nov. 30.042 26.12 Dec. 26. 167 moons and two consecutive new moons, are given in col- umns 3 and 4. Because it is desired to determine the length of that synodic month which most nearly brackets each case of perigee-syzygy, it becomes necessary to consider the period of time between two succeeding occurrences of the oppo- site phase of syzygy. That is, to determine the length of the synodic month which contains, midway in the month, a perigee-syzygy alignment at full moon, it is necessary to calculate the period of elapsed time between the most closely bracketing new moons. To determine the length of the synodic month in which the date of a perigee-syzygy at new moon is centrally located, the procedure involves taking the difference in time between successive full moons. A synodic month is, by convention, 11 defined as the pe- riod of time between new moon and new moon. Because of the shift in dates and in the position of the Moon in its elliptical orbit, different values for the length of the syn- odic period will be obtained if the month is reckoned from full moon to full moon. The possibility of mutual commensurability varies as either the synodic or anomal- istic periods vary. The lengths of the synodic months will show either a maximum or minimum value according as the period chosen contains the date of perigee or apogee, respectively. For analytic purposes, this nonconventional procedure of computing both periods is used here. b See Explanatory Supplement to the Astronomical Ephemeris and The American Ephemeris and Nautical Almanac, London, 1961, p. 107. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy Maximized Lengths of Those Months Bracketing Perigee-Syzygy The lengths of synodic months listed in table 1 7 reveal the considerably different values which pertain for those dates which bracket a date of perigee-syzygy compared with those which bracket an apogee-syzygy situation. For every condition of full moon occurring nearly coinciden- tally with perigee, the next following (or preceding) new moon will occur reasonably close to the time of apogee one-half of an anomalistic month later (or earlier). The interval represented is J/ 2 of 27.55455=13.77728, while the exact alternation of syzygy phases occurs in l / 2 of the synodic month of 29.53059 days= 14.76530 days. This gives a difference of only 0.98802 day between new moon and apogee in the new position. In terms of the limit of ±1 day between components established for a standard perigee-syzygy situation (table 16), the latter case can, with consistency, be classified as a typical apogee-syzygy alignment. From immediately adjacent values in columns 3 and 4 of table 1 7, it will be noted that each condition of perigee- syzygy at full moon (marked by a maximum length of the synodic month) is very nearly matched, in the next suc- ceeding or preceding half month, by a near-coincidence of apogee-syzygy at new moon, (having a minimum length of the month) and vice versa. In this 2-week inter- val, the Moon revolves in its orbit through 180° from alignment with the Earth and Sun at perigee-syzygy to an approximate alignment with Earth and Sun again at apogee-syzygy. Since the Sun has moved only about 14° of arc from the line of apsides in this same period, its per- turbative influence is still active thereon. Of most relevant importance to the present discussion, however, is the fact that, because the Moon's velocity in orbit at apogee-syzygy is considerably slower than at peri- gee-syzygy, the necessary catch-up motion by the rotating Earth is less at the apogee position. The duration of each lunar day near the time of apogee-syzygy is less, and the lengths of both the anomalistic and synodic months brack- eting apogee-syzygy are shorter than those bracketing perigee-syzygy. Cycles of Alternation in Perigee-Syzygy Alignments As noted later in this same section, an almost universal tendency exists for cases of close perigee-syzygy alignment to occur in pairs, two in contiguous anomalistic months, followed by two more within about a half-year of the first. An alternate choice of cyclical relationship therefore ex- ists between these two sets of semiannually occurring, noncontiguous cases of perigee-syzygy. One element of each pair will, however, invariably have a smaller sepa- ration-interval between perigee and syzygy than the other. According to the procedure here adopted for establishing the most meaningful perigee-syzygy cycle, the semiannual period is defined as the difference in time between those cases of perigee-syzygy alignment in each of the two pairs having the smallest separation, in hours, between their individual components. The near-coincidence of perigee with syzygy (either new moon or full moon) will, because of recurring, ap- proximately commensurable relationships between the synodic and anomalistic months, result in approximate agreement again within definite cycles. Short-period repe- titions will occur (at the same lunar phase) an average between one anomalistic and one synodic month earlier or later; also (at opposite lunar phases) separated from the first case by an interval established by the average between either 6.25 (to 6.5) or 7.25 (to 7.5) anomalistic and synodic months. The average must be taken between the actual (not mean) lengths of the synodic and anom- alistic months, such as are given in table 17. (Cf., fur- ther page 25, last paragraph of Explanatory Comments to table 1 , and the bracketed repetitions of tidal flooding in table 1 ; also table 4a. ) In the terms of reference used, the first set of two values involving an approximate 6- month period applies to the situation in which two cases of perigee-syzygy — each possessing the smaller separation- interval within its own pair — are located consecutively within approximately one-half year of each other in the comprehensive perigee-syzygy series of table 16. The sec- ond, 7.25- to 7.5-month period applies to those cases separated by one or more intervening perigee-syzygy oc- currences. The 7.5-month pair possesses the smallest, the intervening cases the largest separation-intervals in their respective groups. The range from 0.25 to 0.5 month in each case con- notes an approximate average rather than a specific value. It is due to the varying periodicities (resulting from altered orbital eccentricities) which may span two cases of close perigee-spring alignment. For convenience, only the 0.5-month values in each set hereafter will be referred to, as more indicative of the accompanying change from new moon to full moon or the reverse. It will be implic- itly understood that, wherever this one value is cited to the exclusion of the other, a several-day variation around either 6.25 to 6.5 or 7.25 to 7.5 months as defined above '_'}',() Strategic Role of Perigean Spring Tides, 1635-1976 may actually be represented in the exact interval between successive cases of perigee-syzygy. As seen in table 16, a perigee-syzygy situation at new moon becomes a perigee-syzygy situation at full moon 6.5 or 7.5 months later (or earlier) , with the two remain- ing combinations of perigee-quadrature occurring ap- proximately halfway inbetween. A more detailed anal- ysis of the exact cycles and relationships involved, which are dependent upon variations in the lengths of the syn- odic and anomalistic months and certain other astronom- ically varying influences, is presented in the following pages. The Meaning and Relationships of High and Low Maxima in the Lengths of the Lunar Months With each repetition of a close perigee-syzygy align- ment, the Moon's orbital velocity accelerates to one of its maxima, and the Earth's required rotational catch-up times reach corresponding maximum values. Simultane- ously, the lengths of the synodic months centered around these perigee-syzygy positions increase toward their own maxima. This increase in the lengths of the synodic months ( and their constituent tidal days) to recurrent maxima cor- responding to the times of perigee-syzygy gives support to the premise variously enunciated throughout this monograph : ( 1 ) that the augmentation in height of peri- gean spring tides is produced by the various reinforcing forces enumerated in chapters 3-4 ; and ( 2 ) these forces are contributed to through a prolongation of their period of maximum action, caused by a coincident increase in various astronomical catch-up motions and (as will be seen later in this same chapter) sometimes also by in- creased individual motions in right ascension. The lengths of successive anomalistic months listed in table 1 7 contain the effects of perturbations of the Moon's line of apsides at both perigee and apogee as the appar- ent solar motion brings the Sun into coincidence with this line; also the retrograde motion of the line of apsides induced at both longitudinal positions of the Sun which make an angle of 90° with respect to the lunar line of apsides. Columns 7, 8, and 9 in this table show the influence of the changing speed of the Moon in orbit as it affects the length of the anomalistic month. When the Moon's motion is accelerated at time of perigee-syzygy, the Earth's rotation must necessarily catch up. The length of the anomalistic month which contains the coincidence of perigee-syzygy is proportionately increased. The dates of the closest alignments of perigee-syzygy are indicated in column 9 by the letters P-S. It will be noted that, very nearly opposite each of these P-S sym- bols, the figure in column 7 representing the length of the anomalistic month also reaches a corresponding maximum — usually one of two possible maximum values in the calendar year. (There are necessarily two such maxima within each 15 anomalistic months.) The cir- cumstance that the lengths of these particular anomalistic months within each approximate 15-month period are increased to a maximum value confirms the fact that the rotational catch-up motions of the Earth are the greatest at these times. For each successive approach to, and recession from, a case of close perigee-syzygy alignment, a set of square brackets encloses all values of the anomalistic month in column 7 which are in excess of the standard mean value (27.55455T 1 ) used in astronomy. In the long-period, net motion of perigee depicted in figures 28, 30, and 32 (as opposed to its short-period motion occurring immediately in the vicinity of perigee-syzygy) another fact is note- worthy in this table: During each of the anomalistic months contained within the square brackets, the net motion of perigee is forward; during the remaining anomalistic months (whose lengths are all less than the established mean value) the net motion of perigee is retrograde. The anomalistic month (or average of two equal anomalistic months) of longest duration in each bracketed series is indicated by a bold dot (bullet) placed directly to the right of its value in column 7. It is, of course, possible to obtain the separation- interval representing the actual near-coincidence in time between the occurrences of perigee and syzygy at each such alignment by simply taking the difference between columns 2 and 8 of this table for the appropriate P-S date. The values should be subtracted in the sense perigee date minus syzygy date to maintain consistency in alge- braic sign. Because of the two-component relationship re- quired to establish the condition of perigee-syzygy, a close (if not exact) correlation also will be observed between any synodic month of maximum length and the anoma- listic month of maximum length occurring in the same close proximity to perigee-syzygy. The maximum lengths of the synodic months determined between successive oc- currences of both new moon and full moon are set in boldface in columns 3 and 4. By noting the number of days separating each succeeding boldface value, the ap- proximate 6.5 or 7.5-month time span between consecu- Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 287 tive alignments of perigee-syzygy is immediately evident. The typical alternation from perigee-syzygy at new moon to perigee-syzygy at full moon can be seen by comparing columns 7, 8, and 9 with columns 3 and 4 and 2 or 5, respectively. Supporting a previous statement regarding the closely related sequence of perigee-syzygy and apogee-syzygy, the maximum length of a synodic month is inevitably accom- panied in the adjoining column — and within a period not to exceed 2 weeks earlier or later — by a corresponding minimum. Inherent within the effects of solar perturba- tions are those altering the lunar period of revolution. Consistent with such dynamic influences, the varying lengths of the synodic months considered as a whole are, of course, a function of their separation in time from perigee-syzygy. Likewise, individual variations in the maximum lengths of the synodic months are a function of the smallness of the separation-interval between perigee and syzygy, the synodic (and anomalistic) months becoming longer as this separation-interval becomes shorter. 1. Variation in Length of the Anomalistic Month The mean value of the anomalistic month is based upon an assumed mean motion of the Moon with respect to perigee amounting to 13.176396°/ d — 0.1 1 1404°/ d = 13.064992°/ d . However, because of the increased angu- lar velocity of the Moon at perigee-syzygy, while the Moon is close to this position the Earth requires a small extra portion of each day's rotation to catch up with the Moon and enable it to transit the meridian to complete a lunar day. The maximum absolute angular velocities of the Moon (occurring at proxigee-syzygy ) can be as high as 15. 4° /day. It is obvious that the necessary catch-up motion of the rotating Earth resulting from such accelerated motions of the Moon can account for the consistent lengths in excess of that of the mean anomalistic month found in the case of those months which contain a very close perigee-syzygy alignment. At the same time, a small additional modification is introduced by the net, long-term progression of perigee. The anomalistic month is measured from perigee to perigee. It therefore contains the extra catch-up motion due to the net forward motion of perigee, but calculated for an assumed mean rate of only +0.1 11404°/day. Ac- cordingly, the true anomalistic month also will be length- ened to a slight extent because of the extra motion re- quired for the Moon to catch up with the greater net forward motion of perigee during those anomalistic months bracketing close perigee-syzygy alignments. The relative lengthening of the anomalistic month will be more, the larger is the net forward motion of perigee with respect to its assumed mean motion. 2. Variation in Length of the Synodic Month On the other hand, the synodic month is ordinarily measured from new moon, which implies an alignment of the Moon with the Sun. The synodic month by defini- tion already contains the effect of the Moon's catch-up motion with the Sun, viewed from the rotating Earth. Its period is measured in terms of the extra number of rotations of the Earth required to achieve the simultane- ous meridian transit of the two bodies. The resulting mean value is based upon an assumed mean daily synodic motion of the Moon amounting to 13.176396°/ d — 0.985647°/ d = 1 2. 1 90749°/ d . In this evaluation of the synodic month, the Sun is assumed to move with a mean apparent angular velocity of + 0.985647 °/day. In the Sun's apparent motion, the variations from its mean value are much smaller than those of the Moon from its mean angular orbital velocity. This is due both to the smaller magnitude of the Sun's mean motion and the smaller daily variations therefrom which are cumulatively totaled. (In addition, the varia- tions in the lunar orbital velocity between perihelion and aphelion are of too small a magnitude to have any influ- ence in this connection. ) Consequently, the maximum variations in the length of the synodic month are considerably less than those in the anomalistic month. The greatest individual values for the length of the synodic month will bracket a perigee-syzygy alignment near the time of perihelion (in accordance with the Sun's greater apparent motion then) . The small- est values will occur bracketing an apogee-syzygy situa- tion near aphelion. As a direct corollary, the maximum difference of 0.5555 day in the lengths of the synodic months appearing in this table exists between the months June-July 1960 and Jan.-Feb. 1964 corresponding to periods near aphelion and perihelion, respectively The Correlation Between Smaller Perigee- Syzygy Separation- Intervals and Longer Months From a detailed analysis of table 17, various pertinent relationships may be summarized. 1 . Over any reasonably short span of time, it is appar- ent that: (a) the total number of lunar days in corre- -;;;; Strategic Role of Perigean Spring Tides, 1635-1976 sponding synodic and anomalistic months (a factor determined by the relative orbital motion of the Moon and the necessity for the rotating Earth to catch up on this motion) ; and (b) the individual lengths of the lunar days contained in each month (again determined by the Moon's changing orbital velocity, as well as relative mo- tion in right ascension) must vary together. The anomalistic months bracketed in table 17 are grouped around those dates on which perigee and syzygy are in close alignment (the separation-intervals for all examples labeled "P-S" are ))-5 28° 612 683 1 g *> smaller 2t - 9 -i-p 4-180° 25-21/ 263 - (665) 26 - o+S 2(y-o)-(V-*J 6+ 7]-3o+o3 Y-2o-(o-5) 13° 398 660 9 ^ M, smaller . s;:„:: +? i--° 1 -v-(Q«) K-v+(Q) 166 (655) [tfj-o,] 8+ T- o+ i7 Y-(o-o) 14' 496 693 9 K J, smaller elliptic (+ A + s-p -90° -V 176 (466) 8+ n+ o- 5 Y+))-5 13° 471 614 5 "i variational [127 (665)] e+37|-4<7 Y+27,-40 /', O principal declinational I— h +90° 163 (656) [S,-A',] 6-7) Y-2t} 14- 958 931 4 X, ([O declinational Meteorological (land and sea breeze) 14- h - 90° Zero 165 (565) [tf.-o,] 6f7] 8 T Y— 1 16° 16° 041 068 6 1 M, ([ (from 4* power of parallax) 365 (555) [JMJxS 143 476 168 3). M, (£ quarter-diurnal IWX4 (er . 968 208 4) Q M, sixth-diurnal x6 ( «6 . 962 312 7) if. eighth- diurnal X8 1115 . 936 416 9) s, O ter-diurnal [S,] X3 , 46 ) w s. quarter-diurnal X4 | BO ) : s, sixth-diurnal eighth-diurnal X6 1 90 (120 ) MS ou (MS), quarter- diurnal [Afj+SJ ( 68 . 984 104 2) 2AfS ou |i; semi-diurnal 237 - (656) [M,-SJ (27" 968 208 4) 3 MS [M,-SJ ( 13' 476 156 3) 2 MS, sixth-diurnal [M.+SJ (87° 968 208 4) H MiV-(MiV), quarter-diurnal [Af^+ATj (57° 423 833 7) Q 2MW, sixth-diurnal [M.+ A-J ( 73° 887 320 7) p (MX), ter-diumal 366 - (456) [Af 1+ X,] t«.-o,] ( 44 026 172 9) g (2 MX), ter-diurnal 345 - (665) [M.-K,] [M,+ 0,] ( 42° 927 139 8) 5 (2SM); semi-diurnal [S.-AfJ ( 31° 015 896 8) o 3SM SO, {SK), diumsl diurnal 183 ■ (666) [S.-MJ 18,-0,] [S,+ K,] ( 16° ( 16° 1 45' 015 895 8) 041 068 6) a - Ml (£ fortnightly 2s -25 076 - (655) [X,-0] 2o- 1° 098 033 1 1 MSI ([O fortnightly synodic variational 073 (665) [S,- MJ ( 1° 016 896 8) Mm (£ monthly s-p Zero 065 (466) [M.-ATJ a-es 0° 644 374 7 ■j Ssa O semi-annual 057 (6S6) [Sa] X 2 ( o° 082 137 3) i So Q meteorological annual (monsoon) * Zero 056 ( ) 1 0° 041 068 6 ASTRONOMIC ELEMENTS FOR THE AEG 1JMENT SPEED OF CHANGE PER MEAN HOUR PER MEAN DAY Y angular speed of Earth's rotat 15° 041 068 6 * hour angle of mean O (mean time). T=<°+A -.-£,. h mean longitude »i Q. « mean longitude ..f {£, J> 1- 16° 360° - 12° 190 749 39 0° 985 647 34 13° 176 396 73 0° 111 404 08 0° 000 047 07 A o d° nent of Q. nent of (J. d° of perigee d° of perigee G .''- 0° 649 016 5 0° 004 641 8 0° 000 002 v right ascension of intersection. v' -/(v, I). V" - / (V, I). / inclination of g orbit on Equator. Figure 43.— This table is reduced from a much larger chart appearing as a foldout in Tide Predicting Machines, Special reference source on the development of analytic constituents pertaining to the harmonic analysis of the tides. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 295 COMPONENTS OF THE TIDE MEAN VALUE OF COEFFICIENT o COM PONENTS AS GIVEN BY THE MACHINES Brit»h TcdUOffiw N°°3 ' ttt Foml Robot. THda Br. N° 4 Predirtiiig (Kelvin) f- . «- 2 K«l.u> Krfvi, Kolra TidJ Tida 0.4543 Af : 12»4206O M, M, m i M 2 m, M, M, M, M, M, Mj Jf 2 if 2 M 2 M 2 0.0871 A» 2 12 65835 N 2 N 2 s i N 2 »j ^2 f, *! H, N 2 »J 2V, iV 2 *: N , 0.0126 L, 12 19162 Li L 2 i, h 4 L l h A Ll A i 2 i, L 2 '-, h 0.0117 2N 12 8783 22V 2N 2N 2» 2 0.012340.0171 v 2 12 62601 v, v 2 V; V2 *i *2 "2 •>i Vi »i v 2 v 2 v, 0.0033 40.0074 X, 12 22177 X 2 (supp.) - - \ \ \ ^1 0.0074 40.0109 p., 12 87186 to to \h ft H-2 to V-2 to \h C! f! fl h I^J 0.2120 S 2 12 hours s , s 2 S 2 s, s, s 2 8, $2 s 2 s z •5 2 s 2 S ! S, S 2 0.0124 t 2 12 01645 1% T; r» T l T l ^ 2 0.0018 fl; 11 98369 *2 00576 1 0,0182 K > 11 96724 K, A'., K 2 *i X; K 2 K 2 K 2 K, K 2 K, ff 2 K 2 ^2 0.1886 0, 26&81935 o, 0, o, Oi o, 0, 0, o, 0, 0, 0, o. 0.0081 22 306 OO 0.0366 0, 26 86836 Q, 0, 0, M, 3 1052 M, M t s> 8 hours s. 6 houre 4 hours 3 hours s. S 8, S, s, petits fonds MS, 6" 1033 MS, MS, MS, MS, MS, MS, MS, MS, MS, MS, MS, MS, MS, MS, 2 MS 12 8718 3 MS 3MS 2 MS, 2MS t UN 6 2693 MN MN MN MN, MN, 2MN, 2MN, MK, 8 1772 MK MK MK MK, 2MK, 8 3863 2MK 2MK 2MK 2MK, 2SM 2 11 6070 2SM 2SM 2SM 2SM 2SM 2SM 2 3SM 3SM SO, 22 420 SO, 0.0783 Mf 13 j. 777 Ml Ml 0.0042 MSI 14 766 MSI MSI 0.0414 Mm 27 655 Mm Mm 0.0365 5m 182 621 Sm Ssa Ssa Ssa Ssa Ssa Sju Ssa Sa 365 242 Stt Sa Sa Sa Sa Sa So S« Sa TOTAL NUMBER OF COMPONENTS 10 20 24 15 .6 ,9 33 37 12 .5 20 16 15 16 + 3 disp. DATE OF CONSTRUCTION 1872-1873 1879 1891 1881 1901 modii .882 .908 1894.1910 19.0 1914 19151916 1918 1920 modi. 1924 .924 1924-25 SERVICE iFF£ V "m * foiZL°' S r ST* TuU Tabla Si "jzbtl ill StJbc' U Sa'-,™ IP §n gig SITUATION W4, ESS aga ST ' (in hours) =0.984 (S° 2 -M° 2 ) (in degrees) That is, the greater is the influence of the Sun on the local tidal waters, tending to detract from the principal effect of the Moon, the greater is the value of . It is important to mention at this point that this par- ticular syzygy influence of the Sun should not be con- fused with another solar gravitational influence occurring at any position in the lunar orbit in connection with the phenomena of tidal priming and lagging. Both of these phenomena are discussed in chapter 8. 2'itt Strategic Role of Perigean Spring Tides, 1635-1976 In the same manner, the augmentation in the range of the tides produced by the passage of the Moon through perigee does not occur exactly at the time of lunar transit across the local meridian of a place. A similar lag known as the age of parallax inequality is involved. This delay factor may likewise be computed from the harmonic con- stants for any location. Two appropriate lunar constants dependent upon the anomalistic period in which the Moon revolves from peri- gee to perigee are indicated by N? and N° , and are termed the larger lunar-elliptic semidiurnal constituents. Because the parallax effect resulting from the Moon's pas- sage through perigee (represented in phase relation by N°) is superimposed upon the principal semidiurnal lunar effect (represented correspondingly by M°), their approximate resultant may be obtained by subtracting the one from the other. Representing by x the parallax age, or interval between meridian passage of perigee and the production of an augmented high tide near the time of perigee : X (in hours) = 1.837 (M%-N° 2 ) (in degrees) Since it is possible for N° to exceed M° (e.g., in parts of the Gulf of Mexico), occasionally the result is nega- tive, and the perigean tides precede the meridian passage of the Moon. As examples of the preceding two phenomena, the phase age at Sandy Hook, N.J., is 0.984 (S° ~M°) = 0.984(244°-222° =+22 h , and the parallax age is 1.837 (M° 2 - N° 2 ) = 1.837 (222°-204°) = +33 h . In the case of a meridian passage of ( 1 ) a new or full moon, or (2) the position of perigee, these are the theoretical intervals of time after which one would expect to find the arrival of augmented high tides associated with syzygy or perigee, respectively. When the two phenomena, syzygy and perigee, occur together, the delay in the resulting tides of increased range following the time of lunar transit is noncumulative but agrees approximately with the average of these two effects. Variation in Tidal Range, and in the Types of Tides An indication of the relative heights of the water levels produced at times of perigee-syzygy is given by the fol- lowing rule-of-thumb analysis: The ordinary spring tide, produced at time of new moon or full moon (i.e., syzygy) alone, can add approxi- mately 20% to the range of the tides above the mean spring range. The passage of the Moon through perigee (creating perigean tides) can also, by itself, increase the range of the tides by approximately 20% above the mean spring range. In the combination of these two phenomena at times of perigee-syzygy, the daily range of the tides is increased nearly as the sum of the two, or 40% above the mean spring range. However, a considerable number of other factors, to be discussed in chapters 7 and 8, can alter this value, and it should be regarded only as a representative figure. Before entering into the discussions of chapter 8 it is logical in the present connection to indicate that two other constants, diurnal in nature, are used to define the declinational effects of the Moon on the tides (includ- ing the diurnal inequality). These are designated as Kx and Ox (representing the lunisolar declinational and prin- cipal declinational constituents, respectively). The pro- duction of the maximum range in the tides resulting from the effects of diurnal inequality undergoes a similar delay following the local transit of the Moon which is known as the age of the diurnal inequality and, if symbolized by A, is expressed in the relationship : A (in hours) =0.911 (K°-0°) (in degrees) Significantly, in conjunction with the harmonic constant M representing the principal lunar semidiurnal constit- uent of the tides, these two constants also may be used to isolate and identify the particular type of tide common to any one oceanographic province. As shown in figure 6 of the appendix, tides in which the diurnal components (represented principally by the tide-raising influence of the Sun) predominate are de- scribed as diurnal tides. Those in which the influence of the semidiurnal constituent due to the Sun (S 2 ) and semi- diurnal constituent due to the Moon (M 2 ) are approxi- mately equally felt are described as mixed tides. Finally, those in which the semidiurnal constituent of the Moon {M->) predominates are termed semidiurnal tides. A quantitative method of classifying local tides into one of these three types is available from the relationships given in table 19. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 2 r,f) Table 19. — Types of Tides {With Index and Range) at Various Locations Along the Atlantic, Pacific, and Gulf Coasts of North America Semidiurnal Tides: ^ f '" l "^ 1 >0.0<0.25 Location of station Value of harmonic constants H(ft) Index: K^ + O, M 2 +S 2 Spring range (ft) Argentia, Newfoundland Quebec, Quebec Halifax, Nova Scotia St. John, New Brunswick Eastport, Me. Portland, Me. Boston, Mass. Newport, R.I. (Narragansett Bay) Bridgeport, Conn. Willets Point, N.Y. New York (The Battery), N.Y. Sandy Hook, N.J. Philadelphia, Pa. Wilmington, N.C. Charleston, S.C. Savannah, Ga. Mayport, Fla. Miami Beach, Fla. 0.289 0. 740 0.340 0.504 0.476 0.459 0.465 0.212 0.295 0.319 0.328 0.318 0.333 0.250 0.335 0.364 0.269 0. 136 0.324 0.690 0. 153 0.374 0.376 0.367 0.380 0. 164 0.212 0.237 0. 177 0. 164 0.244 0.202 0.252 0. 278 0. 193 0. 105 2.281 5.850 2.046 9.943 8.468 4.356 4.422 1.690 3. 185 3.619 2. 138 2. 154 2.602 1. 978 2.445 3.497 2. 143 1.203 0.675 1.380 0.454 1.629 1.413 0. 702 0.717 0.396 0.538 0.616 0.431 0.447 0.298 0.250 0.411 0.542 0.359 0.237 0.207 0. 198 0. 197 0.076 0.086 0. 163 0. 164 0. 180 0. 136 0. 131 0. 197 0. 185 0. 199 0.203 0.206 0. 159 0. 185 0. 167 6.3 15.5 5.3 23. 7 20. 7 10. 4 11.0 4.4 7. 7 8.3 5.4 5.6 (,. 2 4.5 6. 1 8.6 5. 3 3. Diurnal range Anchorage, Cook Inlet, Alaska 2.240 1.251 11.471 3.250 0.237 ",!)(! Strategic Role of Perigean Spring Tides, 1635-1976 Table 19. — Types of Tides ( With Index and R ange) at Various Locations Along the Atlantic, Pacific, and Gulf Coasts of North America — Continued Mixed Tides Mainly Semidiurnal: Kt + O! M 2 +S 2 >0.25<1.5 Location of station Value of harmonic constants Index: Spring K, O l M 2 S 2 M 2 + S 2 St. John's, Newfoundland Harrington Harbour, Quebec Pictou, Nova Scotia New London Conn. Breakwater Harbor, Del. Baltimore, Md. Key West, Fla. San Diego, Calif. Los Angeles, Calif. (Outer Harbor) San Francisco, Calif. (Golden Gate) Astoria, Oreg. (Tongue Point) Aberdeen, Wash. Seattle, Wash. Valdez, Prince William Sound, Alaska Nome, Alaska 0.262 0.213 1. 178 0.486 0.285 3. 5 0.478 0.474 1. 742 0.576 0.411 4. 9 0.667 0.648 1.373 0.354 0.761 3. 9 0.238 0. 166 1. 166 0.228 0.290 3. 1 0.342 0.282 1.916 0.344 0.276 4. 9 0.207 0.204 0.486 0.082 0. 724 1.3 0.290 0.290 0.565 0. 172 0.787 1. 6 Diurnal 0.693 1. 788 0.724 0. 712 range 1.096 5. 7 1. 112 0. 704 1.695 0.665 0.769 5. 4 1. 195 0. 748 1. 796 0.406 0.882 5. 7 1.257 0. 739 3.012 0.676 0.541 8. 2 1.364 0.800 3.425 0.873 0.503 10. 1 2.734 1.503 3.530 0.839 0. 970 11.3 1.601 0.986 4. 521 1.533 0.427 12. 0.317 0.208 0.366 0.038 1.300 1.6 Mixed Tides Kj+O^ 1 c /0 n Mainly Diurnal: M 2 +S 2 ^ Location of station Value of harmonic constants H(ft) Index: K. + O, M 2 + S 2 Spring range (ft) Ki o, M, s 2 South Boca Grande, Fla. St. Petersburg, Fla. Galveston, Texas (Galveston Channel) Victoria, British Columbia Dutch Harbor, Amaknak Island, Alaska 0.410 0.513 0.384 2.056 1.088 0.370 0.477 0.364 1.214 0.729 0.371 0.497 0.309 1.223 0.852 0. 126 0. 159 0.098 0.336 0.091 1.569 1.509 1.838 2.097 1.927 1.7 2.3 L.4 6. 1 3.7 Diurnal Tides. M 2 +S 2 ^ 3 - 3t ° CO Location of station Value of harmonic constants H(ft) Index: M 2 + Sj Diurnal range (ft) K, Oi M 2 s 2 Pensacola, Fla. Mobile, Ala. (Mobile River) Biloxi, Miss. (Biloxi Bay) St. Michael, Alaska Sweeper Cove, Adak Island, Alaska 0.401 0.466 0.568 1.378 1.342 0.384 0.458 0.514 0. 758 0.941 0.062 0.054 0. 112 0.586 0.623 0.021 0.036 0.091 0. Ill 0.074 9.458 10. 267 5.330 3.065 3.275 1.3 1.5 1.8 3.9 3.7 Chapter 7 The Classification, Designation, and Periodicity of Peri- gean Spring Tides, With Outstanding Examples of Accompanying Tidal Flooding From Recent History It has been emphasized frequently in preceding chap- ters that the coincidence of perigee-syzygy with certain lunisolar positional relationships produces the high- est known astronomical tides. The resulting proxigean and perigean spring tides — when associated with strong, persistent, onshore winds — have been responsible for a large number of instances of major tidal flooding expe- rienced over long periods of history (see table 1 ). At the same time, among the examples of table 3, there is empir- ical evidence to show that the ordinary spring tide, when accompanied by sufficiently strong onshore winds, is also capable of causing coastal flooding conditions — although these are, for the most part, of far smaller magnitude. It is imperative, therefore, that an evaluation be made of the particular characteristics which set each close perigee-syzygy alignment apart from other tide-augment- ing circumstances as one especially susceptible to the production of major tidal flooding, when supported by the appropriate meteorological conditions. This analysis must also include other force-modifying factors involving the combination of the gravitational forces of the Moon and Sun — the most important of which are the respective phenomena of priming and lagging. From an initial comparison of spring and perigean spring tides, involving the differences imposed by these latter two factors, a logical follow-on entails : ( 1 ) the establishment of a uniform system of classification for ordinary spring tides, pseudo-perigean spring tides, peri- gean spring tides, proxigean spring tides, and extreme proxigean spring tides, based upon the purely astronom- ical parameters which go into their production; (2) an investigation of various periodicities which govern the recurrence of exceptionally close perigee-syzygy align- ments; (3) the representation of a considerable number of specific examples of tidal flooding associated with the foregoing different classifications of tides; (4) the pro- vision of significant comparative data of astronomical, oceanographic, and meteorological nature relative to these cases of tidal flooding; (5) the development of a basic intensity scale for rating the probable magnitude of the tidal flooding event likely to accompany a given combi- nation of astronomical and meteorological circumstances ; (6) the derivation of a suitable numerical coefficient as a quantitative indicator to assist in evaluating the astro- nomical potential for tidal flooding subject to a given set of perigee-syzygy conditions; (7) a survey of the sig- nificance of rate of tide growth in producing especially intense coastal flooding situations, and of variable wind- coupling conditions in driving the astronomically raised perigean spring tides onshore ; ( 8 ) the determination of a schedule of combined astronomical-meteorological condi- tions which make the coastline particularly vulnerable to tidal attack; (9) an analysis of the relationships be- tween perigean spring tides and other oceanographic phe- nomena — such as the high water lunitidal interval, in- ternal waves, turbidity currents, and the marked increase in the velocity of tidal currents ; and ( 1 ) a consideration of possible correlations between the astronomical occur- rence of perigee-syzygy and various other geophysical, selenophysical, and biological phenomena. These factors will be discussed, in the above order, in this and the following chapter. A suitable system of classi- fication for the various types of tides mentioned in ( 1 ) above must first be developed. Comparison of Ordinary Spring Tides and Perigean Spring Tides Reduced to the simplest terms, spring tides are caused by the reinforcing action of the gravitational force of the Sun with that of the Moon caused by the alignment of these two bodies in celestial longitude (or, alternatively, right ascension) at times of new moon (conjunction) or full moon (opposition). Accordingly, such tides occur without fail on the two occasions of syzygy in each synodic month. At these times, the daily range of the tides is in- creased by approximately 20 percent above the average. The effect of lunar variation (see p. 175) is to add 28" 301 ';02 Strategic Role of Perigean Spring Tides, 1635-1976 to the lunar parallax at either new moon or full moon, regardless of the angular distance from perigee; how- ever, some additional component is also added to the parallax by the lunar evection term, depending upon the Moon's anomalistic angle. Certain other astronomically related factors may oc- cur to cause considerable variations in the relative tide- raising forces associated with spring tides. These include : ( 1 ) the diurnal inequality, resulting from a large declina- tion of the Moon ; ( 2 ) a coincidence of either position of syzygy with (a) the summer or winter solstice, (b) the vernal or autumnal equinox, (c) other times at which the Moon and Sun reach the same declination, or ( d ) the time at which the Earth reaches its closest annual approach to the Sun (perihelion) ; and (3) a large zenith distance of the Moon. Since, however, these same factors may also act to modify perigean spring tides, none of these variable influences may be considered as distinguishing ordinary spring tides from the former type. As in the case of all higher-than-usual tides, ordinary spring tides are subject to the action of sustained onshore winds in lifting the greater water levels produced onto the land. Although spring tides usually possess a much smaller flooding potential compared with tides of the perigean spring type, it must be recognized that they, too, have played a definite, although considerably less prominent and consistent role in major tidal flooding over the course of history. Despite the emphasis given in the present volume to perigean spring tides as a heavily documented contributing cause to coastal flooding as well as the special object of study, there is no intent to detract from the sig- nificance of the ordinary spring tide as an additional source of such flooding, given the necessary supporting conditions of very intense, sustained onshore winds. However, in objectively evaluating the flooding poten- tial of ordinary spring tides compared with that of peri- gean spring tides, certain definite astronomical factors exist which favor the latter for the production of severe coastal flooding when appropriate wind conditions pre- vail. These astronomical differences between ordinary spring tides and perigean spring tides will now be considered. It has been repeatedly pointed out in previous chapters that one of the factors increasing the potential for tidal flooding in the case of perigean spring tides is a greater length of time during which the enhanced gravitational forces of Sun and Moon can act, associated with a longer tidal day. As has been shown, the principal lengthening of the tidal day is due to the increased velocity of the Moon at lunar perigee. By definition, a true ordinary spring tide is one separated in time as far as possible from perigee and thus lacking in the increased orbital velocity and necessary catch-up effects imposed thereby. From this cause alone, therefore, the ordinary spring tide is not ac- companied by an increased tidal day. On the other hand, the astronomical alignment producing spring tides is influenced by the effect of lunar variation (see p. 165) which tends to increase the orbital velocity of the Moon at syzygy (and thereby lengthen the tidal day) and, as a function of lunar phase angle, the effects of priming and lagging which act respectively to shorten or lengthen the tidal . day. Concepts of Tidal Priming and Lagging Although the mass of the Sun is 27,070,000 times that of the Moon, the average distance of the. Sun from the Earth is 389 times that of the Moon. The comparative tide-raising forces of the Sun and Moon are directly proportional to the relative masses of the Sun and Moon and inversely proportional to the cube of their respective distances from the Earth. The effective tide-raising force of the Moon is, therefore, ^Mhs that of the Sun, or the tide-raising force of the Sun is only 5 /nths that of the Moon. In all tidal actions, the Earth's tidal waters accord- ingly more closely follow the position, angular motion, and relative distance of the Moon, but are modified by the corresponding solar factors. Lunar Phase Effects — Qualitative Evaluation In terms of the elongation, or changing angular distance between Sun and Moon in the sky consequent upon the lunar phases, this same tide-raising principle applies. The major axis of the Earth's hypothetical tidal force envelope is always directed toward a position which is the resultant of the gravitational force influences of both the Moon and the Sun. Except at times of conjunction (new moon) and opposition (full moon), when the directions of the Sun and Moon come into coincidence in longitude (or right ascension) the orientation of the resultant force vector in the direction of the combined gravitational attraction of the Moon and Sun always lies between these two bodies as seen from the Earth, but closer to the longitude of the Moon by a factor proportional to its greater tide- raising influence. Priming and Lagging as Shown in Tide Curves The repeating maxima and minima in the two com- posite sets of tide curves (figs. 44a-44b) showing the Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :;o:; variations in the length of the true tidal day may readily be explained by an analysis of the changing phase rela- tionships of the Moon with respect to the Sun. As the result of the annual orbital motion of the Earth around the Sun, the Sun appears to move around the celestial sphere at the same speed as the Earth and in the same counterclockwise direction as viewed from the north pole of the ecliptic. As seen on the vault of the sky, this apparent movement of the Sun duplicates the 360° of the Earth's revolution in 365.25 days, at an average speed of slightly less than 1° per day. The apparent motion of the Sun is also in the same direction as the actual motion of the Moon in its orbit around the Earth. Whereas the Sun's apparent motion is approximately l°/day, the Moon's orbital motion ranges from about 11.78° to 15.3 7° /day, and the Moon therefore achieves two succes- sive alignments with the Sun from one syzygy position (new moon) to the next (full moon) in about 14-15 days. At last-quarter phase, the Moon is 90° to the west of the Sun in celestial longitude but, in its eastward motion in ofbit, the Moon reduces this angular separa- tion at a rate of some 14°/day. Between last-quarter phase and new moon, the configuration of Earth, Moon, and Sun is such that the Sun lies ahead of the Moon (at a greater right ascension or longitude) and the Moon is overtaking the Sun. Because the Sun leads the Moon in the sky, the position of maximum amplitude of the Earth's tidal force envelope resulting from the combined gravitational attractions of the Sun and Moon is dis- placed to a position in advance of a line joining Earth and Moon by a considerable but rapidly lessening amount. Each day, the Moon further closes the angular dis- tance in elongation separating itself from the Sun, and the major axis of the tidal force envelope in turn swings continuously into closer alignment with the Moon (i.e., in a direction opposite to the orbital motion of the Moon and the rotational motion of the Earth ) . The period required for any position on the rotating Earth to align itself twice with the major axis of the tidal force envelope represents the length of the tidal day. Since, with the major axis of the tidal force envelope moving in a direction opposite to the Earth's rotation, it takes any point on the Earth's surface somewhat less time to reach alignment with this force-axis, the tidal day is shortened proportionately. 1. Tidal Priming It has been shown that, following last-quarter phase and with the Moon rapidly catching up on the Sun, the angle of separation (the elongation) between them is reduced. The gravitational influence of the Sun is added increasingly to that of the Moon and in a direction more nearly corresponding to that of the Moon as the two bodies come into closer alignment. From last-quarter phase to new moon, therefore, the tidal day is continually shortened and reaches a minimum at new moon. Exactly the same situation prevails between first-quarter phase and full moon, since the tidal force action is exerted along the line of syzygies. This phenomenon (called lunar "priming") accounts for the successive minima in the length of the tidal day shown in figs. 44a-44b. 2. Tidal Lagging The greater relative speed of the Moon in its orbit compared with the apparent daily motion of the Sun likewise explains the opposite phenomenon which in- creases the length of tidal day following the syzygies and between new moon and first-quarter and full moon and last-quarter phases, respectively. Since the Moon is traveling faster than the Sun at each instant, the latter is effectively falling behind the position of the Moon. The major axis of the Earth's tidal force envelope which, as previously explained, follows the Moon's position far more closely, is in this case continually displaced away from the Sun. This displacement now is in the same di- rection as that of the Moon's revolution, and that in which the Earth is rotating on its axis. A catch-up time is required in the Earth's rotation. Thus, following the minima occurring at new moon and full moon, the tidal day is progressively lengthened between the new moon and first quarter and full moon and last quarter, re- spectively. This relationship is clearly indicated in the curves showing changing lengths of the tidal day in figs. 44a-44b. The shortening process thereafter resumes, as noted under section 1 , above. It is important to observe that the lengthening of the tidal day produced by the phenomenon of tidal lagging occurs prior to neap tides, when the tide-raising forces of Moon and Sun are directly opposed and minimized. The extension of the tidal day resulting from this cause does not, therefore, provide a meaningful contribution in augmenting the daily range of the tides as in the case of : ( 1 ) decreased lunar distance of the Moon from the Earth at perigee-syzygy ; (2) an extreme proximity of the Moon to the Earth at lunar proxigee ; or ( 3 ) the in- creased motion of the Moon in right ascension when it is at higher declinations. m Strategic Role of Perigean Spring Tides, 1635-1976 F-68 (a) 20 VARIATION IN DECLINATION OF MOON AND SUN -1939 JAN 14 21 28 1 FEB MAR 7 14 21 28 7 14 21 28 1 APR 7 14 21 281 MAY 7 14 21 28 1 JUN 7 14 21 28 Figure 44a. — Variation in the length of the tidal day during 1939 January-June, shown as a function of the increment to be added to the time of the previous day's higher high water to establish the time of occurrence of HHW on the current day. The graph for an entire year is presented in figures 44a and 44b. A detailed analysis of these variations is con- tained in the main text. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 305 F-68 (b) 20 VARIATION IN DECLINATION OF MOON AND SUN-1939 JUL AUG SEP OCT NOV DEC 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 Figure 44b. — A graph containing data of the same nature as figure 44a, plotted for 1939 July-December. The technical in- terpretation of the changing maxima and minima of these curves is given in the text. 202-509 0-78-22 106 Strategic Role of Perigean Spring Tides, 1635-1976 QUANTITATIVE ANALYSIS OF THE EFFECTS OF TIDAL PRIMING AND LAGGING As in previous cases, the use of an actual example will serve to illustrate the various quantitative relationships in- volved between neap tides, ordinary spring tides, and per- igean spring tides, as well as the modifications introduced by tidal priming and lagging. Restating the earlier qualitative description, the direct cause of these latter phenomena is the addition of two vector components indicative of the separate gravitational forces of the Sun and Moon, rather than that of the Moon alone. This vector sum representing the com- bined gravitational forces of the Sun and Moon and varying with the lunar phase is hereafter referred to as the resultant force vector. A meaningful evaluation of the effects of these two phenomena may be achieved by reference to figs. 45 and 46, and tables 20 and 21. In the two diagrams, vector arrows indicate, for each succeeding day, the directions and magni- tudes of the combined gravitational forces of the Sun and Moon. The composite of these resultant force vectors (each symbolizing a mean daily magnitude and direction) serves to define the shape of the total tidal force envelope. It should immediately be pointed out that this tidal force envelope representing the combined gravitational attractions of the Sun and Moon on the waters of the Earth during the course of the lunar month is not identical with the envelope of gravitational forces responsible for the instantaneous dis- position of tidal high and low waters and their movements over the surface of the Earth during each tidal day. Both of these force envelopes are ellipsoids, and both are delineated by force components, but the larger force envelope shown in figs. 45 and 46 involves the changing pattern of lunisolar forces over an entire lunar month. The smaller ellipsoidal figure immediately adjacent to the Earth in these same fig- ures (and also shown in fig. 2 of the appendix) represents the combination of all gravitational force components act- ing instantaneously on the tidal waters. This force envelope sweeps daily around the rotating Earth. With certain excep- tions of nonastronomical nature subsequently to be discussed, the major axis of this second force envelope is aligned ap- proximately with that of the Earth's envelope of tidal waters. Although the tidal waters themselves do not actually "ro- tate" around the Earth due to the many inertial and geo- graphic restraints imposed to their passage, the force enve- lope does so rotate once each tidal day. It is in this latter sense that it is safe to use the expression "diurnal rotation" in con- nection with the smaller ellipsoid (shown in elliptical pro- file) in figs. 45-46. With the passage of each succeeding day, the major axis of this smaller force envelope shifts continu- ously to follow the instantaneous orientation of the resultant force vector in the larger force envelope, representing one monthly lunation. Although certain other modifying factors prevent an exact coincidence between the instantaneous ori- entations of the resultant force vectors of these two ellipsoids, their orientations are obviously very closely related for any given position of the Moon and Sun in the monthly cycle of phases. Relative Tide-Raising Forces at Quadratures and Syzygies The instantaneous magnitude of the combined lunisolar force during each lunation is primarily a function of the phase angle of the Moon with respect to the Sun — varying from a minimum at quadratures (when the Moon's gravi- tational force on the Earth is imposed at right angles to that of the Sun) to a maximum at the syzygies (when the vector forces of the Sun and the Moon are applied along the same axis in space to reinforce each other) . These con- ditions result in neap and spring tides, respectively. (See fig. 3, appendix.) Column 7 of tables 20 and 21, in which the relative mag- nitudes of the resultant forces of the Sun and Moon have been computed for various times in a lunar cycle, shows this relationship clearly. For the purpose of convenience, the tide-raising force of the Moon is assumed to be unity, and that of the Sun to have its comparative value of % x or 0.455 that of the Moon. Thus, at quadratures (neap tides ) , the vectorial combination or resultant of the two forces approximates 1.03 to 1.19 and at the syzygies (spring tides) is the simple sum of the two, or 1.455. (See the note at the end of the following section.) The numerical values of the forces specified above are only relative for any given angular orientation between Sun, Earth, and Moon. In terms of a quantitative evaluation, the particular value of these figures is to show the increase in lunitidal forces occurring between the situation producing nean tides and that nroducing spring tides. It must be borne in mind that the absolute magnitude of this resultant force will be modified by the many factors of changing distance, declination, etc., between Earth, Moon, and Sun as these bodies shift in relative position. Confirmation of the Extended Duration of Peak Tide- Raising Forces at Perigee-Syzygy However, column 7 also serves to reinforce one very impor- tant principle in regard to perigean spring tides — namely, the extended period of time within which the stronger com- bined forces of the Sun and Moon at perigee-syzygy are ef- fective in producing higher-than-usual tides vulnerable to wind attack and potential tidal flooding. Such a direct analysis of the basic lunisolar forces acting is possible through a comparison of the normal perigee- quadrature situation occurring on 1962 June 24 (table 21), with the close perigee-syzygy situation contributing to the great coastal flooding of 1962 March 6-7 (table 20). In the first example, with perigee occurring at quadrature, syz- ygy is necessarily more than 5 days away and, under the terms of reference previously established, the ensuing tides at new moon are defined as ordinary spring tides. In this case, the resultant maximum force of Moon and Sun defined by the peak value of 1.455 lasted only 1 day, and this maximum value stands out singularly from a lesser value on either side. During the coastal flooding of 1962 March 6-7, which (as noted later in this chapter) continued for five successive high tides, maximum or near-maximum forces of Sun and Moon (1.452 to 1.455) prevailed through- out a 2-day period and even longer. (Note: In order to standardize the trigonometric-vectorial reductions involved, Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings \W DIRECTION OF MOONS ORBITAL MOTION APOGEE-QUADRATURE FQ SITUATION AS OF 1962 JUNE 18 -JULY 10 THE SHIFTING FORCE-AXIS IN THE HYPOTHET- ICAL LUNISOLAR TIDAL FORCE ENVELOPE, COM- BINING THE GRAVITATIONAL ATTRACTIONS OF THE MOON AND SUN. SEE ALSO 46, BELOW. THE ELLIPTICAL PROFILE OF THE TIDAL FORCE ENVE- LOPE REPRESENTS ONLY THE GENERAL DISTRIBUTION OF FORCES PRESENT, SINCE THE INSTANTANEOUS MAG- NITUDE OF THE COMPOSITE FORCE VARIES WITH LU- NAR DISTANCE AND MANY OTHER FACTORS. THIS TID- AL FORCE ENVELOPE SHOULD NOT BE CONFUSED WITH THE DAILY-ROTATING ELLIPSOID REPRESENTING ACTUAL TIDAL WATER LEVEL (STIPPLED AREA). TO SUN 24 L q 26 PERIGEE-QUADRATURE NOTE : THE DAILY LUNAR MOTIONS SHOWN POSSESS APPROPRIATE RELATIVE ANGU- LAR INCREMENTS AND DECREMENTS, BUT ARE NOT DRAWN TO EXACT SCALE SINCE INCREASINGLY DIVERGENT RADIUS VECTORS OCCUR BETWEEN PERIGEE AND APOGEE. Figure 45. — Graphical representation of the basis for lunar priming and lunar lagging, as these phenomena affect the length of the tidal day. The situation depicted is that at perigee-quadrature. A detailed discussion and quantitative analysis of these effects form part of the main text. ",()!■; Strategic Role of Perigean Spring Tides, 1635-1976 TO SUN t PERIGEE-SYZYGY 7 NM 6 DIRECTION OF MOON'S ORBITAL MOTION F M APOGEE-SYZYGY SITUATION AS OF 1962 FEB 28-MARCH 13 Figure 46. — Partial compensation of the effects of tidal priming and lagging at perigee-syzygy, in relationship to these same effects represented in figure 46 at perigee-quadrature. 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CT> '-. ~- ~. ~ ~ r. 3 3 3 3 3 r 3 3 — r 3 n- i. rt o 3 3 >. 3 3 - X X _ -f 3 _ CO X m z m <* „ 13 n d i c-. in r- -1- -" -1 X 3 r cm X r - 3 -f X 1- X X — 3 d : 3 -1- 3 3 co 3 X X X d d d d "•' -n -i ~l ni 3 "c 3 . s § .s 3. in CM '- en X f 3 co * cr> 3 3 r - X z 3 r. r~» -l 3 3 ni X 3 3 <* -3 -i Tl - 3 co ~i CT) 3 CM r~ m 3 CM 1 i 3 -3 en — CM '- 3 ~r 3 ni 3 CO r ^ 3 m ■* " » CO 1-^ _,' d d ^-' z -' CM m' t^' O) _' X i- r- xs m r^ -z 3' X Z l~» :: :- 3 in ■a 5 1 B-i 3 U U a< i. - 2 fi < 5 3 c E Oh 3 3 -e .2 f! - | 2 5 o C C - 3 o O 3 3 3 3 3 3 3 3 3 o CM ^ in CO ai 3 nj - "I J! -i CM CM -1 CM en — < 3 d ""' c >» >— 1 3 'Q 3 3 M Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■Ml the force magnitudes shown here do not contain any extra allowance above lunar force unity to accommodate this perigee-syzygy situation. Accordingly, in this purely vectorial analysis, the maximum tidal force value at perigee-syzygy calculated with this simplification does not exceed that at ordinary syzygy as is actually the case.) Examples of Tidal Priming and Lagging However, the principal function of these tables is to per- mit a quantitative verification of the manner in which the resultant lunisolar force vector either precedes or follows the position of the Moon in its orbit in the respective phe- nomena of priming and lagging. Although these relation- ships are shown graphically in figs. 45 and 46, it is impos- sible because of the continually changing proportions of an ellipse to represent the appropriate angular motions to a sufficiently accurate degree at the published scale. For de- scriptive purposes only, it is possible — by a smoothed con- solidation of the data appearing in tables 20 and 21 — to in- dicate the resultant force vectors in figs. 45 and 46 in at least approximately their correct positions either ahead of or behind the instantaneous position of the Moon, and with due regard to the phase and apsides relationships of the Moon at the time considered. The next step is to eval- uate the effect of differences in angular orientation of the resultant force vectors upon the Earth's tides. 1. Application to Ordinary Spring Tides With reference to the tide-influencing aspects of the Earth's diurnal rotation, the "catch-up" principle has been thoroughly described in previous pages. From an analysis of this principle, it has been determined that any influence which tends to accelerate the orbital motion of the Moon in the same direction as that in which the Earth is rotating will lengthen the tidal day. Since it is the mass and the gravitational force of the Moon rather than its geometrical figure that is involved in the production of the tides, this principle can be narrowed to permit, in substitution for the words "orbital motion of the Moon" above, the correspond- ing motion of the line of gravitational force action extending between the center-of-mass of the Moon and the Earth's surface. Conversely, any influence which tends to decelerate this line of force action joining the Moon and the Earth — thus increasing its effective displacement in a direction op- posite to that of the Earth's rotation — causes a shortening of the tidal day. A close examination of figs. 45 and 46 and the accom- panying tables 20 and 21 reveals the nature of this particular influence upon the tides. In proceeding from either of the position of syzygy (NM or FM) toward the quadratures (FQ or LQ, respectively) it will be observed that the lon- gitude angle (measured from the center of the Earth) be- tween the direction of the Moon and the direction of the resultant lunisolar force vectors on successive days grows steadily larger. This follows logically from the circumstance that the Moon separates from the Sun through 90° of elongation between syzygy and quadrature. The significant fact, however, is that not only does the angle of separation (elongation) between Sun and Moon grow larger, but the angle separating the Moon from the direction of the result- ant force vector also continuously increases. Between either position of quadrature and the ensuing syzygy, the reverse occurs and both the elongation and the angle between the Moon and the resultant lunisolar force vector diminish in value. (See cols. 6 and 10 in tables 20 and 21.) This is one clue to the phenomena under consideration. The situation is exactly akin to that of the converging step increments by which a function approaches zero as a limit in the integral calculus. Between either position of quadra- ture and syzygy, each day's orbital motion of the Moon results in diminished angle between the Moon and the resultant fdrce vector, approaching zero at syzygy. The in- cremental variations in those angles (second differences) themselves proceed toward increasing values between quad- rature and syzygy, and toward decreasing values between syzygy and quadrature. Accordingly, the Moon is closing up faster on the resultant force vector the nearer it gets to syzygy. By taking differences between the successive values in col. 10 (tables 20, 21 ) , it will be seen that this daily close- up rate is also noticeably greater at perigee-syzygy than at ordinary syzygy. The rise and fall of the tides is very closely related to the times at which the Moon (and by extension, the lunisolar force vector) transits the local meridian of any place on the Earth's surface. The above-mentioned nonuniform dis- placements of the resultant force vector with respect to the position of the Moon therefore are of considerable signifi- cance in establishing not only the times of arrival of high and low water but also the total periods of time in which tide- raising forces of maximum intensity operate. As the resultant force vector moves ahead of the Moon's position through constantly decreasing angular values each day between quad- rature and syzygy, the effect is a slowing down of the monthly rotation of the axis of the combined lunisolar force so that it, in effect, "drops back" in a direction opposite to that of the rotating Earth. A shorter period of time therefore elapses between two successive transits of this force axis across the local meridian of any place. This results, in turn in a contin- ous shortening of the tidal day to a minimum value at the lunar syzygy. As, between syzygy and quadrature, the resultant luni- solar force vector falls behind the position of the Moon, in a motion entailing steadily increasing angular values, the effect is continuously to accelerate this movement in a direction which is the same as that of the Earth's rotation. A longer catch-up time is thus required for any place on the rotating Earth to reach and pass this resultant axis of force. The pe- riod of time between two successive transits of the lunisolar resultant force vector is increased, and the consequence is an extension of the tidal day. As pointed out above, although the orientation in space of the lunisolar resultant force vector and the major axis of the Earth's fluid envelope are not the same, the two normally accompany each other very closely. A circumstance thus arises in which, between quadrature and syzygy, the Earth's tidal bulge lies ahead of — and, subject to the Earth's rotation, reaches the meridian before — the Moon itself. This condition is known in tidal theory as priming. Between syzygy and 312 Strategic Role of Perigean Spring Tides, 1635-1976 quadrature, the tidal bulge transits the local meridian after the Moon, a phenomenon known as lagging. The tidal day is generally defined as the interval of time between the occurrence of two successive higher high waters. The daily displacement of the lunisolar resultant force vec- tor with respect to the Moon's position is in a forward direc- tion near quadrature and retrograde near syzygy. Because the major axis of the Earth's tidal force envelope responds most closely to this motion, the tidal day acquires its greatest length near the, quadratures, and its shortest length near the syzygies. As the result of this decreasing length of the tidal day between quadrature and syzygy and increasing length between syzygy and quadrature, the minimum length of the tidal day from this single cause is established at syzygy. This, then, is the situation as it exists at the time of ordinary spring tide, without any additional tide-raising influence being ex- erted by perigee. 2. Application to Perigean Spring Tides It is important in terms of the classification of perigean spring tides given below to note that, in the case of ordinary spring tides, the greatest gravitational attraction produced by the combination of Sun and Moon (at syzygy) occurs at a time when the tidal day has its shortest length. Also, in figs. 44a, b it will be seen that the peaks of the curves (which rep- resent the maximum lengths of the tidal day at quadratures) are much more uniform in height when at least 5 days separate syzygy and perigee — the classification criterion adopted in this work for an ordinary spring tide. In all cases, the peaks are separated by raised minima (resembling valleys between high mountains) which, however, are subject to a greater elevation in height when the length of the tidal day (e.g., at a time of perigee-syzygy) becomes greater. A further enlightening feature concerning the nature of perigean spring tides is the direct contrast between the shal- lower depths of the curve troughs representing ordinary spring tides and the troughs of perigean spring tides imme- diately preceding or following an uplifted maximum asso- ciated with the latter type of tide. In the case of perigean spring tides accompanying a close alignment of perigee- syzygy, an apogee-syzygy situation must immediately precede or follow, within one-half a lunation, the corresponding con- dition of perigee-syzygy. In terms of the tide-raising force on the Earth, at apogee-syzygy, the gravitationally enhanced tidal effect resulting from the Moon's alignment with the Sun at syzygy is partially offset by the increased distance of the Moon from the Earth at apogee. At the time during which this reduced gravitational force acts, the Moon's orbital velocity is also reduced, due both to its greater dis- tance from the Earth and to its approach to syzygy, shorten- ing the tidal day. The considerably greater net shortening in the length of the tidal day consequent upon both of these causes provides an excellent basis for comparison with the shortening produced primarily by the syzygy effect in the case of an ordinary spring tide. The lengthening of the tidal day and uplifting of the curve minima at perigee-syzygy provides a still further contrast. It will be seen that the difference in amplitude (in units of time representing the length of the tidal day) between the lowest and highest minima of the curves in figs. 44a, 44b amounts to as much as 18 minutes. This difference represents the increase in the length of the tidal day accompanying a situation of close perigee-syzygy compared with a corresponding situation of apogee-syzygy in the same lunation. The uplift effect in the curve minimum at the time of perigee-syzygy and increased depression of the minimum during the immediately preceding or following apogee- syzygy may be attributed to parallactic inequality. When either new moon or full moon coincide with perigee, the shortening of the tidal day described earlier for the ordinary syzygy condition is offset. At such times, the Moon's orbital motion is accelerated by its proximity to the Earth, and the Earth's rotational catch-up motion increases the length of the tidal day. Conversely, the recession of the Moon to its greatest monthly distance from the Earth at apogee reduces the Earth's gravitational attraction for the Moon and slows its orbital motion, decreasing the length of the tidal day and producing a deeper curve minimum. A complete contrast exists in the case of the ordinary spring tide. When perigee coincides with quadrature, and either full moon or new moon is 90° removed from perigee, the average orbital speed of the Moon is only about 13° per day compared with a value which may reach more than 15° per day in the case of perigee-syzygy. The resulting con- siderably shorter length of the tidal day in the case of ordi- nary spring tides is further decreased by the effect of tidal priming previously described, and lacks any compensating increase as in the case of perigean spring tides. A Proposed New System for the Quanti- tative Designation of Perigean Spring Tides It is obvious from the step-by-step analysis of the very numerous astronomical factors which may influence the amplitude and range of perigean spring tides as outlined in previous chapters that various degrees and grades of these tides exist. Consequently, it becomes desirable for scientific purposes to establish a meaningful system for classifying these tides based upon the particular astronomi- cal circumstances which both create them and determine the relative heights of the water they produce. In a suc- ceeding section, the development of a suitable coefficient or index of tidal flooding potential also will be undertaken for these various classes of perigean spring tides, assuming them to be accompanied by the necessary meteorological conditions. In this terminology-assigning process, certain new ex- pressions, not presently in the language of either astronomy or tides, will be introduced which it is felt may be deserv- ing of consideration in order to fill in an existing gap created by many years of comparative neglect of the sub- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 313 ject area — and, in any event, to make the analysis of these tides more understandable. Basis for the Classification of Perigean Spring Tides The common denominator of all such tides, as fre- quently emphasized in the foregoing chapters, is the small time interval between perigee and syzygy, which leads — through solar perturbations of the lunar orbit — to the resulting close proximity of the Moon to the Earth, and a considerable increase in the tide-raising force. The reduced lunar distance from the Earth at times of perigee- syzygy is expediently (but in a mathematically inverse relationship) indicated by the geocentric horizontal parallax (*•) of the Moon. It will become clear in connec- tion with both astronomical and meteorological factors later to be discussed that the lunar parallax alone is in- sufficient substantively to evaluate the various categories of perigean spring tides in terms of their potential flooding ability if they become subject to continuous, strong, on- shore winds. However, this quantity is suitable for a selec- tive classification of such tides, based solely upon astro- nomical parameters. In the subsequent analysis of tidal flooding potential, a practical numerical coefficient will be derived which represents the instantaneous value of the rate of change of the Moon's true anomaly at the time of perigee-syzygy as a function of the small separation-interval a between a It is important to note that the difference between perigee and syzygy can be indicated either as an angular distance or in hours of time. Because of this dual quantification, the expressions separa- tion-time and separation-interval have both been used in this work — the first primarily in part II, chapter 4 and earlier where the time difference was critical, the second in the present chapter and later. The term separation-interval, while at first glance seemingly redundant, is actually the more meaningful, since its two elements are representative of either arc or time. these components, the increased lunar parallax, and the greater speed of the Moon in orbit. The angle of the Moon's orbital motion with respect to the Equator is also considered. As has been seen, all these factors are of con- sequence in the differentiation between perigee-syzygy situations of varying tide-maximizing ability. And it must be emphasized again in terms of a later discussion of hydrographic and oceanographic influences that purely astronomical data are involved in the general classifica- tion scheme for perigean spring tides which follows imme- diately below. (See also figs. 47A, B, C, D, and table 22.) 1. Maximum Perigean Spring Tides (or Ultimate- Maximum Proxigean Spring Tides) ; Maximum Proxigean Spring Tides The theoretically largest possible value of the geocen- tric horizontal parallax which the Moon can attain is 6T32.0" (see fig. 41 ) . The conditions necessary to achieve this very high parallax presume that the full moon shall be simultaneously at proxigee-syzygy, with l h separation- inteival, at one of the lunar nodes (i.e., coincident with the ecliptic, and with the Earth precisely at perihelion. (See pp. 203, 219.) Because this combination has not occurred any time in the past five centuries and will not occur again until A.D. 3300, it may be described as one of maximum perigean spring tides (or, for consistency in the present classification scheme, as an example of ultimate-maximum proxigean spring tides. The designa- tion of maximum proxigean spring tides is appropriately given to those astronomical tides produced under a condi- tion of proxigee-syzygy in which the resulting lunar paral- lax lies below its ultimate value, but within a range of 1 .3". The use of the word "proxigean" in preference to the word "perigean" to distinguish such cases of unusual close proximity of the Moon to the Earth results from the Table 22. — Proposed Classification System for Perigean (Including Proxigean) Spring Tides Range* in lunar geocentric hori- Definition zontal parallax at mean epoch of perigee-syzygy 1. Ultimate maximum proxigean spring tides 2. Maximum proxigean spring tides 3. Extreme proxigean spring tides 4. Proxigean spring tides 5. Perigean spring tides 6. Pseudo-perigean spring tides 7. Ordinary spring tides 61'32.0"±0.1" >61'30.7"<61'32.0' >61'29.0"<61'30.7' >61'21.0"<61'29.0' >60'20.0"<61'21.0' >59'00.0"<60'20.0' >55'00.0"<59'00.0' ♦Because of the complexity of dynamic forces and conditions present, some exceptions to these arbitrarily established parallax ranges may exist on the part of tides otherwise responding to the average daily amplitude variations which occur within these individual categories. 314 Strategic Role of Perigean Spring Tides, 1635-1976 JJJu, in - z J 5 z " -" O o J S " => o S ; ; ■ ».X.r ...?hS Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 315 degree of selectiveness of the Latin and Greek prefixes involved in these respective terms. In a secondary usage to its more familiar concept of "around" (i.e., "circum- scribing"), the Greek prefix peri also has a connotation of "near." The suffix gee (from the Greek ge) designates the Earth, so that the expression perigee properly implies nearness of the Moon to the Earth. In this sense, the word defines the point of the Moon's closest monthly approach to the Earth in its elliptical orbit around it. However, this single term permits no indication of the relative closeness of the perigee position itself which, as has been seen, may vary within significantly wide limits subject to solar perturbations. For more accurate nomen- clatural purposes, the suggested words "proxigee" and "proxigean," with prefix proxi from the Latin superlative form proximus meaning "nearest," connote both a posi- tion and an instant of unusual proximity of the Moon to the Earth. Without altering the time-honored concept of the word "perigee," the additional term "proxigee" allows for the more selective designation of a situation involving a particularly close perigee. Supplementary descriptive modifiers then complete the classification scheme. One factor of immediate note in this connection is that the use of the prefix proxi together with the suffix ge(e) brings a Latin and a Greek root immediately into apposition, a pro- cedure which might be frowned upon by those concerned with the origins and orthography of scientific terminology. An alternate choice for proxi might be the use of the prefix epi, which is itself a Greek root. However, because this prefix possesses such a wide range of possible meanings — including "on" (or "upon"), "at," "besides," "after," "over," "outer," and "anterior," all in addition to "near to" — it is not nearly as suitable, in a semantic sense, as is the prefix proxi. The prefix epi lacks in every way the fine points of distinction which go with the prefix proxi, whose exact meaning is so familiar both to scientific and general audiences in the words "proximal," "proximate," and "proximity." A thorough review of unabridged dictionaries and of words forming, for the most part, a complement of the international scientific vocabulary (ISV) reveals the very large number of early, middle, late, and new Latin words which have come down to the modern period from original Greek sources. Thus, in a very great number of cases, it would appear to be senseless to distinguish between their primary Latin or Greek origins, since the words have appeared, at the same or different times, in both languages with but slight modifications in spelling. Such words are definitely not peculiar to either language and their inter- lingual mixture should provide no major concern. To drive this point home, a brief summary (table 23) is appended herewith containing representative examples from among a large number of similar cases present among Eng- lish scientific and technical vocabularies. This abbreviated table shows clearly that — especially among the words of modern-day origin but formed variously from Greek, Latin, English, French, Spanish, and Arab roots — prefixes and suf- fixes are joined almost indiscriminately. This is particularly true of more recent additions to the scientific vocabulary where the restraints imposed by the origin of a word by any one country are no longer necessary. Table 23. — Examples of scientific and technical terminology in the English language involving interlingual combinations of prefixes peri/martium peri/jove peri/saturnium pseudo/conglomerate pseudo/fluorescence thermo/pile thermo/couple thermo/electric di/sulphide dyna/motor hyper/space auto/mobile meso/tron (meson) photo/electric hemi/demi/semi/quaver Latin-Middle {or Old) English sub/giant infra/red flux/gate multi/foil Satur/day counter/glow ultra/high (frequency) Latin-Arabic alt/azimuth (instrument) co-/azimuth Latin-Spanish (or Old Spanish) circum/zenithal (arc) super/cargo Latin-Greek semi/logarithmic co/logarithm super/adiabatic super/panchromatic non/mathematical extra/atmospheric bi/chloride bi/chromate bin/oxide bin/iodide electro/lyte electro/kinetics electro/phorus spectro/bolometer spectro/heliograph Latin-French (or Middle or Old French) electro/jet gravi/meter multi/stage French-Greek-Middle Latin kilo/par/sec Greek-French thermo/nuclear photo/gravure photo/montage micro/fiche Figure 47, A,B,C,D. — A comparison of four different astronomical configurations and alignments which result — both through the combined lunisolar gravitational force action and an increasingly more exact orientation between the lines of syzygies and apsides — in proportionately higher tides. In conjunction with table 22, a suggested classification scheme for various amplitudes of perigean spring tides is also represented by this composite chart. sift Strategic Role of Perigean Spring Tides, 1635-1976 Without in any way advocating the introduction of such a surficial inconsistency other than by the statement that the use of the prefix proxi in every logical way "belongs," it may readily be seen from the table that ample precedent exists for such apparently discrepant prefix-suffix combinations where the combination involved is more meaningful. It is important in consideration of the specialized and valuable roles of both chemical handbooks and unabridged dictionaries to include one further comment. Actually, if a true adherence to a consistent policy is used, such chemical radicals as chloride, chromate, oxide, or iodide, which origi- nate from Greek words designating the chemical elements chlorine, chromium, oxygen, and iodine, respectively, should possess the corresponding Greek prefix di rather than the Latin prefixes hi or bin(i) which they now have. Similarly, the word sulphide, originating from the Latin word for sul- phur should, for the sake of consistency, possess the Latin prefix bi instead of the Greek di. In the proposed new classification, the position of extraor- dinary recession of the Moon from the Earth along the line of apsides 180° from proxigee (either preceding or follow- ing) would be termed exogee (from the Greek prefix exo, meaning "far from" and suffix ge, "Earth") as the counter- part of apogee. It is emphasized that the preceding two classes of tide require the reinforcement of an extremely close proxigee- syzygy alignment by the other astronomical factors noted in the first paragraph of this section in order to achieve the maximum lunar parallax range cited, in excess of 61'30.7" (the upper limit of the next tidal category). This circumstance has occurred (at instants of proxigee) only 14 times in the past 376 years. Appropriately, there- fore, the use of the word "maximum" serves to distinguish between these tides produced by the combination of ex- tremely favorable circumstances and those belonging to the succeeding category of tides. By contrast, the tides of this next group are in no way related to the position of the Moon at a lunar node. They are, in fact, produced by an entirely different set of astro- nomical circumstances which results in an extraordinarily large value of the lunar parallax. As will be seen, these above-normal tides may be generated even with the Moon at rather high celestial latitudes, so long as it is in the same declination plane with the Sun. 2. Extreme Proxigean Spring Tides Of considerably more consistent, but still infrequent occurrence (see table 13) among the 400-year tabular printout represented by table 16 — and in no way follow- ing a regular chronological pattern — are those perigean spring tides which, for lack of any existing classification system are, in this volume, designated as extreme proxi- gean spring tides. In manner of dynamic origin, they possess certain of the same force-amplifying elements as those described in the preceding section. However, neither the lunar parallax produced, nor the accompanying astro- nomical tides, achieve the absolute maximum values as- sociated with this first category. Through an analysis of all cases recorded in the 400- year printout, the lunar parallaxes characteristic of this group range between > 61 '29.0" and <61'30.7". The greatest separation-interval between proxigee and syzygy encountered among the 39 examples bounded by these parallax limits in table 13 is ±5 h . Of considerable im- portance to the creation of the large parallax values, therefore, is the very consistent, close alignment of proxi- gee and syzygy in all cases. But a second, strongly contributing factor in this cate- gory of tides is the circumstances that the tide-raising forces of the Sun and Moon are also exerted in the same declinational plane in each example, thus reinforcing the gravitational effect of alignment in longitude between the two bodies at proxigee-syzygy. The result of these concurrent lunisolar alignments in two coordinates is to increase the eccentricity of the lunar orbit and thus also the lunar parallax. The proxigee distance of the Moon from the Earth is diminished in proportion. As indicated on page 199, the further location of the Moon at full moon and near solar perigee also play a significant role in this force-enhancing situation. Although the coplanar alignment of the Moon and Sun may ordinarily occur on either the same or opposite sides of the Earth, in the latter case the two bodies are 180° from each other, re- sulting in the force differences previously noted (see p. 214). Although the maximum negative solar declination (solstitial) is -23%°, as seen in table 13 such ap- proximately coplanar gravitational reinforcements can take place at slightly higher positive declinations of the Moon, especially when the nearly coplanar relationship occurs close to the time of perihelion. 3. Proxigean Spring Tides At about 18-month but irregular intervals of time, a more exactly commensurable relationship between the synodic and anomalistic months creates a separation- interval between perigee and syzygy which is considerably less than average. This in turn results in an especially close distance (here termed proxigee) of the Moon from the Earth and a substantially increased lunar parallax. The arbitrarily established values of the parallax for this category lie between < ei'26.5" and <61'29.0". The limiting value of the separation-interval is < 10 h . Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 317 As will be seen by comparison with the immediately succeeding category, a condition of proxigee-syzygy there- fore represents, by definition, a particularly close ap- proach of the Moon to the Earth and, by implication, in order to cause this, an unusually close alignment of peri- gee-syzygy. The tides of exceptional amplitude which result from this reduced distance of the Moon from the Earth and the correspondingly increased gravitational attraction of the Moon on the Earth's tidal waters — coupled with the pull of the Sun at syzygy — are referred to throughout this work as proxigean spring tides. In the computer printout (table 16) covering the 400-year pe- riod 1600-1999, a qualifying value of the parallax (at the time of proxigee ) and corresponding proxigee-syzygy situation occurs, based on an actual average, once in each 1 .46 calendar years. 4. Perigean Spring (or Perigee-Spring) Tides These are the technical expressions which traditionally have been used to designate tides (possessing approxi- mately 40 percent greater mean range) that result from any condition of near-alignment of perigee and syzygy. Either of these alternate terms as heretofore used collec- tively encompasses all of the other categories discussed in this list. For the purpose of the present classification, the term is confined to tides produced by an astronomical con- dition involving a relatively close, but not unusual align- ment of perigee-syzygy. If the separation-interval between perigee and syzygy is chosen as ± 24 hours, such tides oc- cur, on the average, three or four times in each tropical (ordinary) year. Two of the associated perigee-syzygy alignments are invariably closer than the other two, and the tides raised are slightly higher in these cases. Perigean spring tides could, therefore, be regarded as the generic model, of which the other examples included in the present classification system are special adaptations. This category — because of the far greater frequency in the number of cases represented which offer the possi- bility of simultaneous combination with strong, persist- ent, onshore winds — is responsible for by far the greatest number of cases of tidal flooding, but by no means the most severe cases, unless accompanied by a hurricane. As a matter of comparison, the separation-intervals and lunar parallaxes are given in tables 1 and 16, while news accounts of the relative severity of tidal flooding are provided for many cases in table 5. The predominance of major tidal floods at proxigee-springs and the greater frequency in the number of cases of tidal flooding at perigean spring tides are thus easily verified. The mechanism of production of this general category of perigean spring tide has been explained both in the Technical Commentary accompanying part I, chapter 1, and elsewhere throughout the work and need not be repeated here. The arbitrary limits of parallax for this category, established from a detailed analysis of table 1 6 as well as the tidal flooding events encountered in the present study, are from > 60'20.0" to <61'26.5". The perigee-syzygy separation-interval which seems optimally to represent the average situation in this category suscep- tible to tidal flooding (emphasizing again not the most severe cases) ranges from ^±10 h to ^dz36 h . The computer printout of table 16, with an upper limit of ±24 h , does not include all of the perigee-syzygy alignments within ±36 h responsible for perigean spring tides according to the present classification system. From an evaluation of the historic record, this particular cate- gory of tides — when accompanied by the appropriate winds — appears realistically to account for the great majority of cases of coastal flooding (exclusive of those caused by hurricanes). The addition of a 12-hour exten- sion to the present printout data over a period of 400 years would, however, make the list prohibitively long for publication. 5. Pseudo-Perigean Spring Tides This designation has been given in the present work to a group of tides whose perigee-syzygy interval lies just beyond the upper limit for perigean spring tides. How- ever, they are produced close enough to even a compara- tively wide alignment of perigee-syzygy to acquire some of the general characteristics of perigean spring tides in terms of increased amplitude and rapidity of tide growth. Some of the other tide-amplifying factors mentioned in previous chapters (such as coplanar alignment of Moon and Sun, etc.) may provide additional support to the weaker perigee-syzygy effects present. Given sufficiently strong and lasting accompanying onshore winds, some surprisingly high tides and asso- ciated coastal flooding events have occurred among the examples of this type of tides listed in tables 1 and 5. The parallax limits for this category have been set, for the purpose of consistency throughout this work, as be- tween >59'00.0" and <60'20.0". The corresponding separation-interval which seems best to define these cases is from ^ ±36 h to ^±84 h . Some few exceptions of an hour or so in excess of the upper limit have been permitted where the particular characteristics of the tide appear to dictate the logic of these minor extensions beyond the arbitrarily chosen limit. :;if. Strategic Role of Perigean Spring Tides, 1635-1976 6. Ordinary Spring Tides Finally, the category of ordinary spring tides is used to define that situation in which perigee is separated from syzygy by more than ±84 h and up to ±120 h . At a posi- tion more than 5 days away from perigee, an existing syzygy condition will generally converge toward, and be gravitationally weakened by, the increasing lunar distance at the immediately following or preceding position of apogee. An apogee-syzygy alignment ultimately results. The true spring tide, to be completely unaffected by the influence of either perigee or apogee (including factors consequent upon both the lunar distance and velocity in orbit) must be separated by the entire 5 days from perigee and approximately 8-9 days from apogee. (The interval between perigee and apogee is one-half of an anomalistic month, or 13.7774 days, but the Moon moves faster over the portion of its orbit closest to perigee and the distances from perigee and apogee are thus unequally divided in terms of time. ) The parallax limits for this category of tides correspond roughly to a range from >55'00.0" to <59'00.0". Periodic Relationships The various astronomical relationships governing rep- etition of the phenomenon of perigee-syzygy will now be discussed. The Mean Period Between Successive Occurrences of Perigee-Syzygy According to the origin selected from which to meas- ure the motion of the Moon, this body may have several different periods of revolution around the Earth. De- tailed explanations of the synodic and anomalistic months have been included on pages 126, 130 and will not be re- peated. The length of the synodic month is 29.530588 mean solar days. It is the period of time required for the mean moon to orbit from conjunction to conjunction, assuming it has a constant, average daily motion relative to the position of conjunction. However, this position is itself subject to small variations caused by perturbations in the lunar orbit, and the above period is an average for many circumstances, including the effects of parallactic inequality. The length of the anomalistic month is 27.554550 mean solar days. It represents the period of time it takes the Moon to revolve in its orbit from one perigee to the next. The anomalistic month is shorter than the synodic month because of the extra time required in the latter case for the Moon to catch up with the Earth's orbital motion in the same direction and to achieve an alignment in celestial longitude between the Earth, Moon, and Sun at times of new or full moon. The actual difference between the synodic month and the anomalistic month is 29.530588-27.554550=1.976038 mean solar days In consequence, once each synodic month, or lunation, the synodic month gains approximately 2 days on the anomalistic month. This means that, following a situation in which the Moon, Earth, and Sun are closely aligned at perigee-syzygy ( assumed, for this present case, to occur at new moon) the difference between the lengths of the anomalistic and synodic month will cause the positions of perigee and new moon to diverge gradually from each other. In each synodic month, the mean moon revolves through 360° of arc with respect to the position of con- junction, at an average rate of 360°/29.530588= 12.19074947°/day However, this mean daily motion of the Moon does not reveal the wide variations in the Moon's angular velocity previously discussed, and caused by parallactic inequal- ity, solar perturbations, and other factors. During each anomalistic month, the mean moon also revolves through 360° with respect to the position of perigee, at an average rate of 360°/27.554550= 13.064992907day Since this value has been observationally established, it includes the effect of an assumed mean revolutionary motion of the lunar line of apsides (and hence perigee itself) in the same direction as the revolutionary motion of both the Moon and Earth (seep. 177). The daily angular gain of the anomalistic revolution over the synodic revolution is 13.06499290°- 12.19074947° =0.874243437day Since the synodic period is 29.530588 days, at a time ap- proximately 0.5 month or 14.765294 days after new moon, full moon will occur. In this same 2-week period, the gain of the Moon's position over the line of apsides will be the equivalent of 0.87424343 °/day x 14.765294 days = 12.908461° which is less than one day's motion for the Moon. Subject to the previously stipulated conditions, the Moon, in its orbital revolution, cannot attain a position much more (and quite possibly less) than this amount ahead of the position of apogee. When the new moon occurs within less than a day of perigee, the succeeding full moon will Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 31V normally fall within less than a day of the next following apogee. The perturbational motion of the line of apsides itself may be disregarded as of minor consequence during this lunar half-revolution since, over this interval between perigee and apogee, the motion is partially forward and partially retrograde. For this daily gain to add up to the equivalent of one revolution of 360° requires 360°/0.87424343°/day = 41 1.7846216 days The full 411.78-day cycle is known as "the evectional period in the Moon's parallax," and since an early time has appeared variously throughout computational pro- cedures for the tides, in connection with the synodic periods of the semidiurnal and diurnal tidal constituents. (See, for example, page 163 in Manual of Harmonic Analysis and Prediction of Tides, USC&GS (NOS) Spe- cial Publication No. 98 ( 1941 ) ; also table 2 of "Auxiliary Tables for the Reduction and Prediction of Tides," page 1 94 in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1894, Part II) . This inter- val of 411.78 days represents the average period of time required for a perigee-syzygy alignment of Sun, Earth, and either new moon or full moon, once having been attained, to occur next again at the same phase. But since a near-concidence between perigee and syzygy which takes place at new moon results in a second close alignment between the line of syzygies and the line of apsides before the Moon returns to its new phase, suc- cessive occurrences of perigee-syzygy and apogee-syzygy alternate. Alignment of perigee and syzygy at new moon is followed by alignment of apogee and syzygy at full moon. At one perigee-syzygy alignment in each sequence, the two components converge toward a least separation. After this smallest separation-interval is attained, the interval increases with each lunation for some 3 months, then again decreases. Thus, the minimum time for a recurring near- coincidence between perigee and either conjunction or opposition is, on the average 411.7846216/2 = 205.892318 mean solar days (cf., table 39, "Synodic Periods of Constituents," in Manual of Harmonic Analysis and Prediction of Tides.) This average period of time assumes that the mean values for the synodic and anomalistic months previously specified possess a constant and invariant value. The lengths of these individual lunar months actually vary considerably. As has been noted in chapter 6, those syn- odic and anomalistic months which contain the phenom- enon of perigee-syzygy are the longest, but with the anomalistic months increasing considerably more than the synodic months under such circumstances (see table 17). During those anomalistic months whose lengths are in- creased to more than 28.5 days by virtue of a close perigee- syzygy alignment, the mean motion of the Moon is reduced to 360°/28.5° or 12.6° per day with respect to the mean position of perigee. (In the remaining anomalistic months of the lunar year, whose lengths are usually >1 to <5 days shorter than the synodic month, the mean motion of the Moon with respect to perigee varies from about 12.7° to 14.5° per day, on the average.) The previously noted daily angular gain of the anomalistic month over the synodic month is thus decreased from 0.87°/day to 0.5° /day at times of close perigee-syzygy alignments. Because the daily angular gain of the anomalistic mo- tion over the synodic motion is less, the lengths of the corresponding months come more nearly into agreement. In addition, the length of time required for this daily gain to add up to the equivalent of one full revolution of 360° is greater, and the actual minimum period between the closest occurrences of perigee-syzygy is shortened with re- spect to the previously computed mean value of 205.- 892318 mean solar days. This conforms with the observed facts (see table 17). It is also important to note that, for reasons explained in chapter 6, once the position of perigee-syzygy occurs with a minimum separation in time between the two components, it may be accompanied in immediately preceding or following months by similarly close, but gradually diverging, perigee-syzygy alignments. These will, as a rule, take the form of wider spaced perigee-syzygy or pseudo-perigee-syzygy situations. It has been established above that, subject to an as- sumed constant angular speed of separation, a period of 41 1.78462 days is required for the position of perigee, continuously falling behind the position of conjunction, to complete a full revolution of 360° around the lunar orbit. At the end of this period, any previously existing coincidence between perigee and conjunction will repeat itself again, but will not usually occur a second time in succession according to this exact time interval. Because there are numerous disturbing influences affecting the Moon's orbital motion, the immediate repetition of this cyclical period will usually be broken. Short-Period Cycles of Repetition of Perigean Spring Tides It is obvious that, from the standpoint of winter storms, the greatest astronomically induced potential for tidal flooding will exist in those years in which the calendar 320 Strategic Role of Perigean Spring Tides, 1635-1976 arrangement of near-coincidences between perigee and syzyzy permits the greatest number to occur within the most common period of winter storms from November 1 to April 1 . The exact number of occurrences of perigean spring tides in any one year (3-5 having a perigee-syzygy separation-interval of ±24 h ) is a function of the number of close alignments between perigee and syzygy in that calendar year. The number of these close alignments is, in turn, a function of the slow but continuous revolution of the line of apsides (connecting the positions of perigee and apogee) around the Earth in a period of 3,231 days (8.85 years). Other controlling factors include the Moon's revolution around the Earth from perigee to perigee in a period of 27.554550 days, the lunar revolu- tion from new moon to new moon in 29.530588 days, the apparent motion of the Sun around the Earth in an ordi- nary (tropical) year of 365.242199 days, and certain additional astronomical variables. The numerical inter- relationships between these various periods determine the frequency of occurrence of the different classifications of perigee-syzygy alignments. As the result of the relative movements of the Earth, Moon, and Sun, the repetition of tides of similar phase and amplitude — including those of perigean spring origin- — takes place in certain well-defined periods averaging 28.981403, 162.502866, 191.484268, 355.022184, and 384.003587 days," as well as in the previously discussed astronomical cycle of 205.892318 days representing the average motion of perigee around the Earth. Various com- binations of these cycles also occur (e.g., 28.981403 + 162.502866=191.484269 days). The 205.892318-day cycle is the principal one affecting perigean spring tides; the others are subordinate. As has been evidenced in chapter 6, a considerable deviation is present between the lengths of the actual and mean values of both the anomalistic and synodic months in those months containing a close perigee-syzygy align- ment. The magnitude of this deviation increases as the separation-interval becomes smaller. Accordingly, any as- sumed value involving an average period of time between perigean spring tides also will least adequately represent the actual period between these tides when the perigee- syzygy alignments are especially close. The deviation from a mean period also will be the greatest, percentagewise, " Cf., R. A. Harris, Manual of Tides, part V, Currents, Shallow- Water Tides, Meteorological Tides, and Miscellaneous Matters, as Appendix No. 6 in the annual Report of the Superintendent of the Coast and Geodetic Survey for 1907, Washington, D.C., U.S. Government Printing Office, 1908, p. 492. over short periods of time (e.g., one recurring cycle) . Over longer periods, the effect of individual variations will more nearly average out, and a comparison of the actual and the mean intervals of time between perigee-syzygy align- ments will show smaller residuals. The assumed periodic relationships will, for the same reason, more nearly apply. Thus, the mean epoch of the proxigee-syzygy alignment of 1974 January 8.49 (e.t. ), is connected through the 205.89-day perigee cycle (2X205.89=411.78 days) with a proxigean spring tide occurring on 1972 Novem- ber 20.98 (e.t. ) (a Julian Day difference, at mean syzygy, of dt=413.40) . In the chain of cyclical interrelationships, the January 8.49 date is also directly related through the 205.89-day cycle (21X205.89=4,323.7 days) with another proxigean spring tide associated with the proxi- gee of 1962 March 6.375 (e.t.) (dt=4,326.2), in which the extraordinary high waters were further augmented by an intense, wind-driven storm surge to produce extensive flooding along the mid- Atlantic coast (see item 4, later in this chapter). The 1972 November 20.98 proxigee-syzygy date like- wise forms an integral number of multiples of 205.89 (15X205.89=3,088.4 days) with a close perigean spring situation on 1964 June 10.08 (e.t.) (dt=3,086.0 days). Coastal flooding associated with perigean spring tides occurred at Atlantic City, N.J., on 1967 April 27 and December 3, near the mean perigee-syzygy dates April 24.15 and December 1.13 (e.t.). These dates are sepa- rated by a 221.98-day period, which is approximately equivalent to one 191.48- and one 28.98-day cycle (the sum=220.46 days). Similarly, all four of the previously mentioned perigee- syzygy dates form part of a long-period astronomical re- lationship extending backward over 31.010 tropical years (11,326 days) or 55 cycles of 205.89 days (11,324 days). These individual perigee-syzygy dates in 1974 are almost exactly repeated at the end of this long cycle, in each case only 2 calendar days after the perigee-syzygy dates which occurred 3 1 years previously on 1 943 Janu- ary 6, February 4, July 17, and August 15. More will be said concerning this 31 -year period in the immediately following section. Over an even longer period, the four dates of proxigean and perigean spring tides in 1974 also are commensurate with (i.e., an integral number of cycles removed from) proxigean spring tides which were accompanied by severe flooding along the New Jersey coast on 1861 November 2, 113 years earlier (see page 78). The 1861 November 2.69 (G.m.t.) date is separated (dt=40,973.7 days) Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 321 from the 1974 January 8.49, (e.t.) date by 199 cycles of 205.892318 days (total 40,972.6 days). And, as a final example in this representative list, there are 225 cycles of 162.50 days, plus 3 cycles of 28.98 days (total =3 6, 649 .4 days) between the 1861 November 2.69, (G.m.t.) proxigee-syzygy date and that of 1962 March 6.375 (e.t.), accompanied by severe flooding 101 years later (dt=36,647.5 days). The 31 -Year Cycle of Perigee-Syzygy A very significant relationship exists in the 3 1 -year cycle of iteration which governs close perigee-syzygy align- ments. For greater emphasis on the meaning of this re- lationship in terms of recurrent tidal flooding, the astro- nomical factors responsible for a periodicity in tidal ex- tremes will be established by an analysis of ephemeris data. This will be followed by correlations between the cyclical data obtained and examples of repeated coastal flooding from past history. Coincidentally, in followup to a previous section, consideration will be given to the unusually hazardous flooding situation which prevails whenever landfalling hurricanes occur on the same dates as those on which markedly elevated perigean tides exist. Because of the inherent danger for extreme coastal flood- ing produced by the combination of a hurricane plus proxigean or perigean spring tides, this becomes an es- pecially critical aspect in evaluating tidal flooding poten- tial. It has been established over a long period of record that the month in which the greatest frequency of hurri- canes occurs on the Atlantic coast of North America is September. In order to make possible the determination of any desired statistical probability of occurrence incorpo- rating this double threat of hurricanes and high tides, a compilation is included in table 24 of all cases of proxigee- syzygy or perigee-syzygy (P — S<±24 h ) occurring be- tween 1600 and 1999 in the month of September. In con- sequence of the purely astronomical factors expressed in this table, the augmented tide levels resulting are vulner- able to any type of intense offshore coastal storm occurring in this month. The resulting susceptibilities to tidal flood- ing apply, therefore, to either hurricanes or winter storms. Although the data are tabulated for the single month of September, the purpose of this tabulation is to discover the cyclical relationships between successive close perigee- syzygy alignments, regardless of their calendar positions. The periodicities revealed may involve any month of the year, depending upon which month is selected as a start- ing point and whether the repeating cycles are exactly in- tegral ones. In table 24, col. 1 contains the date of syzygy; col. 2 fists the corresponding Julian Date, including in order that the differences between successive dates of syzygy may be taken over long periods without involving the com- plexities of calendar months; those successive differences are tabulated in col. 3. Finally, assuming a synodic month having a mean period of 29.530589 days, col. 4 indicates the corresponding number of synodic months represented by the figure in col. 3. Cols. 5, 6, and 7 repeat the same data for the time of perigee. Some interesting facts emerge from the detailed analysis of this table, and the investiga- tion of the anomalistic period is particularly productive. Table 24. — Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments Calendar date of syzygy Julian date of syzygy Difference between syzygy dates (days) No. of synodic cycles (to nearest 0. 1 ) Julian date of perigee* Difference between perigee dates (days) No. of anomalistic cycles (to nearest 0.1) 9/ 5/1603 2306791. 2 383.8 13.0 2306791. 384.8 14.0 9/23/1604 2307175.0 1077. 9 36.5 2307175.8 1076. 2 39.1 9/ 6/1607 2308252. 9 383.9 13.0 2308252. 384.9 14.0 9/24/1608 2308636. 8 1461.8 49. 5 2308636. 9 1461. 1 53.0 9/24/1612 2310098. 6 1816. 1 61.5 2310098. 1817. 3 66.0 9/15/1617 2311914. 7 1461. 8 49.5 2311915.3 1461.2 53. 9/15/1621 2313376. 5 1461. 7 49.5 2313376. 5 1460. 9 53. n 9/16/1625 2314838. 2 1816.2 61.5 2314837. 4 1817.5 66. See footnote at end of table. 202-509 O - 78 - 23 322 Strategic Role of Perigean Spring Tides, 1635-1976 Table 24. — Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments — Continued Calendar date Julian of syzygy date of syzygy Difference between syzygy dates (days) No. of synodic cycles (to nearest 0.1 ) Julian date of perigee : Difference No. of anomalistic between perigee cycles (to dates (days) nearest 0.1) 9/ 6/1630 2316654.4 2316654. 9 146. 17 49.5 1461.0 53.0 9/ 7/1634 2318116. 1 2318115.9 383.9 1 5. 384.8 14. 9/26/1635 2318500.0 2318500. 7 1077. 9 36. 5 1076. 3 39. 1 9/ 8/1638 2319577. 9 2319577.0 383.9 13.0 384.0 14.0 9/27/1639 2319961.8 2319961.8 1461.8 49. 5 1461.2 53.0 9/27/1643 2321423. 6 2321423. 1861. 1 61.5 1817. 3 66.0 9/17/1648 2323239. 7 2323240. 3 1461.8 49.5 1461. 1 53.0 9/17/1652 2324701. 5 2324701. 4 1461. 7 49.5 1461.0 53. 9/18/1656 2326163. 2 2326162. 4 1816. 1 61. 5 1817. 3 66.0 9/ 8/1661 2327979. 3 2327979. 7 1461.8 4-9. 5 1461.9 53.0 9/ 9/1665 2329441. 1 2329440. 9 383.9 13.0 384.8 14.0 9/28/1666 2329825. 2329825. 7 1077.9 36.5 1076. 2 39. 1 9/10/1669 2330902. 9 2330901. 9 383.9 13.0 384.9 14.0 9/29/1670 2331286.8 2331286. 8 1461. 7 49. 5 1461. 1 53.0 9/29/1674 2332748. 5 2332747. 9 1432. 3 48.5 1432. 6 52. i) 9/ 1/1678 2334180. 8 2334180. 5 383.9 13.0 384. 7 14.0 9/20/1679 2334564. 7 2334565. 2 1461. 7 49. 5 1461. 1 53.0 9/20/1683 2336026. 4 2336026. 3 1461.8 49. 5 1461. 1 53.0 9/21/1687 2337488. 2 2337487. 4 1816. 1 61.5 1817. 3 66.0 9/10/1692 2339304. 3 2339304. 7 1461.8 49.5 1461. 1 53.0 9/11/1696 2340766. 1 2340765. 8 383.9 13.0 384.8 14.0 9/30/1697 2341150.0 2341150.6 1432. 2 48.5 1432. 6 52.0 9/ 2/1701 2342582. 2 2342583. 2 1461.8 49.5 1461. 1 53.0 9/ 3/1705 2344044. 2344044. 3 1461.8 49. 5 1461. 1 53.0 9/ 4/1709 2345505. 8 2345505. 4 383.9 13.0 384.8 14.0 9/23/1710 2345889. 7 2345890. 2 1461. 7 49. 5 1461. 1 53.0 9/23/1714 2347351.4 2347351. 3 1461.8 49.5 1461. 1 53.0 9/24/1718 2348813.2 2348812.4 1816. 1 61.5 1817. 3 i,i,. ii 9/14/1723 2350629. 3 2350629. 7 1461.8 49.5 1461. 1 53.0 See footnote a end of table. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 323 Table 24. — Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments — Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anomalistic of syzygy date of syzygy between syzygy cycles (to date of perigee* between perigee cycles (to dates (days) nearest 0.1 ) dates (daysl nearest 0.1 ) 9/15/1727 2352091. 1 2352090. 8 1816. 1 61.5 1817.4 66.0 9/ 4/1732 2353907. 2 2353908. 2 1461.8 49. 5 1461.0 53.0 9/ 5/1736 2355369. 2355369. 2 1461. 7 49. 5 1461. 1 53.0 9/ 6/1740 2356830. 7 2356830. 3 383. 9 13.0 384.8 14.0 9/25/1741 2357214. 6 2357215. 1 1461.8 49. 5 1461. 1 53.0 9/25/1745 2358676. 4 2358676. 2 1461.8 49.5 1461. 1 53. 9/26/1749 2360138.2 2360137.3 1816. 1 61.5 1817. 3 66.0 9/16/1754 2361954. 3 2361954. 6 1461.8 49.5 1461. 2 53.0 9/17/1758 2363416. 1 2363415.8 1816. 1 61.5 1817. 3 66.0 9/ 7/1763 2365232. 2 2365233. 1 1461.8 49. 5 1461. 1 53.0 9/ 8/1767 2366694. 2366694. 2 1461. 7 49. 5 1461.0 53.0 9/ 9/1771 2368155. 7 2368155.2 383.9 13.0 384.8 11. 9/27/1772 2368539. 6 2368540. 1461.8 49.5 1461. 2 53. 9/27/1776 2370001.4 2370001. 2 1461. 7 49. 5 1461.0 53. 9/28/1780 2371463. 1 2371462. 2 1816. 2 61. 5 1817.4 66.0 9/18/1785 2373279. 3 2373279. 6 1461. 7 49.5 1461. 1 53.0 9/19/1789 2374741.0 2374740. 7 1816.2 61. 5 1817.4 66. 9/9/1794 2376557. 2 2376558. 1 1461. 7 49. 5 1461.0 53. " 9/10/1798 2378018. 9 2378019. 1 1461.8 49. 5 1461. 1 53.0 9/11/1802 237C480. 7 2379480. 2 1816. 1 61.5 1817.4 66. 9/ 2/1807 2381296. 8 2381297.6 1461.8 49.5 1461.0 53. 9/ 2/1811 2382758. 6 2382758. 6 383.9 13.0 384.9 14.0 9/21/1812 2383142. 5 2383143. 5 1077.9 36. 5 1076. 3 39. 1 9/ 3/1815 2384220. 4 2384219. 8 383.9 13.0 384. 5 14.0 9/21/1816 2384604. 3 2384604. 3 1461. 7 49.5 1461.3 53.0 9/22/1820 2386066. 2386065. 6 1816. 1 61. 5 1817.4 66.0 9/12/1825 2387882. 1 2387883. 1461.8 49.5 1461.0 53.0 9/13/1829 2389343. 9 2389344. 1 1461.8 49.5 1461. 1 53.0 9/13/1833 23£0805. 7 2390805. 2 1816. 1 61.5 1817.3 66.0 See footnote at end of table. 324 Strategic Role of Perigean Spring Tides, 1635-1976 Table 24. — Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments — Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anomalistic of syzygy date of syzygy between syzygy cycles (to date of perigee* between perigee cycles (to dates (days) nearest 0.1 ) dates (days) nearest 0.1 ) 9/ 4/1838 2392621.8 2392622. 5 1461.8 49. 5 1461. 1 53.0 9/ 4/1842 2394083. 6 2394083. 6 383.9 13.0 384.9 14. 9/23/1843 2394467. 5 2394468. 5 1077. 8 36.5 1076. 1 39. 1 9/ 5/1846 2395545. 3 2395544. 6 383.9 13.0 384.9 14. 9/24/1847 2395929. 2 2395929. 5 1461.8 49. 5 1461. 1 53.0 9/25/1851 2397391.0 2397390. 6 1816. 1 61.5 1817.3 66. o 9/14/1856 2399207. 1 2399207. 9 1461.8 49.5 1461. 1 53.0 9/15/1860 2400668. 9 2400669. 1461.8 49.5 1461. 2 53.0 9/15/1864 2402130. 7 2402130.2 1816. 1 61.5 1817.3 66.0 9/ 6/1869 2403946. 8 2403947. 5 1461.8 49. 5 1461. 1 53.0 9/ 6/1873 2405408. 6 2405408. 6 383.9 13.0 384.8 14.0 9/25/1874 2405792. 5 2405793. 4 1077.8 36.5 1075. 9 39.0 9/ 7/1877 2406870. 3 2406869. 3 383. 9 13.0 385. 2 14. 9/26/1878 2407254. 2 2407254. 5 1461. 8 49.5 1461. 1 53.0 9/27/1882 2408716.0 2408715. 6 1816. 1 61.5 1817. 3 66.0 9/17/1887 2410532. 1 2410532. 9 1461. 8 49. r > 1461. 1 53.0 9/18/1891 2411993.9 2411994.0 1461. 7 49.5 1461. 1 53. 9/18/1895 2413455.6 2413455. 1 1816.0 61. 5 1815.9 65.9 9/ 9/1900 2415271. 6 2415271.0 1461.9 49. 5 1462. 5 53. 1 9/ 9/1904 2416733. 5 2416733.5 383. 9 13.0 384.8 14.0 9/28/1905 2417117.4 2417118. 3 1077. 9 36.5 1076. 2 39. 1 9/10/1908 2418195. 3 2418194.5 383.9 13.0 384.9 11. 9/29/1909 2418579. 2 2418579.4 1461. 8 49.5 1461. 1 53.0 9/30/1913 2420041.0 2420040. 5 1432. 2 48.5 1432. 5 52.0 9/ 1/1917 2421473. 2 2421473.0 383.9 13.0 384. 9 11. (i 9/20/1918 2421857. 1 2421857. 9 1077.9 36.5 1076. 2 39. 1 9/ 2/1921 2422935. 2422934. 1 383.9 13.0 384.9 14.0 9/21/1922 2423318.9 2423319.0 1461. 7 49.5 1461.0 53.0 9/21/1926 2424780. 6 2424780. 1816.2 61.5 1817.4 66.0 Sec footnote :\\ ■nd of table. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 325 Table 24. — Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments — Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anomalistic of syzygy date of syzygy between syzygy cycles (to date of perigee* between perigee cycles (to dates (days) nearest 0. 1 ) dates (days) nearest 0.1) 9/12/1931 2426596. 8 2426597. 4 1461. 7 49.5 1461. 1 53.0 9/12/1935 2428058. 5 2428058. 5 383.9 13.0 384. 7 14.0 9/30/1936 2428442. 4 2428443. 2 1077. 9 36.5 1076. 3 39. 1 9/13/1939 2429520. 3 2429519. 5 1816. 1 61.5 1817.4 66.0 9/ 2/1944 2431336.4 2431336.9 1461. 8 49.5 1461. 1 53.0 9/ 3/1948 2432798. 2 2432798. 383.9 13.0 384.8 H 9/22/1949 2433182. 1 2433182. 8 1077. 8 36.5 1076. 2 39. 1 9/ 4/1952 2434259. 9 2434259. 383. 9 13.0 384.8 14.0 9/23/1953 2434643. 8 2434643. 8 1461. 8 49.5 1461.2 53.0 9/23/1957 2436105.6 2436105.0 1816. 1 61. 5 1817. 3 66.0 9/14/1962 2437921. 7 2437922. 3 1461.8 49.5 1461. 1 53.0 9/14/1966 2439383. 5 2439383. 4 1461.8 49.5 1461. 1 53.0 9/15/1970 2440845. 3 2440844. 5 1816. 1 61.5 1817. 3 66.0 9/15/1975 2442661. 4 2442661. 8 1461. 8 49.5 1461. 2 53.0 9/ 6/1979 2444123. 1 2444123.0 383. 9 13.0 384.8 1 4. 9/24/1980 2444507. 1 2444507. 8 1077. 8 36.5 1076. 1 39. 1 9/ 7/1983 2445584. 9 2445583. 9 383. 9 13.0 384.9 14.0 9/25/1984 2445968. 8 2445968. 8 1461.8 49.5 1461. 1 53.0 9/25/1988 2447430. 6 2447429. 9 1816. 1 61.5 1817.3 66.0 9/16/1993 2449246. 7 2449247. 2 1461. 8 49.5 1461.2 53.0 -9/16/1997 2450708. 5 2450708. 4 *Note: It has been seen (part II, chapters 3, 4) that certain lunar perturbations are especially critical at times of perigee-syzygy. During the early course of the research for this project, it was discovered that the utilization of a substantial and presumably quite sufficient number of reduc- tion terms among the theoretical expressions for solution of the Moon's orbital position and motion was still quantitatively inadequate. The insuffi- ciency lay in the determination of geocentric horizontal parallax and the times of perigee and syzygy to the accuracy required for consistency with ephemeris data. A corresponding computer reprogramming was introduced, expanding from the partial sequence of analytic terms in table 16A to the full complement of terms given in table 16B. All tables in this monograph involving lunar positions and motions — including the data displayed in the computer printout of table 1 6 — are now based either upon the full reduction expressions contained in table 1 6B, or upon The American Ephemeris and Nautical Almanac. However, table 24 already had been typeset from data computed on the basis of the initial, smaller number of analytic terms. The time differ- ences, perigee minus syzygy, may occasionally vary from 1-3 hours between the solutional accuracies of the short and long methods, if the individual differences are additive in the same direction. Thus the Julian dates of perigee in table 24 (which, as throughout this work, are represented as a function of their intervals from syzygy) may, in some few cases, differ by 0.1-0.2 d from the more precise data obtainable from table 16. Because such slight differences do not materially affect the average values of the long-range cycles of recurrence of perigee-syzygy listed in table 24, these original values calculated from a smaller number of analytic terms have not been altered. The periodic relationships present are quite readily apparent. 326 Strategic Role of Perigean Spring Tides, 1635-1976 The various repeating cycles of anomalistic months between successive perigee-syzygy dates as given in col. 7 are: 14.0, 39.1, (52.0 or 53.0), and 66.0. Assigning each cycle a serial number in this same sequential order it is obvious that, with some few interruptions and irregulari- ties (i.g., wherever 52 instead of 53 cycles occur), the two principal cycles which are systematically repeated are 1-3-3-4-3-4-3-3 and 1-3-4-3-3-4-3-1-2. Adding the total number of cycles contained in each of these repeating series gives 41 1 .0 and 411.1 anomalistic months, respectively. The average between these two values is equivalent to 1 1,326 mean solar days or 31.010 tropical years. As noted in the preceding section, this is also very nearly equivalent (11,324 days) to 55 cycles of the 205.89-day average period between ordinary peri- gee-syzygy alignments. Using this 31 -year cycle, it is now possible to establish an interesting relationship connecting several of the very major tidal floodings on the east coast of North America (see table 1 ) which have occurred at times of large paral- lax ( it) and close perigee-syzygy separations (P— S). These cases are starred in the list below. Table 25. — Cases of Extreme Tidal Flroding Coincid'ng With Long-Term Astronomical Cycles of Close Alignment Between Perigee and Syzygy Lunar Date „. «2P> Strategic Role of Perigean Spring Tides, 1635-1976 weather maps and published newspaper reports relative to the flooding are provided in this work — and two ( F-68 and O-100), supplemented by newspaper excerpts but no tide curves — appear separately in this chapter, where a detailed discussion of these major tidal flooding events is presented. Tide curves for other outstanding examples of coastal flooding (D-57 and E-58) for which news accounts are available — but this time with the omission of the full-page weather maps — are also included in chap- ter 8. Both a weather map and tide curves are published for K-87 in the text, but because of the widely scattered and unusual nature of this event, U.S. Weather Bureau sources are used, and news articles are not included in table 5. Satellite cloud-cover photographs taken by night- infrared and day-infrared cameras are also provided for event N-99. The Correlation of Meteorological and Astronomical Data As has been noted in both the first and present chapters of this work, meteorological factors may act either to sup- port, or to reduce, the effects of astronomically induced tides. Because of the large area of coastal coverage, pro- vided by synoptic weather maps, including the adjoining oceans and ship weather reports, these offer the most con- venient means of determining both the continental and marine pressure and wind patterns in existence at the time of perigean spring tide. The daily synoptic weather maps of the United States used as data sources through- out this work are copies of those compiled and published by the U.S. Weather Bureau (since October 3, 1970, the National Weather Service) as a part of its forecasting analysis and historical record series. The oversize printed maps in all cases have been photographically reduced, and appropriate overlays and spellouts have been applied to emphasize the critical factors of wind direction and velocity (and the movement of relevant low pressure atmospheric pressure systems) as these variously affect the potential for tidal flooding in connection with peri- gean spring tides. GROUPING OF THE WEATHER MAPS The series of synoptic weather maps contained on the following pages consists of four distinct sections, within each of which the maps are chronologically arranged: (a) The first section consists of 20 weather maps show- ing — as closely as can be correlated — the meteorological conditions accompanying a randomly selected group of ex- amples of major tidal flooding. These were observed along either the east or west coasts of North America (or on both coasts, simultaneously). Each such instance of coastal flood- ing represented was associated with the perigean spring tides which occurred on, or very near to, the date of one of these weather maps. The group of weather maps contained in table 26 there- fore involves actual coastal flooding events in which (1) close perigee-syzygy alignments (and resulting perigean spring tides) as well as (2) strong, sustained, onshore winds (usually generated by offshore low pressure centers) joined to become the cause of coastal flooding. As in all examples used, the incidents of tidal flooding were selected, without any systematic predetermination, from the catalog of 100 such representative events compiled in part I, table 1 of chapter 1. (b) A second, control group of 20 weather maps in table 27, chosen with equal randomness in each decade through- out the same 90-year period, show the meteorological condi- tions at times of extreme close perigee-syzygy alignments. The factors producing perigean spring tides also were se- lected to include a variety of solar and lunar positional relationships representative of significant tide-amplifying forces and inequalities, as described in chapter 5. These different circumstances are listed in the "Remarks" column of the table. The resulting astronomical tides were, as in the first series of examples, raised to unusual levels, but no pronounced flooding was observed in these cases, due to the complete absence of persistent, strong, onshore winds at the time. The weather situations portrayed in this category are generally dominated by large high pressure systems, in which wind conditions ranging from light and variable breezes to a complete calm are common. The associated high baro- metric pressure and/or offshore winds are both counter- productive to the generation of additionally augmented and flood-producing high tides. (c) Although, for reasons given in part I, chapter 1, the consideration of coastal flooding resulting from the impact of hurricanes does not form a major part of the present investigation, a few appropriate weather maps depicting conditions in which hurricanes have quite closely coincided with perigean spring tides are included in table 28a. Together with the accompanying explanation in the text of the present chapter, these examples will help to substan- tiate the role of perigean spring tides, when acted upon by the onshore winds of a hurricane. The result is, by com- parison, a much greater amount of water damage through tide-supported flooding — in addition to the hurricane-in- duced wind damage — whenever such hurricanes occur near the times of perigean spring tides. In an example at the opposite end of the scale, a typical case is also included in table 28b in which the unusually high waters associated with perigean spring tides — because of the influence of strong, onshore winds — became a major factor in blocking hydrological runoff. Quite numerous in- stances exist in which exceptional perigean spring tides (even without the support of onshore winds) have, through such blocking action, variously caused, contributed to, or severely aggravated coastal flooding associated with surface runoff of heavy rainfall — or melting ice and snow. A num- ber of such examples are considered in the text. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ., 2U (d) Finally, a special series of eight weather maps repre- senting, like those in table 26, cases in which perigean spring tides accompanied by strong, persistent, onshore winds have caused prominent coastal flooding, are listed in table 29. Together with four other examples of major tidal flooding, they are of sufficient importance or uniqueness to be discussed individually in the text of this chapter. Tables 26-29 thus list the weather maps available in each of the above four groups. Immediately following the pres- ent discussion, a set of Explanatory Comments is provided summarizing the various symbols, descriptors, and techni- cal data used on these synoptic weather charts. To determine the full implication of all meteorological factors, reference also should be made to the text and cross-related graphic materials of this and other chapters for the following per- tinent topics: (a) the practical effects of strong, sustained, onshore winds in driving the amplified waters of perigean spring tides onto the coastline (chapter 7) ; (b) the value of coordination and intercomparison of these weather maps with the computed rate-of-growth tide curves illustrating the astronomically induced, rapid rise in water level at time of perigee-syzygy which provides a natural setup condition for wind-actuated onshore flooding (chapter 8) ; and (c) the possibility of assessing and grading the violence of the coastal flooding resulting from the combination of perigean spring tides and onshore winds by means of contemporary newspaper accounts of the damage produced, as given in table 5 (part I, chapter 1 ) . EXPLANATORY COMMENTS CONCERN- ING THE MANNER OF DESIGNATION OF WEATHER MAPS AND THE CON- CURRENT PERIGEE-SYZYGY DATA The number in the upper left-hand corner of each weather map is a serial number for ease in chronological comparison and evaluation of these maps. All maps con- tain such a serial number. In addition, some of the weather maps are designated by a capital-letter prefix. This is a key letter, to allow a ready intercomparison of a variety of data — in some cases located at different places in the book — but all pertaining to the same example of tidal flooding. Only significant cases of tidal flooding which are the subject of detailed investigation in the present work are designated by a key letter. In this system of computation of standard comparative data for master cases, one such example of coastal flooding associated with perigean spring tides has been chosen, at random, in each decade from 1910 (at which time 37 harmonic components replaced the previous 19 in Coast and Geodetic Survey tidal computations) down to 1970. These sample cases have purposely been selected on both coastlines of North America, representing both semi- diurnal and mixed tides, and distributed throughout a wide range of latitudes as well as varying astronomical, hydro- graphic, climatological, and meteorological conditions. Appropriate tide curves based on predicted tide heights at appropriate nearby tidal reference stations, and showing the accelerated rate of tide growth subject to the influence of perigee-syzygy, have been prepared in figs. 153-163 (table 33) for 16 prototype examples of tidal flooding. These are presented, together with an appropriate discussion thereon, in chapter 8. The corresponding daily synoptic weather map for many of these cases is included in a grouped series of maps fol- lowing these comments (table 26), or may individually accompany the detailed discussion of representative exam- ples of major tidal flooding contained in the text of this chapter (table 29) . In addition, a compilation of newspaper articles covering 50 of the 100 representative cases of major tidal flooding itemized in table 1 graphically describes the extent of the coastal flooding occurring in conjunction with these various cases of perigean spring tides. The latter com- pilation comprises table 5 of part I, chapter 1. The procedure previously mentioned — involving a ran- dom sampling of the tremendous quantities of meteorologi- cal and tidal data available — makes practicable a coordi- nated investigation of the various related, interdisciplinary factors which enter into such cases of tidal flooding. This analysis is expedited through the intercomparison of those various sources of data which, because of their common rela- tionship in time, bear the same alphanumeric designation in the various index lists (tables 1-5, 26, 27, 28a,b, 29, 33). The first date given (in roman type) in the upper right- hand corner of each weather map is the date of the weather map; each map has been chosen to accord as nearly as possible with the date on which coastal flooding occurred. The calendar date is immediately followed by the eastern standard time (e.s.t.) for which the weather map is plotted. [Subtract 3 hours to obtain Pacific standard time (P.s.t.) for cases of flooding on the west coast ; Greenwich civil time (G.c.t.) may be obtained by adding 5 hours to e.s.t.] The second entry (in italics) gives the date and time (e.s.t.) of mean perigee-syzygy; this mean epoch of perigee- syzygy for any occurrence is obtained by taking half the difference between the respective times of perigee and syz- ygy — in the sense perigee minus syzygy — and adding the re- sult algebraically to the time of syzygy. All time values are rounded off to the nearest hour. The last number, in paren- theses, gives the algebraic difference in time, in hours, be- tween perigee and syzygy (likewise taken in the sense perigee minus syzygy ) . Cases in which the difference in time between perigee and syzygy is less than 24 hours are tabulated in the com- puter printout (table 16). In this table, the times are given for syzygy (plus an additive or subtractive value, in hours, to give the time of perigee) . All times given are in ephemeris time (e.t.) — which corresponds very closely with, and for the present purpose may be assumed to be equal to, Green- wich civil time (G.c.t.). Although the times used (imme- diately following the date) have been consistently rounded off to the nearest hour, they are sufficiently accurate for reference use in connection with these weather maps. Wherever the separation-interval between perigee and syzygy is equal to, or greater than 24 hours, the difference has been taken from The American Ephemeris and Nautical Almanac, or from astronomical data contained in annual tide tables. All such values are similarly rounded off to the nearest hour, since the time of perigee is now customarily given only to this accuracy. In earlier years, the times of ■;■;() Strategic Role of Perigean Spring Tides, 1635-1976 both perigee and syzygy were tabulated to the nearest min- ute (or tenth of an hour) . The time difference determined by use of any of the previously mentioned publications may vary as much as 2 hours from those (involving cumulative rounding-oll pro- cedures) contained in the computer printout. However, any influence of this small rounding-off error is inconsequential for the present use. (It should be noted that, in connection with the curves of rate-of-tide-growth included in chapter 8, the more precise perigee-syzygy values derived from tide tahles or The American Ephemeris and Nautical Almanac arc used without exception.) All of the weather maps shown were plotted subsequent to the official adoption of standard time in the United States in 1883 and are, therefore, based on the standard time sys- tem. Each map is plotted from data consistent in time with that of the standard meridian 75 °W., which corresponds to eastern standard time. The wind velocities indicated by the number of barbs (and flags) on the shafts of the wind arrows extending from each station model must be evaluated according to one of two different systems of symbolic representation. These are shown in the accompanying legends titled "U.S. Weather Map Wind Arrow Symbols" as published in the 1949 and U. S. WEATHER MAP WIND ARROW SYMBOLS* BEAUFORT NUMBER ff MILES (STATUTE) PER HOUR KNOTS © CALM CALM 1 v 1-3 1-3 2 >^ 4-7 4-6 3 \v 8-12 7-10 4 w 13-18 11-16 5 \\n 19-24 17-21 6 \\\ 25-31 22-27 7 \\\\ 32-38 28-33 8 WW 39-46 34-40 BEAUFORT NUMBER ff MILES (STATUTE) PER HOUR KNOTS 9 WW 47-54 41-47 10 \\\\\ 55-63 48-55 11 \\\\\\ 64-72 56-63 12 www 73-82 64-71 13 WWWv 83-92 72-80 14 \\ww\ 93-103 81-89 15 wwww 104-114 90-99 16 wwww 115-125 100-108 17 WWWWv 126-136 109-118 LEGEND (ff): % FEATHER = 1 BEAUFORT NO. (F). EACH BEAUFORT NO. CORRESPONDS TO THE WINDSPEED RANGE INDICATED (IN STATUTE MILES PER HOUR AND IN KNOTS, OR NAUTICAL MILES PER HOUR). VELOCITY (MPH) = 1.87^/^ 'Authority: International Meteorological Organization (IMO), Publication No. 9, Fascicule I , Ed. 1949, Chapter m , Suppl. 1,pg. m -3 (1.12) "Wind." icukp, 48.- The system of U.S. Weather Map wind arrow symbols in use between January 1, 1949 and January 1, 1955. This symbolic coding system is applicable to the determination of windspeeds and directions on the earlier sur- face synoptic weather maps which follow. Included among these arc both the charts plotted between the preceding two dates and (with esentially the same wind velocity interpretation) those prepared prior to 1949, until the first few of the 19th century (harts are considered. (See also the accompanying text under "Explanatory Comments . . .") Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 331 1955 editions of the synoptic weather code (figs. 48 and 49) . These wind symbols were officially put into use in the United States on January 1, 1949 and January 1, 1955. Subsequent to the 1955 date, the system of wind representation has remained the same; prior to the 1949 date, winds were sym- bolized essentially according to the procedure indicated in the 1949 code until very early dates are considered. On some of these early weather maps, strong wind velocities are shown by small, solid black squares attached to the shafts of the wind arrows; the squares indicate winds of "caution- ary force." On such earlier weather maps, the numbers fol- lowing the barometric pressure represent the wind speed in miles per hour. Atmospheric fronts were not introduced on U.S. Weather Bureau synoptic weather maps until August 1, 1941. Before that time, although the common wind shifts across a front were not utilized, the prevailing patterns of highs and lows indicate the direction of surface wind flow (in the Northern Hemisphere, clockwise around a high, counter- clockwise around a low). 1. The Tidal Flooding of 1931 March 4-5 The first example (D-57 ) described among the follow- ing individual cases of tidal flooding — that of 193 1 March 4-5 — occurred at a time when the U.S. Weather Bureau's Monthly Weather Review, for logistic reasons, provided only a minimum of offshore and coastal storm informa- tion. It also occurred prior to the dates on which were inaugurated the information sources C 'Urn at o logical Data — National Summary (with its section on "Severe Storms" begun in January 1950 and changed, in January 1954, to "Storm Data and Unusual Phenomena") or the U. S. WEATHER MAP WIND ARROW SYMBOLS* ff MILES (STATUTE) PER HOUR KNOTS © CALM CALM 1-4 1-2 v 5-8 3-7 \ 9-14 8-12 \n 15-20 13-17 w 21-25 18-22 \\\ 26-31 23-27 \\\ 32-37 28-32 \\\\ 38-43 33-37 ft MILES (STATUTE) PER HOUR KNOTS WW 44-49 38-42 WW 50-54 43-47 k 55-60 48-52 L 61-66 53-57 k\ 67-71 58-62 kw 72-77 63-67 k\\ 78-83 68-72 k\\s 84-89 73-77 kks 119-123 103-107 LEGEND (ff): % FEATHER = 5 KNOTS (MEAN WIND SPEED); 1 FEATHER = 10 KNOTS; 1 FLAG = 50 KNOTS. * Authority : First Session of the Commission for Synoptic Meteorology (CSM- 1) April 1953. Recommendation #42 (Adopted in November 1954 by the U. S.). Figure 49. — The system of U.S. Weather Map wind arrow symbols adopted on January 1, 1955 and in force since that time. Note especially the use of flags to replace feathers at higher windspeeds, and the conversion from miles per hour to knots as the basic unit of windspeed. 332 Strategic Role of Perigean Spring Tides, 1635-1976 Table 26. — Surface Synoptic Weather Maps for Twenty Representative Cases of Coastal Flooding Associated With Perigean Spring Tides and Strong, Sustained, Onshore Winds Key letter and serial No. Weather map date and mean perigee-syzygy date (e.s.t.) Perigee -syzygy (in hours) Location of tidal flooding L'-> 1895 February 8 8. Oh (- 4) February 9 10. Oh 27 1896 November 6 8. Oh (-15) November 4 19. 5h vl 1901 November 24 8. Oh (- 9) November 25 15. 5h r> 1908 February 2 8. Oh (- 8) February 2 0. Oh 41 1917 October 1 8. Oh (-27) September 30 2. 5h A-43 1918 April 10 8. Oh (-19) April 10 14. 5h H-V) 1927 March 3 8. Oh ( + 15) March 3 21. 5h c--,i 1927 April April 2 1 8. Oh 20. Oh (- 6) 1,1 1933 December 17 8. Oh (+ 9) December 17 2. 5h 64 1934 August 21 8. Oh (-24) August 24 3. Oh F-68 1939 January 4 7. 5h ( + 14) January 5 23. Oh G-69 1940 April 21 7. 5h (-34) April 21 7. Oh H-72 1945 November 20 1.5h (-13) November 19 3. 5h 74 1948 January 26 1. 5h (+ 4) January 2<, 4. Oh I-83e,w 1959 December 29 1. Oh (-18) December 29 5. Oh 84e,w 1961 January 15 l.Oh (+ 1) January 16 17. 5h Ko 1962 October 13 l.Oh (- 9) October 13 3. 5h L-93e,w 1971 March 26 7. Oh (-10) March 26 9. Oh 94 1971 April 23 7. Oh (-34) April 24 6. Oh M-98e,w 1973 December 11 7. Oh (+21) December 10 7. 5h Staten Island, N.Y.; Providence, Newport, R.I.; Cape Cod, New Bed- ford, Boston, Mass.; Bangor, Pordand, Bath, Me. Pictou, Nova Scotia Asbury Park, Sea Bright, Keyport, N.J. ; Coney Island, N.Y. ; New Haven. Stamford, Greenwich, Conn.; Chatham, Provincetown, Mass. Port aux Basques, Newfoundland ; Harrington Harbour, Quebec Moncton, Sackville, Amherst Harbor, New Brunswick Sea Bright, Atlantic City, N.J. ; Staten Island, Rockaway Beach, southern Long Island, N.Y. New England coast Atlantic City, N.J.; Delaware Hoquiam, Cosmopolis, Aberdeen, Montesano, Wash. Balboa, Malibu, Newport, and Laguna Beaches, Calif. Aberdeen, Hoquiam, Neskowin, Wash.; Astoria, Marshfield, Coos Bay, Delake, Oreg. ; northern Calif. Boston, Minot's Light, Deer Island, Bassing's Island, Hull, Winthrop, Quincy, Mass. Eastport, Machiasport, Portland, Me. Vicinity of San Francisco, Calif. Atlantic City, N.J.; Long Island, N.Y. ; Hull, Boston, Provincetown, Gloucester, Cape Cod, Barnstable, Mass.; Kennebunkport, Me.; San Franciso Bay area, Calif. Adantic City, N.J.; Delaware; Ventura County, Calif. Local estuaries and bay locations, Oreg., Wash., and northern Calif. Vicinity of Sewell's Point, Virginia Beach, Willoughby, Ocean View, Norfolk, Sandbridge, Va. ; Oxnard Shores, Calif. Oxnard Shores, near Oxnard, Calif. Tokeland, Raymond, South Bend, Wash.; Seaside, Astoria, Newport, Oreg. ; Halifax, Nova Scotia full-size monthly report Storm Data (initiated January 1959). Thus, detailed technical data concerning this case of coastal flooding are not available. However, the history and course of the atmospheric storm which added its effects to perigean spring tides to produce tidal flood- ing are included in an article appearing in the New York Times for March 5, 1931, which is reproduced, in partly abbreviated form, below. (See figs. 95, 96.) This example is historically meaningful as an instance of perigean spring tides accompanied by widespread coastal flooding. The March 5 flooding event is of theo- retical significance to this study because of its association with astronomical tides predicted to rise (at Boston) 6.3 ft above mean tidal level at this location and, therefore, particularly vulnerable to wind attack. It is technically important because of the extremely close perigee-syzygy alignment which existed on this occasion (see reference note 4 to chapter 4, part II at the end of this volume) and which was responsible for the greatly enhanced astro- nomical high tides experienced. As an example, the value of the astronomically pro- duced higher high water predicted for Boston, Mass. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 333 334 Strategic Role of Perigean Spring Tides, 1635-1976 h ! 1 14 1 f ? i f ?! Ififrllifff ii | Iff ill I f 1 f I Mi mi I f f f ki|i Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 335 :;% Strategic Role of Perigean Spring Tides, 1635-1976 iffffftiintfTfTnin ^tM0 ■ mm-lfff B!i . - Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :nv a 1 t, -j "S —-fj—T \ I X V^ i f^IillHillllilpi 202-509 0-78-24 :v,H Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :,:vi iiaff« sjj" I'ili. is** So«?|: :■!!() Strategic Role of Perigean Spring Tides, 1635-1976 M Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 341 i : *;:: ::|;: - : - '!■ :..,■■: '.;••: ::::::::;: j | fi^^M 1 1 I >-» i I I ! I Mai - " - 'i .§ «j I *• liilfitiiillS » j J I | if' 1 1 > J U fill! i II 11 m ] if .fiif i -PI? II 111 it if ne I 1 . jiff! if |i !| |||s 1 1 ■;r_- Strategic Role of Perigean Spring Tides, 1635-1976 X l i j 1 1 lilii! illlifiii j i i i 1 triiniini ^ ■-' .i.^i:,!!,^.,. « ssii.-.i .-=sa»s=ji : B* 1 ' -\i s;si;i km : , i j jj |i:t|J|j m w H § s ^=T«*S£ If tp fen I Mil ill fjJl lllfi i l Ml! ft Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :m 344 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 345 :;ib Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 317 :;i,", Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :m<» :m Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 351 132 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 3!) 3 Table 27. — Surface Synoptic Weather Maps for Twenty Representative Cases of Nonflooding Conditions Associated With Perigean Spring Tides Which Were Accompanied by Light and Variable Winds and High Atmospheric Pressure Weather map date and mean perigee-syzygy date Perigee -syzygy (in hours) 151 1893 December 23 20. Oh (- 2) December 22 23. Oh 152 1899 January 12 8. Oh (+3) January 1 1 19. 5h 153 1912 January 5 8. Oh (+6. 5 mm.) January 4 8. 5h 154 1922 September 22 8. Oh ( + D September 21 0. 5h 155 1923 November 9 8. Oh (-27™.) November 8 10. Oh 156 1928 November 28 8. Oh (+5) November 27 6. 5h 157 1930 January 15 8. Oh (+2) January 14 18. Oh 158 1935 September 13 8. Oh (-2) September 12 14. Oh 159 1940 October 2 7. 5h (+3) October 1 9. 5h 160 1944 October 2 1.5h (-11) October 1 17. 5h ll.l 1950 May 3 1. 5h (+2) May 2 l.Oh 162 1950 December 9 1.5h (-8) December 9 l.Oh 163 1951 June 20 1. 5h ( + D June 19 8. Oh 164 1953 September 24 1. 5h ( — 15 min.) September 22 23. Oh 165 1954 November 10 1. 5h (-D November 10 9. Oh 166 1966 September 14 l.Oh (-2) September 14 13. Oh 167 1967 March 27 l.Oh (+5) March 26 0. 5h 168 1968 December 19 7. Oh (-6) December 19 10. Oh 169 1972 December 20 7. Oh (-21) December 19 18. 5h 170 1974 February 6 7. Oh (-24) February 6 6. Oh Near-maximum parallax and declination, occurring at the winter solstice and near perihelion. Large parallax; close to perihelion. Near maximum parallax; occurring at perihelion; very close separation- interval. Total solar eclipse; autumnal equinox; and Moon very nearly on Equator. Large parallax; very close separation-interval. Large parallax and positive declination. Near maximum parallax and high positive declination, occurring near perihelion. Very large parallax; Moon very nearly on Equator. Total solar eclipse ; Moon near Equator. Moon very nearly on Equator. Large parallax; close separation-interval. Large parallax; very high negative declination (ascending node at the vernal equinox). Summer solstice and maximum declination of Sun (+) and Moon (— ); close separation-interval. Autumnal equinox, large parallax, and Moon near Equator; very close separation-interval. Large parallax; close separation-interval. Large parallax. Moon near vernal equinox and on Equator. Large parallax and high negative declination. Near winter solstice; full moon at high positive declination, nearly co- planar with negative declination of Sun. Declination of full moon (+15°19') nearly coplanar with declination of Sun (-15°39'). (Commonwealth Pier) on 1931 March 6 at 1243 h (e.s.t.) —55 hours after the mean epoch of perigee-syzygy on 1931 March 4 at 0530 h (e.s.t.)— was 11.0 ft. The maximum tidal range on March 6 was 13.0 ft. These values compare respectively with 10.3 ft for mean high water springs and 10.9 ft (or 11.0 ft in the 1977 tide table ) for the spring range of the tide at Boston. It will be demonstrated in chapter 8 that the likelihood of an increased amount of tidal flooding is associated, not alone with the predicted amplitude and range of perigean spring tides, but with their accelerated rate of growth in reaching this maximum. Thus figure 96, which depicts the predicted rate of tide rise (in ft/min X 0.0001 ) at Willetts Point, N.Y., during successive lunations bracket- ing 1931 March 4-5, is far more meaningful in indicating the potential for the tidal flooding which actually oc- curred. The use of such rate-of -growth tide curves of perigean spring tides and the determination of their re- spective "windows for potential flooding" will be dis- cussed further in part II, chapter 8. The peaking of those portions of the tidal curve con- taining perigean spring tides at a level considerably above the baseline representing the average rate of tide growth throughout the entire year at this location is clearly evi- -509 0-78-25 354 Strategic Role of Perigean Spring Tides, 1635-1976 & .; TiXSm MjWjWttsV'V . li .....,.... i _,...;., ej ..... ......; _^. t k ">■ . 11: ""*. ;■- ■------ = -—-.: :._•'■ .- -■■_■: ; - : ... : : ■ \ -"■- V \ t » — 4^;;liiili:Z.;;;:.:.; :;::".'...',:."; ..." w "'"*" Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■m ■M>b Strategic Role of Perigean Spring Tides, 1635-1976 ^3S ■ v ■"■ '-■ 4m -rf M 1 1 f i u 1! lit Hii ii 111 I ! i ! i 1 l !i)''Mil|ill?i ill "tJiiiPi! Biffii isi='j i,yt ■:..-■,■",>..■ J l! Ii-sij II (lllf 1 L L ;;"!! \ iLidk n . - itim ij« »"" iBlipiitiill : S| : - ; r / / ■■ v ] / ' ; a I ■MyO Strategic Role of Perigean Spring Tides, 1635-1976 IMP Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 361 :u>: Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :K?, _ it 1 Si Pill Kl 1 ! 8 ill ill i^ifiteS! 11 M'A Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :s(, r » :m Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 367 !',(,» Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :k> ( ! 202-509 0-78-26 370 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 371 :;72 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings V3 ss-vW ■SlNpi iSfe'Ti . :;:^ Strategic Role of Perigean Spring Tides, 1635-1976 Table 28a. — Surface Synoptic Weather Maps for Four Representative Cases of Hurricanes Occurring in Near-Coincidence With Perigean Spring Tides Serial Weather map date and mean Perigee — No. perigee-syzygy date s Y z ygy (hours) Region of impact 266 1878 October 23 l.Oh October 25 9. 5h August 20 8. Oh August 20 20. 5h September 2 7. 5h September 2 12. Oh October 15 1.5h hurricane Hazel) October 12 10. 5h (■ — 17) All sections of New England and the mid-Atlantic States, Oct. 23-24, starting off the S.E. coast of Florida and the Carolinas, Oct. 21-23 ( — 7) Coasts of Virginia, Delaware, and New Jersey, Aug. 18-19 (+26) Cape Hatteras, N.C., on Sept. 1, then northeastward to eastern Maine and Nova Scotia (+21) Entire mid-Adantic region and Carolinas, Oct. 15 Table 28b. — Representative Surface Synoptic Weather Map at a Time During Which a Perigean Spring Tide Caused Blocking and Backup of Hydrological Runoff Serial Weather map date and Perigee — No. mean perigee-syzygy syzygy date (hours) Region of impact 466 1936 March 21 8. Oh ( + 5) Newburyport and tidewaters of Merrimack River, Mass. March 23 1. 5h dent. Where supporting winds are present, the vulner- ability to tidal flooding on both March 4-5 and April 1 at Willetts Point (and additional east coast locations having similar tidal characteristics) is directly confirmed thereby. The coastline near Boston, Mass. also has been shown to be susceptible to tidal flooding at this time, if subject to the correct meteorological conditions. As described in the accompanying newspaper account (fig. 95 ) , the combination of both wind and astronomical effects lifted the tides at Boston on 1931 March 4 to an actual height of 13 ft 8 in. The tides at the Naval Yard, Portsmouth, N.H., were raised to a height of 13 ft 10 in. Regional effects of these storm tides occurring near peri- gee-syzygy are described both in the other news articles re- produced in figs. 95, 96, and in those of table 5, part I, chapter 1 . The circumstance of occurrence of a series of astro- nomically produced perigean spring tides related in a commensurable pattern to this 1931 March 4 flooding event, each of which was itself accompanied by tidal flood- ing (Key Nos. 56w, D-57, E-58, 59, and 60) already has been mentioned as of special consequence in reference note 4 supplementing part II, chapter 4. This example of proxigean spring tides therefore substantiates, in every way, the particular influence of such tides in causing coastal flooding when reinforced by the prerequisite wind conditions. 2. The Tidal Flooding of 1939 January 3-5 The next case of coastal flooding to come under con- sideration from a combined meteorological-astronomical viewpoint — that of 1939 January 3-5 (Key No. F.-68) on the west coast — is notable because of the extent of its occurrence, nearly simultaneously, from Long Beach, Calif., to Aberdeen, Wash. This fact substantiates the effectiveness of perigean spring tides in producing coastal flooding in various latitudes on either the east of west coasts of North America — wherever the correct tidal har- monic constituents, adequate tidal range, a low-lying coastline, and persistent, strong, onshore winds combine to provide the conditions requisite to flooding. A surface synoptic weather map for the former map plotting time of 0430" (P.s.t.) on 1939 January 4 is in- cluded among the group of maps following table 26. As indicated by the several newspaper accounts of this flood- ing event which appear below and in table 5, part I, chap- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings •Mj ii'iosa {tiA H— I i M6 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 377 DC CO ' Xi-^ / \^vf^;^ ^*5FW ■MS? Mil j iiliii ;H ; Iptllllil]) WjikwH 4 ? ill s i Mil :*78 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings . - -— --^n. z. 3 379 380 The New York Times Thurs., March 5, 1931 Page 20, Cols. 3-6 Strategic Role of Perigean Spring Tides, 1635-1976 was so high over the pier that the gang- plank, when put down, was tilted at a crazy angle . . . SEABOARD IS LASHED BY TIDE AND STORM Tide and storm had an interesting his- tory, with the Weather Bureau acting as recorder. It appears that on the night of Feb. 27 a little storm was cradled out in the open spaces of Utah. At first it tried its comparatively puny strength on the northeastern part of Mexico, whooped it up over the Gulf of Mexico and made a vicious turn toward Tampa, reaching there Monday morning. Takes to the Atlantic. Here it developed an extremely violent temper and began to vent its wrath on the Atlantic. By Tuesday morning it had ar- rived at Cape Hatteras, rolling tremendous waves before it, toward the shore, from points as far as 1,000 miles out. Rushing northeast while growing to a sixty-mile gale, it worked all Tuesday night and yes- terday morning, driving the foaming green water toward the coast. This continued drive from the east would ordinarily have been enough to create a high tide, but to make matters worse, the moon is at full, exerting its maximum strength on the ocean. Thus, between the two. New York, New Jersey and other coastal States felt the power of the worst tide in four years . . . New Jersey Resorts Battered. Atlantic City, Margate, Ventnor City, Ocean City and Sea Isle City received a tremendous battering from the tide and reported heavy damage. Rushing into the inlet and thoroughfare the waters spread out over the long meadows back of Atlan- tic City, until they were completely sub- merged. Only the shore line trolley tracks remained clear. In Longport and the inlet district the water -was six inches deep in the streets, marooning families in their cottages and sloshing into cellars every- where . . . In New York Harbor not only the ferry- boats but the large ocean liners were affected. Commuters were delayed while the ferryboats maneuvered for the best position for the placing of gangplanks, and on the New Jersey side of the Hudson the tide was so high that passengers had to splash through several inches of water. Behind the Erie station in Jersey City automobiles and persons on foot virtually had to ford their way to cross the streets. When the giant liner Europa docked yesterday morning at the army base pier, foot of Fifty-eighth Street, Brooklyn, she . . . Last night remote shore villages in New Jersey and on Long Island were still send- ing in reports of floods in the streets, hoats carried to sea and homes undermined by the tide . . . . . . EAST HAMPTON, L. I., March 4.— Ring Lardner's Summer home on the dunes here was hanging over the cliff tonight after the high tide had undermined the house. It is feared that the house will top- ple into the sea if a heavy tide rolls in tomorrow . . . HEAVY DAMAGE AT BOSTON Loss From Flood and Waves Said to Be Enormous. BOSTON, Mass., March 4. — A huge tide driven to heights unprecedented in two decades lashed the shores of New England today, causing havoc among shore cottages, demolishing sea walls and rolling up a damage which could not be estimated. The tide rose three feet above normal. Eighty-two structures were damaged in Revere alone, seven of them being com- pletely wrecked and washed away. Seas rolling through carried away all cottages, furniture, ripped up floors and undermined foundations. Damage at Revere was esti- mated at $1,000,000. At Roughan's Point, in the Beachmont section, cottages were loosed from their locations and floated to- gether like packing boxes . . . . . . The Revere Beach & Boston suspended operations for an hour before and nearly two hours after high water, at 11 o'clock. Two East Boston lines of the elevated were suspended for a time. The Portland division of the Boston & Maine was held up nearly two hours by tracks under water. Sections of the New Haven tracks were washed out between Neponset and Milton, and between Norfolk Downs and Atlantic. All communication between Lynn and Boston was suspended during the flood tide. Whole sections of rail were under water. Shore roads, washed by seas or flooded entirely by the record tide, were left impassable because of debris when the waters receded . . . . . . Today's tide went to a height of 13 feet 8 inches . . . . . . From everywhere came reports of the appearance of myriads of sea rats, driven out of the burrows near normal high tide marks by the rising flood. At Portsmouth Navy Yard the highest level ever recorded was reported, 13 feet 10 inches . . . ... At Newburyport the 30,000 clam puri- fication plant was undermined by rushing high water and nearly wrecked. At Salis- bury, cement walks and miles of board- walk along the beach were washed away. Nahant was turned into an island. Every- where boat yards were endangered . . . ... At Hingham thousands of feet of lumber floated to sea when the yards of J. H. Kimball & Co. and of E. E. Whitney were flooded to the tops of the piled boards. At Yarmouth, the town bathhouse, town pavilion and town dock were distrib- uted over several back yards. With half of the Nantasket Beach Rail- way undermined and destroyed, with prac- tically every cottage and Summer resi- dence on the ocean side of the Nantasket peninsula damaged and with Hull cut off from communication, damage from Nan- tasket to Pemberton w r as estimated at more than $1,000,000. Gloucester suffered more heavily than at any time within recent years, with waterfront streets submerged, train serv- ice completely cut off and cellars flooded. No trains operated between 9 A. M. and 5:50 P. M. At Rockport a heavy surf washed away the new sea wall completed a few months ago. CITY OF LYNN IS ISOLATED LYNN. Mass., March 4 (AP).— Lynn was virtually isolated by the storm and tide. Transportation lines were paralyzed. The harbor front was flooded. Children were taken from a flood-surrounded school in ambulances. The adjacent town of Nahant was made an island when the ocean waters rose above the isthmus for the first time since 1909. The high waters swept into Lynn sewers and breaking waves sent water bursting out of manholes like geysers . . . ... At Swampscott. adjoining Lynn on the north, the tide swept in over shore roads, bringing up dories and fishing equipment with it. 1931 Mar. 4 5.5h e.s.t. ( ) D-57 The New York Times Mon., March 9, 1931 Page 1, Cols. 1, 2 HIGH SEAS BATTER COAST HIGH TIDES LASH BEACHES In and about New York a high wind that accompanied heavy rains and a high tide caused at least seven deaths, scores of injuries and millions in property damage Figure 95. Newspaper articles in connection with the 1931 March 4-5 tidal flooding in New England. Classification, Designation and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 381 METROPOLITAN AREA HIT HARD At least seven deaths, millions of dollars in property loss and scores of injuries were caused by the gale that scourged New York and New Jersey Saturday night and all day yesterday. D-57 (a), E-58 (a) The gale, as earlier in the week, was assisted by the waning moon, in rolling up tremendous tides that gnawed away long stretches of waterfront, undermined Sum- mer homes and flooded streets and high- ways . . . ... at the Battery the tide rose to within a foot of the top of the sea-wal first time in many years . . . 1931 Mar. 4 5.5h e.s.t. ( ) D-57 8.4 Ok WILLETS POINT, NEW YORK 1931 8.3 • T 8.6 8.9 T • 9.0 k > T • 8.7 k O 8.2 • A O "WINDOW" FOR POTENTIAL — TIDAL FLOODING AVERAGE OF CURVE MAXIMA FOR 1931 JAN 7 14 21 28 1 FEB 7 14 21 28 7 MAR 14 21 28 1 APR 7 14 21 281 MAY 7 14 21 28 1 JUN 7 14 21 28 Figure 96. — Continuation of newspaper items relative to 1931 March 4-5 tidal flooding event. The appended graph also shows the accelerated rate of astronomical tide growth accompanying this event. The tidal enhancement is associated with an alignment of perigee-syzygy within 6 minutes at the mean epoch of 1931 March 4.23 e.s.t. (See pt. II, ch. 8 for an explanation of these curves indicating rate of tide rise.) V>2 Strategic Role of Perigean Spring Tides, 1635-1976 ter 1, tidal flooding of major consequence had begun along the Washington and Oregon coasts as early as Jan- uary 3. However, this weather map for the very next day, midway in the tidal flooding period, reveals no deep low pressure system, intense precipitation pattern, strong winds, or other active weather indicators either along the coast or offshore. Despite this, the tidal flooding was con- tinuing along the Washington coast and beginning in southern California. (It is important to remember in this connection that atmospheric fronts were not introduced on official U.S. Weather Bureau synoptic weather maps until August 1, 1941.) The general summary of weather conditions over this Pacific coast region appearing in the Monthly Weather Review for January 1939 solves the mystery of the me- teorological contribution to this tidal flooding event. The answer is inherent within a circumstance which occurs often along the Pacific coast of North America, but which (before satellite weather photographs became available) confounded many an early weather forecaster in this area attempting to determine the cause of such surging up- lifts of water along the coastline — determined as not due to seismic sea waves (known alternatively as tsunamis). ( Cf., for example, Key No. 64 in table 5. ) A contributing element to such coastal inundations, es- pecially at times of perigean spring tides, can lie in deep atmospheric low pressure systems existing possibly many hundreds of miles at sea. These low pressure systems, with their associated steep atmospheric pressure gradients, pro- duce very strong surface winds. The winds, in turn, gen- erate an active swell on the sea surface. The speed of movement of such a deep low pressure system can far ex- ceed that of the swell it generates. Thus the low pressure center, accompanied by strong winds, can move rapidly onshore and be out of the area before the swell ever reaches the coast. Conversely, a strong high pressure sys- tem can block the forward movement of a low pressure cell. As a result, the swell which the latter has produced is propagated along the sea surface and may strike the coastline while the low center maintains its position many hundreds of miles at sea. In either case, if a very strong swell arrives along the coastline at the same time that perigean spring tides rise to their greatest levels at high water, the reinforcing action between strong swell and augmented tides can only cause tidal flooding — while the apparent cause (lacking im- mediate strong winds) remains obscure. The present in- stance of coastal flooding seems to have involved both circumstances, the first over Washington and the second in southern California. (See fig. 97 ) . Numerous other examples of each type are contained among the newspaper accounts of tidal floodings along both the east and west coasts contained in table 5. On certain parts of the California coastline, notably from Point Conception south, a frequently observed tendency exists for a channeling of a northeasterly directed swell — apparently by similarly oriented bathymetric configura- tions on the ocean floor. This influence has been variously noted by marine engineers writing in Shore and Beach magazine 1 , by coastal resource engineers in the Los An- geles District Office of the U.S. Corps of Engineers, and by a beachguard with many years of observational exper- ience at Imperial Beach, Calif. The effects of the strong swell generated by a hurri- cane located even far to the southwest in the subtropical regions of the Pacific can sometimes be felt as an active series of ocean surges impacting on the California shore- line. The swell may appear in an otherwise calm sea, un- swept by wind or waves, under a perfectly clear sky, and with no visible generating source, having been propagated from its distant origin, losing little in flooding potential on the way. From an astronomical viewpoint, while the perigee - syzygy alignment ( + 14 h ) which produced the perigean spring tides in case F-68 was not nearly so precise as in case D-57, the astronomical high tides resulting were of considerably augmented amplitude and range with respect to their average values. On 1939 January 5 at 0802" (P.s.t.), for example, the predicted higher high water at Los Angeles (Outer Harbor) was 7.0 ft. The predicted maximum tidal range for this same date was 8.6 ft. The latter value is signifi- cantly in excess of either the diurnal range (that between mean lower low water and mean higher high water) of 5.4 ft or the mean tidal range of 3.8 ft at Los Angeles. At Aberdeen, Wash., the HHW predicted to occur at 1 2 1 8 h ( P.s.t. ) on January 5 was 11.2 ft and the predicted maximum range for this date was 12.7 ft. By contrast, the diurnal range at Aberdeen is only 9.9 ft. At Astoria (Tongue Point) , Oreg., the HHW predicted for 1233 h (P.s.t.) on January 5 was 9.8 ft and the maxi- mum range 1 1.2 ft, whereas the diurnal range at Astoria is only 8.1 ft. These unusual tidal elevations, combined with the reinforcing influence of strong onshore winds, resulting high seas, and ground swell confirmed by the following general weather summary, could only produce Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■MM The Oregon Daily Journal Fri., Jan. 6, 1939 Page 1, Col. 7 Sea Unruly in California Three Homes Washed Into Pacific; Others Damaged Long Beach, Cal., Jan. 6— (AP)— Three modest beach homes in the Alamitos pe- ninsula area southeast of Belmont shore were washed to sea today as giant break- ers, riding in from the Pacific on high tide ground swells, crashed over the low sea wall . . . . . . The tide also brought extensive dam- age to Manhattan and Hermosa beaches, where the highest water in years flowed as far as 180 feet inland. But the Alamitos peninsula below Long Beach was hardest hit. William E. Ross, boat builder there, said the tide was the worst in his 35 years' ex- perience. Mrs. I). H. Collins stood by and watched the tide carry her two-story dwelling into the Pacific . . . . . . More than two feet of water roared in at some Santa Monica bay points, sweeping out the board walk along the strand between Manhattan and Hermosa beaches . . . Tillamook Area Raked By Sea Surge Wheeler, Jan. 6. — Devastation was left by surging seas that hit Tillamook county beaches Thursday noon. High water marks were broken. The Southern Pacific track at Barview, washed out Tuesday and re- paired Wednesday, was torn from the roadbed and rails and ties strewn along the Coast highway . . . . . . The seawall was washed inland 50 to 250 feet from Manhattan to Barview . . . 13-Foot Tide Recorded at Newport Newport, Jan. 6.— A 13-foot tide, one of the highest ever recorded here, washed the water fronts Thursday. Yaquina Bay was covered with heavy logs and timbers, kept moving away from boats and buildings by coastguardsmen . . . . . . Several hundred feet of the trestle work of both jetties left standing by former contractors was washed to sea . . . . . . The surging breakers cut off lights, water and traffic from the Bayocean pen- ninsula and washed out the highway at Oceanview, marooning those on the pe- ninsula. The surf almost demolished the seawalls at Netarts . . . 1939 Jan. 5 20b P.s.t. (-\ F-68 14) Figure 97.- -Representative news articles relative to the tidal flooding of 1939 January 3-5 occurring in Washington, Oregon, and southern California. the damaging tidal flooding along the coast which took place. From: Monthly Weather Review, Vol. 67, No. 1, January 1939 F-68 — Coastal Flooding of 1939 January 5, Central Oregon to Southern California "The early part of January may be characterized as one of the stormiest periods in recent years on the North Pacific Ocean. At the opening of the month low pressure extended across the northern half of the ocean, with three distinct and powerful centers, one east of Japan, another in upper middle longitudes, and a third off the west coast of the United States and British Columbia. In connection with these specific storms and the generally unsettled weather existing generally to the northward of the 30th parallel during the 1st to 5th, gales, many of which were of hurri- cane or near hurricane intensity, occurred over wide areas, some being experienced almost as far south as the 25th parallel. However, in east longitudes, the greater part of the high winds reported occurred between latitudes 30° and 45°N., and in west longitudes, between 35° and 45°N., except along the American coast, where they were experi- enced also in much higher latitudes. "The easternmost Pacific storm was of unusual severity. It was damaging on the Washington, Oregon, and California coast, from the standpoint of both heavy winds and high seas, which continued with varying intensity from the 1st to the 5th. At the entrance of the Strait of Juan de Fuca, the Swiftsure Bank Lightship reported winds of forces 9 to 10 on the 1st, 2d, and 4th. At sea several vessels were delayed in passage, and a number of passengers on the American steamship Lurline were injured, according to press reports, when a huge sea swept the decks. The American steamship Mauna Ala reported southerly winds of forces 11 to 12 on the 2d and 4th while proceeding southwestward some 100 to 200 or more miles west of the Oregon coast, lowest barometer 29.08 inches, on the 2d. Much farther at sea, near 43°N., 148°W. the Japanese motorship Genyo Maru encountered strong gales to hurricane winds, lowest barom- eter 28.71, on the 3d." 3. The Coastal Flooding of 1959 December 29-30 This case of coastal flooding (I-83e,w) is the first among the present examples for which specialized in- formation as compiled in the U.S. Weather Bureau (now :W4 Strategic Role of Perigean Spring Tides, 1635-1976 the National Weather Service) publication Storm Data is available. It also provides an example of two nearly concurrent tidal floodings which resulted from perigean spring tides produced on both the east and west coasts of North America. Although the respective floodings on op- posite coasts were separated by a day, in each case the event was a function of strong onshore winds acting upon the astronomically produced perigean spring tides. Other such instances of near-simultaneous tidal flooding on both coasts exist in Key Nos. 56e,w, 84e,w, L-93e,w, and M-98e,w. (See table 1.) A surface synoptic weather map plotted for 1959 De- cember 29 at 0100 h (e.s.t.) is included among the group of maps following table 26. This map clearly shows that the meteorological factor which contributed to the east coast tidal flooding was a large low pressure system with two centers located just inland from the mid-Atlantic coastline. The easternmost of these two centers contained a nonoccluded frontal wave. The peak of this wave was centered, at map time, over the Delmarva Peninsula, with its warm-front portion extending east-northeast along the entire southern New England coast. This resulted in a strong wind circulation from the east-northeast and hence directly onshore from the sea at coastal points to the north of the front — a typical setup condition for the familiar New England nor'easter in winter. The effect upon the rising perigean spring tides, whose mean epoch occurred on 1959 December 29 at 0500 h (e.s.t.) was also typical. Tidal flooding ranged along the coast from New Hampshire to Maine. The severe magni- tude of this tidal flooding and the associated damage in New Hampshire, Massachusetts, and Maine are described in the following summaries from Storm Data. Further in- formation is available in the accompanying newspaper articles (fig. 98), with an additional news account ap- pearing in table 5. Considerable data in connection with this instance of coastal flooding, an event described by the U.S. Coast and Geodetic Survey as produced by "the The Boston Herald Wed., Dec. 30, 1959 Page C3, Cols. 2-4, 6-8 7959 Dec. 29 5h e.s.t. (-18) l-83e South Shore Areas Lose Northeaster Lashe * A,f c »p* Co(I Power; Streets Flooded 1 5-Foot Tides Smash A 100-foot section of the seawall at Lighthouse Point, near Rebecca road where the Italian freighter Etrusco went aground in 1956 was washed away and homes on the point were isolated for sev- eral hours. Stores in the Scituate Harbor area were flooded, with a foot of water pouring both in and out of the First National Store on Front street. The street, main business thoroughfare, was closed during the morn- ing. In Marshfield, 50 families were evacu- ated for several hours from the beach areas at Rexhame, Ocean Bluff, Brant Rock and Green Harbor. DIKE GIVES WAY The situation was particularly tense in the Brant Rock area where the famed esplanade was under three feet of water after a dike on the Green Harbor River gave way at 11 a.m. . . . Provincetown, Barnstable Storm tides 15 feet high crashed across waterfronts of Provincetown and Barn- stable while the whole Cape Cod area was lashed with a heavy rain driven by north- east gale winds. Peak of the flood tides hit at 11 a.m. and flooded scores of cellars in both towns and washed out stretches of some high- ways and made others impassable for sev- eral hours. VILLAGE THREATENED In Barnstable the sea flooded to within 50 yards of the main street of Barnstable Village. In Provincetown, Commercial street was hip-deep at. one point and a number of stores and dwellings were damaged. Both Barnstable and Provincetown po- lice estimated damage in the thousands of dollars but no injuries were reported. Police and firefighters stood by to evac- uate 60 families in the Common Field area of Barnstable as water flooded Commerce road and isolated a big freezing plant. The water receded before evacuation became necessary. In Provincetown the crashing tide sent spray roof-high over buildings on Mac- Millan Wharf and nearby piers. Crews of fishing vessells were kept busy strengthen- ing moorings. In East Dennis, Bridge Street was washed out. It was repaired several hours later by highway crews. In Wellfleet, the heaviest water damage hit Mayo's Beach road . . . . . . Water breaking over the boulevard seawall on Western avenue, Gloucester, drenched the area, and at Pavilion Beach, in the inner harbor, it climbed the back walls of a plant of the BirdsEye division of General Foods. The bridge leading into Annisyuam was awash and cars were re- routed. The water reached to within one foot of the windows of the Gloucester House on the Gloucester waterfront . . . Figure 98. — A newspaper account of the due east-west coast tidal flooding of 1959 December 29 the vicinity of Boston, Mass. -30, as it was experienced in Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :W5 highest tides in 108 years," are contained in the latter article. The perigee-syzygy separation-interval at the time of this flooding was — 18 h . The peak of the flood tides — indicated in the second of the immediately succeeding news articles as occurring in the vicinity of Cape Cod at 1100 h on December 29 — closely followed the predicted high water for Boston (Commonwealth Pier) of 11.9 ft at 1016 h (e.s.t.) on this date. The corresponding predicted maximum range was 14.1 ft. For comparison, the tide level at mean high water springs is 10.3 ft, and the mean spring range is only 1 1 .0 ft. These rising perigean spring tides reached a slightly higher level of 12.0 ft at Boston at HHW ( 1 109 h e.s.t. ) on December 30 ( as the result of the time lags introduced by phase age and parallax age ) , and then receded. * * ■* On the west coast, the tidal flooding produced was occasioned by the same condition of perigean spring tides that prevailed on the east coast, coupled with strong onshore winds. To show the basis for these winds, the synoptic weather map for 1959 December 30 would have to be used, since the coastal flooding on the west coast occurred on this date. However, on the 1959 December 29 map, a low-pressure trough is already seen to be moving from the south along the California coast, intruding be- tween two high pressure cells — one off the coast and the other centered over northeastern Nevada and southern Idaho. The strong winds produced over San Francisco Bay on December 30 resulted from the steepening pressure gradi- ent associated with this low pressure system approaching the mid-California coast from off the Pacific. Since no strong winds are indicated at San Francisco on the weather map of December 29, those mentioned in the Storm Data report must have been of relatively short duration, with the principal flooding effects being due to the augmented perigean spring tide. These tides reached their highest level of 6.9 ft at San Francisco (Golden Gate) on 1959 December 29 at 1023 h (P.s.t.). The maximum range for this date was 8.4 ft. The predicted higher high water at Golden Gate on De- cember 30 at 1 1 12 h (P.s.t.) was 6.7 ft, and the predicted maximum range on this date was 8.2 ft. The correspond- ing values of mean higher high water and diurnal range at Golden Gate are 5.4 ft and 5.7 ft. Because the onshore wind movement was neither sus- tained for a long period over San Francisco Bay, nor of extreme intensity, the accompanying flooding damage from the perigean spring tides was not nearly as con- sequential here as in the vicinity of Boston. From: STORM DATA, Vol. 1, No. 12, December 1959 I-83e,w — Coastal Flooding of: 1959 December 29- 30, Maine, Massachusetts, New Hampshire; San Francisco Bay Area, California Coastal "Dec. 29 — Abnormally high tides flooded waterfront along entire coast. Major damage south of Rockland over area with eastward exposure to the sea. Coastal streets and highways were flooded. Water poured into cellars of homes and busi- ness establishments. Five summer cot- tages were demolished by the huge waves in the Biddeford area. Small craft were reported lost all along the coast. A num- ber of roads were washed out. The tide also backed up the Kennebunk River, flooding Dock Square at Kennebunkport. Hundreds of lobster traps were wrecked or washed away. MASSACHUSETTS Coastal "Dec. 29 — Unusually high normal tides, strong to gale-force easterly winds, and a full moon, combined to produce the high- est tides in at least 50 years, and possibly as much as 108 years. Central and northern portions of the coast bore the brunt of the tidal attack. Tidal flood waters engulfed all immediate coastal areas, and towering waves battered coastal installations and leaped seawalls. Water reached a depth of about 6 feet in the streets of Hull. At Nan- tasket Beach the waves tore out a 100 foot section of parking area pavement to a depth of 10 feet. Several thousand families were evacuated from their homes by the Coast Guard, Harbor Police, or Fire De- partments. Thirty families were evacuated because of a flood-induced gas leak. Heavy stones and debris were hurled onto shore areas by the giant waves. Plows were used to clear the affected area. Lobstermen lost many traps. Small boats were washed away, and others were engulfed. Some beach areas were markedly eroded by the pound- ing surf. Flooded cellars crippled heating equipment in several thousand homes and caused heavy losses of inventory at business establishments. Many homes were badly damaged by flood and surf. 202-509 0-78-27 386 Strategic Role of Perigean Spring Tides, 1635-1976 NEW HAMPSHIRE Coastal "Dec. 29 — Combination of spring tides and winds produced tide levels up to 14 feet above mean low water. Giant breakers smashed coastline. At Rye, wind-swept waters spilled over, damaging a seawall, flooding roads, and hurling shale piles to a depth of 3 feet across a half-mile stretch of highway. Lobstermen and fishermen counted heavy losses from the abnormally high tides and surf. CALIFORNIA San Francisco "Dec. 30 — Strong winds combined with Bay Area. high tides to flood low-lying areas of the southern San Francisco Bay area. One man was drowned when his small boat capsized. A painter lost his life when he was blown from a scaffold at the sixth story of a Palo Alto building." 4. The Tidal Flooding of March 6-7, 1962 The great tidal flooding ( Key No. J— 85 ) which struck the entire coastline of the United States from South Caro- lina to Maine (with the principal damage being experi- enced between Long Island, N.Y., and Hatteras Outer Banks, N.C.) on March 6-7, 1962 is, without doubt, the most widespread nonhurricane-induced coastal flood- ing which has occurred along the North American eastern coastline during the entire period of coverage of this study, 1635-1976. So thoroughly has this event been documented since its occurrence (cf., the reference source list opposite J— 85 in table 1 ) that, with appropriate narrative excerpts in- cluded from Climatological Data — National Summary and Storm Data, it is additionally necessary only to assem- ble certain facts in resume. Of first importance is the consideration that, with the initial severe flooding occurring in the dark of the Moon and in the early morning hours of winter predawn, as well as under completely cloudy and snowswept skies, this catastrophe resulted in the loss of 40 lives and property damage estimated at 0.5 billion dollars. Incalculable loss was incurred as a consequence of coastal erosion. Second in significance is the very near coincidence of this flooding event with a proxigee-syzygy alignment having a mean epoch of 1962 March 6 at 0430" (e.s.t.), just 3.5 hours before the initial peak reached by the inflooding tides at Sandy Hook, N.J., (see fig. Ill) and some 28 hours before the highest tidal peak reached on the follow- ing day. This latter flooding included the normal delay factor induced by phase age and parallax age at times of perigee-syzygy. The separation-interval between prox- igee and syzygy in this occurrence was only — 31 minutes. The parallax of the Moon at the mean epoch of proxigee- syzygy was 61 '26.6". The third fact of significance is the manner in which reinforcement was given to the high tides already present at proxigee-syzygy by the merging of two atmospheric low pressure systems at a point midway along the east coast, followed by the easterly movement of the combined system offshore, and its subsequent blocking by a strong, nearly stationary high pressure system which had moved south- ward off the east coast of Canada. The atmospheric pressures at the centers of both of the initially converging lows was 1,008 milibars. Although the central pressure of the combined low was only 992 mb as it left the coast, the cyclonic cell deepened and inten- sified after it left the coast. By 0100 h on March 7, the cen- tral pressure had dropped to 984 mb. The process of successive buildup of this active wind- producing system is shown in the series of three accom- panying surface synoptic weather maps for 1962 March 5, 6, and 7, each plotted for 0100 h (e.s.t.). (See figs. 99, 100,101.) On the March 5 map, an extratropical low pressure center with accompanying frontal wave is seen to be de- veloping off the southeast coast of the United States, centered at about 30°N. latitude and 75°W. longitude. A second low pressure system is centered at the same time over southern Ohio. Falling pressures and the isallobaric gradient indicate its projected movement to be almost directly eastward. The weather map of March 6 shows that the two low pressure systems, on a collision course, have merged, with the center of the combined system being located at a point some 100 nautical miles east of Chesapeake Bay. The pres- sure at the center of the new single low has deepened to 992 mb, and the winds have intensified strongly, with average easterly and northeasterly winds onshore from 32- 37 mph (28-32 knots) at map time, increasing as the day goes by, including isolated peak gusts to 81 and 84 mph (70 and 73 knots). The weather map for March 7 shows that the center of the low pressure system has moved only slowly east-south- eastward to an offshore location centered at about 35°N. latitude and 70°W. longitude. Its forward motion has become blocked by a strong, near-stationary high pres- sure cell which has intruded southeastward from off the Canadian coast and which, while not appearing on this weather map of the United States and surrounding Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings Table 29. — Surface Synoptic Weather Maps for Cases of Tidal Flooding Receiving Special Attention in the Text 387 Key letter Weather map date and and serial mean perigee-syzygy date No. J-85 1962 March 5 l.Oh March 6 4. 5h J-85 1962 March 6 l.Oh March 6 4. 5h J-85 1962 March 7 l.Oh March 6 4. 5h 86 1962 October 12 l.Oh October 13 3. 5h N-99 1974 January 7 7. Oh January 8 7. Oh N-99 1974 January 8 7. Oh January 8 7. Oh N-99 1974 January 9 7. Oh January 8 7. Oh O-lOO 1976 March 16 7. Oh March 16 6. Oh Perigee - syzygy (hours) Location of tidal flooding ( — 31 min.) Entire mid-Atlantic coast from Long Island, N.Y. to Outer Banks, N.C. (-31 mm.) Do. (-31 min.) Do. ( — 9) Local estuaries and bay locations, Oreg., Wash., and northern Calif. ( — 2) Santa Barbara, Santa Monica, and San Clemente; Newport, Capistrano, and Malibu Beaches, Calif. (-2) Do. (-2) Do. (4-16) Beaches in Massachusetts, New Hampshire, and Maine, and northward to Halifax, Nova Scotia. waters, lies over the Atlantic to the east of the blocked low. This low pressure cell has meanwhile expanded and elon- gated along a southwest-northeast axis. The resulting "fetch" of overwater surface wind movement directed, on the north side of the low, from the sea onto the land, has thus been extended to several hundreds of miles. During the time that this offshore low pressure system had been deepening (979 mb being the lowest pressure actually recorded at sea) the barometric gradient had been steepening. Greatly strengthened, gusty winds re- sulted, blowing onshore from directions originally north- east over the North Carolina and Virginia coasts to final east and east-northeast components over the New Eng- land coastline. Because of the impaired movement of the low pressure center, these intensified winds continued with little diminishment, but with changing locations of maximum onshore intensity, along the coastline for some 65 hours, throughout five successive high tides. Although, as mentioned, peak gusts up to 84 mph (73 knots) were recorded, the average coastal onshore winds during the height of the storm ranged from about 21 to 49 mph ( 1 8 to 42 knots). The devastating effects of the severe offshore storm, plus augmented proxigean spring tides, are illustrated in various forms among the accompanying graphic mate- rials. Representative scenes of extensive inundation of the coastline, severe beachfront erosion, flooding of both suburban homesites and coastal industrial facilities, de- struction and toppling of beach homes (and their trans- port to sea ) , and the complete demolition of waterfront condominiums, are shown in figs. 102-109. The frontis- piece of the book also contains a very meaningful rep- resentation of the extent of damage that such severe tidal flooding can cause. The various contemporary newspaper accounts included in the present section and in table 5 provide valuable supporting information in connection with the 1962 catastrophe. A technical analysis of the time-rate of buildup of this flooding event is also possible from a study of the accom- panying graphs. Fig. 110 shows the progress of an ac- celerated rise in the coastal flooding waters resulting from proxigean spring tides plus onshore winds at Atlantic City, N.J., over a 5-day period bracketing the actual flooding event. The various sets of broken lines in this figure represent individual plots of observed (i.e., re- corded ) hourly heights surrounding the time of each day's higher high water in the period from March 5 to March 9. (Note that the vertical tidal height is plotted in meters as well as feet. ) For comparison, the two solid curves indicate the predicted, or purely astronomically induced tide for March 6 and 7. In all cases, the appro- priate curve is plotted for a 10-hour period in each day, centered on HHW. The accelerated rates of growth of these storm tides, in excess of those which are astronomically induced, are obvious from the shifting of the observed curves to the left of the predicted curves along the time scale of each diagram. The considerably greater amplitudes of these observed curves, in consequence of the sustained wind action, and the resultant sharp peaks, rather than pre- Strategic Role of Perigean Spring Tides, 1635-1976 l Figure 99. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :w) Figure 100. :iou Strategic Role of Perigean Spring Tides, 1635-1976 *t£- • Figure 101. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :m Courtesy of U.S. Army Corps of Engineers (Philadelphia District) Figure 102. — The inundating effects of the great mid- Atlantic coastal storm and tidal flooding of 1962 March 6-7 upon the Grandview Beach section of the City of Hampton, Va. A very close perigee-syzygy alignment oc- curred on 1962 March 6.188 e.s.t. Courtesy of U.S. Army Corps of Engi (Philadelphia District) Figure 104. — Beach homes at Rehobeth Beach, Del., knocked over and reduced to rubble by the impact of the 1962 March 6-7 tidal flooding. rtmurhu, Courtesy of U.S. Army Corps of Engineers (Philadelphia District) Figure 103. — Devastation caused by the wind-driven tidal assault of 1962 March 6-7 at Bethany Beach, Del. Note the completely toppled homes. This aerial photograph was taken on March 11. Courtesy of U.S. Army Corps of Engineers (Philadelphia District) Figure 105. — Nearly total demolition of the Atlantic Sands Resort Apartment at Rehobeth Beach, Del., by the 1962 March 6-7 tidal onslaught. 392 Strategic Role of Perigean Spring Tides, 1635-1976 Figure 106. — Severe erosion of the shoreline along the south coast of Long Island, N.Y., caused by the tidal flooding in- cursion on 1962 March 6-7. The coastal highway was rendered impassable by huge, wave-transported mounds of sand. Courtesy of U.S. Army Corps of Engineers (Norfolk District) Figure 108. — Onshore encroachment of seawater at Nor- folk, Va., associated with the 1962 March 6-7 tidal flood- ing. The area shown is on Moran Avenue between Princess Anne Road and Olney Road. U.S. Coast and Geodetic Survey (Aer Survey) I'hotngrammetric Cnurti'sy of U.S. Army Corps of Engineers (Norfolk District) Figure 107. — Portion of barrier beach south of Mecox Bay, near Southampton, Long Island, N.Y., breached by the tidal flooding of 1962 March 6-7. Figure 109. — The Building 27 warehouse and pier at Fort Norfolk, Va., were extensively inundated by the 1962 March 6-7 coastal flooding event. Note the top of the submerged car in the middle distance. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 393 GREAT MID-ATLANTIC COASTAL FLOODING -1962 PLOT OF OBSERVED AND PREDICTED HOURLY HEIGHTS (HHW) ATLANTIC CITY, N.J. MARCH 5-9 , ' § -~- LEGEND OBSERVED Mar 5 Mar 6 Mar 7 Mar 8 Mar 9 PREDICTED Mar 6 03 2.44 1.83 Z 2 \ % 0.91 07 08 09 HOURS OF THE DAY 11 12 Figure 110. dieted plateaus, of tidal maxima on March 6 and 7 also are clearly evident. Fig. 1 1 1 illustrates the observed rapid buildup and less rapid subsidence of the higher high water phase of the tides at Sandy Hook, N.J., over 7 successive days from March 4 through March 10. The considerable damage to the piers at Atlantic City caused by these repeated extreme rises in water level, and the hurling of ponderous masses of water against the piers by strong winds, is shown in fig. 1 1 3a. Fig. 115a depicts tidal flooding of the streets in Nor- folk, Va., during the earlier phase of the low pressure center's offshore movement when the surface winds at Norfolk were still directed onto the coast. Appropriate newspaper accounts (figs. 112-115) as well as official analyses from Climatological Data — National Summary and Storm Data relative to the meteorological circumstances accompanying this coastal flooding are included on the following pages. ■M 14 Strategic Role of Perigean Spring Tides, 1635-1976 ± 6 SE GREAT MID-ATLANTIC COASTAL FLOODING -1962 PLOT OF OBSERVED HOURLY HEIGHTS (HHW) 6 ,•' SANDY HOOK, N.J. ^ 7 7 ""~^ MARCH 4-10 /'" / \ \ / /' \ N / /' 8 \ \ / /' ,-- V- . \ / ■' ,'''^ \ N v - LEGEND /' / / /' \ \ x . OBSERVED Mar 4 / / /"' \ \ "■ Mar 5 Mar 6 / / /' \ \ X - Mar 8 / /' 5 / \ \ \ / / ....-•• >C \ \ \ Mar 10 / / / -"" ''' '•■■• 9 \ \ \ / / / \ .....- p^"^ \\ / /■' i '■'•• .•*"" /' '"'• ^ s \ * N / / /' 4 / .••' •' \ \" N N ^ / /./' s^" 7^\ V /' \ \%» / //' yS / >V / \ / \ \ \ / /'/' jS / >v /* / '\ \ / /'/ / \ /' X' '''■■".: / 4/ / \./ / \ / ,f / / x' \ /.'•''/ / / / \ " / // / / / \ / / '' /' /' \ / / / ••■''" / \ "'■•■ / / / /' / / \ \ 2.13 1.83 Z 1.52 02 03 04 05 06 07 08 HOURS OF THE DAY 09 10 11 0.61 Figure 111. Fig. 161a in chapter 8 further represents the predicted rate of tide rise at Breakwater Harbor, Del., as a func- tion of the proxigean spring tide which — acted upon by supporting winds — precipitated this tidal flooding event. It is especially noteworthy that this method of analysis reveals the March 6.19 proxigee-syzygy alignment to lie centrally within a "window" of potential tidal flooding, with the peak of the tidal growth curve well into the potential danger zone. To conclude the list of items under substantive review, it is, therefore, also significant for the future in connection with such tidal floodings to note that this circumstance was in no way predicted. (See the "Today's Forecast" and "Five-Day Forecast" columns from the New York Times in fig. 112.) Despite the very close proxigee-syzygy alignment ( -31 minutes) accompanying this event, and the considerable potential for tidal flooding, the event was later described in all public announcements only as being associated with "spring" tides. With the appropriate use of the data contained in table 34, the computer printout of table 16, and the de- velopmental predictor equation of chapter 8, such a seri- ous tidal flooding eventuality, it is to be hoped, can in the future be avoided. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings :m The New York Times Tues., March 6, 1962 Page 70 L+, Cols. 2-5 The Summary Snow fell yesterday from the North Atlantic States to the Mississippi Valley and in the higher parts of the Pacific States. Rain fell in the North Atlantic States and the Pacific States. Low pressure will dominate the East and the Pacific Northwest today. High pressure will extend from the Mississippi Valley to the plateau region. Snow is the forecast today for the north- ern plateau region. Snow mixed with rain will fall from the North Atlantic States to the Appalachians. Rain will fall in the western plateau region and the Pacific States. It will lie colder in the Atlantic States, the Ohio and Mississippi Valleys and the lake region. Today's Forecast United States Weather Bureau (As of 11 P. M.) NEW YORK CITY, NEW JERSEY, LONG ISLAND, LONG ISLAND SOUND, ROCKLAND AND WESTCHESTER COUNTIES, SOUTHEASTERN NEW YORK, EASTERN PENNSYLVANIA AND CONNECTICUT— Snow today and tonight, highest temperature today in the 30's, northeasterly winds 35 to 45 miles an hour ; lowest temperature to- night near 30. Cloudy and cold tomor- row. (As of 5 P. M.) MASSACHUSETTS, VERMONT, NEW HAMPSHIRE AND NORTHEASTERN NEW YORK — Snow, except snow or rain southeast portion today ; snow north portion, snow or rain southwest portion tonight. Day's Records NEW YORK Eastern Standard Time 0£3 C£3 OtfS,0£VQ£% Os£>Os3oO££ QSS Q£$r Figure beside Station Circle indicates cur- rent temperature (Fahrenheit) ; a decimal number beneath temperature indicates pre- cipitation in inches during the six hours prior to time shown on map. Cold front: a boundary line between cold air and a mass of warmer air, under which the colder air pushes like a wedge, usually advancing southward and eastioard. Warm front: a boundary between warm air and a retreating wedge of colder air over which the warm air is forced as it advances, usually northivard and eastward. Stationary front: an air mass boundary which shoxos little or no movement. Occluded front: a line along which warm air has been lifted from the earth's surface by the action of the opposing wedges of cold air. This lifting of the warm air often causes precipitation along the front. Shading on the above map indicates areas of precipitation during the six hours prior to time shown. Isobars (solid black lines) are lines of equal barometric pressure and form patterns which control air flow. Labels in millibars and inches. Winds are counter-clockwise toward the center of low-pressure systems, and clockwise and outward from high-pressure areas. Pressure systems usually move eastward at an average movement of 500 miles a day in summer and at a rate of 700 miles a day in the winter. Temp. Midnight 30 1 A.M 30 2 A.M 30 3 A.M 30 4 A.M 30 5 A.M 30 6 A.M 30 7 A.M 31 8A.M 31 9 A.M 32 10 A.M 35 11 A.M 36 Noon 36 1 P.M 36 2 P.M 37 3 P.M 38 4 P.M 37 5 P.M 38 6 P.M 39 7 P.M 38 8 P.M 36 9 P.M 36 10 P.M 36 11 P.M 34 Midnight 35 1 A.M 35 Hum. 53 56 55 56 56 56 63 61 63 66 67 69 72 79 79 79 85 82 79 78 85 85 85 92 89 89 Wind (M.P.H.) N 8 N 6 N 5 N 6 N 6 N 5 N 8 N 8 N 6 NE 9 NE 11 NE 11 NE 13 NE 15 NE 16 NE 17 NE 16 NE 16 NE17 NE 18 NE 19 NE21 NE23 NE25 NE27 NE27 Bar. 30.05 30.04 30.04 30.02 30.02 30.03 30.04 30.05 30.06 30.05 30.06 30.05 30.04 30.00 29.98 29.95 29.93 29.98 29.98 29.98 29.93 29.93 29.91 29.86 29.82 29.81 Five-Day Forecast (March 6 through March 10) SOUTHEASTERN NEW YORK, EAST- ERN PENNSYLVANIA, NEW JERSEY AND CONNECTICUT — Temperatures will average near normal, except 2 to 4 degrees below normal in extreme south- ern sections. It will be cold today and tomorrow with warming toward the end of the period. (Some normal high and low temperatures are : Albany 39-21, At- lantic City 46-33, Hartford 44-24, New York 46-31, Philadelphia 49-33 and Scranton 42-25.) Snow inland and snow or rain along the coast today and rain Friday or Saturday may total more than one-half an inch melted. 1962 Mar. 6 4.5h e.s.t. (-31 min.) J-85 Figure 112. 396 Strategic Role of Perigean Spring Tides, 1635-1976 The New York Times Wed., March 7, 1962 Page 24 L-f, Cols. 1-4 (Continued from Table 5) Snow, Rain, Gales, Tides Lash Mid- Atlantic States (Continued from Page 1, Col. 3) . . . The northeast storm developed with multiple centers, according to the Weather Bureau, including one low pressure area in Virginia and another southwest of Ber- muda. It stalled in the face of a cold, high- pressure area from Canada . . . . . . Twenty-three persons in Far Rock- away and six in Breezy Point were evacu- ated when high tides threatened their homes . . . . . . Ferry service between Staten Island and Sixty-ninth Street, Brooklyn, was halted from 8:15 A. M. until 10:26 A. M. because high tides made loading of ve- hicles and passengers impossible . . . . . . The Brooklyn-St. George ferry ceased operations again during high tide last night, starting at 7 :30 o'clock . . . . . . Flooding forced scores of families from homes in south shore communities. Sections of Franklin D. Roosevelt Drive, the Belt Parkway in Brooklyn and the Hutchinson River Parkway in the Bronx were flooded and closed to traffic part of the day . . . . . . High tides in the morning and evening Halted service on the railroad between Island Park and Long Beach . . . . . . The Erie-Lackawanna ferry to Barclay Street was closed from 7 :25 to 10 :30 A. M., and again during evening high tide, start- ing at 6 :55 . . . . . . The Jersey Central Railroad ferry from Jersey City to Liberty Street was halted from 7 to 10 :15 A. M. Flooding later halted the line at Jersey City and Bayway, so that until noon, service ended at Bay- onne. Jersey Central normally handles 10.- 000 passengers each morning. Ferry service was also suspended by the Jersey Central last night during high tide . . . . . . Flooding in the Atlantic resort area and neighboring communities was exten- sive. A fifty-foot section at the end of the Steel Pier, used for a water circus, was washed away, and a thirty-foot section in the midway portion of the pier was de- molished. So was a 200-foot section of the boardwalk in the Inlet section while a sixty-five-foot boardwalk approach there was washed across Maine Avenue . . . . . . The staff of The Atlantic City Press, a morning newspaper, worked with its composing room and much of its editorial office covered by water at high tide . . . . . . Municipal offices in Asbury Park's Convention Hall were flooded. Several hun- dred feet of the boardwalk were damaged as tide-driven sand made the structure bulge upward. The Loveland Town bridge over the In- land Waterway Canal in Point Pleasant between the Manasquan River and Barne- gat Bay collapsed when racing waters un- dermined its pillars. Almost every house in Sea Isle City. X. J., which has 1,200 residents, was re- ported flooded by four to five feet of water. Seventy-five families were evacuated fromTsland Park, Oceanside, Bellmore and Seaford, L. I., when water rose two to three feet. Wind-driven waves twenty feet high stormed Fire Island, carrying away sand dunes on the ocean side and wreck- ing some Boardwalk and other facilities . . . The barrier beaches of Long Island, from Coney Island to Montauk Point, were battered heavily. Many streets in Coney Island were covered by up to two feet of water last night. In Nassau County, flooding cut off sec- tions of Merrick, Baldwin Harbor, East Rockaway and Point Lookout. High seas took a heavy toll of the dunes from Fire Island to Montauk. At West- hampton Beach, three luxurious summer homes were demolished . . . ... In Fairfield County, Conn., several families were evacuated in shore homes in Norwalk, Darien and Westport . . . 7962 Mar. 6 4.5h e.s.t. (-31 min.) J-85 Figure 113. (Aerial Photogrammetrlc Figure 113c -Aerial photograph taken over Atlantic City, N.J. at 1030 e.s.t. on March 25, 1962, showing damage to Steel Pier by severe tidal flooding of March 6-7. Flight altitude, 10,000 ft; scale 1 : 20,000. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 397 The New York Times Thurs., March 8, 1962 Page 1, Cols. 6, 7 (Late City Ed.) Storm Hits Coast 2d Day; 27 Dead, Damage Heavy By Russell Porter At 7 o'clock last night the ocean broke through Long Beach Island, cutting off Beach Haven. Police Chief Jerry Sullivan of Atlantic City predicted the damage would he "much more" than the $5,000,000 damage the city sustained in a hurricane in 1944. The re- sort city was swept by tides six feet high and winds that hit eighty-four miles an hour in gusts . . . The heavy storm that swept the mid- Atlantic states Tuesday struck again yes- terday with high tides and winds along the coast. At least twenty-seven persons were reported dead in its wake as the storm swept out to sea. Thousands of homes were wrecked or damaged from Virginia to New England, and thousands of persons were evacuated. Hundreds were marooned without electric- ity, gas or drinking water, and food ran low. Rescuers used trucks, cars, boats, am- phibious vehicles and helicopters . . . . . . The Weather Bureau predicted that strong, gusty winds and above-normal tides would continue through the night, but that the wind and water would sub- side today. Tidal waters in this area were expected to rise three to five feet above normal dur- ing the night, and two to three feet higher than usual in the early morning. There may be more flooding . . . . . . The New York metropolitan area was hit hard yesterday by extremely high tides, heavy surf, violent, winds, flooding and power failures. Ferry, rail and high- way traffic was disrupted. Winds up to fifty miles an hour blew across the city. Streets in lower Man- hattan, and sections of the East River Drive, the Hutchinson River parkway and the Belt parkway were closed by flooding. Coney Island was flooded and hotels and apartment houses in the Rockaways were evacuated . . . 1962 Mar. 6 4.5h e.s.t. (-31 min.) J-85 The New York Times Thurs., March 8, 1962 Page 22 L++, Cols. 3-8 . . . Cape May, Monmouth and Ocean Counties declared states-of-emergency. All 700 residents of Long Beach Island were evacuated, and nine houses were seen floating in Barnegat Bay . . . . . . State officials in Trenton last night estimated the damage in coastal areas at $30,000,000. Winds as high as forty miles an hour and abnormally high tides were still battering the coast. NEW YORK Sayville ^o Westhampton Beach irV/t - ^ a tl Shore; $#£:-■£ Babylon I iNew \ -~y^ Ocean Beach The New York Times March 8. M62 HAVOC: Storm swept houses at (1) and (2) into ocean, inundated Rockaway area (3), routed Long Beach Island residents (4), and pounded Atlantic City (5). . . On Long Island. Suffolk County Ex- ecutive H. Lee Dennison also said damage was in the hurricane class. He asked Gov- ernor Rockefeller to declare the South Shore, along the Atlantic, a disaster area. Mr. Dennison declared a state of emer- gency along the shorefront. He estimated property damage at more than $2,000,000. More than seventy houses, including thirty-five on Fire Island, were destroyed on the barrier beaches of the county. Fif- teen summer houses on the dunes at West- hampton Beach were undermined and swept out to sea. About twenty other houses were lost in near-by coastal re- sorts . . . . . . Most ferries morning rush In high tidal waters, failures . . . stopped running as the ur started, because of heavy winds and power . . . The rising tide forced the suspension of ferry service between Staten Island and Manhattan between 8:05 and 9:18 P. M. Two boats with about 2,000 passengers Figure 114. 398 NEW YORK (Cont.) Strategic Role of Perigean Spring Tides, 1635-1976 each stood off St. George. S. I., unable to dock because of high water . . . . . . Service on the Tubes was suspended again last night when high tides flooded the tracks between Newark and Jersey City. The rising waters also forced cancel- lation of the Erie-Lackawanna ferry serv- ice between Hoboken and Manhattan at 8:50 P. M. The Greenwood Lake and Newark lines of the Erie-Lackawanna Railroad were put out of commission by flooding. The Penn- sylvania Railroad reported some commuter trains from North Jersey shore points de- layed by high water, some as much as thirty minutes . . . . . . Power on the Long Beach line of the Long Island Rail Road was cut at 8:25 A. M. for the third time in two days as third rails were flooded . . . . . . Service was resumed at 1 P. M. but was interrupted again last night by the rising tide. It was expected to go back to normal when the tide receded. Much of the East River Drive was closed. At noon a foot of water covered the roadway between Eightieth and Nine- tieth Streets . . . . . . The eastbound lane of the Belt was closed because of high tides at 9 P. M. over a three-mile section from Fort Hamilton Parkway to Bay Parkway. The westbound lane was closed at 10 :30 and the police said the road would be reopened after the tides diminished. Some streets in downtown Manhattan were also closed by flooding, including Pearl Street from John Street to Maiden Lane. The east side of Whitehall Street from the tip of Manhattan island to Front Street was under water. The worst of the flooding in the city was in the Rockaways and near-by sections. Water covered the tops of parked automo- biles in some areas. Water from Jamaica Bay was so deep at Howard Beach that commuters were unable to wade through it to the subway and buses were unable to get to Hamilton Beach. About 100 marooned families were evacuated from Breezy Point at the west end of the Rockaway peninsula . . . . . . Flood waters inundated Wallops Island, Va., a launching site of the Na- tional Aeronautics and Space Administra- tion. In Chincoteague, Va., 1,000 residents were evacuated after their homes began to break up under the pounding of the surf. At least five persons lost their lives there . . . TIDE CYCLE AND WIND BLAMED IN FLOODING WASHINGTON, March 7 (AP)— Winds from one of the worst winter Atlantic storms ever recorded, at a time of normal- ly high tides, combined to produce the devasting high water today on much of the East coast. The main path of the wind, out of the northeast, was along a line extending from about 300 miles off Cape Cod to the Vir- ginia-North Carolina coast. In a meteor- ologist's or sailor's term, this is a long fetch of about 600 miles. Such a long fetch gives time and opportunity for the winds to pile up water before them. The rush of wind, pushing and dragging water, came at a time when tides in the normal course would have been high. In the twenty-eight-day moon cycle there is a period when the gravitational forces of the moon and the sun. acting on the oceans, pull in opposite directions, dimin- ishing the tides. There is another period when these forces pull together and give higher tides. This storm happened to come in such a period . . . 7962 Mar. 6 4.5h e.s.t. (-31 min.) J-85 Figure 115a. Figure 115a. — The corner of Bank Street and City Hall Avenue in downtown Norfolk, Va., showing the tidewaters reced- ing after the great mid- Atlantic coastal flooding of March 6-7, 1962. Note the dark 3-foot highwater mark on the wall at the right. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 399 Abstracted from: Cooperman A. I., and Rosendal, H. E., "Great Atlantic Coast Storm, 1962, March 5-9," U.S. Weather Bureau Climatological Data — National Sum- mary, vol. III. 1962, p. 137. "A slow moving late winter coastal storm combined with springtides (maximum range) wrought tremendous destruc- tion to coastal installations from southern New England to Florida on March 6-9. This storm, which consisted of a series of LOWS, has been described as one of the most dam- aging extratropical cyclones to hit the United States coast- line. Although gale-force winds, and at times hurricane- force winds, accompanied the storm, this is not unusual for a North Atlantic winter extratropical cyclone. It was the long fet^h and the persistence of these strong northeasterly winds which raised the spring tides to near record levels. The tidal flooding which attended this storm was in many ways more disastrous than that which accompanies hurricanes. The storm surge in tropical cyclones generally recedes rapidly af- ter one or two high tides, but the surge accompanying this storm occurred in many locations on four or five successive high tides. In addition, many places reported runup of waves 20 to 30 ft high. "This successive onslaught of wave and tidal action for over two days weakened and undermined even the more permanent shoreline structures, and after a period of time some suffered structural damage and collapsed. . . . "The erosive effect of wave and tidal action changed the face of the immediate coastline, and on many of the well- known beaches the most severe loss was often the sand of the beach itself. In addition many new channels and inlets were cut in the shoreline. . . . "Preliminary estimates of damage total about $200 mil- lion; 1,893 dwellings were destroyed, 2,189 sustained major damage, and 14,593 minor damage. Thirty-three persons are known dead; 340 received major injuries and 912 minor injuries. ". . . This storm, although it first appeared as a wave on the polar front on the 4th off the Florida coast, did not deepen to any extent until it reached the Hatteras area. . . . "When the coastal storm started to form as a wave on the polar front off the Atlantic coast of Florida on the 4th, the dominating features on the weather map were a strong block- ing HIGH centered over the Canadian Arctic Archipelago with a ridge extending south-southeastward over the Middle Atlantic States and a moderate LOW located over the upper Mississippi Valley. On the 5th the interior LOW with a very deep circulation aloft moved along the southern fringes of the Canadian HIGH to the Ohio Valley, where the surface LOW began to dissipate. In the meantime, a wide area of low pressure with several separate centers had developed be- tween the Carolina coast and the wave off the Florida coast. The deep LOW aloft which was associated with the dissipat- ing interior LOW continued its eastward movement, and by the 6th it was located over the Carolina coast. This triggered the intensification of the coastal LOW which still consisted of several ill-defined centers. The usual northeastward move- merit of such a system was retarded by the presence of the blocking HIGH which was now centered near Labrador. On the 7th and 8th this HIGH continued to move southward to- ward northern New England, as the intensifying coastal storm started to drift east-northeastward. This resulted in the LOW elongating in a roughly east-west direction with a very steep pressure gradient. ... A long fetch of north- easterly winds was set up by the configuration of this elongated LOW. This pattern persisted from late on the 6th to the 8th, and the resulting strong northeasterly winds piled up additional water on top of the high spring tides and cre- ated mountainous seas which pounded savagely at the coastline- ". . . [A sea-condition analysis revealed] a significant wave height of more than 40 ft at 0000 G.m.t. of the 8th. The cause of such high seas from the east . . . was the slow move- ment of the system and its elongated shape. Furthermore, the westward traveling seas were already set up, by the previous LOW, across the entire ocean to Europe, . . . [facilitating the breakdown of the] . . . easterly winds and rebuilding of waves traveling in the opposite direction. "The pressure gradient near the center of the system was not very steep, and the lowest pressure recorded was only about 979 mb which is deep for an extratropical LOW in the western North Atlantic, but not too unusual. Within this "shallow" and fairly large region of the lowest pressures, two or three separate low pressure cells could be detected during the first few days of the storm by analyzing the wind and pressure data received from ships in the area. These cells appeared to rotate within the primary system with the for- ward one weakening and a cell toward the rear generating and taking over. This caused the movement of the system as a whole to be rather erratic, and at times the storm appeared to move backward or loop. Any single track is thus difficult to construct. "Precipitation was heavy over the Middle Atlantic Coast with interior portions of Virginia and Maryland receiving up to three feet of snow accompanied by some thunderstorm activitiy during the development stage of the storm. As the LOW became more mature, only light precipitation fell to the north of it, and in New England the storm was known as a "dry northeaster." Much of the driving energy was prob- ably caused by the transformation of potential energy stored in the large warm HIGH into kinetic energy along the steep pressure gradient of this LOW. . . . "NEW ENGLAND.— Central and northern New England escaped relatively lightly the effects of the coastal storm. Seas came crashing over walls along all parts of the coast south of Portland, Maine. Low lying coastal highways were flooded and closed to traffic as tides ran up to 5 ft above nor- mal. Damage to seawalls was slight along the Maine coast but was heavier along the New Hampshire shore. Complete sections of old seawalls were washed out at the New Hamp- shire resort towns of Rye, North Hampton, and Hampton. Some structural damage to waterfront installations, mostly of minor nature, occurred in New Hampshire and Massachu- setts, and many cellars in low-lying districts were flooded. Most damage in Connecticut and Rhode Island was con- fined to beaches along the south coast and Block Island. There was some flooding in low susceptible places in Bridge- port, East Haven, and Greenwich, and the Quinnipiac River overflowed in North Haven doing some damage. An oyster !()(.) Strategic Role of Perigcan Spring Tides, 1635-1976 boat and barge were sunk near New Haven. The highest winds reported on the East Coast occurred at Block Island. The Weather Bureau Airport Station recorded a peak gust of 84 mph and a sustained wind of 76 mph on the morning of the 6th. "Preliminary damage figures for the New England States: Maine, $25,000; New Hampshire, $27,000; Massachusetts, $250,000; Rhode Island and Connecticut, $1 million. No lives were reported lost in the New England area. "NEW YORK. — The strong winds pushed the ocean waters onshore, producing severe flooding. At the time of high tides on the 6th and part of the 7th, the waters reached between 4 ft above mean sea level along the western end of Long Island and 7 ft above in New York Harbor. On top of the high water the storm sent huge waves, estimated at 20 ft high in places, to break against beachfront installa- tions. Damage was greatest on the south shores of Rich- mond, Brooklyn, and Queens Boroughs in New York City, and along the barrier beaches of Nassau and Suffolk County, eastward to Montauk Point. On Long Island's South Shore about 100 houses were swept into the sea, 35 of them on Fire Island alone. Numerous other buildings suffered water damage, and cellars, streets, and highways in waterside areas were flooded. There was also wind damage to utility lines, trees, signs, and windows, but these losses were compara- tively minor. "Preliminary and unofficial damage estimates are in the $10-$ 15 million range. Fortunately, no loss of life or injuries were directly attributable to the storm, although many families were forced to evacuate threatened dwellings. "NEW JERSEY. — . . . The major damage was re- stricted to property facing the beach itself. The entire coast- line and even the Delaware Bay area suffered from the high tides. Highways along the coast were cut in many places or buried under several feet of sand. Thousands of homes along the coast were damaged or destroyed. One of the hardest hit areas was Long Beach Island. At Atlantic City the major damage was the cutting of the famed Steel Pier. The storm swept away the quarter-mile section of the pier which connects the auditorium at the end of the pier with the mainland boardwalk. . . . "The storm did an estimated $80 million damage in New Jersey. Deaths mounted to 14 with 12 other persons, in- cluding nine aboard two fishing trawlers, missing and pre- sumed dead. "DELAWARE AND MARYLAND.— The Atlantic coast resort towns bore the brunt of the storm in these States. Four or five consecutive high tides with 20— 30— ft waves right against the coast caused serious beach erosion and de- struction of shoreline property along the Delmarva Penin- sula from Cape Henlopen and Cape Charles. At Rehoboth Beach, Del., and Ocean City, Md., complete destruction to severe damage was inflicted to many resorts on the immedi- ate coast while tidal flooding occurred farther inland. Tides at Ocean City were estimated to be 5 to 6 ft above nor- mal. . . . The boardwalks were reduced to splinters early in the storm, . . . and in . . . resort areas much of the sand was washed away. . . . Less serious flooding occurred in the Bay areas. The rain-soaked soil of late winter prob- ably prevented severe damage to inundated farmlands far- ther inland or in the Bay areas. It is estimated that from 1.2 to 1.5 million broiler chickens and an unknown number of incubator eggs were lost chiefly due to power failures in the Delmarva production area. "Preliminary estimates on damage for the Delaware- Maryland shore are about $50 million. Seven deaths were reported in Delaware and three in Maryland. "VIRGINIA. — The intense coastal storm brought as se- vere damage to the Atlantic coastline of Virginia as any extratropical storm in modern times. The resort areas near Virginia Beach in particular had heavy property losses. Many hundreds of homes on the beaches were totally de- stroyed and thousands were damaged. The fishing pier at Virginia Beach was destroyed. The largest pile driver in the world, a $l 1 /o million machine, was turned over on its side in deep water. One of the communities hardest hit along the Virginia section of the Delmarva Peninsula was Chinco- teague Island. Extensive damage was done to the fishing boats and nets, homes and livestock. . . . Many ponies on Chincoteague drowned. More than 1,000 persons were air- lifted by helicopter to the mainland during the storm. The NASA installation on Wallops Island also suffered consid- erable damage. High tides inundated large areas inside the Bay, and sections of Hampton Roads were under several feet of water. The 8.9 ft tide above mean low water, 5.6 ft above normal, was the highest tide caused by an extratropi- cal cyclone and the third highest of record. More than 1,000 automobiles were flooded in the metropolitan area alone. The Chesapeake Lightship of the Coast Guard while on station at 36°59'N., 75°42' W., or 17 mi east of Cape Henry Lighthouse was damaged by a 50-ft wave early on the 7th and forced to leave the station. At this time sustained winds were above hurricane force. "Damage in Virginia is estimated at $30 million; however, the full extent is not known. In the city of Virginia Beach alone, damage amounted to about $16 million. Five deaths were reported in Virginia. "NORTH CAROLINA.— The most destructive effects of the storm took place on Hatteras Island and northward. On the entire stretch to the Virginia line, a large percentage of the protective sand dunes along the ocean side of the elongated islands which constitute the Outer Banks were washed flat. A 200-ft wide inlet was cut, by waves and strong currents at the change of the tides, across Hatteras Island about 2 mi north of Buxton. The highway along the shore was destroyed or undermined in many places or cov- ered with sand up to several feet deep. Many cars were stranded with only the rooftops appearing above the sand. Most of the damage to private property occurred in the Kill Devil Hills-Kitty Hawk-Nags Head area north of Oregon Inlet where many motels and summer homes suffered. "Preliminary damage figures are estimated at $12 million which does not include the devastation to the land itself. Two deaths were reported in North Carolina. "SOUTH CAROLINA.— Damage from the coastal storm in this State was mainly limited to tidal flooding and some beach erosion. A few cottages along the beaches were de- stroyed and others damaged. All beaches along the coast Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 401 suffered in varying degrees from loss of sand in certain sections. Folly Beach is estimated to have lost 100 to 200 ft in width for one-quarter mile in an uninhabited area near the east end. . . ." RHODE ISLAND From: Storm Data, Vol. 4, No. 3, March 1962 J-86 — Coastal Flooding of: 1962 March 6-7, East Coast of U.S., Maine-South Carolina Coastal South of "Mar. 6-8 — This area received fringe Portland. effects of a vast ocean storm that wreaked havoc along coastal areas far- ther south. Flooding of coastal lowlands and some road washouts were reported. Slight damage was reported to seawalls. NEW HAMPSHIRE Coastal "Mar. 6-8 — This area received fringe effects of a vast ocean storm that wreaked havoc to coastal areas farther south. A combination of wind-driven tidal surges and spring tides brought seas crashing over and damaging walls erected against them. Coastal lowlands were flooded and some road washouts were reported. Foundation of a beach- front home was washed out. MASSACHUSETTS Coastal Areas "Mar. 6-8 — This area was relatively lightly affected by the vast ocean storm that wreaked havoc over coastal areas to the south. A combination of wind-driven tidal surges and spring tides brought seas crashing over and damaging walls erected against them. Complete sections of some old seawalls were washed out. Low-lying areas were flooded. Some structural damage to waterfront installa- tions occurred and many cellars were flooded. About 100 residents of Ken- berma Park, Hull, Mass., were evacu- ated as a precautionary measure. Winds reached and maintained gale force for long periods on the 6th and 7th. How- ever, wind damage was scattered and mostly light and was generally limited to broken windows and downed signs. Many flights out of Logan Airport, E. Boston, were cancelled because of the winds there and the weather at other airports along the coast. A boy was in- jured when struck by a wind-blown storm door. Coastal Sections. Shore Areas. Coastal sections extending from the New York City area throughout Long Island and Montauk Pt. "Mar. 6-7 — Four successive high tides, 2-4 feet above normal, with gale-force winds and gusts to 80 mph in southern sections of the mainland and hurricane winds with gusts to 85 mph on Block Island, combined with surging waves to batter seawalls and destroy beaches as a great storm moved eastward in the Atlantic well south of Rhode Island. Strongest winds occurred on March 6, and highest tides on the morning of March 7. Considerable flooding in New- port, South Kingston, Bristol, Barring- ton and Warren. Many piers and boats damaged. Heavy waterfront sand ero- sion and some property damage with 3-5 feet of sand being stripped from beaches between Point Judith and the Pawcatuck River. CONNECTICUT "Mar. 6-7 — Four successive high tides, 2-4 feet above normal, with gale-force winds battered seawalls as a major storm moved eastward in the Atlantic well south of the State. Greatest damage due to tidal flooding in Fairfield and eastern New London Counties with minor dam- age along rest of Coast. Sand erosion moderate along easternmost beaches. Wind damage confined to tree branches and downed powerlines. NEW YORK "Mar. 6-8 — A great Atlantic storm was centered off the Maryland-Delaware coast during the period. The extensive intensifying storm finally encompassed much of the North Atlantic and caused destructive winds, tides, and waves over much of the Atlantic seaboard from southern New England to Florida. The gale- to hurricane-force northeast winds from this great storm pushed the ocean waters onshore during at least five suc- cessive high tides in an unprecedented manner. On top of the near-record tides was repeated wave action of heights be- tween 20 and 30 feet. Great and un- precedented damage was done to barrier dunes, beaches, and all types of shore installations. Damage was greatest on the south shores of Richmond, Kings, and Queens Boroughs in New York City, along the barrier beaches of Nassau and Suffolk counties, eastward to Montauk Point. One hundred or more houses were 202-509 O - 78 - 28 •11)2 Strategic Role of Perigean Spring Tides, 1635-1976 swept into the sea. Many hundreds of buildings suffered water and structural damages. Streets and highways, utility lines and boats were severely damaged or wiped out. Much of the area lost its bar- rier dunes and beaches and left further inland properties exposed to future storms. Property damage expected to be well up in [the range from $5 million to $50 million.] NEW JERSEY Entire coastline "Mar. 6-8 — A severe coastal storm, of State, in- moving very slowly, combined with high eluding Dela- tides on five consecutive occasions in a ware and Ra- three-day period, wrought tremendous ritan Bay. destruction to coastal installations. Hun- dreds of summer homes were demol- ished. The sand from beaches was washed away, changing the shoreline in many areas. Many new channels and inlets were cut in the shoreline. High- ways were cut in many places, or buried under several feet of sand. A Navy de- stroyer, the MONSSEN, was beached about a half mile north of Beach Haven after breaking its tow. The destroyer was unmanned and was being towed to Philadelphia from Bayonne Navy Yard. Loss of life from the storm includes 6 persons missing and presumed dead. Five of those six were aboard a fishing trawler off the New Jersey coast. Agri- cultural losses were chiefly due to flood- ing of around 1,000 acres of Cumberland County, on Delaware Bay. DELAWARE Coastal Areas "Mar. 5-8 — The storm deepened and nearly stagnated off the Virginia Capes giving sustained northeasterly winds for over 24 hours. The highest windspeed at Delaware Breakwater was NE 72 mph at 9PM on the 5th. The storm tide piled on top of the high spring tides to make the water up to 5 feet above normal. In addition, 20 to 30 foot waves broke against the coast causing very serious beach erosion and destruction of shore- line property. Many beach homes and commercial properties were damaged or destroyed. In some places the beach sand was completely washed away. Salt damage to flooded farmlands in north- ern Delaware is considerable. Coastal Areas. Eastern Shore and Tidewater areas. MARYLAND "Mar. 5-8 — The storm deepened and nearly stagnated off the Virginia Capes, giving sustained northeasterly winds for over 24 hours. Ocean City Coast Guard reported 40-45 mph wind with gusts 55- 65 mph for 18 hours. The storm tide piled on top of the high spring tides to make the water up to 5 or 6 feet above normal. Four or five such high tides with 20 to 30 foot waves broke against the coast, causing serious beach erosion and destruction of shore property. Many beach homes and commercial properties were damaged and destroyed. Other property was damaged by water and sand. Nearly 1.5 million broilers and an unknown number of incubator eggs were lost due to power failure. Salt damage to flooded farmlands was minimized by the rainsoaked soil. Direct wind damage was small. Greatest and longest lasting dam- age is to beaches where the sand was washed away. "Mar. 6-8 — The combination of the long fetch of strong onshore winds and the 'spring tides' caused greater wave and surf damage and tidal flooding than any other coastal storm of recent record. The islands Chincoteague and Assa- teague were completely covered with water and more than 1,000 residents were evacuated by military helicopters. Hundreds of homes on the beaches were totally destroyed and thousands were damaged; many residents were evacu- ated by boats and amphibious equip- ment. The fishing pier at Virginia Beach was destroyed and the largest pile driver in the world (a one and one-half mil- lion dollar machine) was turned over on its side in deep water. Hampton Roads Harbor experienced the highest tide on record for an extratropical storm, that of 5.6 feet above normal, which was less than a foot below the record tide during a hurricane of 1963. All Eastern Shore and Tidewater region was de- clared a disaster area by the Governor. Removal of sand by waves and tide has in many cases changed the configuration of the shoreline. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings •id:-; NORTH CAROLINA Northern Coast _ "Mar. 6-8 — Large and persistent low pressure storm caused greater alteration of coastline from Hatteras northward than any previous known storm, includ- ing hurricanes. Miles of protective dunes destroyed and several breakthroughs entirely across Outer Banks from Ocean to Sound. Completely new inlet 200 yards wide dividing Hatteras Island in two parts will require bridging. Miles of paved highway destroyed by washing out or buried in several feet of sand. Hundreds of beach homes destroyed or damaged, hundreds of autos submerged in water or buried in sand. Many resi- dents evacuated by helicopter. Two el- derly persons died from excitement and exposure due to rigors of the storm. Ship broke in two 100 miles off Hatteras with one person lost. Most of damage due to high water and pounding surf. Highest recorded wind gusts near 70 miles per hour, lowest barometer 29.20 inches at Nags Head. Highest tides about ten feet above mean low water with seas of about 20 ft. height. Number of persons in- jured estimated. SOUTH CAROLINA Coastal "Mar. 7-9 — The Great Atlantic Coast Storm of March 5-9, 1962 did limited damage in this state. Damage was mainly in the form of tidal flooding and beach erosion. Some beach cottages were de- stroyed, others damaged. All beaches suf- fered from loss of sand." 5. The Aborted Tidal Flooding of 1962 October 13 The tidal flooding of 1962 October 13 (Key No. 86) is of definite parallel interest to the preceding discussion of the 1962 March 6-7 tidal flooding. This is because the event is cyclically related to the latter perigean spring tide through the 221.5-day average period of recurring alignments. The October perigee-syzygy alignment also occurred nearly simultaneously with a very active weather disturbance along the Pacific coast now familiarly known in that area as the "Columbus Day Storm of 1962." Although some flooding damage was experienced in connection with the near-coincidence of these events, it was nothing like that which accompanied the March 6-7 catastrophe. Contradictingly, the associated storm on the west coast was, if anything, much more severe. An entire book has been written describing the widespread effects of this natural disaster. 2 Since an immediate question is raised as to why this case of perigee-syzygy, accompanied by a severe storm, did not produce the same marked degree of tidal flooding resulting from the very similar storm tide of March 6-7, a detailed comparison is in order. The surface synoptic weather map (fig. 66) for the date 1962 October 13 at 0100 h (e.s.t.) is included to make the analysis easier. (For the local tidal flooding effects observed around this date, see table 1 . ) It is obvious from all evidence that the catastrophic effects of the 1962 Columbus Day storm on the Pacific coast were largely the result of wind damage rather than any major tidal flooding. This event nevertheless is dis- cussed in detail here because of : ( 1 ) its local coastal flood- ing influences, including tidal impairment of hydrological runoff; and (2) the latent potential for extremely violent tidal flooding by the proxigean spring tides present, had the weather and wind been but slightly different. Considering first the atmospheric low pressure system responsible for this storm, it is noteworthy that the deep cyclonic system that was located just offshore along the northern California and southern Oregon coasts on Oc- tober 12 had basically a northerly component of move- ment and, further, that the storm center hugged the coast very closely. This low pressure center also possessed an elongated north-south axis and moved very rapidly north- ward parallel to the coast. This situation provided a limited fetch in wind move- ment over the surface of the water. The coastal winds pos- sessed directional components primarily from the south (parallel to the coast) shifting only slightly to south- westerly components inland, with their directions still channeled strongly by the north-south oriented valleys here. Those portions of the Oregon coastline which were exposed to any onshore component of the wind are char- acterized by cliff topography, with no lowland portions susceptible to flooding except in small bays and estuaries. In addition, the pressure gradient both in front of and behind the low pressure system was so steep, the alternat- ing fall and rise in pressure as the system passed so rapid, gusting winds so prominent, and the whole system's move- ment over the water comparatively so brief, that the principal air-water interaction was evidenced in high waves and spindrift rather than long-period onshore swells. The entire storm intensified and swept through coastal points, with winds shifting into directions parallel to the coast and even offshore as the storm's center moved slightly inland. The intense central core of the low pressure 101 Strategic Role of Perigean Spring Tides, 1635-1976 system was narrow and produced southerly winds along its eastern side and easterly winds along its northern extremities as it moved inland. The strongest winds in the Willamette Valley, Oreg., were from the south. The storm system and its associated atmospheric front moved almost directly northward from the vicinity of Crescent City, Calif., to Portland, Oreg., in less than 5 hours 'traveling at something less than 50 mi/hr). The storm center with its cyclostrophic winds remained just inland of the coastline during the early portion of its passage, then erratically shifted offshore again in the latter portion (see fig. 66 ) . The entire course of this move- ment along the Pacific coast lasted barely 1 .5 days. Thus, in recapitulation, the comparatively low flooding potential of this storm, despite the setup tidal condition present, is attributable to : ( 1 ) The relatively small size of the low pressure center and the fact that it did not intensify until just inland of the coast; (2) Its general south-north path, even recurving slightly offshore in the final phases of its movement up the coast; (3) The rapidity of movement, and corresponding quickness of dissipation of this young storm system. This combined situation is, by strong contrast with that of the relatively slow-moving storm systems, responsible for the extensive coastal floodings which occurred on 1931 March 4-5, 1939 January 3-5, and 1959 December 29 (see the preceding discussions). Similarly, the 1962 Octo- ber 13 storm is at sharp variance with the 1962 March 6-7 storm on the mid-Atlantic coast. In consequence of a high pressure system which remained almost stationary over the North Atlantic on these latter dates, blocking an active low pressure system over the ocean waters, a long fetch and strong onshore wind movement were established for 2.5 days along the mid- Atlantic coast. By contrast, the Columbus Day storm on the west coast traveled nearly 1 ,800 miles in 1 .5 days. 6. The Tidal Flooding of 1974 January 8 (N-99) Perhaps one of the more interesting aspects in regard to this case of tidal flooding on the west coast — produced in conjunction with a tide-amplifying astronomical align- ment designated in table 22 as extreme proxigee-syzygy — is that it was the first such tidal event whose indicated coastal flooding potential was verified according to the principles enumerated in the present work. The astronomical situation involved was discovered during an early analysis of the data of table 16, and its considerable potential for tidal flooding in lowland coastal regions was recognized, should strong, persistent, onshore winds simultaneously prevail. As noted in table 16, the mean epoch of extreme prox- igee-syzygy in this case was 1974 January 8 at 1200 b ( G.c.t. ) , 0700 h ( e.s.t. ) , or 0400 h ( P.s.t. ) . The astronomi- cal alignment occurred at full phase of the Moon. The separation-interval between proxigee and syzygy was — 2 h , and the lunar parallax corresponding to this proxigee was 61 '30.0". The parallax indicated is especially sig- nificant in that comparable values in table 16 — either equal to, or in excess of, this figure — have occurred only 29 times in the 373-year period ( 1600-1973; prior to this date, and 34 times in the entire 400-year period (1600- 1999) of the computer printout. (The instants of proxigee are here compared, rather than the mean epochs, to ensure a maximum parallax in each case. ) The predicted tidal ranges at representative stations along the east and west coasts of the United States, for those dates displaying the largest values of higher high water resulting from this proxigee-syzygy alignment were : Boston, Mass., January 8, 14.2 ft; Willetts Point, N.Y., January 9, 10.4 ft; Breakwater Harbor, Del., January 9, 6.5 ft; Savannah, Ga., January 9, 10.8 ft; also, Aber- deen, Wash., January 8, 14.1 ft; Astoria Tongue Point), Oreg., January 8, 11.7 ft; Los Angeles 'Outer Harbor), Calif., January 8, 8.9 ft; and San Diego, Calif., January 8, 9.8 ft. These ranges compare with corresponding values for spring ranges at the same east coast locations as follows : Boston, 1 1.0 ft; Willetts Point, 8.3 ft; Breakwater Harbor, 4.9 ft; and Savannah, 8.6 ft. The matching diurnal ranges for the west coast stations are: Aberdeen, 10.1 ft; Astoria, 8.2 ft; Los Angeles, 5.4 ft; and San Diego, 5.7 ft. The buildup to this considerable increase in tide-rais- ing force at time of proxigee-syzygy was further substanti- ated by cyclically related tidal flooding 'Key Xos. M-98e,w) occurring approximately one anomalistic month earlier on 1973 December 11 on both the east and west coasts. ( See the news article of fig. 1 1 6 which follows, describing tidal flooding along the coast of Washington in connection with the perigean spring tides near this date.) The mean epoch of perigee-syzygy in this instance was 1973 December 10 at 1230 h (G.c.t.) or 0430" (P.s.t.). The lunar parallax at this time was 61' 12.8", and the separation-interval was +21\ Confirming the increased eccentricity of the Moon's orbit during the lunation containing the proxigee-syzygy alignment of 1974 January 8. a total annular eclipse of the Sun took place on 1973 December 24 at 1508 h (G.c.t.). Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■m The Oregonian Wed., Dec. 12, 1973 Page 24, 3M, Cols. 4, 5 Tidewaters floods Washington towns; winds to ease off Strong coastal winds Tuesday blew water from a near-record 16-foot tide over the seawall at Tokeland, Wash., leaving water a foot deep throughout town. Flooding caused by the tide and winds also was reported at nearby Raymond and South Bend. Police said water reached depths of four feet in the streets of the two communities. No injuries were re- ported. The touchy period came between 2 and 3 p.m. at the peak of the high tide when winds of 75 miles per hour were reported at Seaside. The wind-caused flooding at Tokeland pushed a large trailer house out into a street and washed another house off its foundation. Waves breaking over the seawall near the general store and post office threw logs against the store and littered the road with rocks, driftwood and debris. 1973 Dec. 10 4.5h P.s.t. (+21) M-98w Figure 116. This failure of the apparent image size of the Moon to cover the Sun because of the extreme lunar distance from Earth at the opposing exogee-syzygy position in the lunar orbit occurred very close to the mean epoch of this latter phenomenon (new moon on December 24 at 1507 h G.c.t., exogee on December 25 at 2200 h G.c.t.). A suitable precautionary note to the public concerning the flooding potential of the astronomically amplified January 8 tides — carefully stressing the necessity of ac- companying winds possessing the characteristics to induce coastal flooding — was felt desirable. The following NOAA advisory article (with two slight clarifications added here in square brackets) was released on December 26, 1973. United States Department of Commerce, Washington, D.C. 20230 NEWS RELEASE: WEDNESDAY DECEMBER 2 6, 197 7 East Coast tides to be unusually high on Jan. 8 and Feb. 7 ; NOAA warns of coastal flooding if Atlantic storms oc- cur then. "Unusual astronomical conditions will bring high tides on January 8 and February 7, 1974, the Commerce Depart- ment's National Oceanic and Atmospheric Administration said today. "Should these conditions be combined with severe At- lantic storms — a development which cannot be predicted at this time — extreme flooding might strike low-lying coastal areas- "By themselves, the astronomical tides will not produce problems, weather being the controlling factor. However, similar astronomical conditions, accompanied by an offshore storm and onshore winds, generated much higher than usual water levels on March 6 and 7, 1962, which resulted in the death of 40 persons and wrought an estimated $500 million damage from Long Island, N.Y., to the Outer Banks of North Carolina. "NQAA's National Weather Service alerted its forecast- ers along the Atlantic coast to be especially aware of meteor- ological conditions which produce 'north-easters' or other offshore storms which, if combined with the unusual astro- nomical conditions, could prove hazardous to low-lying areas. Other low-lying regions on the earth could be similarly affected. "A combination of unusual astronomical conditions will occur on January 8 and February 7. On these days the moon, whose gravitational pull is the major influence on the tides, will be full, causing 'spring tides,' a higher than nor- mal rise in the water which occurs twice monthly. But around these two particular days the tides will rise even higher than normal because of two phenomena: the moon will be 1137 miles closer to the mid-Atlantic coast on Jan- uary 8 and on February 7 within 800 miles of the distance it was on March 6, 1962. In addition, the sun, whose gravitational pull also influences the tides, will be in ap- proximately the same longitudinal plane as the moon. This alignment further enhances the astronomical effect on the tides. The earth will also be near its closest annual approach to the sun. Therefore, spring tides during these periods will be particularly high. "The Coastal Environmental Studies Group of NOAA's National Ocean Survey has found that destructive high waters along the Atlantic coast occurred close to such ex- treme spring tides on April 27 and December 3, 1967 and have been traced as far back as November 2, 1861, Novem- ber 1-2, 1877, and November 23-26, 1885. " 'Should a sustained onshore wind occur during these high waters, a destructive water level could result around January 8,' pointed out Fergus J. Wood, a research scientist with the study group. 'The same could hold true also around February 7.' Wood added that similar spring tide conditions and wind-induced water crests could result in extraordinarily high tides along coastal areas around July 19 and August 17 next year, during the hurricane season. "Wood said that his investigation reveals that in 1974 there will be an above-average number [5] of longitudinal alignments of the moon and sun which are associated with close approaches of the moon to the earth. As a result, he stated, there will be a greater than usual number of extreme spring tide situations in 1974. "As a typical example, he cited predicted tidal conditions during 1974 at Atlantic City, N.J., which is being used as a •Kit) Strategic Role of Perigean Spring Tides, 1635-1976 representative test center for his studies. The [tide table] predictions are for 79 days of high tide, up to 1.3 feet higher than the normal spring tide of 4/ 2 feet above mean low water, compared with 53 in 1954 and 1968, the greatest and least number of days of such tides during the past two dec- ades. In 1973, the total will be 61 days and in 1975 it will be 77. Twenty-four of these days in 1974 are clustered around January 8, February 7, July 19 and August 17 when the moon and the sun will be in approximately the same longitudinal plane. "Wood noted in a report that 'from a statistical point of view, 1974 bears close watching.' The NOAA scientist added this 'careful reservation' that 'without the association of the necessary meteorological events producing sustained onshore winds, only higher than usual high tides will be noted on these dates.' "At Atlantic City, in March 1962, the 5.2-foot spring tide, reinforced by a 40-knot wind, with gusts to 70 knots, reached a total height of 9.5 feet above mean low water. The wind blew continuously from the sea for five consecutive high tides over a 2/2 -day period and that set up the condi- tions for the ensuing devastation. Waves as high as 20 feet were recorded on the storm-lashed shore. "Wood stressed that the combination of unusually high spring tides and meteorological conditions could affect other coastlines around the earth to varying degrees. In the United States, he added, this would be true along the West Coast. The danger would not be as great along the Gulf Coast, ex- cept during the hurricane season, since the tides there are generally small. . . ." A representative example of one of the conditional warnings of high tidal flooding potential which could oc- cur in the event of supporting winds, as reported by the United Press International in the Los Angeles Times for December 26, 1973, two weeks before the actual tidal flooding which resulted, is given in fig. 117. A consider- able number of similar rewrite articles, some not ade- quately emphasizing the necessity for supporting winds; others — apparently in the interests of sensationalism — positively stating that extraordinary tidal flooding would occur, were published in the news media on both the east and west coasts. The major tidal flooding (Key No. N-99) which did occur as the result of the combination of these proxigean spring tides and supporting meteorological conditions is graphically presented in the front page article from the Los Angeles Times of January 9, 1974, also reproduced here (fig. 117). A NOTE ON STORM TIDE ANNOUNCEMENT EFFECTIVENESS Before proceeding with a more detailed discussion of the nature and extent of the coastal onslaught associated with this 1974 January 8 tidal flooding — including il- lustrations of the damage produced thereby — certain information-disseminating procedures encountered in con- nection with this event are deserving of mention. The im- mediate issue relates to the optimum manner of informing those segments of the general public, maritme commerce, and shoreline industry which are variously residing, va- cationing, engaged in marine transportation, or conduct- ing business activities within the coastal zone, in regard to such potentially hazardous or damaging tidal flooding conditions. Environmental, coastal wildlife preservation, and ecological interests are also deeply affected. As indicated in the preceding section, almost no ad- vance information was made available to the public at the time of the 1962 March 6-7 disaster. By contrast, in consequence of the ensuing advances in knowledge of tidal flooding, an overwhelming media response (in- cluding, unfortunately, some too terse misinformation) was directed toward assuring a general appreciation of the potential flooding hazards involved in the 1974 January 8 event. Somewhere between these two extremes, through a program of public education and enlightment, lies an optimum procedure for providing awareness of the neces- sary dependence of severe tidal flooding upon a variety of meteorological contingencies in addition to predicted tidal extremes. One of the principal aims of the present work has been to delineate the very complex nature of a major tidal flooding and the numerous factors which go into its pro- duction. It is virtually impossible to encapsulate any proper explanation of these many variables within a neces- sarily abbreviated news announcement just prior to the tidal flooding. Manifestly, it must become the responsibility of civil defense organizations, beachguards, harbormasters, the Coast Guard, beach and coastal highway preservation units, and other groups concerned with the coastal en- vironment, as well as public safety therein, to acquaint themselves fully with the varying aspects of tidal flooding potential. At the same time, these parties should become intimately familiar with the use of marine advisory serv- ices providing other current or updated hourly data on the direction and velocity of coastal winds. These same sources also continuously monitor offshore storms which might combine with astronomically produced perigean spring tides to cause coastal flooding. In this concept of providing continuing public en- lightenment both in the resource aspects and environ- mental problems of the coastal zone, the New England Marine Resources Information Program (NEMRIP) — a Sea Grant project of the University of Rhode Island — Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 107 The Los Angeles Times Wed., Dec. 26, 1973 Part I, Page 4, Cols. 3-6 Moon, Sun to Produce 2 Unusually High Tides WASHINGTON (UPI)— A rare rela- tionship of the earth, moon and sun will cause unusually high tides on Jan. 8 and Feb. 7, and forecasters have been alerted to watch for Atlantic storms that could cause severe flooding along low-lying coast- al areas. The National Oceanic and Atmospheric Administration said Tuesday that similar astronomical conditions accompanied by an offshore storm on March 6 and 7, 1972, caused 40 deaths and $500 million in flood damage extending from Long Island, N.Y., to the outer banks of North Carolina. Fergus J. Wood, a research scientist for the agency, said that without sustained onshore winds, only higher than usual tides would occur on Jan. 8 and Feb. 7. He said there also would be more than the usual number of particularly high tide sit- uations in the upcoming year and "from a statistical point of view, 1974 bears close watching. The moon's gravitational pull is the major influence on the tides. On Jan. 8 and Feb. 7, the moon will be 1,137 miles closer to the mid-Atlantic coast than usual. In addition on those dates, the sun — which also influences the tides — will be in about the same longitudinal plane as the moon, adding to the moon's effect. Further, the earth will be near its closest annual approach to the sun. "Therefore, spring tides during these periods will be particularly high," the agency said. A spring tide is higher than normal and occurs twice a month when the moon is full. The agency said other low-lying coastal areas also could be affected to varying degrees, particularly along the Pacific Coast . . . 1974 Jan. 8 4h P.s.t. (-2) N-99 The Los Angeles Times Wed., Jan. 9, 1974 (CC Ed. Part I, Page 1, Cols. 2, 3 Giant Waves Pound Southland Coast, Undermine Beach Homes Sandbag Barriers Erected to Ward Off Tidal Assault; Five-Day Storm Tapers Off After 7.69-Inch Rainfall BY DICK MAIN and TOM PAEGEL Times Staff Writers Giant wind-driven waves riding on surg- ing high tides battered the Southern Cali- fornia coast Tuesday, damaging homes and flooding nearby areas. Occupants of many beachfront homes from Santa Barbara to San Clemente erected sandbag barriers throughout the day in preparation for the next high tide at 10 :08 a.m. today. The wave and tidal assault came as rainfall from a five-day storm tapered off after dropping 7.69 inches in the Los Angeles Civic Center. Mostly fair weather was forecast for today and Thursday and chances of a new storm Friday, feared earlier, appeared to be remote. Floodwaters and mud and rock slides continued to menace many low-lying areas in foothill and coastal valleys, however. A local emergency was declared for all of Los Angeles County earlier Tuesday by the Board of Supervisors. "Conditions of extreme peril to the eafety of persons and property have arisen," the board said in its resolution. Board Chairman Kenneth Hahn said the proclamation, which was forwarded to the state director of the Office of Emergency Services, may clear the way for state financial assistance for storm damage to public property. In Orange County, supervisors proclaim- ed a "local emergency" for wave-battered coastline sections . , . Part I, Page 29, Cols. 2 ... At least eignt homes in the Beach Road community of Capistrano Beach, were damaged, as waves washed sand away, exposing or damaging seawalls, foundations and pilings. Waves up to 8 feet high slammed into some Orange County beaches during the morning high tide Tuesday. Sheriff's officers and county firemen were dispatched to endangered beach properties and helped in sandbagging op- erations. Breakers wiped out wide sections of many beaches, exposing the pilings of life- guard headquarters at both San Clemente and Newport Beach. Part of Pacific Coast Highway was flooded in Huntington Harbor and in New- port Beach. The morning tides are abnormally high because the present alignment of the earth, sun and moon exerts a stronger than usual gravitational pull upon the ocean. Tuesday morning's peak tide came at 9:22 a.m. and measured 7.1 feet. A 7-foot tide is expected this morning and Thurs- day's tide is expected to measure 6.5 feet. The high tides and battering w T aves also damaged beachfront homes in Los Angeles County, particularly in Malibu, where oc- cupants of two residences were evacuated . . . Sheriff's deputies said earth fill was washed out from in back of two homes on pilings facing the ocean at 27036 and 27054 Malibu Colony Cove Road. Heavy erosion was reported under homes at 25036 Malibu Road and 27308 Escondido Beach Road, but the structures were not evacuated. Minor damage to sea walls, patios and other outdoor improvements was reported to at least three structures in the Malibu Colony. At Zuma Beach, waves dug out much of the sandy beach, forcing lifeguards to move four portable lookout stations away from the surfline. The high tide and waves uprooted more than 20 old pilings from the abandoned and often-burned Pacific Ocean Park pier at Santa Monica. They were towed out to sea to prevent their crashing into Santa Monica Pier. Roger Pappas, National Weather Serv- ice forecaster, said winds which created the towering waves during high tide early Tuesday should subside by this morning, lessening chances of coastal damage. A small-craft advisory warning of high winds between Point Conception and the Mexican border was lowered at 8 p.m. The National Weather Service earlier said ocean swells were expected to drop from 4 to 6 feet during the night to 2 to 4 feet today and Thursday. A storm system in the mid-Pacific which had been expected to arrive in Southern California by Friday apparently has been blocked off by a high -pressure ridge ex- tending southward from the Gulf of Alaska, Pappas said . . . 1974 Jan. 8 4h P.s.t. (-2) N-99 Figure 117. Strategic Role of Perigean Spring Tides, 1635-1976 publishes a monthly bulletin of ocean-oriented facts titled Information. In August 1975, this publication very ap- propriately included a communicated explanation of why flooding conditions did not materialize on the east coast of the United States in connection with the 1974 Janu- ary 8 perigee-syzygy alignment, although structurally damaging tidal flooding conditions existed on the west coast : "A continuous, strong, offshore wind tends to lower water level and negate the effects of a perigean spring tide. The one which occurred on the northeast coast on January 8 [1974] . . . was negated ... by a combination of offshore winds and an atmospheric high pressure sys- tem. The atmosphere and the ocean . . . act together like an inverted barometer. As the atmospheric pressure rises, water level goes down; as atmospheric pressure dimin- ishes, water level rises. The adjustment in ocean level in either direction is approximately 13 inches for each change of one inch in barometric pressure. "Thanks to weather conditions, the east coast escaped flooding on both dates of predicted proxigean spring tides, but California did not. On January 8, 1974, giant wind-driven waves combined with extraordinary high tides battered the southern coast, creating a state of emergency." This article also pointed up the advantages of remain- ing actively alert to the possibility of tidal flooding under such conditions, and of taking precautionary measures when necessary : "Damage would have been far greater if local officials hadn't heeded NOAA's warning and taken defensive measures. Because the action of tides is world-wide, origi- nating from the same astronomical positions, the proxi- gean spring tide that pounded Southern California rose four days later off the English and Scottish coasts. (Ocean water has a specific period of resonance that creates a time delay. ) "Coinciding with a strong onshore gale off the south- west coasts of England and Wales, it breached sea walls and caused widespread flooding there as well as in the outer Hebrides. On February 9 through 11, the second period predicted for perigean spring tides, conditions were also propitious and southern England was clobbered again. "In 1962, residents of the mid-Atlantic United States had not been as lucky as they were in 1974 . . . [since] there was no warning that conditions could be ideal for disaster on March 6 and 7. As it happened, proxigean spring tides prevailed and the flood waters along the At- lantic coastline resulted in 40 deaths and $5 hundred million property damage." Finally, the important matter of dissemination of complete and accurate information — which includes the various contingencies for tidal flooding — was brought out, reiterating and supporting the comments made several paragraphs above : "News accounts of [the] '74 prediction alarmed the public unnecessarily ... by oversimplifying NOAA's press release and failing to stress that onshore winds as well as high tides are required for flooding. They often failed to mention, too, that only lowland coastal regions or those with a sufficiently large daily tidal range would be affected. (Perigee-syzygy adds about 40 percent to the tidal range.) Thus the entire coast of the Gulf of Mexico and much of the southeastern coast of the U.S. would not be in danger, except during hurricanes. "Perigean or proxigean spring tides [likewise] do not necessarily occur on the central day of perigee-syzygy, . . . but can show up within several days before or after it." DATA ON TIDAL FLOODING AND ASSOCIATED DAMAGE On-the-scene observations, scientific data, and photo- graphs recorded in connection with this tidal flooding circumstance were obtained from various sources located in the coastal area between San Clemente and Ventura, Calif., which felt the greatest impact of the destructive tides. Some of the most graphic illustrations showing the extent of the damage produced (figs. 118-131), as well as extracts from official and nonofficial reports concern- ing the protective measures taken in an attempt to pre- vent this damage, have been included on the following pages. a. The Department of Harbors, Beaches, and Parks of Orange County, Calif., for example, provided the Na- tional Ocean Survey with a copy of a preliminary but well-detailed report covering the January 8 tidal flooding. Abstracting only the appropriate technical information from this partially administrative report, the following summary is representative of the tidal flooding conditions at one of many similarly affected coastal communities, Capistrano Beach. It also demonstrates the effectiveness of well-organized protective measures applied to counter tidal flooding. It was practicable to place these into early operation in consequence of the 1973 December 26 NOAA information release — with 2 weeks' advance indi- cation of the potential flooding threat. The prevention of extensive flooding damage despite high tides which Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 100 .!,.. WG2&BA IT ^ Courtesy of U.S. Army Corps of Engineers (Los Angel Figure 118. — Workers filling sandbags at Newport Beach, Calif., in consequence of NOAA forewarning of tidal flooding potential resulting from the extremely close perigee-syzygy alignment of 1974 January 8. Courtesy of U.S. Army Corps of Engineers (Los Angeles District) Figure 120. — Backfilling of the shoreline at Newport Beach, Calif., to create sand barriers during the buildup of the tidal onslaught of 1974 January 8. Courtesy of U.S. Army Corps of Engineers (Los Angeles District) Figure 119. — Sandbags being emplaced at Newport Beach, Calif., as protection against the predicted extreme peri- gean spring tides of 1974 January 8. were already several feet above their mean value is clearly evidenced. This record also" points up the fact that, de- pending upon location as well as meteorological and other circumstances, the flooding effects from perigean spring tides may occur from one to several or more days on either side of the epoch of perigee-syzygy (or proxigee-syzygy ) which is responsible for the astronomical portion of the unusual tidal uplift. Courtesy of Marine Safety Department City of Newport Beach, Calif. Figure 121. — The perigean spring tides contributory to the 1974 January 8 coastal flooding event completely cover the beach and begin to intrude onto the Dory Fleet's Beachfront fish market facility, far above the normal high water mark. Storm-Surge Damage at Capistrano Beach, Calif., Janu- ary 7-9, 1974 "The storms of early January were accompanied on occasion by strong winds. These winds were especially strong on Friday, January 4 and again on the evening of Monday, January 7, with gusts of 50 miles per hour re- corded at both Newport and Dana Point Harbors. 410 Strategic Role of Perigean Spring Tides, 1635-1976 Courtesy of Marine Safety Department City of Newport Beach, Calif. Figure 122. — Scene showing the encroaching sea responsible for the extreme tidal battering experienced at Newport Beach, Calif., on 1974 January 8. The municipal fishing pier is in the background; the lifeguard station is at the right. Note the severe damage to the thickly layered as- phalt parking lot in the foreground. Courtesy of U.S. Army Corps of Engineers (Los Angeles District) Figure 123. — The wind-driven tidal assault of 1974 January 8 sweeps away sandbags emplaced at the lifeguard station, Newport Beach, Calif., and begins erosional breakup of the surfaced parking lot. "The strong winds were from the southeast, causing waves to strike the shore at an angle, commonly called an upcoast angle. Indeed, in Newport Harbor, the waves came in almost directly in the harbor mouth between the breakwaters .... Courtesy of U.S. Army Corps of Engineers (Los Angeles District) Figure 124. — The complete destruction of the beach front parking lot fronting the lifeguard station, Newport Beach, Calif., caused by the pounding action of the surf accom- panying the extreme tides of 1974 January 8. Courtesy of The Orange Coast Daily Pilot, Costa Mesa. Calif. Figure 125. — Severe undercutting, subsidence, and cracking of the marina wallkway at Newport Beach, Calif., caused by high waters associated with the tidal flooding of 1974 January 8. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 411 Courtesy of The Los Angeles Times Figure 126. — Picture taken along the coast just west of Los Angeles, Calif., at approximately 9 a.m. on 1974 January 8, coinciding with the time of the unusually high perigean spring tide of this date. ■« 4* Courtesy of The Orange Coast Daily Pilot, Costa Mesa, Calif. Figure 127. — The augmented perigean spring tides of 1974 January 8 break destructively against the El Moro Trailer Park between Corona del Mar and Laguna Beach, Calif. "The beach began to disappear at Capistrano Beach, and by January 7, waves were pounding against the seawalls in front of some homes there. Then on Tuesday morning, January 8, one of the highest tides of the year occurred. The approximate +7.4 foot tide was fortu- nately not accompanied by large waves, but because the seawalls had previously been exposed, the battle was on. The waves damaged some sections of the wall, and ap- peared to be undermining other sections. Courtesy of Department of the Los Angeles County Engineer Figure 128. — View from the landward side, showing ex- treme damage to the seawall at Malibu Beach, Calif., pro- duced by the wind-reinforced erosion, and undercutting of the seawall from the rear caused by these augmented high tides. Courtesy of Department of the Los Angeles County Engineer Figure 129. — Dislocation of an access stile surmounting the seawall at Malibu Beach, Calif., as the result of undermin- ing and toppling of the wall by storm-amplified perigean spring tides on 1974 January 8. ■112 Strategic Role of Perigean Spring Tides, 1635-1976 Courtesy of Department of the Los Angeles County Engineer Figure 130. — View of a section of the beachfront at Malibu Beach, Calif., following the tidal flooding of 1974 Janu- ary 8, showing the extensive damage to the seawall caused by wave overtopping. A closeup of the rear portion of this same seawall at a point in the center distance is included in figure 128. tHIflHS! • - Courtesy of Department of the Los Angeles County Engineer Figure 131. — Detail of the breaching of the seawall at Malibu Beach, Calif., by the perigean spring tides of 1974 January 8. The deep cavitation behind the wall is pro- duced by erosional action resulting from the overspilling "At this point, some of the residents called the Harbor Patrol for assistance. A representative was dispatched to investigate the situation. At first, it didn't look too bad, but when the tide receded and it was possible to walk in front of the seawalls, it was found that consider- able erosion had occurred behind the walls, in some cases clear up under the beach side of a home. "Due to the fact that another high tide was expected the next day and storm conditions were forecast which could result in big waves on top of the tide, it was decided that protective measures must be taken. Residents got together and obtained sandbags from the County Fire De- partment and began sandbagging, and also called a con- tractor to deliver and place large rocks in front of the sea- walls. The residents also requested County assistance .... "Things then happened fast. The County Departments of Communications, Road, Flood Control, Fire Protection and Sheriff were contacted. Communications dispatched a mobile communications van to the site with complete radio and telephone service, as well as portable electric generators. The Road Department sent dump trucks and drivers, which, on the way, stopped at a sand and gravel plant and picked up 50 tons of sand. Fire Protection dis- patched trucks and crews for filling sandbags. Harbors, Beaches and Parks sent men, trucks and a tractor. Flood- ing Control sent thousands of sandbags and the Sheriffs Department provided deputies for security and crowd control. "Almost immediately telephone lines at the District Headquarters began to ring with reporters asking ques- tions. Eventually, crews from all three television networks would visit the site and film reports. Coverage by news- papers was complete .... "An approximate 7.2 foot high tide arrived at 10:20 a.m. Pacific daylight time, on January 9. The sea was very calm, waves only 2-A: feet. "Approximately 13,000 sandbags had been placed in front of approximately 1 2 homes. Generally, the bags were placed behind wooden seawalls which already existed. The day before, the sand behind the seawalls had been eroded away. In some cases, it was necessary to cut holes in wood decking or patios to gain access to behind the sea- wall for sandbag placement. "One section of seawall had to be cut down, as it had been damaged to the point where the 1 /9 high tide could be expected to break it loose, and then it would become a battering ram tossed about by the surf. This section was the width of one lot, fortunately the lot was vacant. During the night of 1 /8 crews replaced this wall with a sandbag barrier, several bags deep and approximately 7 feet high. "In addition, some homeowners contracted for the de- livery and placement of large granite boulders in front of their seawall. Many had been put into place before the high tide of 1/9, with more to be put in after the tide recedes. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floo dings ■m "The high tide of 1 /9 resulted in no further damage. All seawalls and sandbags remained in place. As the waves rolled in, they would send surges of water to the seawalls, but they and the bags held . . . ." b. In addition, official data were obtained from the Los Angeles office of the National Weather Service rela- tive to the prevailing wind velocities and directions, and state-of-the-sea at the time of the tidal impact. Damage reports from coastal communities were also compiled by the Los Angeles weather station on the basis of reports from local beachguards or similar authorities which are summarized below : As can be seen from the synoptic weather maps of the United States for 1974 January 7, 8, and 9 at 0400 h (P.s.t.) in figs. 132, 133, and 134, the contribution of wind to the unusually high tides already present was the result of a fairly shallow low pressure system (central pressure, approximately 1004mb) approaching the south- west coast of California from off the Pacific Ocean. The January 7 weather map indicates a warm front extending southeastward from the low pressure system. However, the absence of either an open or an occluded wave, as plotted, seems to indicate that this frontal ex- tension did not form part of a series of "feeder" waves which often impinge on the southern California coastline, one after the other, during the winter season. The satellite weather photos in figs. 135, 136 show the offshore situation to better advantage, and reveal that this weather front was (on January 7) an extension of an intense occluded frontal system over the southeast Pacific, and probably, indeed, part of a feeder-wave system. The counterclockwise rotation within this low pressure center, with the surface winds blowing in northerly and northeasterly directions on the eastern side of the low, ac- counts for the prevailing winds from southerly and south- easterly components during the entire period of onshore movement of the system. As shown on the January 8 map, the warm front has moved very rapidly eastward and has been modified into an occluded front. It is the strong, gusty, surface winds associated with the passage of this front which were re- sponsible for the meteorological contribution to the storm surge experienced along the southern California coast. However, neither the surface waves nor the sea swells produced along this coast were very high, nor was their maximum height of long duration. It was the already extraordinarily high tides, driven en masse against the coastline by these short-lived but powerful winds, that caused the ensuing damage. Marine weather observations obtained at 20 stations, ranging from Point Arguello on the north to San Diego' on the south show the maximum swell height reached (at Avalon Harbor at 2000 h (P.s.t.) on January 7) to be about 7 ft ; the average swell height at all other points was 4-5 ft. The peak-velocity ESE to SE winds experi- enced along the southern California coastline in advance of the eastward-moving low pressure center were strong and gusty, but their duration of movement over the water was relatively brief. Their velocities built up slowly during the morning and afternoon of January 7 to an average range of 15-30 knots at various locations, with continuing rain throughout the day. By 2000" on January 7, practically all of the marine weather stations reporting indicated wind velocities of 20 knots and greater from S to SE components, with addi- tional gusts to 30-35 knots, and with the barometric pressure reduced to 999-1,005 mbs. During the late night of January 7, the maximum wind velocities were attained at Avalon on Catalina Island and were carried over to other coastal points. Fortunately, this period coincided with that of an extremely low water accompanying the proxigean spring tides. The astronomical higher high water was predicted to reach 7.1 ft at Los Angeles (Outer Harbor) on January 8 at 0822" (P.s.t.). The maximum tide height actually reached here, as reduced from marigram records, was 7.8 ft, corresponding very nearly to the time 0800 h (P.s.t.) on January 8. This value is 2.6 ft above that of mean higher high water (5.2 ft ) at Los Angeles. In a telephoned communication from the harbor- master at Avalon on Catalina Island to the Los Angeles weather station, the extreme height of the tides on the morning of January 8 was confirmed. It was stated that, at this time of higher high water, the anchor lines of the mooring buoys to which many small boats were tied (ordinarily containing some slack cable and hence in- clined in the water) were standing straight up, with the buoys resembling "buttons ready to pop." It was affirmed that, had the high winds of the previous night occurred instead during this period of morning high tides, a dis- astrous situation might have resulted. With the water- piling action of the winds added to the unusually high astronomical tides, many of the small boats unquestion- ably would have been snapped from their anchor cables and have been released to drift freely around the harbor, collide with each other, or smash on the shore subject to the strong winds and currents present. Onshore, where strong winds and very high astronom- ical tides did more nearly coincide (fig. 126), problems 411 Strategic Role of Perigean Spring Tides, 1635-1976 Figure 132. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 415 Figure 133. 418 Strategic Role of Perigean Spring Tides, 1635-1976 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings msssum ■1 1 7 Source : National Environmental Satellite Service, NOAA Figure 135. — This composite mosaic of Northern Hemisphere cloud cover was compiled from infrared "night photog- raphy" images secured by a NOAA weather satelliteduring the period between 1974 January 7 1259 P.s.t. and 1974 January 8 1007 P.s.t. The approximate times corresponding to the geographic positions of satellite photography are indicated around the equatorial margin of the grid overlay. The situation represented off the Pacific coast of North America as of January 7 2248 P.s.t. shows an intense low pressure system marked by a strongly occluded frontal wave, with an associated cloud cover extending from Hawaii to the Gulf of Alaska. The southeasterly extending warm front portion of the occlusion merges into a long, recurving cold front. This joins a second warm front and to- gether they form a second, rapidly eastwardly moving "feeder wave" whose cloud-cover effects are already noticeable over northern Baja California. (See also figs." 132-133.) Astronomically induced proxigean spring tides, raised during the early morning hours of January 8, reached their maximum heights locally along the southern Cali- fornia coast between approximately 0800 and 1000 P.s.t. The southerly and southeasterly winds encircling this sec- ond low-pressure system prior to the onshore arrival of the warm front (shifting to strong southwesterly winds with passage of the front) further raised the proxigean spring tides to coastal flooding conditions. Moderate swells also had been generated many miles at sea, adding to the tidal flooding potential. 202-509 0-78-29 Strategic Role of Perigean Spring Tides, 1635-1976 BBSKS Source: National Environmental Satellite Service, NOAA Figure 136. — Approximately 24 hours after the meteorological situation depicted in figure 135, the large offshore oc- clusion is still essentially stagnant, but the rapidly moving feeder wave which contributed to the coastal flooding already has moved over Arizona. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 419 of another sort had arisen. Since the maximum height of the sea swell running at this time was estimated by vari- ous observers as 4-5 ft, this means that the crest of the swell would ride 2.6+4.0 or 6.6 ft above the level of mean higher high water. Assuming any seawall would be built with its base at the level of MHHW to afford maxi- mum protection against tidal flooding, the wall would have to be at least 6.6 ft high to keep the sea from surg- ing over its top. As attested by the previous report in connection with Capistrano Beach, by various among the illustrations of the 1974 January 8 tidal flooding which conclude this chapter, and the summary of tidal damage at southern California coastal communities which immediately fol- lows, such a violent overspilling and breaching of sea- walls actually did happen, with consequent damage to beach homes. c. The estimated amounts of damage caused by the unusually high tides of 1974 January 8 at various loca- tions on the southern California coast, (See fig. 15 1A.) as obtained (together with related information) by Na- tional Weather Service forecasters at the Los Angeles office, were as follows: ( 1 ) Newport Beach (a) The first floors of 20 homes were inundated by tidal resurgence within Newport Bay, with corresponding structural damage to plaster walls, etc. (b) A 300-ft portion of a concrete seawall collapsed. (c) A 500-ft section of the shoreline was eroded back a distance of 120 ft along an elbow of the bay. (d) An asphalt parking area on the seaward side of the lifeguard station was severely broken up by wave erosion and undercutting. (e) The total structural damage to the area was estimated at $100,000. (f) Additional damage occurred to a boat of the Dory Fleet and to the beachfront fish market facility. (g) The measured maximum tides in this area throughout the period of tidal onslaught were 7.7- 8.3 ft above mean lower low water. (2) Capistrano Beach (a) Structural damage was incurred to 12 homes, involving especially that caused by erosion beneath concrete foundations and damage to wooden patios. (b) The total loss due to structural damage in the area was estimated at $25,000. (c) A one-half mile stretch of beach also was eroded back a distance of 75 ft. ( 3 ) Malibu Cove Colony, Malibu (a) Erosion occurred along one-half mile of the waterfront, including overspilling and undercutting of 700 ft of seawall from the rear. (b) Structural damage also was caused to this same seawall. (4) Malibu Film Colony, Malibu (a) An estimated $20,000 in damage to home properties resulted through seawater penetration, sand leaching, flooding of cesspools, downing of power poles, and overtopping of protecting bulk- heads. (b) The erosion around, and saltwater corrosion to, the steel foundation beams of two condominiums required $20,000 for their replacement. (5) Mission Beach A 1.7 mi. stretch of beach was eroded back a dis- tance of 100 ft. ( 6 ) South Laguna Beach A 200-ft section of beach was eroded back a dis- tance of 25 ft. ( 7 ) San Clemente A seashore gas main was broken by attrition due to the strong tidal action; four or five house trailers in a coastal trailer park were lost in the fire resulting therefrom. d. As noted in the NEMRIP bulletin quoted in an earlier portion of this same section, no prominent coastal flooding accompanied the proxigean spring tide of 1974 January 8 on the east coast of the United States. The reasons are made very clear by reference to the daily synoptic weather map of the United States for this date (fig. 133). A very large high pressure cell (central pressure 1,028 mb) was centered over the Great Lakes. The 1,024-mb isobar of this cell reached eastward as far as the Atlantic coast and extended along it from Long Island to central South Carolina. The associated clockwise circulation around a high pressure system in the Northern Hemisphere resulted in a light offshore wind movement at all coastal points from the Chesapeake Bay north to the Gulf of St. Lawrence. Those winds along the coast from the Chesa- peake Bay south to Florida likewise possessed relatively small velocities, with components parallel to, or directed 120 Strategic Role of Perigean Spring Tides, 1635-1976 just off the shoreline, and (in the extreme south) having gentle landward components. In addition, the eastward movement of a high pressure (1,024-mb) ridge over the middle and southern portions of the Atlantic coastline caused the pressures here to rise from that of an atmospheric "col" (1,012-1,016 mb) on the previous day. This circumstance tended slightly to depress the rising tides, by approximately 1.3 in. for each 0.1 in. rise in barometric pressure (0.1 in. of mercury rise=4.06 mb). The January 9 synoptic weather map shows that the inmoving 1,024-mb isobar was still along the coast at map time on this date, but subject to the ad- vance of a rapidly moving, dual low pressure system and two associated cold fronts over the eastern portion of the country (fig. 134). In the Pacific Northwest, where certain lowland por- tions also are susceptible to tidal flooding, a moderate high pressure system (central pressure 1,020 mb) re- mained relatively stationary over eastern Oregon and Washington between January 7 and January 8. Light and variable winds prevailed on this portion of the coast throughout the foregoing period. Consequently, despite the unusually high astronomical tides present, no reinforcement by strong, onshore winds conducive to tidal flooding was provided either in the Pacific Northwest or along the Atlantic coast on Janu- ary 8. A case of ordinary perigean spring tides followed this proxigean spring event of 1974 January 8 by approx- imately one anomalistic month. Although its perigee- syzygy separation-interval was a full — 24 h , it was closely watched for tidal flooding propensities. Again, how- ever, high pressure systems prevailed on both the east and west coasts, shoreline winds were light and variable, and flooding was not induced in the considerably height- ened astronomical tides around February 6-7 (fig. 89). In summary, three principal factors can greatly re- duce, or even cancel out the rather severe damage threat to a coastline posed by the astronomical production of a proxigean spring or similar extraordinarily high tide which is subject to further uplift through the action of intense and persistent onshore winds : (1). The substitution of a strong, sustained, offshore wind, resulting in a negative storm surge, or partial de- pression of the existing astronomically raised tidal waters. This occurs as the result of the amplified tidal waters being distributed toward the deeper, more open sea rather than landward, involving runup over shallow bottom slopes and channeling into constricted coastal passages. Light to calm surface winds also usually exist in a high pressure system. Such winds have very little effect in mov- ing (or raising) the surface waters of the oceans. ( 2 ) . An increase in atmospheric pressure prior to and/ or during the period of the enhanced astronomical tidal uplift tends to depress the tide by virtue of the added weight of the overlying atmospheric column. At this same time, such a rising barometric pressure — as the result of gradual "filling" of the system and production of a smaller atmospheric pressure gradient from the high pressure center outward — is accompanied by a reduction in surface wind velocities. Subsidence of the air within the high pressure system rather than a vortex uplift motion which frequently occurs in an atmospheric low also tends to stabilize the air mass present and to resist the effects of cyclogenesis and frontogenesis associated with a low (both conducive to strong surface winds ) . (3 ) . As mentioned in part I, chapter 1, the addition of outlying breakwaters, organized and renewable coastal berms, dikes, dunes, and groins (artificial barriers built out perpendicular to the shoreline to resist alongshore current movements) have, in more recent years, reduced much of the severe damage caused by the combination of strong onshore winds and astronomically amplified tides. The planting and maintenance of appropriate species of saltwater-tolerant spartina grass on the slopes of barrier sand dunes located above the mean high water mark also have served as an aid against irremedial coastal erosion by these tides. n . Tidal Flooding in the British Isles on 1974 January 11-12 and February 9 The foregoing instance of tidal flooding on the west coast of the United States on 1974 January 8 was di- rectly related through the astronomical perigee-syzygy cycle to two other tidal floodings on the west and south coasts of Great Britain. These incidents occurred in con- nection with the same proxigee-syzygy alignment of 1974 January 8, having a mean epoch of 1200 h (G.c.t. ), and a second perigee-syzygy alignment of February 6 at 1100 h (G.c.t.). The actual floodings occurred on January 11-12 and February 9-11, with the already amplified astronomical tides being reinforced by the necessary strong onshore winds on these dates. This delay in the rise of maximum astronomical tides experienced in the British Isles to a date approximately 3 days later than that in which these same amplified tides became evident on the east and west coasts of the United States is caused by a dynamic phenomenon. Simply put, the ocean waters in each given locality possess a specific resonance response to their local- ity which, in this instance, results in the maximum tidal effects of the proxigee-syzygy (or perigee-syzygy) align- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings •121 Source : National Environmental Satellite Service, NOAA Figure 137. — This photomosaic is compiled from "daytime infrared" images of global cloud cover obtained by a NOAA weather satellite between 1974 January 11 0754 G.m.t. and 1974 January 12 0654 G.m.t. (a malfunctioning signal is responsible for the blank, saw-toothed area off the east coast of the United States). A large, bent-back frontal oc- clusion associated with a deep low pressure center is seen to be approaching the west coast of Great Britain along a southwest-northeast track. In the eastern portion of this low pressure system, because of its steep pressure gradient strong winds would subsequently blow from the south against the southern English coast; in the warm front section of the occluded wave, winds would likewise blow from the s outhwest and west, directed onshore along the west coast of England. This atmospheric storm system, and the proxigean spring tides simultaneously present, were together respon- sible for the active coastal flooding experienced along the western and southern lowland shores of Great Britain during high tides on January 11-12. 422 Strategic Role of Perigean Spring Tides, 1635-1976 Source: National Environmental Satellite Service, NOAA Figure 138. — As subsidiary weather satellite coverage useful in nephanalysis, a Northern Hemisphere "visual image" photo- mosaic is included here, covering the same period of record as figure 137. This mosaic also illustrates the somewhat greater sensitivity of infrared photography in representing diffuse and peripheral cloud cover compared with photography in the visual range of the spectrum. Note the considerably sharper delineation of cloud boundaries (although cloud areas of cor- respondingly smaller extent) in the present figure compared with figure 137. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■m ij Courtesy of The Guernsey Press Co., Ltd. Figure 139. — Tidal flooding at North Beach Street quay, Stornoway, Scotland, on January 11, 1974 produced by a wind-driven storm surge accompanying perigean spring tides on this date. With the quay inundated, the boats have been lifted to the level of the over-street flooding. Figure 141. — Surf breaking over the seawall at Guernsey in the Channel Islands off the south coast of Great Britain on January 11, 1974, in consequence of strong onshore winds combined with augmented tides produced by the close perigee-syzygy alignment of 1974 January 8. The arrival of the maximum perigean spring tides is affected by a com- posite delay resulting from approximately 3-day phase- and parallax-lags at this location. (See chapter 6.) Courtesy of The Stornoway Gazette, Ltd. Figure 140. — As a major spillover from the inner harbor into South Beach Street, Stornoway, caused by the storm- amplified perigean spring tides of January 11, 1974 begins to recede, business traffic resumes. The photograph was taken about 10:30 a.m. Courtesy of The Stornoway Gazette, Ltd. Figure 142. — Seawater lifted by the perigean spring tides of January 11, 1974 extends inland onto the wooded area at Porter's Lodge, entrance to Lady Lever Park on Lewis Castle Grounds, Stornoway, Scotland. Such an extraor- dinary incursion by tidal flooding was reported by The Stornoway Gazette to have occurred for only "the second time in living memory." 421 Strategic Role of Perigean Spring Tides, 1635-1976 ment being felt about 3 days later in the British Isles than on the southern coast of California. Since it is not the purpose of this treatise to intrude on the analysis of tidal waters in other areas than the United States and, to a very limited extent, Canada (many other more definitive works having been produced, with far greater local knowledge, by experts in the countries in- volved) this instance will be summarized in very brief terms. The extreme bent-back atmospheric occluded front and the very deep low pressure system which produced strong onshore winds along the entire west and south coasts of Great Britain on January 11-12, 1974 is distinctively marked by the cloud-cover pattern approaching the southwest coast in the weather satellite photographs taken at 0754 h (G.c.t.) on January 11 (figs. 137-138). With these winds arriving at the same time as the amplified, astronomically produced proxigean spring tides, flooding of low-lying coastal regions was inevitable (figs. 139- 142). Seawalls were breached along the western coasts of both England and Wales, and tidal flooding extended from the District of Lewis in the Outer Hebrides on the north to Guernsey in the Channel Islands on the south. The effects of such rampaging storm surges were felt at Mine- head, Somersetshire; at Appledore in north Devonshire; and at Amroth in Pembrokeshire. Coastal flooding also occurred in Devonshire at Ilfracombe, Bideford, and Lynmouth. The town of Barnstable described the flooding there as the worst in 25 years, while in Stornoway, Outer Hebrides, the tidal inundation covered a considerable section of a coastal airfield. A similar tidal inundation occurred on the southern coast of England between February 9-11, 1974, as on- shore winds reinforced perigean spring tides raised around these dates. 8. Tidal Flooding of 1976 March 16-17 This coastal flooding event (Key No. O-100) is sig- nificant as the second test case in which an accurate con- firmation was made of the principles of tidal flooding potential enumerated in this work. Advance warnings also were released to responsible agencies in this instance, and appropriate flooding-protection measures were taken. (Cf. The Boston Globe, March 17, 1976, p. 1, cols. 2-6, and especially p. 42, cols. 1-6. ) The associated perigee-syzygy alignment (P — S= + 16") had a mean epoch of 1976 March 16 at 0600 h (e.s.t.). Between March 16 and March 17, the progress of a strong, swiftly moving offshore storm (with accom- panying low pressure system ) was carefully monitored as its center moved northward from the New Jersey coast, some 50 miles at sea. The storm system deepened steadily in intensity as it proceeded, causing onshore winds (to the north of the low ) of increasing velocity along the New England coast (fig. 143). By the time the northern edge of the low pressure cen- ter had reached a point opposite Massachusetts, the com- bined tide-amplifying and storm surge effects were begin- ning to be felt in lowland coastal areas. Likewise, in sand embankment regions along the coast from Plum Island. Mass., to Saco and Popham Beach, Me., cottages and summer homes built on pilings overlooking the water had their foundations undercut by erosion, dropping the houses onto the lower beach or into the sea. Tidal flooding and erosional damage was reported from such coastal communities as Marblehead, Newbury, and Provincetown, Mass.; New Castle, Rye, Hampton Beach, and Portsmouth, N.H.; and Ogunquit, Popham Beach, Saco, and Kennebunkport, Me. At Saco, the tidal flood- ing washed out a coastal road, destroyed a seawall, and caused an estimated $102,000 in damage to property. Even on the afternoon of March 16, hurricane-force winds were predicted off Narragansett Bay. By the time the low pressure center reached Halifax, Nova Scotia, in its northward movement, the central pressure had dropped to about 962 mb. The system continued to in- tensify as it proceeded northward over Newfoundland. With storm surge effects due to the intense winds adding to the already high perigean spring tides, the eastern sides of bays and harbors near Halifax were subjected to active tidal flooding from the strong westerly winds in the south- ern portion of the low. As quoted from the front page of the Halifax Chron- icle-Herald for March 18, 1976: ". . . Unusually high tides recorded along the eastern side of Halifax Harbour and at Eastern Passage caused unestimated damage, with roads, fishing wharves, and a number of houses flooded and isolated. The high tide sub- merged some areas under 5 feet of water. ". . . Ferry service between St. John, N.B., and Digby as well as sailing of the ferry Bluenose from Yarmouth for Bar Harbor, Maine, were cancelled . . . The South Korean oil tanker Ocean Park was unable to dock at the Gulf Oil Refinery at Pt. Tupper because of high tides and heavy wind . . . ." The rapid northerly movement and deep intensification of this low pressure system over the waters of the North Atlantic are described in the accompanying abstract from the Mariners Weather Log for September 1976. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 425 ■126 Strategic Role of Perigean Spring Tides, 1635-1976 From: Mariners Weather Log, Vol. 20, No. 5, September 1976 O-100 — Coastal Flooding of: 1976, March 16-17, Maine to Nova Scotia "This storm moved out of New Mexico as a frontal wave. It did not develop until late on the 16th as it approached the U.S. East Coast. By 1200 on the 17th, it was 962 mb near Yarmouth, Nova Scotia. On the afternoon of the 16th, storm warnings were issued for the New England coast with hurricane-force winds in the Narragansett Bay area. Up to 14 in. of new snow accumulated in some areas of Maine, with 20 in northern Maine. Boon Island, along the coast of Maine, reported gusts to 75 mi/h. Ships off the east coast were observing 40- to 50-kn winds with the highest being measured as 52 kn by the BIBB near 42.2° N, 65.2° W. Seas and swells of over 30 ft were reported by four ships with the highest of 35 ft by the BALTIMORE TRADER near 37.4° N, 72.6° W. "At 0000 on the 18th, the 957-mb LOW was near Corner Brook, Newfoundland. Four ships reported 40-kn winds from Cape Cod northward. St. Pierre measured 60-kn winds. A ship at 51° N, 50° W, reported 60-kn winds just prior to passage of the occlusion. The ATLANTIC CHAM- PAGNE, at 40° N, 51° W, and east of the cold front, was tossed by 20-ft seas and 28-ft swells. At 0000 on the 19th, the center was approaching Kep Farvel with a pressure of 592 mb. Ocean Weather Station Charlie measured 50-kn winds and 26-ft seas. Waves were forming on the front south of the center and moving northeastward around the perim- eter. Forty knots was the strongest wind on the chart, but the ANNA WESCH reported 33-ft swells near 50° N, 42° w." Miscellaneous scenes of perigean spring tides, photo- graphed at both extreme high and low water, and the dam- age caused by such augmented astronomical tides in asso- ciation with severe onshore winds and /or sea swell, are shown in figs. 144-151, on the following pages. Courtesy of The Paciflca Tribune, Pacifica, Calif. Figure 144. — The extreme low water occurring during the negative-amplitude phase of perigean spring tides on 1962 October 13. The scene is photographed from offshore at Pacifica, Calif. The vastly greater amount of beach ex- posed at such extreme low waters is a boon for marine biologists, marine archaeologists, beachcombers, and certain engineering projects. At the same time, however, very shallowly submerged reefs, rocks, and bottom slope present a hazard to navigation. Courtesy of The Paciflca Tribune, Pacifica, Calif. Figure 145. — A matching scene photographed from the same location during the extreme high-water phase of these perigean spring tides. Despite a protecting seawall, the beach cottage shown already has been flanked by the incoming tide and is in danger of serious flooding. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 427 Courtesy of The Paciflca Tribune, Pacifica, Calif. Figure 146. — A second view looking slightly to the left of figure 144 during the extreme low water on this same date, showing the large extent of foreshore uncovered. The existing stream drainage channel in the foreground is seen to be completely unimpaired, permitting free hydro- logical runoff of rainfall or other surface waters to the sea. Courtesy of County of Ventura, Calif., Public Works Agency Figure 148. — Representative damage to porch and front of beach home at Oxnard Shores, Oxnard, Calif., caused by wind-impelled waves and swell piling on top of perigean spring tides resulting from a perigee-syzygy alignment on 1971 March 26. II Js»^_->- f fl 1*'™ J% fjp-"*! Courtesy of The Pacifica Tribune, Paciflca, Calif. Figure 147. — Corresponding view from the same position as figure 146, photographed during the high-water phase of the tides. The drainage outlet to the sea is now completely covered and blocked by the incoming tide. Thus, whereas sometimes perigean spring tides do not result in actual salt- water inundation, the impairment of strong hydrological runoff by such extraordinarily high tides can cause the backup and/or overflow of normal drainage channels into surrounding areas. Courtesy of The Orange Coast Daily Pilot, Costa Mesa, Calif. Figure 149. — Damage to the seawall and protecting parapet at Capistrano Beach Club, Capistrano, Calif., consequent upon the wind-reinforced amplification of already high waters produced in association with the perigee-syzygy alignment of 1962 February 5. (See table 16.) ■1L'8 Strategic Role of Perigean Spring Tides, 1635-1976 Courtesy of The Orange Coast ixiiht Pilot, Costa Mesa, Calif. Figure 150. — Detail of destruction of the concrete walkway and driveway at Capistrano Beach Club resulting from erosion and attrition of the underlying foundation ma- terials by storm-amplified perigean spring tides occurring around the 1962 February 5 date. Courtesy of County of Ventura, Calif., Public Works Agency Figure 151 A. — Section of the coastline in Ventura County, Calif., photographed on January 8, 1974 during the coincident ar- rival of wind-driven surf and perigean spring tides associated with the close perigee-syzygy alignment of this date. Note the extensive log debris in the foreground and the fact that waves arc pounding against fenced areas normally well above the waterline. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings ■12' i It is significant in terms of a further verification of the principles of tidal flooding potential enunciated in this work to include four other examples of severe tidal flood- ing which took place subsequent to preparation of the preceding text covering the period 1635-1976. These more recent examples are especially noteworthy since, in appropriate pairs, they occurred nearly simultaneously on the east and west coasts of the United States, exactly one anomalistic month apart. The respective cases, happening in 1978, are outlined below. Additional information re- garding the full extent of the flooding damage sustained and the exact times and locations of these flooding events may be had from the newspaper sources cited in each instance. 9. The Tidal Flooding of 1978 January 8-9 On 1978 January 8-9, severe coastal flooding obviously related to perigean spring tides was experienced, in turn, along both the coast of southern California and the south- east coast of New England — and, 3 days later, on the west coast of Great Britain. Interestingly, this circumstance was, in the latter respect, very nearly a repetition of the tidal flooding of 1974 January 8 described earlier in this same chapter. The 1978 flooding event was directly associated with an alignment between perigee and syzygy having a mean epoch of January 8 at 1500" (e.s.t.), for which P~S = -16 h , 7r = 6H8.2". As the result of the particular oceanic resonance factors appropriate to the west coast compared with the east coast, major tidal flooding oc- curred in connection with these perigean spring tides one day earlier in the former location, aided by coincident strong onshore winds. These winds were generated in con- junction with a long, southward-extending, cold-front portion of an occluded atmospheric wave centered in a deep low pressure cell over the Gulf of Alaska. Particularly hard hit by tidal flooding in the lowland coastal regions of southern California were the beaches at El Segundo and Manhattan, as well as numerous others between Malibu and Ventura. At many such locations, sandbagging was resorted to, but failed to stem the in- coming tides and storm-raised surf on January 8. Very extensive damage was caused to seawalls, homes, and beachfront property in these areas. (See the Los Angeles Times, Monday, January 9, pt. I, p. 1, col. 4; p. 3, cols. 1-4. ) Considerable flooding damage also was experienced at Mission, South Mission, La Jolla, Ocean, and Del Mar beaches. (See The Evening Tribune, San Diego, Janu- ary 9, p. 1, col. 5; p. 6, cols. 1-2.) These initial instances of tidal flooding were succeeded on January 9 by further tidal inundation at Malibu, Rincon, and Solimar beaches as well as, further north, at Seacliff State Beach and Capitola. (See the Los Angeles Times, January 10, pt. I, p. 1, cols. 3-4; p. 3, col. 4; p. 19, cols. 1-4.) Because of the average 0.5 d -1.5 d phase- and parallax- ages on the east coast, perigean spring tides prevailed here on January 9. And, successively, along the entire Atlantic coast from Virginia to Maine, these tides were accom- panied during the period of their rise by strong onshore winds produced in the northern portion of a deep low pressure system which moved up the coast from the south. Tidal flooding and/or severe erosion of the coastline was felt prominently at Provincetown, along Cape Cod, and at Revere Beach, Mass., during the times of high tides on January 9 (see the Boston Evening Globe, Jan- uary 10, pp. 1,8); also at Southampton, Long Island, and the Rockaways, Queens, N.Y., and in various other coastal lowland regions between Virginia and Maine. (See the New York Times, January 10, p. 20, cols. 2-6; p. 25, cols. 5-8). In keeping with the individual resonance factors pecu- liar to the west coast of Great Britain noted in example 7 of this same chapter, the effects of these augmented perigean spring tides, raised further by strong onshore winds, were felt 3 days later in various coastal regions. The gale- to near-hurricane force winds (gusting to 82 mph at London) were produced by a steep atmospheric pressure gradient between a 1,032-millibar high pressure system in the eastern North Atlantic and a 892-millibar low pressure cell over the north of Europe. (See The Times, London, England, Thursday, January 12, p. 2, cols. 5-7.) High tides breached seawalls at Cleethorpes in Hum- berside, and invaded the town. A portion of a road at Ilfracombe on the north Devon coast was washed into the sea by the combination of high tides and heavy rainfall. Other tidal flooding occurred at Rhos-on-Sea in Colwyn Bay, Clwyd, and at Llanfairfechan, Gwynedd. A coastal road at Sandgate in Kent was closed by the coastal innundation. (See The Times, London, January 12, p. 1, cols. 5-6.) Elsewhere, the effects of these exceptionally high astronomical tides, coupled with strong storm winds, were observed on the Thames River, England, which came within 19 inches of breaching its floodwalls, and in wave and tidal flooding which surmounted dikes in Bel- no Strategic Role of Perigean Spring Tides, 1635-1976 gium. (See the Reuters dispatch in the Los Angeles Times, January 13, pt. I, p. 7, cols. 5-6.) 10. The Tidal Flooding of 1978 February 6-7 Yet another confirmatory instance of coastal flooding produced by perigean spring tides in conjunction with supporting onshore winds — which is also indicative of a series relationship between such tidal flooding events and the times of successive perigee-syzygy alignments — came, significantly, exactly one anomalistic month later, on 1978 February 6-7. Again, the situation is made more mean- ingful in strengthening previous evidence with regard to the significant role of perigean spring tides in coastal flooding by a nearly coincident occurrence of tidal flood- ing on both the east and west coasts of the United States. In this case, a pseudo-perigean spring tide (defined ac- cording to the terms of reference given earlier in this chapter) was produced by a perigee-syzygy alignment whose mean epoch was 1978 February 6 at 1300' 1 (e.s.t. ), with P - S=— 42 h . This astronomical circumstance was accompanied, on the east coast of the United States, by a violent storm which has been variously described as every- thing from "the worst storm in 30 years" to "the most severe storm ever to strike New England," depending upon the particular location affected. At Cape Cod, wind velocities as high as 92 mph were recorded. As in the January 9 case, the shoreline flooding consequent upon wind-driven high tides was felt in coastal lowlands from Virginia to Maine on February 6-7. (So severe was the resulting damage that, for some days, local newspapers were unable to publish or distribute their regular editions. But cf., the Los Angeles Times, Wednesday, February 8, pt. I, p. 1 , col. 1 ; p. 29, cols. 1-5 ; February 1 2, pt. I, p. 1 , cols. 1-2; p. 6, cols. 1-3.) The sections hardest hit by tidal flooding were those around Revere, Scituate, (See fig. 15 IB.) Hull, Salem, and Winthrop, Mass. In Revere alone, an estimated 2,000 homes were flooded. At Monmouth Beach, 85 families were evacuated, and at Winthrop, 50 families had to be reached by amphibious vehicle. At Revere, 20-ft tides topped the seawall, and were prevented from returning by the rising high waters. Also feeling the flooding effects of the high tides on February 6 7 were Falmouth, East Falmouth, Woods Hole, Eastham, and Rockport, Mass. Other extensive tidal flooding occurred at Belman, Sandy Hook, Sea Bright, and Monmouth Beach, N.J., and at Coney Island, N.Y. The Cape Cod coastline suffered very damaging beach erosion. Tidal flooding damage likewise was heavy along the southeast- ern coast of Maine. It has been estimated that, through- out the entire coastal region of New England, 1 1 ,000 per- sons were forced to leave their homes due to the flooding waters. [See The Boston Herald American, February 9, p. 1 (entire page) ; p. 2, cols. 5-6 (pictures) ; p. 3, cols. 1-4; p. 4 (entire page); also this same newspaper's Storm Souvenir Edition under "The Flooding," pp. 7-13 (pictures. Cf., further, The San Diego Union, February 9, p. A-3, cols. 1-4 (pictures) ; p. A-14, cols. 4-8.] This tidal flooding on the east coast was matched on the west coast on February 6-7 by major tidal flooding re- sulting from exceptionally high tides coupled with pound- ing waves and surf. The latter two conditions were created by successive storm fronts associated with a series of inmoving meteorological "feeder waves" from off the Pacific Ocean. And, in a manner similar to that demon- strated one anomalistic month earlier, the astronomically elevated tides, reinforced by gale-force winds, swept over protecting sandbag barriers at Surfside, Sunset, and Seal beaches, Calif. Tidal flooding also occurred along Balboa Peninsula, on Balboa Island, and at Pacific Beach. Severe tidal erosion was encountered at South Mission Beach. (See the Los Angeles Times, February 8, pt. I, p. 1, col. 5; p. 32, cols. 1-3.) Such recurring coincidences between perigean spring tides and violent coastal storms possessing strong onshore winds capable of supporting severe tidal flooding — as evidenced throughout history, and often occurring on both coastlines simultaneously — is a scientifically intriguing cir- cumstance. From evidence at hand, these coincidences appear to exceed a normal probability distribution, con- sidering the far greater number of occasions within each year when such strong onshore winds could occur other than in the relatively narrow "windows" of perigean spring tides. The seemingly above-average frequency of such con- current events raises the question whether some possible interrelationship between the respective astronomical (gravitational) and meteorological phenomena might exist which has not as yet been established. From the available, documented occurrences, a certain statistical relationship also seems to hold between the most severe cases of tidal flooding and the second or third alignment in a given perigee-syzygy series. Under these latter circum- stances also, repeated flooding events often occur within consecutive anomalistic months. These and other yet un- proven astronomical-geophysical issues will receive further attention in chapter 8. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 431 Photocredit : The Boston Herald American Figure 15 IB. — Section of shoreline at Scituate-Marshfield, Mass., showing the extensive tidal flooding damage to homes caused by the combination of strong onshore winds and the elevated perigean spring tides of February 6-7, 1978 associated with the pseudo-perigee-syzygy alignment of 1978 February 6, P — S=— 42 h . (See item 10.) Chapter 8. Tidal Flooding Potential, and the Relationship of Perigee- Syzygy to Other Oceanographic and Geophysical Factors and Influences The data of table 1, the news accounts contained in table 5, and the detailed evidence of chapter 7 provide ample support to a strong positive correlation between perigean spring tides and coastal flooding, when these tides are accompanied by the correct conditions of wind. The many examples of tidal flooding previously cited also in- dicate that a considerable multiplicity exists among the astronomical conditions of perigee-syzygy which are capa- ble of raising tides to the point of vulnerability to attack by strong onshore winds. The changing right ascensions, declinations, orbital an- gular velocities, and distances of the Moon, when subject to correspondingly varying dynamic conditions imposed during each revolutionary period and the perturbations produced in the lunar orbit by the Sun, themselves result in a diversity of tide-raising forces at times of perigee- syzygy. In addition, the reinforcing gravitational forces of both the Moon and the Sun are involved in the production o. unusually high tides at these times. Add to the Moon's complexities of motion ( 1 ) those of the Sun's apparent motion due to the annual revolution of the Earth, and ( 2 ) further modifications affecting the attraction of the Sun upon the Moon caused by the Earth's changing heliocen- tric distance in its elliptical orbit — and the variety of cir- cumstances of perigee-syzygy builds up accordingly. The magnitude of the combined lunisolar tide-raising force also can vary at perigee-syzygy alignments occurring at different times of the year. Finally, the fluctuating veloc- ity of the Moon at different points in its orbit, and the par- ticular component of this velocity measured parallel to the Earth's Equator, are of importance in the production and duration of perigean spring tides. In columns 5-6 and 11-12 of table 16, four sets of figures have been included for each case of perigee-syzygy whose meaning has not yet been fully explained. These data, examined analytically, incorporate the effects of at least the majority of the above-mentioned factors and, in so doing, provide a quantitative measure of the gravita- tional forces tending to amplify the astronomical tides. Grouped in consecutive pairs, they constitute the astro- nomical portion of an index of tidal flooding potential. An unusual proximity of the Moon to the Earth, to- gether with a corresponding variation in the tide-raising force inversely as the third power of the distance, is the most important single determinant in raising the tides to a significantly higher level. However, the use of the geocentric horizontal parallax of the Moon is not the most representative astronomical indicator of tidal flood- ing potential. Moreover it has been repeatedly pointed out that an increase in the interval of time during which these near-maximized forces act also plays a contributing role in augmenting the tide-raising influence. It thus be- comes necessary to select, as an appropriate coefficient, some indicator which combines the distance, velocity, declination, and relative inclination of the Moon's motion with respect to the celestial equator (thus allowing for amplified tidal duration effects) and which includes the influence of the Sun's gravitational attraction as well. Such a composite astronomical index to tidal flooding potential, known as the Aw-syzygy coefficient (or Aa>-S) will be proposed in the present chapter. In this particular usage, Aw represents a comparative measure of the changing or- bital angular velocity of the Moon, selectively referenced to ( 1 ) perigee, and (2) the vernal equinox, and including the effects of numerous other astronomical factors. 433 202-509 O - 78 - 30 ■m Strategic Role of Perigean Spring Tides, 1635-1976 Certain necessary qualifications and restrictions on the universal application of such a coefficient, related to the existing type of tides, a limited daily range, or a predomi- nant solar modification of the harmonic constituents at a given locality — as well as other special exceptions resulting from geographic and hydrographic considerations — are also presented. Development of a Numerical Index Desig- nating the Astronomical Potential for Tidal Flooding In establishing some quantitative measure of the pos- sibility of any one perigean spring tide producing coastal flooding when accompanied by the requisite wind condi- tions — and hence the flooding potential of one perigean spring tide compared with another — the astronomical cir- cumstances present must be individually evaluated. The four principal conditions affecting the production of all categories of perigean spring tides are : ( 1 ) a closer prox- imity of the Moon to the Earth as a result of (a) solar perturbations of the Moon's orbit when the Sun in its apparent motion approaches coincidence with the line of apsides (in this case, specifically, the perigee position) and (b) a smaller separation between perigee and syzygy produced by a closer commensurability between the syno- dic and anomalistic months under certain conditions; (2) the effect of changing declination upon the Moon's com- ponent of motion in right ascension ; ( 3 ) the longer in- terval of time required for a point on the rotating Earth to catch up with the physically advanced positions of lunar transit resulting from accelerated orbital motions of the Moon at the time of perigee-syzygy ; and (4) the retro- grade motion of perigee at this same time. The varying distance of the Sun from the Earth is also relevant in terms of the increment of force acting on the Earth's waters at perihelion; however, as has been seen, at solar perigee the Moon's orbital velocity is decreased and the Earth's necessary rotational catch-up motion is reduced. Among all of the tide-raising factors present, the Moon's distance from the Earth has the greatest influence in pro- ducing a significantly amplified rise of the tides. It might readily be assumed, therefore, that the use of the Moon's instantaneous parallax as interpolated from The American Ephemeris and Nautical Almanac for the various occa- sions of close perigee-syzygy might be the most logical single indicator of tidal flooding potential associated with such astronomical alignments. This is not the case. An increased value of the lunar parallax does represent the reduced distance of the Moon from Earth at perigee- syzygy in a closely matching fashion. However, this quan- tity as tabulated in the ephemeris does not represent the corresponding effects of changing orbital velocities of the Moon with distance from the Earth, the influence of the changing lunar declination in this same connection, nor the combined (coplanar) tide-raising actions of the Moon and Sun. Neither does it in any way indicate the corresponding requirements for catch-up motion by the rotating Earth, and resulting extensions in the duration of time over which stronger gravitational forces act, con- sequent upon any given perigee-syzygy alignment. Simi- larly, the value of p , the radius vector from the center of the Earth to the center of the Moon, which is numerically equal to cosecant -k , is not a useful indicator for the pres- ent purpose. 1. The Need for Combined Lunisolar Representa- tion In assigning some quantitative measure to the increased potential for tidal flooding resulting from the astronom- ically amplified higher waters at times of perigee-syzygy, the preceding factors and failings must be taken into ac- count. It is obvious that it is necessary to find some coeffi- cient which includes the dynamic effects of both the Moon and Sun, since the gravitational forces of both are in- volved. The increase in tidal range due to the alignment of Moon and Sun at syzygy has been shown to be about 20 percent, and that due to the approach of the Moon to the Earth at perigee amounts to another 20 percent. Ac- cordingly, the combined gravitational forces of the Moon and Sun at times of perigee-syzygy are, on the average, responsible for an increase in tidal range of about 40 per- cent above the mean spring range. As derived from The American Ephemeris and Nauti- cal Almanac, daily apparent angular velocities of the Moon and Sun in celestial longitude (A) or in right ascen- sion (a) are basically a function of: ( 1 ) their respective parallaxes; (2) their instantaneous and changing declina- tions (8), and (3) the actual or real (as well as pertur- bationally disturbed) motions of the Moon and the Earth, respectively. All three of these factors are among those whose effects are being sought after for consolidation in a single index of enhanced tide-raising activity. The daily motions of the Moon and Sun in celestial longitude must, therefore, be regarded as useful indicators in the task of finding such a meaningful index of amplified astronomi- cal tide-raising force and associated tidal flooding poten- tial. Of even greater significance in the first case, however, is the angular motion of the Moon in its own orbital plane. The daily apparent motion of the Moon in right ascension becomes an equally valuable indicator for the Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena ■VXi present purpose, since the Moon's angular motion is there- by referred to the plane of the celestial equator. Sig- nificantly, this is also a plane perpendicular to the axis of the Earth's rotation — and that plane in which the frequently described catch-up effects of the Earth's rota- tion must occur. 2. Significance of the Aco-Syzygy Coefficient In the light of all aspects of the preceding discussion, it is apparent that the necessity exists for the establishment of some quantitative indicator which represents not only the increased gravitational effects of the Moon on the Earth's tidal waters caused by the reduced separation between them at the time of perigee, but also : ( 1 ) the combined gravitational forces of the Moon and Sun at (perigee-) syzygy; (2) the increased tide-raising force of the Sun exerted at solar perigee; and (3) the enhanced tidal forces introduced by a coplanar alignment of the Moon and Sun in declination. It must also include the various effects, at perigee-syzygy, tending to lengthen the periods of time during which the previously mentioned augmented gravitational forces exert their influences, and the special significance of the retrograde motion of perigee. Such a numerical quantifier is achieved, in part, through the determination of the rate of closure of the Moon's angular motion in orbit with respect to the position of perigee. Because the Moon's velocity of revo- lution is always far greater than the angular motion of perigee along the orbit as the result of solar perturba- tions, the Moon will in every case be catching up on the position of perigee. Expressing the appropriate angular velocities as differential rates of motion in one day of time, as a first component of the total expression for Aw-S, the relative motion Awj of the Moon with respect to perigee is given by : where ra^ represents the rate of angular motion of perigee (or rate of angular change in the true anomaly) and v<£ the rate of angular motion of the Moon. Both motions, ex- pressed in degrees per day, occur along the Moon's orbital plane. The selection of these particular parameters permits representation of : a. The lunar parallactic effect: The increased orbital angular velocity of the Moon as a function of close prox- imity to the Earth at the time of perigee- (or proxigee-) syzygy — this reduced separation being caused by the solar perturbational influences exerted on the Moon's orbit by the perigee-syzygy alignment. (The magnitude of this component of the Aw-S coeffi- cient therefore bears a direct relationship with the in- creased values of the lunar parallax at times of perigee- syzygy. ) b. The motion of perigee: Of particular importance is the maximum retrograde motion of perigee which oc- curs as the Moon reaches the position of perigee-syzygy. This effect will be evident as an increase in the rate of closure between the Moon and perigee, since the two are moving in opposite directions. The relative velocity is, therefore, represented by the vector sum of the two ve- locities, whose magnitude will always have its greatest value at the time of perigee-syzygy (see pp. 177-182) . c. The solar parallactic effect: This negative velocity of perigee is further augmented at the time of perihelion by an added lunar proximity to the Sun and an increase in the perturbational influences consequent upon the heightened solar gravitational force present. The value of the rate of closure will increase accordingly, providing an indication of the effect of solar perigee. d. The effect of the annual equation : Conversely, the reduction in the Moon's velocity near the time of solar perigee caused by perturbational influences will, of its own accord, be reflected in a diminished relative velocity between Moon and perigee. Thus, in its total effect, proximity to solar perigee will be represented by the net difference between c and d. Since the effect of c is always larger, the resultant influence will always be an increased value of Awl e. Coplanar lunisolar alignment: A coplanar align- ment of the Sun and Moon in declination, or the possible joint alignment of these bodies in declination and longi- tude at the equinoxes, are both conditions which create increased gravitational forces. The corollary production of an augmented lunar parallax is manifest, in turn, by an increase in orbital velocity of the Moon, and hence a larger value of the Ao^-S coefficient. Thus, in each of the above cases, the Aon-S coefficient responds directly to those factors whose existence pro- duces an enhancement of the tide-raising forces on the Earth's waters. A large value of the Ao^-S coefficient is directly indicative of conditions which are conducive to an increase in such tide-raising forces. Of considerably less consequence in its influence, and subsequently so weighted, a second component of the total Aio-S coefficient is required in order to include the effects of a lengthening of the period of increased gravi- tational force associated with each alignment of perigee- syzygy. Such prolongations of the intervals of tide-raising force application result from the necessity for equivalent 436 Strategic Role of Perigean Spring Tides, 1635-1976 catch-up motions by the rotating Earth to compensate for increased orbital motions in right ascension at the time of perigee-syzygy, especially when the Moon's declination is large. This second component involves the actual daily rate of motion of the Moon in right ascension. The influences of (a) a closer approach of the Moon to the Earth at perigee-syzygy, with a resulting larger parallax and faster lunar motion and (b) a large lunar declination, will al- ways be reflected in a correspondingly high value of A±18°, approximately). Above this declination, a graph of declination as the ordi- nate versus right ascension (or time) as the abscissa re- curves more rapidly toward the horizontal (figs. 44a, b), indicating a proportionately larger component of motion in a. The latter motion creates the necessity for a corresponding catch-up motion by the rotating Earth, and results in a longer interval of amplified gravitational force action if the high lunar declination is coincident with perigee- syzygy. The greater number of cases of such coplanar forces occurring at larger lunar declinations (up to ±28.5°) com- pared with those occurring at or very near declination 0° likewise increases the statistical probability for coincidence of these high declination cases with meteorological condi- tions of strong, onshore winds contributory to tidal flooding. It has been amply demonstrated in table 13, and can be even more fully corroborated by an analysis of table 16, that by far the greater number of cases of a large lunar parallax occur with the Moon at a relatively large declina- tion — especially when the Moon s also coplanar with the Sun. The resulting closer approach of the Moon to the Earth (with the accompanying tide-raising force increasing inversely as the cube of the distance) caused by the orbital perturbations becomes of considerable significance. The coin- cidence of the Moon and Sun on the celestial equator can- not occur at solar perigee (i.e., perihelion) because the Sun is then near its maximum negative declination. It is less cogent that the Moon's presence on the celestial equator is manifest in a reduction of its apparent angular velocity in right ascension (i.e., in the value of a the instantaneous angular velocity of the position of perigee (negative around the time the Moon reaches perigee) must be algebraically subtracted from the velocity of the Moon at this same time. The latter, direct motion is always positive. The vectorial sum thus yields an increased angular velocity of the Moon (still positive) relative to perigee. The individual values of this relative velocity at the instants of (a) syzygy and (b) perigee are tabulated in columns 5 and 1 1, respectively, of table 16. Because a purely dimensionless coefficient is to be established, the units of angular velocity in °/ d are dropped, per- mitting an otherwise incongruous combination of values possessing completely variant units in the several parts of the subsequent evaluating formula. In determining the second component, Au 2 S, the values of the instantaneous rate of change of the Moon's motion in right ascension (including the effects of declination) are computed by use of the expression for a^ given in paragraph 4 on page 226. These values, corresponding to the instants of syzygy and perigee, appear in the computer printout of table 16 in columns 6 and 12, respectively (the time units of right ascension being reduced, for consistency, to °/ d )- It is obvious that a further measure is necessary to establish the relatively greater importance assignable to the tide-raising forces resulting from the close lunar proximity to the Earth at perigee-syzygy (indicated by Awi-S) compared with the effect of the prolongation of these forces at the same time (indicated by A.o> 2 -S). The procedure used also serves to define a more explicit comparative influence of lunar proximity over the range between apogee-syzygy, perigee- or apogee-quadrature, perigee-syzygy, and proxigee-syzygy. It further main- tains an appropriate relative perspective between astro- nomical contributions to tidal flooding and the hydro- logical and meteorological factors which follow. From empirical considerations, the data of columns 5 and 1 1 are multiplied by 4, with those of columns 6 and 1 2 being left the same. The total expression for the Aw-S coefficient then becomes : A w-S= 4 V c + ac The sum of these two terms will subsequently become the astronomical portion of a multiparameter empirical formula applicable to the evaluation of tidal flooding potential — which includes the effects of local harmonic constituents, tidal range, and various meteorological circumstances as well. Establishment of a Combined Astronomical- Meteorological Index to Potential Tidal Flooding The speed of the wind, its direction, and duration of overwater movement are, of course, further aspects of importance in the production of tidal flooding. Strong winds, onshore winds, and those with a long fetch — or total distance of airflow over the sea surface — are all con- tributing factors to coastal flooding when added to astro- nomically amplified tidal conditions. Offshore winds pro- vide a negative or subtractive effect. Low pressure atmospheric systems create an additional rise of water level by an amount equal to about 13 inches for each inch of barometric depression (i.e., approximately 1 centimeter per millibar), while high pressure systems cause a reduc- tion in water level by the same amount. Meteorologically, therefore, a correction must also be applied to account for any deepening or filling of the overlying atmospheric pressure system during the 3-hour period since the preced- ing synoptic weather map. With consideration to the foregoing and other factors, it is now possible to develop a single equation incorporat- ing the various astronomical, meteorological, physical, and hydrographic elements which together serve to establish a greater or lesser potential for tidal flooding. Specifically, these elements include : ( 1 ) the effect of a perigee-syzygy alignment in increasing the tide-raising forces present, represented by the Aoj-syzygy coefficient ; ( 2 ) the response of the local tide to the semidiurnal lunar influence, which is that most prominent in connection with perigean spring tides, and here expressed for mathematical conven- ience by the term M 2 — 1 ; ( 3 ) the value of the mean spring (or diurnal) range of the tides at the place under con- sideration, representing a further aspect of local dynamic response to astronomical tide-producing influences, and incorporating as well a quantitative indication of the degree of constriction of tidal estuaries, shallowing of the ocean floor, and other variables; (4) the average velocity of the strong (usually >25 knots), persistent, and direc- tionally steady wind movement over the sea surface neces- sary to support tidal flooding. The effects of the wind ac- tion on the sea surface are manifest in waves produced in the shallow waters immediately adjacent to the coastline, but may also persist in the form of swell hundreds of miles from the coastline ( the total distance of such uninter- rupted wind movement is known as the fetch) ; (5) the angle-of-attack of this overwater wind movement with r,:: Strategic Role of Perigean Spring Tides, 1635-1976 respect to the shoreline, measured by the angle 6 between the direction from which the wind is blowing and a normal or orthogonal line to that immediate section of coastline under consideration; (6) the duration of the overwater wind movement, expressed as a time factor a rather than in terms of distance, as in the case of the fetch; and ( 7 ) the atmospheric pressure gradient during the past 3 hours. Thus, where: n=a combined astronomical-meteorological coefficient of potential tidal flooding (the capitalized symbol is derived from the first letter of the Greek word 7rAi?MMpa meaning "flood-tide" or "inundation," and should not be confused with the lower-case symbol w universally used for astronomical par- allax throughout this volume). (As a nu- merical index only, IT is dimensionless.) y(£ = the rate of angular change in the Moon's true anomaly at the instant of syzygy (or perigee) (Vectorially, & c =v c — « c . The units of all three quantities are °/ d -) J-£=the rate of angular motion of the Moon in its orbit ra c = the rate of angular motion of the lunar perigee along the orbit aj^the rate of lunar angular motion in right ascension (i.e., as projected on the celestial equator) at the instant of syzygy (or perigee) Au-S=4:U ([ -\-a ( r M 2 =the principal lunar semidiurnal component of the tides at the location under consider- ation (in feet) i? s =the mean spring (or diurnal) tidal range at the same local station (in feet) F=the mean velocity of the surface wind during at least a 3-hour period at a nearby reference coastal weather station (in knots) 0=the angle measured between an axis ex- tended to seaward perpendicular to the general coastline and the direction from which the wind is blowing (in degrees of arc) "The reason for use of the dimensional unit of time rather than distance is obvious when an actual example such as the great mid- Atlantic tidal flooding of 19G2 is considered. Because of stagnation of the onshore low pressure center, the distance of overwater wind movement remained relatively constant. However, the onshore wind- flow persisted timewise through 2.5 days and 5 successive high tides, during each of which continuously height-accelerating effects were felt. D=the duration of a strong, sustained, on- shore windflow over the body of water lying directly seaward (but with no limit on its total outward extent) from the coastal station (in hours) AP=the change in barometric pressure at the coastal weather station, during the past 3 hours (in millibars) A meaningful index quantifier describing the active potential for coastal flooding resulting from the com- bination of astronomical and meteorological causes may be represented by : IL=Au-S+(M 2 -l) + (&-0 + Vcos6+D-34:(±AP) The final coefficient, 34 millibars, is approximately equivalent to an atmospheric pressure change of 1 inch of mercury — that required to raise or lower the water level by 1 foot. For simplification, the small effect of a rapidly moving atmospheric pressure system in itself altering the level of the sea surface is ignored in the above equation. The remaining numerical constants are arbitrary ones, based both upon empirical data and analytic convenience in establishing an average index value centered around 100. The units in which the individual functions comprising this equation are customarily derived are specified in the preceding legend, but are not carried into the computa- tions associated with this formula. Since the index is itself dimensionless and constitutes a purely relative measure, the various components of the equation may be safely combined, with their different units being ignored. In this equation, it will be seen that the first term on the right — that expressing the effect of a perigee-syzygy alignment — is always positive. So also, in successive order are M 2 , Rs, and V, the magnitude of the wind velocity. The cosine function in the fourth term automatically takes care of the tide-raising or tide-reducing effects created by onshore or offshore components of the wind, respectively. The corresponding additive or subtractive functions are indicated by the algebraic sign customarily assigned to this trigonometric function in the quadrant concerned. The value of D is again always positive, but the algebraic sign of the last term varies respectively from plus to minus with rise or fall in atmospheric pressure (the corresponding correction being taken care of by the minus sign in front of the parentheses). The greater the amount by which the numerical value of this index is in excess of 100 (representing an average Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena n<) condition) the greater is the potential for tidal flooding. Examples demonstrating the application of this index to the determination of tidal flooding potential, and showing in the relative magnitude of II a very close agreement with the severity of the flooding conditions actually encountered are given in table 30. These and other desired historical examples for which II has been evaluated may be compared with the extent of tidal flooding described for specific cases in chapter 7 and in the newspaper accounts comprising table 5 of part I, chapter 1. This index to potential tidal flooding is presently in an analytic stage of development and largely dependent upon correlations with empirical data. Appropriate ad- justments within the individual portions of the formula will undoubtedly occur as additional comparisons are made with future coastal flooding events. With this un- derstanding, the expression for II is to be regarded as a provisional one, pending the realization of such a definitive indicator. The incorporation of the various contributing causes to tidal flooding in such a single numerical index is in- tended principally to achieve a generalized descriptor term leading toward an awareness of the increased tidal flood- ing potential occasioned by tide-amplifying astronomical conditions, where supporting meteorological conditions are also present. In connection with meteorological investi- gations of hurricanes and storm surges, N. Arthur Pore, Chester P. Jelesnianski, and others (see bibliography — category 18) have derived various theoretical, empirical, and modular formulae for predicting the height of waves, wave setup conditions, swell, and storm surges under con- ditions of strong, onshore winds. These formulae are based upon such factors as wind stress vectors, offshore surface- pressure fields, maximum storm winds, and the magnitudes and distributions of these and related meteorological ele- ments within rectangular grid systems covering the coastal waters. Such formulae will prove more satisfactory for detailed analytical evaluations, bearing in mind an earlier clarification that a storm surge analyzed for meteorological purposes does not necessarily imply coastal flooding potential. The numerical evaluation of II is designed to provide an expedient and, where appropriate, a timely forewarn- ing of astronomical tidal flooding potential should critical meteorological conditions also prevail. A more compre- hensive evaluation is achieved when most of the terms in the expression are employed. However, where certain elements are lacking — or in the exigencies of the mo- ment — a partial indication of any pending tidal flooding threat to the shoreline may be secured by the combined utilization (or separate analysis of) all parameters in the equation which are immediately available. Table 30. — Examples Involving the Use of the Aco-S Coefficient in Establishing a Combined Astronomical-Meteorological Index (II) of Potential Tidal Flooding The astronomical coefficients are computed for the mean epochs of perigee- (proxigee-) syzygy and are combined with the most representative meteorological data available for the cases evaluated.* Key No. Date; flooding location (or that of the nearest tide station) Astronomical-Tidal Parameters Meteorological Parameters Potential for tidal flooding Aco-S coefficient (table 16) M 2 -\ (table 19) 3.5 (table 19) V cos (kt) D (h) 34 ( ± P) Index n Intensity rating D-57 F-68 -I-83e J-85 N-99 O-100 1931, Mar. 4-5, New York (The Battery), N.Y. 1939, Jan. 3-5, Aberdeen, Wash. 1959, Dec. 29, Boston, Mass 1962, Mar. 6-7, Entire mid- Atlantic coast (Breakwater Harbor, Del.). 1974, Jan. 8, Malibu Beach (Los Angeles, Calif.).' (Willets Point, N.Y.) 1976, Mar. 17, Halifax, Nova Scotia. 82. 178 84. 056 84. 105 83. 025 84.611 84.611 82. 371 1. 138 2.425 3.422 . 916 .695 2.619 1.046 0.5 . 9 3. 1 .4 . 5 1.4 . 5 52 43 56 30 35 -8 43 36 48 20 65 24 10 171.8 168.4 166.6 179.3 144.8 80.6 136.9 Extreme. Severe. Severe. Extreme. Strong. Insignificant. Moderate. Intensity rating scale: n > 1 70— Extreme. n > 120— Moderate. TI> 160— Severe. n> 100— Slight. n> 140— Strong. n< 100— Insignificant. *Note: Precise values for the rates of barometric pressure change in the past 3 hours at local stations are best obtained from original hourly weather data in each case and, accordingly, have not been inserted in the above table. 4111 Strategic Role of Perigean Spring Tides, 1635-1976 One further requirement for extensive tidal flooding is, of course, the involvement of a lowlying coastal area, whose mean elevation is only some few feet above the level of mean high water spring tides, and in which any upward slope (positive gradient) extending inland from the sea is also small. Empirical Support for the Validity of the Delta Omega-Syzygy Coefficient Provided by Predicted and Observed Tidal Height Data Comprising the next step in an evaluative process to determine the reliability of the Aw-syzygy coefficient as one factor in a multiple-parameter indicator of tidal flooding potential, it is desirable to subject this coefficient to appro- priate quantitative tests. In this process, certain cases of perigee-syzygy alignment possessing unusually high Aoj- syzygy coefficients computed directly from the data in table 16 are compared with predicted tidal data for the same dates contained within official government tide ta- bles. Dates on which tidal flooding has been observed to occur are selected for such analyses. In this comparison with examples of known tidal flood- ing, the objective is that of discovering all consistent rela- tionships between the Aw-syzygy coefficient and predicted or observed tide data which either give support to, or con- tradict, the interpretations made from the previously con- sidered, purely astronomical data. A necessary preliminary to the establishment of factors of correlation between the astronomically related A -0.2 r24 0515 0.0 9 0000 4.5 T24 0549 -0.1 o 9 0109 3.9 :. 24 0054 i.r 1.200 3.7 1114 3.5 0627 0.1 1 1 ol 3.5 0733 0.4 P 1 9 -0.2 1800 0.1 1712 . 2 1240 3.3 1746 0.2 1.0;, G 3.3 1 0,58 .-.'J 0000 4.0 1824 0.5 1040 0.8 1940 0.2 54 54 54 53 61 no 0029 4.5 W25 0604 0.1 no 0054 4.2 1 oo 0011 4.6 S10 0202 3.7 M25 0155 4.2 0653 ] 3 16 0.1 3.4 lou'i 1800 0.0 0.0 OVOO lO-lo 0.3 3.2 0643 125( 0.0 3.5 Ff|0822 ■ M1450 0.4 3.4 1 f\ 0816 ^M 1443 -0 . 2 4.1 1855 0.4 1923 0.7 1847 0.2 2043 0.8 0, 48 o.: 58 54 58 59 53 65 .1 i ( i 1 : : V 4.2 126 0029 4.4 i J 1 0152 3.9 ! 126 0110 4.4 01 j 1 000 3.6 1 26 0300 4.1 N in i 0.4 3.2 s o'O.l 10' ,0 ' .2 3.3 0819 11 10 0.4 3.2 0741 10-0 0.0 3.6 A 0000 1041 t .4 3.6 E ,0915 lo-o: -O.O 4.4 64 T12 1956 oooo 0.6 4.0 60 F27 1902 0129 0.3 4.3 59 S12 2026 0251 0.8 3.7 64 S27 1954 0214 0.3 4.3 48 10 21 1 0349 i .7 3.5 61 0.10 V .,40.3 . 1 3.9 - .: 4.0 O.C ■ IJ1520 66 21 ° 2 0.5 3.2 0.8 66 GO.,1 1409 0008 . .0 0.4 i .3 r Vl540 2129 58 0.5 3.3 0.8 1 f>0840 t Xi502 2103 66 -0.1 3.9 0.2 E 45 0956 1629 2233 0.3 3.8 . 62 1009 16-17 2302 F13 0337 3.8 S28 0235 1.0 SI 3 03 1 9 looo 1632 3.7 0.5 3.5 OOo 0320 4.2 a/13 439 O.: T28 1505 3.8 1002 1622 0.5 3.3 1 f\ 0904 0.1 3.6 000 10 )o -0.2 4.2 104( 1714 i'.3 4.1 1 1 04 rcic ;. :-:;■;■ ii 0.7 2118 0.2 000:, 0.7 221( 0.1 o; 23 0.-1 60 68 45 57 43 52 .1 1 ■ ;:■/, 3.8 S29 0343 1 . Oil 0441 3.7 1 0.0 0424 4.2 iM 0526 3.5 : o 1 ., ii IE -0.1 ;■ .o: - .3 loOO 1714 0.5 3.4 o . o; -0.1 ;•'. . o A 1049 1V1V 0.4 3.8 E loOG 1704 -0.3 4.5 1123 1757 0.2 4.3 i "'-:_- 5 1.0', 2304 0.6 221 5 l;.o ; ,4o 0.5 2314 -0.1 L835 5.0 51 63 41 56 41 50 SI 5 0528 3.9 M30 0446 1.1 [J;. i ooo 3.7 .G.v, 24 4.2 F15 001 o .0 -.< 0056 - .: ] 1 i 0.4 1102 -0.3 1130 0.3 p .1 OO -0.4 .0,11 0.: 0658 3.( 1 759 3.7 1723 4.4 1758 4.0 1800 4.9 1204 0.0 10,1V -0.3 ; :. ,; , 1 0.4 : .: ,: ( -0.3 1838 4.6 1925 o.l 45 55 37 51 01 i ioi: 0620 101 9 -0.3 4.2 -0.5 41 46 50 1 -" '-: -1 5.1 Time meridian 75° W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena -Ho Table 31a, b, c, d. — Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy {Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December, 1962 78 BREAKWATER HARBOR, DEL., 1962 Times and Heights of High and Low Waters JULY AUGUST SEPTEMBER Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Day Day Day Day Day Day h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. 771. ft. S 1 0148 -0.3 M16 0115 -0.1 W 1 0255 -0.1 T16 0223 -0.6 S 1 0331 0.0 S16 0330 -0.9 0749 3.7 0711 3.6 NM 08 3.7 FIV 08 4.3 941 4.0 0946 3.1 1334 -0.2 1303 -0.3 "1446 0.0 ■1427 -0.7 1542 0.0 1558 -0.0 2011 5.1 1938 5.1 2114 4.6 2053 5.3 2157 4.2 2209 4.0 44 46 38 47 3S 52 M 2 0235 -0.3 T17 0201 -0.3 r 2 0332 0.0 F17 0310 -0.8 K 04 03 0.0 Ml 7 0417 -0.8 MM0836 3.7 s 0759 3,7 0937 3.7 P 0917 4.5 1016 4.0 1030 6,0 glT- "1421 -0.2 en_ ■ 1352 -0.4 1528 0.1 1519 -0.8 ■ 1622 0.1 165 2 -0.6 N 42 2055 5.0 FJV12024 5,2 37 2152 4.5 SO 2140 5.2 fc2232 38 4.0 54 2302 4.4 I 3 0319 -0.2 W18 004 7 -0.4 F 3 0408 0.0 210 0357 -0.8 M 3 0439 0.1 no 0506 -0.5 0921 3.6 0847 3. C J 1015 3.7 1007 4.6 1054 4.0 1132 4.9 1506 2137 0.0 1442 -0.5 m 2:1 1612 -0.7 1703 0.2 174 9 -0.3 4.8 2110 5.3 2221.M 4.3 11 OH 0.0 1114 4.4 0600 0.3 114 4 4.6 0625 0.8 163b 0.1 1732 -0.3 1744 0.3 1235 4.4 1816 0.1 1254 4.0 2230 3.6 2337 3.8 3338 3.2 1905 0.2 1918 0.3 40 W 3 0437 0.2 56 ue (i031 -0.1 49 3 s : '334 0.3 60 S18 0117 3.3 56 M 3 0013 3.4 53 T18 0134 8.3 1000 4.2 1 2( i4 4 . 7 1203 4.3 0.3 0659 0.6 "613 0.2 0723 .7 1719 8:5 1831 0.0 1838 1335 4.1 1240 4.4 1347 8.8 231 2004 0.3 1911 0.1 2008 '.,.4 44 1 4 0517 0.2 61 1 19 0038 3.3 59 3 4 0O34 3.2 0.4 4.3 0.3 62 M19 0222 3.2 rt 0117 3.5 55 W19 0230 3.4 1142 1807 4.2 0.4 N 0-0:7 1303 0.2 4.4 ('■630 1302 1 f\ 0803 ■- X 1437 0.7 3.9 716 134': 0.3 4.3 1 f\ 0822 L V 1442 ..3 8,. 6 1930, 0.2 1937 2103 0.4 8' 3,0 0.0 2058 C.5 50 66 63 59 65 54 f 5 0002 3.2 S20 0140 3.3 M 3 0137 3.2 T20 0324 3.3 W 5 "223 3.7 T20 0325 3.3 0602 1232 0.4 4.1 1 f\ 0730 HJ14II 0,3 4.1 P {\ U734 r " 1^05 0.4 4.2 0909 1536 0.8 3.7 P O 0824 ■ V 1445 0.3 4.2 C 0921 fc A 1536 A 2145 J. 8 8.3 1902 0.5 2044 0.4 3('38 0.2 2155 0.4 2108 -0.1 '-,.4 58 68 67 53 64 51 S 6 0057 3.1 S21 0238 3.2 T ('243 3.4 W21 0418 3.5 T 6 0329 4.0 F21 0416 3.7 06, 07 0.4 0838 0.7 0843 0.3 1010 0.7 "933 0.2 1017 0.7 1330 4.1 1519 4.0 1313 4.3 1629 3.7 1549 4.2 1627 3.3 20(i3 0.5 2148 0.4 2137 0.0 2240 0.4 28! '4 -0.3 2230 -.3 64 61 63 47 62 47 0800 3.1 M22 0403 3.3 W 7 o331 3.7 T22 0505 3.7 F 7 0431 4.4 S22 0503 3.9 C 0759 0.4 0940 0.7 O901 if 13 0.1 1103 0.6 E 1"39 0.0 "^1715 ! .6 ..1434 4.1 L0 20 3.9 4.4 1716 3.7 1031 4.2) 6.0 FO2106 0.4 2244 0.4 2334 -0.2 2320 0.3 2239 -0.4 2313 0.2 65^ 53 , 5 ? 41 57 43 M 8 0308 3.2 1 23 0439 3.3 T 8 04 02: 4.2 F23 0546 4.0 3 8 0328, 4.7 S23 0546 4.2 m 2:1 3 07 1713 0.0 3.9 1,6,6 1714 -0.1 4.5 A 1149 M —1759 t2357 0.4 3.7 1141 174 9 -0.2 4.2 1158 1801 o.4 8.3 3206 0.2 2328 0.3 3336 -0.5 0.1 8338 -0.6 2354 8.1 62 46 55 38 54 42 I 9 0414 3.5 W24 0544 ii >o 3.7 F 9 0547 4.6 S24 0624 4.2 8 9 06 88 3.1 M24 0628 4.4 Ml' 0.1 0.3 E 1136, -0.4 1231 0.2 P 1238 -0.4 1243 . 3 1641 4.5 1759 4.0 1809 4.6 1837 3.7 1844 4.2 1843 3.3 2303 -0.1 58 W10 0313 3.9 39 T25 0005 0.2 52 S10 0016 -0.7 37 S25 0033 0.1 52 0042 -0.7 39 T25 0035 o.O 1112 -0.2 1)6 34 3.9 0639 5.0 0701 4.4 ('714 5.3 0707 4.6 1730 4.7 1222 0.3 1331 -0.6 1310 0.1 13.0 -0.5 1325 0.1 3303 -0.4 1838 4.0 1901 4.6 1915 3.7 1030 4.2 1925 3.3 53 11 1 0007 4.4 35 F26 0039 0.1 51 "103 -0.9 35 M26 0107 0.0 48 Til 0130 -0.7 41 W26 0115 - .1 1210 -0.5 A 0600 4.1 P 0730 5.3 0736 4.6 PM0802 5.4 0748 4 . 8 1832 4.9 1301 0.1 13,44 -0.8 1350 0.0 rrr 11424 -0.6 1408 0.0 1913 4.(1 1033 4.6 1952 3.7 2027 4.1 2004 3.6 si 33 48 36 49 40 11." 0043 -0.7 S27 0111 0.0 0151 -0.9 T27 0144 -0.1 W12 0218 -0.6 T27 0156 EF m i451 -0.2 0658 1 3,i '4 4.8 -0.8 E 0732 1337 4.3 0.0 r in -l^ 5.5 -0.8 MM 1 ■^•"MSO 4.7 0.0 0851 1311) 5.4 -0.5 4.9 -6.1 1923 5.0 1043 4.(1 2042 4.4 2029 3.6 8116 4.0 5 2046 3.0 48 ,13 0120 -0.9 33 S28 014 3 O.o 49 113 0239 -0.8 W28 0220 -0.1 47 113 0303 -0.5 F28 0239 -0.3 E. o740 5.1 0800 4.4 0907 5.5 0849 4.8 N 0938 5.2 0908 0.4 k 1358 -0.9 1414 0.0 1338, -0.7 1511 -0.1 1(3,3 -0.4 1534 -,-.:: K2011 5.0 2021 3.9 2132 4.2 2107 3.5 2204 3.8 2129 8.7 49 34 49 38 47 44 SI 4 0216 -1.0 M29 0217 -0.1 Wll 0326 -0.6 T29 0259 -0.1 F14 1 334 -0.3 S29 0324 -0.3 FM0837 ■"■1450 5.4 -0.9 •JM 0839 Ull" 1452 4.5 0.0 O03G 1,0-'" 5.3 -0.5 0927 1553 4.8 0.0 1025 1038 5.0 -0.2 0952 1618 3." -0.: 2101 4.8 .On;,,, 3.8 3323 3.9 2147 3.5 8884 3.6 2215 3.7 49 34 50 41 F30 0340 49 46 M15 0302 -0.9 KO.i O201 -0.1 T 1 5 1'4 14 -0.4 -0.1 SI 5 0442 0.0 S30 0411 -0.2 U030 5.4 0913 4.6 1O4 5.0 C 1008 ^ 1637 4.8 1114 4.6 1038 4 . 9 134 2, -0.8 1531 0.0 1713 -0.3 0.0 1730 0.0 1704 -0.2 31 00 4.5 2131 2..0 32,17 3.7 2231 3.4 88,46 3.5 2304 3.7 50 36 W31 40 0326 ('04 1012 2208 0.0 4.6 0.0 3.5 53 46 49 49 M31 0308 1127 1754 -0.1 4.7 -0.2 Time meridian 75° W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 445 and Sun at perigee-syzygy, which act to produce aug- mented high waters and thus enhance their susceptibility to tidal flooding. Accordingly, its influence should be re- flected in the calculated value of the Aw-syzygy coefficient, if this is to become a meaningful index of astronomical tidal flooding potential. One of the worst instances of tidal flooding in recorded history occurred along the mid-Atlantic coast on 1962 March 6-7. The unusually high proxigean spring tide created at this time, assisted by an increased tidal day, was raised to severe flooding proportions by strong, persistent, onshore winds which lasted through five successive high tides. (See chapter 7 for the flooding details published in newspaper accounts of this catastrophic event, as well as associated weather maps, pictures of the flooding, and hourly height tide data corresponding to the dates in- volved. ) The astronomical contributions to this extremely vulnerable tidal flooding event are revealed among the various data and graphs covering this case. The evaluation of the flooding potential n is shown in table 30. Table 32a gives the predicted tide heights. Fig. 161a depicts the corresponding rate-of-growth tide curves. Similar data are provided for the rest of the year in tables 32b,c,d and fig. 161b to provide a controlled basis for comparison. In this example, an extremely close proxigee-syzygy alignment which occurred at a mean epoch of March 6.1975 (e.s.t.), having a separation-interval of only — 31 m , resulted in a lunar parallax value of 7r = 6r26.6" on March 6.19 (e.s.t.). The position of perigee (labeled P in table 32a) occurred at March 6.1868; syzygy (labeled NM in the same table occurred at March 6.2083 (e.s.t.) . The highest high water (5.3 ft at Breakwater Harbor) was predicted for 0813 (e.s.t.) on March 6. The next succeeding higher high water (of the same height) was predicted for 0902 (e.s.t.) on March 7. The difference between these two times is 49 m which, when added to the 24 1 ' of elapsed time between the consecutive days, ex- presses the total interval separating the peaks of immedi- ately succeeding higher high waters. This period is equiva- lent to the length of the tidal day. In fig. 152a, it will be noted that this increment of 49 m represents the minimum value in a curve trough located between two peaks. As described in the discussion on similar tide curves (p. 303), each minimum in the series of which this is a part is due to the effect of tidal priming in reducing the tidal day. However, among the total array of minima appearing throughout the year, it will be ob- served that those occurring close to a time of perigee- syzygy are located farthest above a baseline corresponding to the next succeeding apogee-syzygy. This uplifting of a curve trough between two crests is clearly due to the com- pensating effect of perigee in speeding up the Moon's orbital velocity, increasing the necessary catch-up time of the rotating Earth, and thus lengthening the tidal day. Further, the large tt defines a condition of proxigee. The maximum increase in the tidal day at proxigee- syzygy (NM) on March 6.1975 (e.s.t.), compared with that at exogee-syzygy (FM) on March 20.3944 (e.s.t.) is 16"'. The difference involved is larger than that for any other lunation except that containing the date September 14.2374 (e.s.t.), when another perigee-syzygy alignment occurs at full moon. This case has a separation-interval of 11.8 1 ' with an accompanying parallax of ir = 61'22.233" on September 14.2. The difference in the length of the tidal day between perigee and apogee is again 16 m (fig. 152b). The incremental values of 15 m on February 5.2541 (e.s.t.), and April 4.1406 (e.s.t.), correspond to two other perigee-syzygy dates in the year, with separation-intervals of 21.8" and — 22.8 11 , respectively. The third 15'" incre- ment on October 13.1156 (e.s.t.) is associated with yet another perigee-syzygy alignment in this same unusual year, having a separation-interval of — 9.6' 1 and a value of 7r = 61 , 25.808' / on October 12.8 (e.s.t.). The corresponding values of the Aw-syzygy coefficients for each of the above dates, as derived from table 16, are all above average. Thus, the Aw-syzygy coefficients not only indicate very accurately the times of production of perigean (or proxigean ) spring tides but (as a direct func- tion of their magnitudes) denote, in relative degree, the amplified heights of the high waters which result. Various other astronomical influences resulting from the changing interrelationships of the Moon and Sun may be studied in detail by the combined use of tables 31a,b,c,d and figs. 152a,b. In these tables, the follow- ing symbolic designations are used : S = the date on which the Moon is at its greatest declination south of the Equator E = the date on which the Moon crosses the Equator N = the date on which the Moon is at its greatest declination north of the Equator P=the date of perigee (or proxigee) A = the date of apogee ( or exogee ) NM=new moon FQ = first quarter moon FM=full moon LQ=last quarter moon VE = the vernal equinox ■lib Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a) VARIATION IN DECLINATION OF MOON AND SUN- 1962 •A O T TO A« TO A« T O A 80 BREAKWATER HARBOR, DELAWARE 1962 20 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 152a. — (Discussed in text.) Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena •147 J-85 (b) VARIATION IN DECLINATION OF MOON AND SUN-1962 T OA •T 80 BREAKWATER HARBOR, DELAWARE 1962 20 T • AO T • JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 Figure 152b. — (Discussed in text. 148 Strategic Role of Perigean Spring Tides, 1635-1976 SS=the summer solstice AE=the autumnal equinox WS=the winter solstice The symbols used in figs. 152a,b are indicated in the legend accompanying fig. 153a. At the top of each of these composite diagrams, the continually varying decli- nations of both the Moon and Sun are plotted to the same scale as that used for the changing lengths of the tidal day in the bottom portion of the diagram. A direct analysis of any contribution to the length of the tidal day made by the changing lunar declination, or by the declinational influence of the Sun, is thus possible. An obvious disruption of the otherwise uniform, double crests of the curves which occur individually near the Moon's semimonthly positions of quadrature is evident at the time of the summer solstice. The resulting curve irregularities are clearly due to a superposition of the diurnal influence of the Sun, exerted at a time when the solar body is at its maximum positive declination (i.e., at its greatest incursion into the Northern Hemisphere) while the Moon is at a large southern declination. In fig. 152a, a bifurcated curve peak occurs shortly after the summer solstice on June 21, 21 h 24 m . This is followed by a jagged and not readily identifiable mini- mum about the middle of July as the Moon and Sun again move to nearly maximum opposing declinations. This effect is not as pronounced when the Sun reaches its maximum negative declination at the winter solstice (December 22, 08"15 m ). Since the Sun is then in the Southern Hemisphere, its influence on the Northern Hemisphere tides is somewhat reduced. With the Sun and Moon nearly at the same declina- tions and crossing the Equator on March 21 and 22, re- spectively, the heights of the two adjacent crests on either side of these dates are very nearly equal. As the dates of the summer and winter solstices are approached, the heights of any two contiguous peaks become the most disparate. Accelerated Rate of Tide Rise as an Indica- tion of Increased Tidal Flooding Potential The most significant of the empirical factors giving credibility to the use of the Aw-syzygy coefficient is its close relationship with a significantly increased rate of tide rise at times of perigee-syzygy. Curves of rapidly ac- celerating tide growth may, in turn, be demonstrated to have a very real positive correlation with actual tidal flooding events. The point of departure for verifying this relationship is, again, basic data abstracted from the annual tide tables. In contrast with the previously constructed curves involv- ing the length of the tidal day, however, the present curves utilize the average rate of tide rise at a given station during any day of the year as the ordinate value. Depend- ing upon the characteristic type of tide found at the station, one of two different procedures is used in the ensuing analysis. 1. Semidiurnal Tide To achieve the appropriate curve-plotting values in this case, the difference (in feet or meters) is taken between the predicted level of the lowest low water for any given date and that of the highest high water next following it (even if this HHW occurs early in the morning of the next succeeding date). As will be explained in the next section, if — as frequently happens on the west coast of North America — the lower high water (LHW) sequen- tially follows the lowest low water, a slightly different procedure is used. Negative low-water values (indicating water levels below the standard chart datum) are, of course, treated algebraically in making the subtraction leading to the total maximum rise in water level. (See tables 32a, b, c, d.) To obtain the average rate of rise, it only remains to subtract the time of LLW for any date from the time of the next succeeding HHW, and to divide the difference into that giving the corresponding change in water level over this same time interval. The resulting quotient is plotted against the appropriate date on the abscissa axis of the diagram. Because of the sizable task of extracting and plotting these differences and quotients in each case for 365 days in the year, various representative examples from among the 100 cases of tidal flooding noted in table 1 have been used to show the resulting correlations. Table 33 lists appropriate standard tide-prediction stations either at the scene of the flooding or close thereto. The principal re- quirement in the selection is that these examples be vari- ously typical of observed tidal flooding conditions. The examples are randomly distributed in time, including one from each decade over the 56-year period from 1918 to 1974, in latitudes ranging from Halifax, Nova Scotia (44°40' N.), to Los Angeles, Calif. (33°43' N.), are lo- cated on both the Atlantic and Pacific coasts of North America, occur during all winter months of the year from October to April, and at various times of the day and night. Tables 32a,b,c,d show a sample of the method of tak- ing the requisite time differences (the tidal height differ- ences are similarly established for these same intervals). Figs. 153-163 depict the predicted curves of astro- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena ■149 Table 32a, b, c, d.- 74 -Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December, 1962 BREAKWATER HARBOR, DEL., 1962 Times and Heights of High and Low Waters JANUARY FEBRUARY MARCH Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Day Day Day Day Day Day h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. M1 !83§ 8:8 T16 0504 4.4 T 1 0504 1125 4.5 F16 0631 4.4 T 1 0330 4.2 F16 (1515 4.0 1124 0.3 0.2 1253 0.3 0954 0.4 1138 i ) ,. 5 1612 3.5 1727 3.6 1725 3.5 1855 3.5 1558 3.3 1747 5,4 2217 0.2 2320 0.1 2323 -0.2 2158 0.1 2534 0.5 99 113 127 107 109 92 T 2 0450 4.1 W17 0600 4.6 F 2 0558 4.8 5 17 0041 0.2 F 2 0433 4.4 S17 0G05 4.1 1102 0.4 1222 0.2 1220 0.0 0715 4.4 1057 0.2 1223 0.4 1704 3.5 1822 3.5 1820 3.7 1333 0.2 1701 3.5 1832 3.5 2304 0.0 1936 3.6 2300 -0.1 112 115 140 113 122 101 W 3 0538 4.4 118 0010 0.1 S 3 0016 -0.4 MM 0123 0.1 S 3 0533 4.7 S18 0021 0.3 1155 0.2 0649 4.7 0650 5.1 0754 4.5 1 i 55 -0.1 0649 4 , 2 1755 2352 3.6 1312 0.1 1312 -0.3 I t08 2012 0.1 1800 3.9 15ol n.,3 -0.2 1911 3.6 1913 4.0 3.7 2:55" -0.4 1910 3.7 127 119 151 116 138 104 T 4 0625 4.8 F19 0057 0.0 S 4 0109 -0.6 M19 0202 0.0 S 4 0629 5.0 Ml 9 0102 0.2 1245 1843 0.0 3.7 0733 1355 1954 4.7 0.1 3.6 m 2003 5.3 -0.5 4.2 m 2046 4.5 0.1 3.8 L24S 1854 -0.4 4.2 0728 1334 1945 4.2 0.2 3.9 137 119 162 114 152 113 F 5 0039 -0.4 S20 0139 0.0 M 5 0201 -0.8 "120 0239 0.0 M 5 0054 -0.7 120 0140 0.0 0712 5.0 0814 4.7 0830 5.5 0904 4.4 0722 5.2 0802 .7 1333 -0.2 1434 0.1 1451 -0.7 1516 0.1 1338 -0.6 1.4 07 0.1 1932 3.8 2034 3.6 2054 4.4 2120 3.9 1947 4.5 2017 4.0 148 120 164 113 161 116 S 6 0127 -0.5 S21 0220 0.0 r 6 0254 -0.9 U21 0317 0.0 T G 0148 -0.9 W21 0217 -0.1 0759 5.3 0852 4.7 0919 5.4 0938 4.3 0813 5.3 0836 4 . 3 1421 -0.4 1511 0.1 1539 -0.8 1548 0.1 1427 -0.8 1439 0.0 2020 4.0 2111 3.6 2144 4.5 2154 3.9 2036 4.8 2050 4.2 153 118 159 111 165 115 S 7 0215 -0.6 M22 0300 0.0 W 7 0346 -0.8 122 0355 0.0 W 7 0241 -1.0 122 0254 -0.1 0846 5.4 0929 4.6 1009 5.3 1013 4.2 0902 5.3 0909 4.2 1510 -0.5 1.5 17 2148 0.1 1627 -0.7 1622 0.1 1511 -0.9 1511 li,l) 2109 4.0 3.6 3236 4.6 2229 4.0 21 26 5.0 2123 4 . 2 157 114 149 107 161 115 M 8 0305 -0.7 7 23 0339 0.1 T 8 0439 -0.7 F23 0434 0.1 1 8 0333 -1.0 1 23 0331 -0.1 0934 1600 5.4 m 4.5 1101 1716 5.0 1049 4.1 0951 1602 5.1 4.1 -0.6 0.1 -0.6 1657 0.2 -0.8 1545 0.0 2200 4.1 2225 3.6 2330 4.6 2307 4.0 2215 5.0 2158 4.3 153 109 132 100 149 112 T 9 0358 1024 ■°5: 6 3 W24 0419 0.1 F 9 0535 -0.4 S24 0515 0.2 F- i -0.8 1210 0.0 1553 -0.4 1320 -0.1 1703 0.3 1639 -0.2 2154 5.2 21 29 4.6 2,22:o 5.1 2144 4.9 8331 4.4 2303 4.9 147 121 127 125 89 123 S 7 0410 -0.8 22:2 2,4 V -0.2 M 7 0444 -0.4 122 0412 -0.2 T 7 0558 0.1 F22 0532 -0.3 1(121 4.5 093o 3.7 1031 3.8 1009 3.5 1204 3.4 1138 3.7 m ■fc! 124 7 0.0 1641 -0.1 1(9,8 0.0 1753 0.5 1734 0.0 22i)6 4.6 22,08. 4.8 2227! 4.8 2337 4.7 129 115 100 122 93 no S 8 0502 -0.5 M23 0429 -0.1 T 8 0535 -0.2 w; :.'. 0459 -0.1 F 8 0019 4.1 223 0624 -0.3 1112 4.1 1030 1627 3.6 1144 3.5 1038, 3.5 0645 0.3 1236 1708 -0.2 0.1 17 3o 0.2 1652 0.0 1303 3.3 1835 0.1 2335 4.8 22.48, 4.3 281 7 4.7 184 7 0.7 105 112 110 — 84 116 M 9 0555 -0.2 r 24 0212 0.0 2 0000 4.5 1 24 034 9 -0.1 S 9 0109 3.9 224 0054 4.5 1 2< .0 3.7 1114 3.3 (,62V 0.1 1131 3.5 0733 0.4 0719 -0 . 2 1800 0.1 1/12 2332 0.2 4 . 2 1.24 1824 3.3 0.5 174 2 0.2 1336 1945 3.3 0.8 1388 1242 3.9 0.2 113 95 114 77 107 no 1 1029 4.5 222 0604 0.1 T10 0054 4.2 1 23 0011 4.6 810 (.1202 3.7 M83 0135 4.2 0653 0.1 12m 4 3.3 0723 0.3 064 3 0.0 0822 0.4 0816 -0.2 1306 3.4 1803 0.3 12/1'"' 3.2 1 220 3.5 148(4 3.4 1443 4.1 1855 0.4 12 23 0.7 1847 0.2 204 3 0.8 80 4 8 0.2 97 106 82 110 82 117 Wll 0127 4.2 1 26 0029 4.4 i 11 0152 3.9 326 0110 4.4 Mil 0283 3.6 T 26 (.'•300 4.1 (.72b 0.4 0701 . 2 0819 0.4 0741 0.0 0909 0.4 0913 -0.2 I'll ' 3.2 1 3i ,3 3.3 1442 3.2 1355 3.6 1541 3 . 6 1946 4.4 193o 0.6 1902 0.3 2026 0.8 1954 0.3 2140 0.7 2127 0.1 86 103 75 105 89 121 T12 0231 4.0 F27 0129 4.3 SI 2 0251 3.7 227 0214 4.3 112 034 9 3.5 W27 (J433 3.9 O'Kj] 0.5 08,', J 0.2 0914 0.5 0840 -0.1 932 0.3 1009 -0 . 2 1520 3.2 14(22 3. 1 1340 3.3 1502 3.9 1629 3.8 14,47 4 . 6 2102 0.8 2()o8 0.3 2129 0.8 2103 0.2 2233 0.6 128 2302 0.0 76 103 76 114 96 1 1 3 0227/ 3.8 : 128 0235 4.3 S13 0349 lo ,:-, o 3 .^ 22:8 038,0 4.2 1/18, 0439 3.5 1 3 i 0505 3.8 1002 1622 0.5 3.3 ( 191 <4 1518 0.1 3.6 . -0.2 1040 0.3 11 o4 -0.8 1632 3.5 looo 4.2 1714 4.1 1743 4.8 79 2206 0.7 106 2118 0.2 88 2225 0.7 123 2210 0.1 104 2323 0.4 133 SI 4 2'4.'7/ 3.8 222 0343 4.3 Ml 4 0441 3.7 129 0424 4.2 114 032:8 3.5 i 89 0003 -0.1 1(22, 0.5 1004 -0.1 1049 0.4 lo2,0 -0.3 1123 0.2 0603 3.8 1 7 1 •; 3.4 12 22 3.9 1717 3.8 1704 4.5 17., 7 4.3 1137 -0.3 22/ ,-1 0.6 2225 0.0 2316 0.5 2(2,14 -0.1 1883 5.0 86 120 95 135 117 136 12 222(2 3.9 M30 04 4'-, 4.4 11:, uo:i8 3.7 W30 0224 4.2 1 12 0010 0.2 S30 0038 -0.2 1140 0.4 1102 -0.3 1 ! 2,( , 0.3 1128 -0.4 061 1 3.5 0658 3.8 1759 3.7 1723 4 . 4 1728, 4.0 1800 4.9 1204 0.',' 1247 -, ' . 8 2.2,1 0.4 23:;: -0.3 1838 4.6 1982 3.1 95 138 103 143 ,24 147 0013 06 2:o 1219 1831 -0.3 4.2 -0.5 5.1 125 134 Time meridian 75° W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 4-51 Table 32a, b, c, d. — Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December, 1962 76 BREAKWATER HARBOR, DEL., 1962 Times and Heights of High and Low Waters JULY AUGUST SEPTEMBER Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Day Day Day Day Day Day h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. S 1 0148 -0.3 Ml 6 0115 -0.1 W 1 0255 -0.1 T16 0223 -0.6 S 1 0331 0.0 S16 0330 -0.9 0749 3.7 0711 3.6 0859 3.7 0828 4.3 0941 4.0 0946 5.1 1334 -0.2 1303 -0.3 1446 0.0 1427 -0.7 1542 0.0 1558 -0.8 2011 5.1 1938 5.1 2114 4.6 2053 5.3 2157 4.2 22U9 4.8 132 143 115 157 107 152 M 2 0235 -0.3 T17 0201 -0.3 T 2 0332 0.0 F17 0310 -0.8 S 2 0403 0.0 Ml 7 0417 -0.8 0836 3.7 0759 3.7 0937 3.7 0917 4.5 1016 4.0 1 138 5.0 1421 -0.2 1352 -0.4 1528 0.1 1519 -0.8 1622 0.1 1652 -0.6 2055 5.0 2024 5.2 2152 4.5 2140 5.2 2232 4.0 2302 4.4 123 149 108 151 104 140 T 3 0319 -0.2 W18 0247 -0.4 F 3 0408 0.0 S18 0357 -0.8 M 3 0439 0.1 T18 0506 -0.5 0921 3.6 0847 3.9 1015 3.7 1007 4.6 1054 4.0 J lb:: 4.9 m 0.0 4.8 1442 2110 -0.5 5.3 m 2:1 1613 2230 -%:l 1703 2309 0.2 3.7 L749 2357 -0.3 4.0 116 148 104 141 100 125 W 4 0402 -0.1 T19 0334 -0.5 S 4 0444 0.1 SI 9 0445 -0.7 T 4 0516 0.2 W19 0558 -0.2 1004 1551 3.6 0.1 m -8:8 m 1:1 1100 1708 4.6 -0.0 1135 1748 4.0 0.4 1230 1850 4.7 0.0 2218 4.6 2158 5.2 2307 4.1 2322 4.6 2350 3.5 109 141 94 136 94 108 T 5 0442 1049 0.0 F20 0421 1027 •fci S 5 0521 0.2 M20 0534 -0.6 W 5 0556 0.3 7 20 0058 3.7 3.5 1135 3.7 1155 4.6 1220 3.9 <}(,bb 0.1 1636 0.2 1626 -0.4 1736 0.4 1805 -0.2 1837 0.5 1333 4,4 2301 4.4 2248 5.0 2347 3.9 1959 0.2 97 132 93 123 90 99 F 6 0523 1134 0.1 S21 0510 -0.5 M 6 0600 0.2 T21 0017 4.3 T 6 0036 3.3 F21 0205 3.4 3.5 1121 4.2 1218 3.7 0626 -0.3 0642 0.4 0758 0.3 1722 0.4 1722 -0.3 1823 0.5 1255 4.5 1310 3.9 1441 4.3 2343 4.1. 2340 4.7 1908 0.0 1933 0.6 2111 0.4 88 122 89 114 92 92 S 7 0603 0.2 S22 0601 -0.4 T 7 0030 3.6 W22 0117 3.9 F 7 0129 3.1 S22 0319 3.2 1219 3.5 1218 4.2 0642 0.3 0722 -0.1 0733 0.4 0901 O.b 1810 0.5 1821 -0.1 1305 1914 3.7 1358 4.4 1406 4.0 1549 4.2 0.6 2017 0.2 2033 0.6 2220 0.4 90 120 87 107 93 93 S 8 0028 3.9 M23 0037 4.4 W 8 0117 3.4 T23 0222 3.6 S 8 0229 3.1 :;23 0429 3.3 0646 1307 °3.-5 3 0654 -0.3 0727 1357 0.4 0822 0.1 0831 1508 0.4 1012 ().-.'.> 1318 4.3 3.8 1504 4.4 4.1 1652 A ;. ; : 1902 0.7 1925 0.1 2010 0.7 2129 0.3 2136 0.5 2319 0.3 80 115 89 103 101 97 M 9 0115 3.7 T24 0136 4.1 T 9 0208 3.3 F24 0333 3.4 S 9 0334 3.1 M24 Ob 2V 3.4 0731 0.3 0750 -0.2 0816 0.4 0926 0.2 0931 0.3 1112 0.4 1356 3.6 1421 4.3 1451 3.9 1612 4.4 ■ (9 4.3 1745 4.2 1957 0.7 2033 0.2 2109 0.7 2239 0.3 3235 0.3 84 113 95 101 114 101 T10 0203 3.5 W25 024O 3.8 F10 0305 3.2 S25 0441 3.3 M10 0437 3.3 T25 OUOb %:i 0817 0.4 0848 -0.1 0908 0.3 1029 0.3 1032 0.1 0614 1448 3.7 1526 4.4 1548 4.1 1713 4.4 1707 4.6 1203 0.3 2054 0.7 2143 0.2 2207 0.6 2340 0.2 2331 0.0 1830 4.2 91 112 102 108 127 107 171 1 0257 3.4 T26 0346 3.6 Sll 0404 3.2 S26 0542 3.4 Til 0534 3.7 W26 0U45 0.1 0904 0.3 0946 0.0 1002 0.2 1128 0.2 1130 -0.2 0655 3.8 1540 3.9 1629 4.5 1643 4.3 1806 4.5 1803 4.8 1246 0.2 2150 0.7 2251 0.2 2305 0.3 1910 4.3 95 117 113 109 144 110 T12 0351 3.3 F27 0452 3.5 SI 2 0502 3.3 M27 0032 0.1 W12 0023 -0.3 T27 0119 0.1 0952 0.3 1045 0.0 1058 0.1 0634 3.5 0628 4.0 0730 3.9 1630 4.1 1728 4.7 1736 4.6 1219 0.2 1 :.';.«, -0.5 1325 oa 2245 0.5 2353 0.1 2359 0.1 1854 4.5 1854 5.1 1946 4.3 103 119 129 112 153 111 F13 0443 1040 3.3 S28 0552 3.5 Ml 3 0557 3.5 T28 0114 0.1 T13 0110 -0.6 F28 0150 0.0 0.2 1140 0.0 1151 -0.2 0718 3.6 0718 4.4 0802 4.1 1719 4.3 1822 4.8 1827 4.9 1304 0.1 1319 -0.7 1402 0.0 2337 0.3 1936 4.5 1944 5.2 2020 4.2 116 120 140 116 161 112 S14 0534 3.4 S29 0047 0.0 T14 0049 -0.2 W29 0151 0.0 F14 0157 -0.8 S29 0221 0.0 1128 0.0 0646 3.5 0649 3.8 0757 3.8 0807 4.7 4,,; 1804 4.6 1232 0.0 1243 -0.4 1345 0.0 1412 -0.9 i t3 1 0,0 1911 4.8 1916 5.1 2013 4.5 2032 5.2 ;«!)3 4.1 126 121 152 115 159 115 S15 0027 §15 M30 0134 0.0 1715 0136 -0.4 T30 0225 0.0 Sib 0243 -0.9 S30 0253 0.0 0623 0735 3.6 0739 4.0 0832 3.9 0857 5.0 0908 4.3 1216 -0.1 1319 0.0 1335 -0.6 1425 0.0 1504 -0.9 1516 0.0 1852 4.9 1955 4.8 2004 5.3 2049 4.4 2121 5.1 2125 4.0 137 120 T31 119 0216 0819 1403 2036 -0.1 3.6 0.0 4.7 155 113 F31 112 0259 0906 1503 2123 0.0 3.9 0.0 4.3 160 114 Time meridian 75° W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. 452 Strategic Role of Perigean Spring Tides, 1635-1976 Table 32a, b, c, d. — Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December , 1962 BREAKWATER HARBOR, DEL., 1962 77 Times and Heights of High and Low Waters OCTOBER NOVEMBER DECEMBER Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. Day Day Day Day Day Day h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. M 1 0326 0.0 T16 07551 -0.8 T 1 0404 0.1 F16 0506 0.0 S 1 04 23 0.0 316 0532 . 3 094 5 4.3 1016 5.3 1029 4.5 1139 4.7 1054 4.7 1203 4 . 3 1065 0.0 16 30 -0.6 1636 0.1 1808 0.0 1725 0.1 1828 . 2 211.9 3.8 224 2 4.2 227.0 3.3 2520 3.4 111 141 109 120 121 102 T 2 (1400 0.1 WL7 04 39 -0.5 F 2 0447 0.2 517 0014 3.4 S 2 0615 0.1 M17 0039 3.4 1018 4.3 1108 3.0 ■ 4.4 0600 0.3 1144 4.6 0625 0.3 16 :5b 0.1 1732 -0.3 1744 0.3 1235 4.4 1816 0.1 1254 4.(7 105 2230 3.6 122 2337 5.8 103 2338 3.2 104 1903 0.2 116 90 1918 0.5 W 3 04:57 0.2 T18 03:51 -0.1 S 3 0534 0.3 518 0117 3.3 M 3 0015 3.4 T18 0134 3.3 1,»,8 4.2 12(i4 4.7 1 2i >3 4.3 06b9 0.6 (.16 12 0.2 07: 3 ".7 171'J 0.3 1831 0.0 1838 0.3 1333 4.1 1243 4.4 1347 3.8 104 ;-:-u g 3.4 106 99 88 2004 0.3 108 1911 0.1 81 2008 0.4 T 4 0517 0.2 F19 0038 3.5 S 4 0034 3.2 M19 0222 3.2 T 4 0117 3.5 W19 0230 3.4 1 14 ;: 4.2 07.27 0.2 0630 0.4 0803 0.7 0.3 ( '83 2 ' .3 lfK.V 0.4 1303 4.4 1302 4.3 3.9 1340 4.3 1442 3.6 95 90 1937. 0.2 97 1937 0.3 81 2103 0.4 104 2" 09 0.0 74 2058 7.5 F 5 0002 3.2 S20 014 6 ."77,(i 3.3 M 5 0137 3.2 T20 0324 3.3 W 5 0223 3.7 T20 0325 3.5 0002 0.4 0.5 (J 7 34 0.4 0909 0.8 0824 0.3 C7:i 0.6 1232 4.1 14 11 4.1 1405 4.2 17,7.7 3.7 1445 4.2 1336 5.6 94 1902 0.5 82 2044 0.4 103 2(758 0.2 75 W21 2133 0.4 102 21 08 -0.1 78 2145 0.4 S 6 0057 3.1 S21 0258 3.2 T 6 0243 3.4 0418 3.5 T 6 0329 4.0 F 21 0416 5.7 of.;, v 0.4 0838 0.7 ' 0.3 1010 0.7 0933 0.2 1' 17 6.7 135<> 4.1 1519 4.0 1512 4.3 1629 3.7 134 J 4.2 16:7 5.3 2003 0.5 2148 0.4 112 2137 0.0 2240 0.4 2204 -0.3 2230 0.3 94 81 79 106 84 S 7 0200 3.1 M22 0403 3.3 W 7 0331 3.7 T22 0505 3.7 F 7 0431 4.4 522 0503 3.9 0759 0.4 0946 0.7 0931 0.1 1716 0.6 1039 0.0 111. 7 . 6 14 771 4.1 17.7(1 3.9 L61! 4.4 3.7 1631 4.2 1715 5.6 21 ( if 0.4 2244 0.4 2234 -0.2 2320 0.3 2237 -0.4 231.) 0.2 101 85 112 86 113 92 M 8 0308 3.2 T23 0459 3.3 T 8 0452 4.2 -0.1 F23 054 6 4.0 5 8 0528 4.7 5 25 0546 4.2 m 2:1 1047 0.6 114 9 0.4 1141 -0.2 1158 0.4 1713 3 . 9 1714 4.5 1759 3.7 4.2 1801 3.3 22o6 0.2 2328 0.3 2326 -0.5 2337 0.1 2332 -0.6 2554 0.1 113 92 122 96 131 102 T 9 0414 3.5 W24 0544 1138 3.7 F 9 034 7 4.6 524 0624 4.2 S 9 0622 5.1 M24 0628 4.4 1010 0.1 (J. 5 1135 -0.4 i ; ;;■'. l 0.2 1238 -0.4 1243 0.2 1641 4.5 1759 4.0 1809 4.6 18717 3.7 1844 4.2 184 3 5.5 2303 -0.1 127 98 130 106 146 109 W10 0513 3.9 T25 0003 0.2 S10 0016 -0.7 S25 0033 0.1 M10 0042 -0.7 T26 0035 0.0 1112 -0.2 06 24 3.9 0639 5.0 0701 4.4 "714 5.3 ( 7( 7 4 . 6 1739 4.7 1222 0.3 1231 -0.6 4.6 1310 0.1 1332 -0.5 13: ; 0.1 277.7, -0.4 1838 4.0 1901 1915 3.7 1956 4.2 1925 3.5 141 105 149 111 153 117 Til 0607 4.4 F26 (JO 3 9 0.1 511 0103 -0.9 M26 0107 0.0 Til 0130 -0.7 w: 6 0115 -,.1 1210 -0.5 0637 4.1 077,., 5.3 0736 4.6 08-2 5.4 0748 4.8 1832 4.9 1301 0.1 134 4 -0.8 1350 0.0 14 771 -0.6 14 08 0.0 1913 4.0 1952 4.6 1952 3.7 2027 4.1 2004 3.6 153 113 160 118 156 125 i i:; 0043 -0.7 S27 Oil] 0.0 M12 0151 -0.9 T27 0144 -0.1 W12 0718 -0.6 T27 0156 -0.2 (,./,;,(: 4.8 0732 4.3 0818 5.5 0812 4.7 (i8;31 5.4 0828 4.9 1304 -0.8 15,37 0.0 1 4 57 -0.8 14 30 0.0 1515 -0.5 14: 1 -7.1 1923 5.0 1948 4.0 204 2 4.4 27)29 3.6 2116 4.0 2 04 6 3.6 158 115 16S 124 153 130 S13 0129 -0.9 S28 014 3 0.0 T13 0239 -0.8 W28 022O -0.1 113 0305 -0.5 F28 0239 -0.3 0748 5.1 08o5 4.4 0907 5.5 0849 4.8 0938 5.2 ,.'70b 5.0 1358 -0.9 1414 0.0 1328 -0.7 1511 -0.1 1603 -0.4 1534 -0.2 2011 5.0 2021 3.9 2132 4.2 21 oV 3.5 2204 3.8 2129 3.7 168 120 162 126 145 136 S14 0216 -1.0 M29 0217 -0.1 W14 0326 -0.6 F2.9 0259 -0.1 F14 0334 -0.3 3:77 ' 324 -0.3 0837 5.4 0M30 4.5 0956 5.3 0927 4.8 1025 5.0 0962 5.0 14 50 -0.9 1432 0.0 1730 -0.5 1553 0.0 1.752 -0.2 1618 -0.2 2101 4.8 2056 3.8 2223 3.9 214 7 3.5 2 264 3.6 21 16 3.7 164 123 151 126 136 137 M15 0302 -0.9 T30 0251 -0.1 T13 0414 -0.4 F3o 0340 -0.1 S15 ('4 4 2 0.0 S30 0411 -0.2 0926 5.4 0913 4.6 1046 5.0 loot) 4.8 1114 4.6 1038 4.7 1543 -0.8 1531 0.0 1713 -0.3 107.7 0.0 173'.. 0.0 1704 -0.2 2150 4.5 2131 3.6 2317 3.7 2231 3.4 234 6 3.5 2.7 4 3.7 158 120 W31 114 1)5,26 7194 9 1 6 1 : : 22H8 0.0 4 .6 0.0 3.3 138 126 117 132 M31 125 0502 1177 173 1 -0.1 4.7 -0.2 Time meridian 75° W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 4.W Table 33. — Sixteen Instances of Major Tidal Flooding JVear a Time of Perigee-Syzygy, Represented (in Figs. 153-163) by Plots Showing the Predicted Rate of Rise of the Astronomical Tide at Nearby Tidal Reference Stations (Listed in the Table) Tidal reference station used Dates of flooding Key letter and serial No. SANDY HOOK, N.J., 1918 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 NEWPORT, R.I., 1927 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 PORTLAND, ME., 1940 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 EASTPORT, ME., 1945 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 HALIFAX, NOVA SCOTIA, 1973-74 Part (b): Oct. 1-Mar. 31 ABERDEEN, WASH., 1973-74 Part (b): Oct. 1-Mar. 31 WILLETS POINT, N.Y., 1931 Part (a): Jan. 1-June 30 Part(b): July 1-Dec. 31 BOSTON, MASS., 1959-60 Part (a): Jan. 1-June 30 Part (b): July 1-Jan. 7 BREAKWATER HARBOR, DEL., 1962 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 ASTORIA, OREG., 1962 Part (a): Jan. 1-June 30 Part (b): July 1-Dec. 31 LOS ANGELES, CALIF., 1974 Part (a): Dec. 1-May 31 Part (b): June 1-Nov. 30 4/10-12 11/18 A-43(a); 44(a) A-43(b); 44(b) 3/3-4; 4/2 12/5 B-50(a); C-51(a), 52(a) B-50(b); C-51(b), 52(b) 4/21 G-69(a) G-69(b) 11/20 H-72(a) H-72(b) 12/11 M-98e 12/11 M-98w 3/4-8; 4/1 D-57(a); E-58(a) D-57(b); E-58(b) 12/29 I-83e(a) I-83e(b) 3/6-7 11/10-14 J-85(a); K-87(a) J-85(b); K-87(b) 10/13 86(a) 86(b) 1/8 N-99(a) N-99(b) 454 Strategic Role of Perigean Spring Tides, 1635-1976 A-43 (a), 44 (a) JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Note: The bracketed "windows" of potential tidal flooding pertain only to the higher of the two peaks indicating maximum rate of tide rise in each lunation, and their corresponding dates The position of the line representing the "average of curve maxima" is computed (see excep- tions noted in text) from a 13 lunar-month mean of the higher of these two monthly maxima A perigee -syzygy series may thus overlap successive calendar years. A Lunar perigee T Lunar apogee O Full moon • New moon .... - Maximum tide height in each lunation, in feet and tenths above standard datum -13 Difference, in hours, perigee minus syzygy 1 "One-back" computation method involving tidal phases 3 "Three-back" computation method involving tidal phases Figure 153a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena A-43 (b), 44 (b) 4 r n JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 Figure 153b. 1 16 Strategic Role of Perigean Spring Tides, 1635-1976 B-50 (a), C-51 (a), 52 (a) 4.3 • A 4.3 O T OY 4.3 4.6 f TO 4.8 TO NEWPORT, RHODE ISLAND 1927 "WINDOW" FOR POTENTIAL — TIDAL FLOODING ===== 4.8 4.6 k% TO A • AVERAGE OF CURVE MAXIMA FOR 1927 1 7 JAN FEB MAR APR MAY JUN 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 154a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena B-50 lb), C-51 (b), 52 (b) 4:37 4.4 O A 4.4 OA • T 4.6 'i 4.9 5.0 4.9 T« NEWPORT, RHODE ISLAND 1927 "WINDOW FOR POTENTIAL = TIDAL FLOODING — T • JUL AUG SEP OCT NOV 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 Figure 154b. 1 58 Strategic Role of Perigean Spring Tides, 1635-1976 G-69 (a) 50 40 30 g20 o & 10 Z >300 cr LU 9 80 i- u_ °70 1X1 uj 50 40 30 20 10 200 90 180 PORTLAND, MAINE 1940 10.7 • T 10.8 10.8 10.9 ?• T • 10.7 10.4 A O T "WINDOW" FOR POTENTIAL — TIDAL FLOODING JAN -FEB MAR 7 14 21 28 1 7 14 21 28 7 14 21 28 1 APR MAY JUN 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 155a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 459 G-69 (b) 180 JUL AUG 1 7 14 21 28 1 7 14 21 SEP OCT NOV DEC 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 460 Strategic Role of Perigean Spring Tides, 1635-1976 H-72 (a) 700 80 60 o 40 o 20 600 £80 DC Q 60 i- u_ O 40 uj 20 lu500 80 60 40 20 400 80 20.4 • A 21.3 •A OT 21.7 A ^r 22.0 A T° 21.8 T O 21.1 A« T O EASTPORT, MAINE 1945 "WINDOW" FOR POTENTIAL = TIDAL FLOODING — = JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 156a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 461 H-72 (b) Figure 156b. 1(32 Strategic Role of Perigean Spring Tides, 1635-1976 -70 o o o HALIFAX, NOVA SCOTIA 1973-74 7.2 7.5 OA 04 • T 7.8 7.8 7.5 V 7.3 AO T • "WINDOW" FOR POTENTIAL TIDAL FLOODING = AVERAGE OF CURVE MAXIMA 10/1/73-3/31/74 OCT 1 7 14 21 NOV 7 14 21 281 7 DEC JAN FEB 14 21 281 7 14 21 28 1 7 14 21 28 7 MAR 14 21 28 Figure 157. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 463 M-98 ABERDEEN, WASHINGTON 1973-74 11.3 12.1 12.6 12.7 12.1 11.4 O A • Y OA • T ° k m y ^ T# j? T# AO Y • 40 "WINDOW" FOR POTENTIAL — TIDAL FLOODING = —^ AVERAGE OF CURVEMAXiMA 10/1/73-3/31/74 OCT NOV DEC JAN FEB MAR 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 1 7 14 21 28 7 14 21 1 7 Figure 158. 464 Strategic Role of Perigean Spring Tides, 1635-1976 D-57 (a), E-58 (a) 90 80 ^ 70 8 o • 60 x I 50 5 10 cc LU ^200 cc LU < 90 WILLETS POINT, NEW YORK 1931 8.4 8.3 OA • T 8.6 8.9 9.0 8.7 8.2 O A T* A T • A i T • A O T • A O 'WINDOW" FOR POTENTIAL = TIDAL FLOODING = AVERAGE OF JAN 1 7 14 21 FEB MAR APR MAY JUN 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 159a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena D-57 (b), E-58 (b) 465 II u. 20 O •5 10 CO ai ^ 90 80 70 60 50 40 130 WILLETS POINT, NEW YORK 1931 8.3 8.3 • A O Y or 8.8 9.1 r to 9.0 A* T O 8.6 km t o "WINDOW" FOR POTENTIAL = — TIDAL FLOODING — AVERAGE OF JUL AUG 7 14 21 28 1 7 14 21 SEP OCT NOV DEC 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 Figure 159b. 202-509 0-78-32 466 Strategic Role of Perigean Spring Tides, 1635-1976 l-83e (a) 11.4 10.7 11.0 A* T O A • T OA 11.4 11.9 12.1 V 12.0 WINDOW" FOR POTENTIAL = TIDAL FLOODING ===== JAN FEB MAR APR MAY JUN 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 160a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena -167 1 7 JUL AUG SEP OCT NOV DEC JAN 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 Figure 160b. 468 Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a), K-87 (a) -175 O o o BREAKWATER HARBOR, DELAWARE 1962 5.4 5.5 5.3 •A O T __ "WINDOW" FOR 5.3 5.4 TO T O 5.3 km ▼ o a AVERAGE OF CURVE MAXIMA FOR 1962 JAN FEB MAR APR MAY JUN 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 161a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 469 J-85 (b), K-87 (b) -175 O o o • T BREAKWATER HARBOR, DELAWARE 1962 5.3 5.3 OA • T OA •T 5.2 5.4 °i % A° » | ~ "WINDOW" FOR L P< 5.5 T • 5.4 AO T JUL 7 14 21 28 1 AUG SEP OCT NOV DEC 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 Figure 161b. 470 Strategic Role of Perigean Spring Tides, 1635-1976 86(a) O 8 20 10 >200 K 90 Ui Q 80 70 60 3 £50 20 10 100 •a or « A 9, r ASTORIA, OREGON 1962 TO A« TO A • T O A AVERAGE OF CURVE MAXIMA FOR 1962 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 162a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 471 86(b) 100 1 7 JUL AUG 14 21 28 1 7 14 21 28 1 SEP OCT 7 14 21 281 7 14 21 NOV DEC 1 7 14 21 281 7 14 21 28 Figure 162b. 472 Strategic Role of Perigean Spring Tides, 1635-1976 N-99 (a) LOS 10 §100 7.1 90 80 c/> 70 ANGELES, CALIFORNIA 1973-74 7.1 % 2 » "WINDOW" FOR POTENTIAL TIDAL FLOODING = 6.8 T • 6.1 T • iO 5.9 O T 6.4 AVERAGE OF CURVE MAXIMA 12/1/73-TI/30/74 DEC JAN FEB MAR APR 7 14 21 28 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 MAY 14 21 28 Figure 163a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phe 473 N-99 (b) 10 LOS ANGELES. CALIFORNIA 1973-74 6.9 7.1 6.9 6.3 6.6 6.7 8100 O T \ OT • 9 • I TO f TO A« T O A • T C X . 90 z "WINDOW" FOR POTENTIAL ^ 80 LL AVERAGE OF w 70 LU Q 60 °50 s A L 1 \ r°\ Ak CURVE MAXIMA 12/1/73- A 11/30/75 / \ i £ 30 \ 20 m If 3 JUN JUL AUG SEP OCT NOV 7 14 21 281 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 Figure 163b. 474 Strategic Role of Perigean Spring Tides, 1635-1976 nomical tide growth at the times of 16 representative cases of tidal flooding, plotted from such data. Where direct tidal predictions are not customarily made at the location of the tidal flooding, the nearest standard (ref- erence) tide-prediction station has been chosen. The growth rates on the ordinate axis are given in ft/min ( X 0.0001 ). The abscissa axis represents calendar dates, labeled at 7-day intervals. The average of the curve max- ima for one lunar year is obtained by dividing the sum of the values for the 13 peaks by 13 lunar months. Across the top of each chart is indicated the height, in feet and tenths, of the highest tide in each calendar month. The symbols used on each chart are again those coded at the bottom of fig. 153a and are inserted directly above the appropriate dates. Thus, a close alignment of perigee- syzygy is indicated by the symbol of a new or full moon resting centrally on the narrow tip of the perigee symbol. A condition of apogee-syzygy is denoted by either of these lunar symbols located within the upturned cup of the apogee symbol. As one of the lunar-phase symbols and the perigee symbol draw further apart along a horizontal axis, the corresponding astronomical configuration changes from a proxigee- or perigee-syzygy alignment to the situa- tion described earlier as pseudo-perigee-syzygy. Finally ( as either the new or full moon becomes separated by its maximum angular distance from perigee ) , a condition of ordinary syzygy ( or spring tides ) results. The plus or minus values located inside the highest of the curve peaks indicate the separation-intervals, in hours, between the time of occurrence of the two phenomena involved — in the algebraic sense perigee minus syzygy. To provide a totally representative basis for compari- son, all of the data being evaluated at any given tidal sta- tion are plotted for an entire lunar year of 13 lunations (resulting, in some cases, in an overlapping of successive calendar years ) . Those immediately adjacent curve peaks which pro- trude appreciably above the average line are, in keeping with the context of the present investigation, bracketed and labeled cumulatively as a "window for potential tidal flooding." At times corresponding to the highest points of each of the peaks within these bracketed intervals, the tide is rising the most rapidly (the lower peak in each pair is, of course, automatically excluded ) . It will be ob- served that, among all the examples plotted, these "win- dows" of potential tidal flooding contain not only all of the highest peaks indicating maximum rate of tide rise within the lunar year, but all cases of proxigee-syzygy, perigee-syzygy, and some cases of pseudo-perigee-syzygy. With one or two exceptions made to avoid repetition and conserve space, both of the "windows" in each year containing close perigee-syzygy alignments are included, for completeness, among the examples of figs. 153-163, irrespective of the half-year in which tidal flooding actually occurred. It is quite obvious, however, that the observed tidal flooding was associated, in every single example represented, with the peak of a curve located within one of these "windows," and hence with a situation of perigee-syzygy having a large Atu-syzygy coefficient. The flooding event did not, in every case, coincide with the highest peak in a "window," nor, in every case, with the absolute peak of the curve. But, without exception, the coastal inundation occurred near the time of one of these peaks. The reason that (despite repeat cases later to be noted) tidal flooding did not occur at the other peaks in the "window" is, of course, the fact that no supporting strong, persistent, onshore winds were present at these times. From the standpoint of the unusually high astronomical tide generated, the conditions present at these times were entirely favorable to coastal flooding, but lacked the neces- sary associated meteorological factors. On the other hand, realistic support is given to the premise that such tidal flooding situations are a definite function of perigean spring tides when accompanied by the previously noted conditions of winds through a consi- deration of the following facts : (a) At Newport, R.I., in 1927, extreme tidal floodings occurred on both March 3-4 and April 2, one synodic- anomalistic month apart. The same relationship holds true for Willetts Point, N.Y., on 1931 March 4 and April 1 in conjunction with two consecutive occurrences of peri- gee-syzygy. (b) On 1933 December 11, in conjunction with a common astronomical alignment of perigee-syzygy, tidal flooding occurred simultaneously on both the east and west coasts of North America — at Halifax, N.S., and Aberdeen, Wash. (c) Other examples of both of the above types are to be found in table 1, and are appropriately designated in this table. 2. Mixed Tides (Affected by the Diurnal In- equality) On the west coast of North America, a secondary dy- namic factor often intrudes at certain locations to alter the tidal situation typical of the east coast where (with some few exceptions) tides of the semidiurnal type pre- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 475 vail. Diurnal inequality is common at many west coast stations, and mixed tides result. Along the east coast, the tides are generally character- ized by two highs and two lows in each day. Although a higher high water and lower high water as well as a lower low water and higher low water exist, within each pair of high waters and low waters the tides are not extraordi- narily different in height. (It must be noted, however, that at very high latitudes the phenomenon of diurnal inequality manifests itself to increase the difference in height between higher high water and lower high water. ) At certain stations on the west coast a tidal situation frequently exists in which, at the Moon's maximum dec- lination, one high water is much higher than the other. This effect, occurring at large southerly or northerly lunar declinations, almost disappears when the Moon crosses the Equator. (See, for example, the general tide curves for Los Angeles in fig. 164.) For those tide stations especially subject to the influence of diurnal inequality, therefore, when the Moon is located at a high declination at time of perigee-syzygy, allowance must be made for this phenom- enon. In taking the previously noted differences between the times and heights of LLW and HHW in order to plot the curves of rate of tide rise, a slight modification in pro- cedure is necessary. Instead of subtracting from the height of HHW (or the time thereof) the value for the low water immediately preceding it, the corresponding value for the low water three entries back is used. This "three-back" method reduces the discrepancy en- countered if the method for semidiurnal tides is used, and more accurately assures the representation of a period of water level rise from lowest minimum to highest maximum in accordance with the above-mentioned principles. Not all west coast stations require this adjustment, but those strongly subject to diurnal inequality (e.g., Los Angeles, Calif.; Aberdeen, Wash.) definitely do. Some high-lati- tude stations on the east coast (e.g., Halifax) also require this special method of solution at times when the lunar declination is large. Among the examples of this type included in the ac- companying group of rate-of-tide-rise curves, those cases using the "three-back" method (figs. 157, 158, 163) are indicated by a boldface number 3 in the lower right corner of the chart. Examples using the "one-back" method are similarly identified by a number 1. Figures 153-163 con- tain 1 1 examples of both types, covering the broad range of coastal locations previously noted. It has been indicated that such rapid and extreme rates of tide rise are present and demonstrable only where the type of tide involved is one affected strongly by the Moon. In this respect, three further considerations are note- worthy in connection with the foregoing analysis aimed at establishing a positive correlation between perigean (or proxigean) spring tides, accelerated rate of tide rise, and astronomical tidal flooding potential. These items are by way of qualification on the previous discussion : (a) Between 1885 and 1911, only 19 harmonic constit- uents were used in the computation and prediction of tides by the U.S. Coast and Geodetic Survey. These did not include the 3 second-order semidiurnal and diurnal constituents, the 2 smaller elliptic terms (semidiurnal and diurnal), the larger evectional diurnal term, the tridi- urnal constituent, and 3 overtide constituents, and in- cluded only 1 component in each case among 5 dealing with compound tides and 5 representative of long-period tides. (See fig. 43). The 18 additional components were introduced and first became a part of the harmonic solu- tions forming the basis for the tide tables published in 1912. Accordingly, the use of the previously described method for determination of rate of tide growth (which is sensitive to a greater level of accuracy) is not entirely effective when the tide data were published prior to this year. ( b ) Sufficiently large mean spring ranges must be pres- ent at the stations utilized in such computations to indicate a characteristic responsiveness to lunar influences and a corresponding rapid rate of tidal buildup. From a large variety of tidal growth curves plotted for both the east and west coasts, it is apparent that those tide stations whose mean spring range is less than 5 feet do not lend themselves readily to this test analysis. By the same token, however, such coastal locations are not strongly prone to tidal flood- ing at times of perigee-syzygy. (c) The determination of astronomical tidal flooding potential by the above methods (employing the closely corresponding Aw-syzygy coefficient) is, of course, not possible for tides which are more responsive to solar than lunar influences. An Independent Check on the Validity of the Aw -Syzygy Coefficient Since first proposing the use of the A«j-syzygy coeffi- cient as an indicator of vulnerability to tidal flooding con- ditions, it has been left to substantiate that the daily rate of lunar motion in right ascension — the secondary element of the A^-syzygy coefficient — is itself a parameter accu- rately representative of tidal flooding potential. In the immediately preceding section, the conditions of predicted and actual flooding have been positively cor- related with the accelerated rate of tide rise associated 476 Strategic Role of Perigean Spring Tides, 1635-1976 • A E SEPTEMBER 12 3 4 5 E O P ©3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 UUMimm StfffiBffi K mi •, new moon; ), first quarter; O, full moon; C , last quarter; E, moon on the Equator; N,S, mooi farthest north or south of the Equator; A,P, moon in apogee or perigee; Oj.sun at autumnal equinox • chart datum. Figure 164. — Representative daily tidal curves of different types (see p. 298 and fig. 6 in appendix) at selected stations throughout the world. Note the individual, varying effects of the perigee-syzygy align- ment (plus proximity to the autumnal equinox) on September 23. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena All with perigee-syzygy. To complete the circle of analysis, it is finally necessary to demonstrate that the unusually rapid rate of tide rise at times of perigee-syzygy can be directly correlated with the daily velocity (and hence change of position ) of the Moon in right ascension. Such an analysis can be accomplished by the use of figs. 165a and 165b. These diagrams, in their inherent nature, constitute a parallel reconstruction of the tide curves contained in figs. 161a- 16 lb, which represent the varying daily rate of tide rise thoughout the year 1962. However, for comparative purposes, these curves are plotted entirely from astronomi- cal data in The American Ephemeris and Nautical Al- manac and are, therefore, independent of any particular tidal stations. The ordinate values and curve amplitudes accordingly will not change from tide station to tide sta- tion as in the rate-of-tide-rise curves, but the properties of the purely astronomically derived curves can prove to be very meaningful in relationship to the tide curves. Figs. 165a-165b represent graphs of daily lunar motion in right ascension plotted with declination as ordinate against the time as abscissa (indicated to exactly the same scale as that previously used ) . For correlation purposes, the present curves may be directly compared with the matching curves of figs. 161a— 161b, plotted completely from tide table data. Specifically, the ordinate axis in these present figures represents the angular distance in right ascension through which the Moon appears to move on each day of the year in consequence of both real and apparent motions. The movement is expressed as a difference between the Moon's position in right ascension at h of date and its position at a time 24 hours earlier. The tabular differences calculated from The American Ephemeris and Nautical Almanac are converted uniformly to minutes of time. The final reduc- tion takes into account corrections for lunar declination ( 1/cos 2 8) and for the effects of the Earth's diurnal rota- tion. The result is, therefore, the projection on the celes- tial equator of the apparent daily motion of the Moon. The horizontal dotted line labeled "Average of Curve Maxima for 1962" is obtained by taking the mean of the ordinate values for all peaks throughout a 13 -month pe- riod and dividing by 13. The effect of acceleration of the Moon's apparent mo- tion in right ascension in increasing the length of the tidal day at times of perigee-syzygy is clearly manifest in the fact that the peaks of the curves extend perceptibly above the average line at these exact times. A further salient factor is the very exact correlation be- tween the portions of these curves protruding above the line in figs. 165a and 165b, and the matching extreme peaks in figs. 161a and 161b. The even greater significance of this circumstance is that, whereas the first curves are plotted entirely from astronomical tables and the second from tide tables, the profiles of the respective curves are an almost identical match for all dates throughout the year. The close resemblance between the positions, shapes, and augmented amplitudes of the curves at times of perigee- syzygy is particularly noteworthy. Since the lunar phase relationships do not directly affect the Moon's daily mo- tion in right ascension as they do sensibly affect the tides, figs. 165a and 165b do not contain the series of dual maxi- ma (one of which is elevated) and minima shown in figs. 161aandl61b. Finally, an item of major importance should be men- tioned in connection with the search for a suitable coeffi- cient of tidal flooding. Throughout the entire series of curves representing a considerable variety of tide stations in figs. 153-163, the only major tidal flooding events ob- served among the 56 years of record covered, occurred at one of the peaks extending above the respective "average of curve maxima" lines. As an aid to the determination of astronomical condi- tions which are especially conducive to tidal flooding when they exist concurrently with strong, persistent, on- shore winds, all examples of perigean spring tides occur- ring between 1977 and 1999 in which the perigee-syzygy separation-interval is < 24 hours are summarized in table 34. Those cases of proxigee-syzygy and extreme proxigee- syzygy leading to the production of exceptionally high tides, and thus particularly vulnerable to severe coastal flooding when supported by the correct meteorological conditions, are identified for quick reference. Summary and Conclusions In summary, the following facts have been made evi- dent throughout the preceding chapters : A. The Tidal Aspects of Perigee-Syzygy Alignment 1 . The coincidence of perigean spring tides and strong, persistent, onshore winds must inevitably result in active coastal flooding, a statement amply confirmed by table 1 . By contrast, perigean spring tides alone, without support- ing winds, are usually insufficient of their own right to cause major flooding. (See table 27.) Because of this re- quired combination of events, at no time has the word "prediction" of tidal flooding been used in this publication. The astronomically induced tides can be computed for thousands of years into the future with extreme precision. 478 Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a) 43 VARIATION IN DECLINATION OF MOON AND SUN EFFECT OF PERIGEE -SYZYGY ALIGNMENTS IN ACCELERATING THE MOON'S APPARENT MOTION IN RIGHT ASCENSION AND LENGTHENING THE TIDAL DAY -1962- JAN 1 7 14 21 28 1 FEB MAR APR 7 14 21 28 7 14 21 28 1 7 14 21 281 MAY JUN 7 14 21 28 1 7 14 21 28 Figure 165a. — (Discussed in text. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 479 J-85 (b) • Y OA • T 58 43 VARIATION IN DECLINATION OF MOON AND SUN • T ° k % 2 T« AO T • iO T • EFFECT OF PERIGEE-SYZYGY ALIGNMENTS IN ACCELERATING THE MOON'S APPARENT MOTION IN RIGHT ASCENSION AND LENGTHENING THE TIDAL DAY -1962- JUL 1 7 14 21 28 1 AUG SEP OCT NOV DEC 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 Figure 165b. — (Discussed in text. 480 Strategic Role of Perigean Spring Tides, 1635-1976 Table 34. — A Checklist of the Central Dates {Mean Epochs) of Perigean Spring Tides (P—S< ±24 b ) Occurring Between 1977 and 1999 [Proxigean spring tides are indicated by the letters "Pr." before the date, and extreme proxigean spring tides by the letters "Ext. Pr." See table 16 for full astronomical details.] Mean epoch of perigee-syzygy Perigee Mean epoch of per gee-syzygy Perigee minus minus Year Date Hour (e.s.t.) syzygy ( h ) Year Date Hour (e.s.t.) syzygy ( h ) 1977 5/3 1900 (+16) 1988 2/17 0730 (-7) 1977 6/1 1 300 (-6) 1988 8/27 0900 (+6) Pr. 1977 12/10 1530 ( + 5) 1988 9/25 0630 (-15) 1978 1/8 1500 (-16) 1989 3/7 2000 (+14) 1978 9/20 2330 (+15) 1989 4/5 1830 (-9) 1978 7/19 1700 (-5) Pr. 1 989 10/14 1830 ( + 5) Pr. 1979 1 /28 0300 ( + 4) 1989 11/12 1 700 (-16) 1979 2/26 0230 (-19) 1990 4/25 0530 ( + 13) 1<)79 8/8 0600 (+16) 1990 5/24 0230 (-9) 197') 9/6 0300 (-6) Ext. Pr. 1990 12/2 0430 ( + 3) 1980 2/16 1600 ( + 24) 1990 12/31 0430 (-19) 1980 3/16 14.30 (+D 1991 6/12 1 300 (+12) 1980 4/14 1230 (-21) 1991 7/11 0930 (-9) 1980 9/24 1430 (+15) 1991 12/21 1700 (+24) Pr 1 980 10/23 1230 (-7) Ext. Pr. 1992 1/19 1630 (+D 1981 4/5 0230 ( + 23) 1992 2/17 1600 (-22) 1981 5/3 2330 (+D 1992 7/29 2100 (+12) 1981 6/1 2000 (-22) 1992 8/27 1730 (-9) 1981 11/12 0030 (+13) 1993 2/7 5000 (+20) Pr. 1981 12/10 2330 (-9) Ext. Pr. 1993 3/8 0400 (-2) 1982 5/23 1100 ( + 22) 1993 4/6 0200 (-24) 1982 6/2 1 0700 (0) 1993 9/16 0400 (+12) 1982 7/20 0300 (-22) 1993 10/15 0200 (-10) 1982 12/30 1200 (+10) 1994 3/27 1 530 (+19) 1983 1/28 1130 (-11) 1994 4/25 1330 (-3) 1985 7/10 1800 ( + 22) 1994 11/3 1400 (+10) 1983 8/8 1430 (+D 1994 12/2 1300 (-12) 198 5 9/7 1100 (-22) 199.5 5/15 0100 (+18) Pr. 1984 2/17 0000 ( + 8) 1995 6/12 2130 (-3) 1984 3/16 2230 (-13) Pr. 1995 12/22 0100 (+8) 1984 8/27 0100 ( + 22) 1996 1/20 0100 (-14) 1 984 9/24 2200 (0) 1996, 7/1 0800 (+18) 1984 10/23 2000 (-22) 1996 7/30 0430 (-3) 1985 4/5 1000 ( + 6) Pr. 1997 2/7 1300 (+6) 1985 5/4 0730 (-15) 1997 3/8 1200 (-16) 1985 10/14 1090 ( + 20) 1997 8/18 1500 (+18) Pr. 1985 11/12 0830 (-D 1997 9/16 1230 (-3) 1985 12/11 0800 (-24) 1998 3/28 0000 (+4) 1986 5/25 1900 ( + 6) 1998 4/25 2200 (-18) 1989 6/21 1530 (-15) 1998 10/5 2330 (+17) 1989 12/1 2100 (+18) Pi. 1998 11/3 2200 (-14) Pr. 1986 12/30 2000 (-4) 1999 5/15 0830 ( + 3) 1987 7/11 0200 (+6) 1999 6/13 0500 (-18) 1987 8/8 2130 (-15) 1 ***** » 11/23 0930 (+15) 1988 1/19 0800 (+16) Pi. 19')') 12/22 0930 (-7) However, sea-surface winds — especially under the most changeable offshore storm conditions, and with only ship weather reports and weather satellite photographs as guides — can rarely be accurately predicted more than sev- eral days in advance. Major tidal flooding is dependent upon such support- ing wind action as well as the coexistence of high tides (in the cases being investigated, further heightened by the in- fluence of perigee-syzygy alignment). Accordingly, care- fully chosen phrases indicative of this astronomical situa- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena tion as "enhancing the dynamic potential for," or "in- creasing the vulnerability of the shoreline to ," severe tidal flooding in the presence of strong onshore winds have been used. Severe erosion of the coastline in low, sandy regions is an attendant factor in any situation involving the simul- taneous occurrence of intensified onshore winds and astro- nomically heightened tides. 2. Hurricane winds in combination with any state of the tide are usually intense enough to cause coastal flood- ing. However, to a degree which is variable with the dis- tance of the hurricane's center from the coastline, the strength of the storm (i.e., the existing pressure gradient) , the actual wind velocities present, their angle-of-attack to the shoreline, the duration of their movement over the water, the time of a hurricane's landfall with respect to high water, and the daily range of the tides at the location in question, the severity of the flooding may vary over a wide range. Disregarding for the moment the high- and low-water extremes produced by perigean spring tides, a hurricane entering the coastline at low tide — although causing ex- treme wind damage — will not cause as severe flooding as one impacting the coastline at high tide. A landfalling hurricane will likewise, during any period of average tidal range, cause much more severe flooding than an offshore hurricane. In the case of an offshore hurricane, the duration of onshore surface wind movement is not usually as long as that associated with an offshore winter storm, because of the generally far more rapid forward movement of the hurricane in its recurving path at higher latitudes. An overwater, deep low pressure system of extratropical na- ture, accompanied by strong onshore winds, may be totally blocked by the presence of a stationary high-pressure sys- tem and the winds may thus persist in onshore movement, creating a long overwater fetch. Because of the great ki- netic energy contained within a hurricane, it is rarely so blocked, and rather than coming to a complete standstill, is only diverted in its path, split into components, or baro- metrically filled and weakened in intensity by the blocking high pressure center. On the other hand, in the case of the coincidence of a hurricane with perigean spring tides, the extra rise in the high water level accompanying this type of tide acts as an astronomically produced setup condition, and provides a factor of consequence in the production of extreme coastal flooding. In recapitulation, cases of record show that, when land- falling hurricanes have arrived on the coast at times of low water — or even in conjunction with moderately high tides — the principal damage sustained frequently is wind damage. The coincidence or near-coincidence of hurri- canes and perigean spring tides inevitably have resulted in extreme coastal flooding (see table 2). Interestingly, although the range of tides at Galveston, Tex., is not suffi- ciently large to support a major astronomical height-in- ducing influence at perigee-syzygy, the great historical tidal flooding associated with the hurricane of September 8, 1900 at Galveston, which drowned some 6,000 persons, occurred on the same day as a perigee-syzygy alignment (P-S=14 h ). 3. The coincidence of strong, persistent, onshore winds with ordinary spring tides can cause major beach erosion and seawall damage if the winds are sufficiently strong and occur very close to the times of high water. Unless the velocity of the surface winds is high and the path of their onshore movement is long-continued over the water, the magnitude of coastal flooding produced is, however, never as large as that created by the same circumstances of strong onshore winds, plus perigean spring tides. b A considerable increase in tide-raising power occurs when the Moon reaches a position at or near perigee, be- cause of the proximity of the Moon to the Earth. How- ever, for true perigean tides to occur, with the least rein- forcement from the gravitational attraction of the Sun, they must be produced with the Moon at one of its quad- rature positions (first or third quarter) when the gravita- tional forces of the Moon and Sun are opposed. The addi- tional tide-raising force at lunar perigee, although con- tributory in enhancing the tides, is not as effective when thus acting alone as when a simultaneous perigee-syzygy alignment occurs. If strong onshore winds coexist with a high phase of the tides produced at times of perigee-quad- rature, some minor flooding may result, but the principal damage is that created by wind and associated high waves directly along the coast, without strong flooding inland. [Cf., for example, the instance of the coastal storm of February 11-12, 1973 at Nags Head, N.C., and vicinity described in Mariners Weather Log, vol. 17 (May 1973), pp. 188-189.] Theoretical analysis indicates that wind- induced coastal waves of the breaking type are raised to b Pseudo-perigean spring tides, at their upper limit of perigee- syzygy separation (±84 h ), also merge rather indistinguishably into ordinary spring tides. A major destruction to seawalls and the piles supporting beach homes and patios occurred at Malibu Beach, Calif., during the pseudo-perigean spring tides (P— S=— 82 h ) of 1978 March 3-7. This occurrence was the third in a series of such destructive tides following upon the two already discussed at the end of chapter 7. But the immediate and subsequent attritional dam- age by pounding, wind-driven surf piled on top of moderately above- average spring tides was not accompanied by significant tidal flooding. -509 0-78-33 482 Strategic Role of Perigean Spring Tides, 1635-1976 greater heights the more intense is the wind action and, somewhat anomalously, the shorter the duration of storm growth and period of wave rise [Cf ., Geoffrey L. Holland, "Effect of the Rate of Storm Growth on Subsequent Surge Elevation," Journal Fisheries Research Board of Canada, 26, (8), 1969, pp. 2223-2227]. The fractional coupling action between the wind and the sea surface is also greater, the steeper is the windward slope of the waves produced. [See also the bibliography, category ( 18) .] 4. Yet another coastal flooding influence of considerable consequence is the combination of perigean spring tides with hydrological runoff from near-coastal uplands. This circumstance may cause severe flooding of coastal regions as the result of an impairment of normal river or drainage runoff to the sea during a period of unusually high tides. The increased water levels produced at times of perigee- syzygy may provide such an effective barrier to hydrolog- ical runoff and force the rising waters to flood over the banks of rivers or drainage channels leading to the sea. The necessarily intense initial watershed drainage is, of course, created by the melting of thick layers of snow and ice at higher elevations, by heavy and sustained precipitation, and by the especially rapid and unimpeded runoff of water from slopes denuded by strip logging and mining. Freshets and flash floods are the result. Aque- ducts, storm sewers, and natural feeder channels sufficient to take care of ordinary drainage situations may, under such conditions, prove entirely inadequate to accommo- date the intense runoff which, in encountering the rising tide, is caused to back up into gutters and streets [Cf ., table 5, key no. 79(2) col. 2]. This is especially true if the peri- gean spring tides, lifted further by strong onshore winds, rise to the actual height of the outlets which comprise the sewer and drainage outfalls to the sea, thus physically pre- venting the effluent discharge. Significantly, however, an effective blocking action of extreme hydrological runoff can occur as the result of perigean spring tides alone, with- out the coincidence of strong onshore winds, provided in this same respect that intense and persistent offshore winds do not prevail. Proper awareness should be observed by climatologists to any coincidence between years of heavy snowfall and years of proxigean tides (as defined earlier in this volume) , and attention should be given by hydrologists to the possi- bility of runoff from snowmelt or heavy precipitation on upland slopes coinciding with periods of perigean spring tides. A correlation between simultaneously rapidly in- creasing readings on river gages and tide gages can provide an appropriate short-range warning. 5. Important practical and environmental influences of perigean spring tides, even without the support of strong onshore winds, include their action in : ( 1 ) bringing salt- water farther up estuaries, thus modifying or even destroy- ing the equilibrium conditions required by various forms of marine fauna and flora (the destruction of birds' nests in saltwater marshes or seacoast wildfowl sanctuaries also may result from the insurging water) ; (2) hastening the breakup of river ice in consequence of their strong associ- ated currents; and (3) facilitating navigation through coastal shoals and over rivermouth bars. All these factors are well substantiated by examples cited in chapters 2-3. Other miscellaneous influences, both adverse and utili- tarian, have been suggested in these same chapters and are further amplified below. B. The Subsidiary Effects of Extreme High and Low Waters and Strong Tidal Cur- rents at Times of Perigee-Syzygy Several practical but — because of the complex accom- panying circumstances — not always directly provable con- sequences of perigean spring tides will next be considered. Among these are: (a) the possible contributions of the extreme low-water phase of such tides to instances of ship grounding; (b) the increased chance of ship collisions im- posed by the strong currents associated with such tides; and (c) the effects of the accompanying extreme high and low waters and intense tidal currents upon marine life in the intertidal zone. The same gravitational forces responsible for unusually high waters in conjunction with perigean spring tides also produce extremely low waters at the opposite tidal phase. There is no question but that an inherent danger exists in regard to ship grounding at such times of excessive low waters. This is especially true since the actual water level is then considerably below the levels of mean low water or mean lower low water on which chart datums (in the United States) are based. Closer inshore, in the tidewater belt, entire schools of fish also can be left stranded by the unusually low water. Because of the large number of possible alternative rea- sons for ship groundings, such as pilot's or navigator's error, adverse weather, failure of navigation equipment, mechanical breakdown of the engines or rudder, confusion of warning signals, etc., it is manifestly implausible to des- ignate this critically reduced low water as more than a possible contributing cause in any one accident. The num- ber of shipmasters' claims to "water level being lower than anticipated" mentioned in a footnote in chapter 3 as a rea- son for the respective grounding casualties is, however, too Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena •IK', sizable to ignore. The overriding factor for consideration is that, even aside from these numerous direct attributions of grounding due to unexpectedly low water, such cir- cumstances do provide a special hazard for deep-draft and only slowly maneuverable supertankers. The likeli- hood for accompanying oilspills, with serious damage to the coastline and the natural environment, cannot be emphasized too strongly. A contiguous navigational threat to the same large, cumbersome ships consequent upon the existence of peri- gean spring tides lies in the much stronger tidal current flows which must necessarily accompany such tides. It is an incontrovertible fact that these unwieldy craft will be sub- ject to increased navigation problems under the afore- mentioned conditions, particularly when the vessels are underway in narrow coastal rivers or channels where the currents are running even more strongly and there is little room for maneuvering. Should sudden course-correcting movements be required as the result of confused signals, improperly identified targets, misinterpreted orders, or poor visibility, the danger that this action will not be ac- complished in time is directly increased. Collisions may result. Actual examples of such tidal influences follow : REPRESENTATIVE INSTANCES OF SHIP GROUNDINGS IN SHALLOW DEPTHS PRODUCED AT THE LOW-WATER PHASE OF PERIGEAN SPRING TIDES Ship groundings due to sudden encounter with unusually shallow water depths naturally occurred more frequently in earlier times when vessels — many still under sail — lacked the quick response of engine power and engine-steering control. This early navigational deficiency, while not carried over into present day ship dynamics is, however, in certain re- spects replaced by the ponderousness, large moments of inertia, and correspondingly reduced maneuverability of modern supertankers and other deep-draft vessels. Among the following representative examples of ship groundings, instances have been chosen in which a direct correlation is possible with the phase of the tides at the time of the grounding. Although strong surface winds and/or impaired visibility may also prevail during the times of ship groundings, these meteorological conditions taken together with the extremely low tides present simply complete a triad of mutually con- tributing causes to such accidents. [If the winds are offshore, they may depress the tides still further; if onshore, they may raise the tides, but at the same time force an unsteerable ship shoreward toward the danger area of the astronomically lowered tides.] In all of the examples cited below, either an astronomi- cally induced extreme low water or strong tidal currents (or both) were present at the time of the disaster. To what de- gree these factors might have contributed to each accident is a matter of open conjecture — as in all cases of this type where possible multiple causes exist. In keeping with any such partially uncertain evaluation in this work, the only rational answer is that "under such tide and current condi- tions, a greatly increased potential for danger is present, and proportionately increased safety measures should, in conse- quence, be observed." Two outstanding historical cases of ships running aground subject to the circumstance of especially low water associ- ated with perigean spring tides are contained in appropri- ate New York City newspaper articles for June 3, 1871 and February 10, 1895 as abstracted below: ". . . On June 3, 1871 .. . the ship Pacific [bound from Glasgow to New York] . . . went aground off South- hampton, Long Island . . . 1,000 tons of pig iron which was her cargo was thrown overboard, after which she floated again ..." A very close perigee-syzygy alignment (P — S= — 1 1] ) oc- curred on this same date, having a mean epoch of 1871 June 3, 0130' 1 75°W.-meridian time. The resulting greatly depressed tidal waters at low-water phase and associated strong tidal currents were accompanied by a stiff surface wind. In the news article, this wind — because of its more obvious effects — was mistakedly given as the cause of the very low (ebb) tide and strong currents. This supposition totally ignores the facts, later indicated in this same article, that both the flood and ebb currents (incoming and out- going) were very intense at their respective times, without the wind having shifted through 180°. Continuing with the news article: "Yesterday [6/3] ... a low ebb tide resulted from the gale, and it was impossible for the ferryboats to cross river in a direct course ... so strong was the tide in the middle of the stream . . ." (New York Evening Post, June 7, 1871, p. 4, col. 8) It was subject to these treacherous tide and tidal current conditions that the Pacific grounded at Southhampton. ***** Similarly, during the low-water phase on February 9, 1895, tides occurred which the New York Times described in a headline (see table 5, key No. 25) as the "lowest tide in twenty years." This extremely low tide was produced by a perigee-syzygy alignment having a mean epoch of 1895 February 9 at 1000 h e.s.t. — together with a northwest wind. The New York Times further relates : "Sandy Hook, N.J., Feb. 9 — The large four-masted steam- ship Patria of the Hamburg-American Packet Steamship Company, while proceeding to sea this evening, grounded in the main ship channel, [!] near the southern edge of Pales- tine Shoal . . ." (New York Times, February 10, 1895, p. 1, cols. 3, 7) Since high water occurred at 7 : 47 p.m., e.s.t. at New York (Governors Island) on February 9, 1895, this case of grounding probably was contributed to more by the strong currents than by the unusually low tide situation associated with perigee-syzygy. ■IK-1 Strategic Role of Perigean Spring Tides, 1635-1976 Dense fog or heavy precipitation combined with the low- water phase of perigean spring tides also can provide a particularly hazardous combination for a ship. Drifting off course by virtue of reduced visibility, the vessel may come unexpectedly into waters of unusually shallow depth. Among representative examples of ship groundings known definitely to have occurred during the low-water phase of perigean spring tides (although other factors may be attributable) are those of: March 13, 1918 ". . . The steamship Kersaw with 121 passengers and four crew ran aground early yesterday [morning] [3/13] . . . the steamship was bound from Boston to Philadelphia, and cause of the accident was that the Captain lost his bearings. When aground, the Kersaw was between the inner and outer bars . . ." {New York Herald, March 14, 1918, p. 2, col. 1 ) "Easthampton, L.I., Mar. 13 — The Merchant and Miner's Liner Kersaw with 1 1 7 naval reservists aboard as well as other passengers struck a sandbar during a heavy fog last night [actually, very early in the morning] and is still held fast . . . Fortunately, the weather was calm and practically no sea was running when the accident occurred . . . [the vessel] apparently lost her way in the fog . . . the ship had strained her plates badly when she struck the bar and all idea of pulling her out this [late morning or evening] high tide was abandoned . . . Kersaw lies just inside the outer bar on the beach . . . Leaks are being fixed in time for her to float out at next high tide . . . Kersaw displaces 2,600 tons and is 224 feet long." {New York Tribune, March 14, 1918, p. 14, col. 1 ) [The predicted lower low water at New London, Conn., on March 13, 1918 was at 3:35 a.m., e.s.t. ; the mean epoch of perigee-syzygy was 1918 March 12, 1600 h e.s.t., P-S= +2 h .] ***** 1930 February 15 ". . . Inbound with 45 passengers and crew of 65, the liner Admiral Benson went aground at 6:40 p.m. Saturday [2/15] near the mouth of the Columbia River . . . Black fog ham- pered the movements of the rescue craft and made it ex- tremely difficult for them to locate the liner . . ." {Oregon Sunday Journal, February 16, 1930, p. 1, col. 8) ". . . Cause of the wreck will not be known until official investigation . . . thus far it remains a mystery to those on shore and not even plausible conjectures seemed to have been advanced . . . The mouth of the Columbia River is a wide and safe entrance, guarded by navigation aids of all kinds . . . Lightship southwest of entrance in line with the first channel, lights day and night, with lights visible 1 1 miles . . . this vessel is in good shape ... it has submarine signal devices, foghorn, and radio compass equipment . . . Beyond the jetty markings there are whistles, [and] slightly north of North Head, flashing lights, everything marked and signaled . . . Benson went on in the fog, just why remains to be seen . . ." {Oregon Daily Journal, February 17, 1930, p. 1, cols. 7, 8) [The predicted lower low water at Astoria, Oreg., on Feb- ruary 15, 1930 was at 9:28 p.m., P.s.t. (higher high water had occurred at 2:58 p.m., and the tide was falling) ; the mean epoch of perigee-syzygy was 1930 February 12, 1500 h P.s.t., P-S=-20M Despite all that has been said in previous pages of this work concerning the advantage offered by perigean spring tides in facilitating the passage of ships over sandbars and through inshore shoals and shallows, a word of caution must be sounded where modern deep-draft vessels (especially those subject to underway "squat") are involved. It must be clearly emphasized from a safety standpoint that the high-water phase of perigean spring tides does not provide a navigational panacea for easing modern supertankers or other deep-draft bulkcarriers into ports or harbors around which reefs and sandbars exist. A typical case in point is illustrated by the grounding of the oil-carrying supertanker Lake Palourde (of 125,831 deadweight tons) just inside Los Angeles (San Pedro) Har- bor on November 20, 1976. This date marked the beginning of a period of perigean spring tides, and came just prior to a perigee-syzygy alignment having a mean epoch of 1976 November 21, 0030 h P.s.t. (P-S=-13 h ). Quoting from the Los Angeles Herald-Examiner for No- vember 21 (p. 1, col. 1) : "A 974-foot long supertanker loaded with 880,000 barrels of crude oil has run aground just inside the Los Angeles Har- bor in San Pedro and immediate action was begun to free the vessel and gvrd against a potentially disastrous oil spill. The Lake Palourde . . . became locked in the sand at dawn yesterday while [enroute] ... to port . . ." As noted, grounding occurred "at dawn." Sunrise for this latitude and date occurred about 6:38 a.m. The ship obvi- ously was trying to take advantage of the extra high tide af- forded by the perigee-syzygy alignment. At Los Angeles Outer Harbor, this morning's higher high water was pre- dicted to reach its crest of 6.9 ft above the datum of mean lower low water at 7:23 a.m. on this date. The tidal range (from LLW to HHW) on this date was 8.1 ft, which, subject to the action of the perigean spring tides, is 2.7 ft greater than the diurnal range of 5.4 ft (from MLLW to MHHW) at this location. The predicted height of 6.5 ft is also 1.1 ft above the value of mean higher high water at Los Angeles Harbor, based on a 19-year period of observations. However, as the events attest, even this appreciable tidal rise at time of perigee springs is often inadequate to accom- modate ships of such unusually large draft over shallow ocean bottoms. Tidal currents probably played no major role in the grounding of this vessel, in spite of their usual acceleration at times of perigee-syzygy. As noted in the National Ocean Sur- vey's Tidal Current Tables, Pacific Coast of North America and Asia — 1976, p. 203: "In Los Angeles and Long Beach Harbors the tidal current is weak. It is reported, however, that three minute surge waves are responsible for major ship movements and damage." No surface winds sufficient to cause strong surges were present at the time of this grounding. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 48.') REPRESENTATIVE INSTANCES OF THE EFFECTS OF STRONG CURRENT FLOW ASSOCIATED WITH PERIODS OF PER- IGEAN SPRING TIDES A perigee-syzygy alignment having a separation-interval of only -8 h occurred at 2300 (e.s.t.) on February 3, 1939. Although the winds were not right to cause tidal flooding on this date, the influence of the astronomical alignment in pro- ducing strong tidal currents is indicated by the following ex- cerpts from the New York Times of February 4 (p. 20, col. 3): ". . . The Cunard White Star liner Aquitania, due to dock at 8 a.m., was not made fast until 3 : 10 p.m. because of an extremely strong ebb tide running at 7 miles an hour that held her at the pier head and carried away 4 wire hawsers . . ." [With total objectivity in mind, the already strong, as- tronomically induced current might also have been added to, in a meteorological sense, by preceding heavy rains, possible runoff from snowmelt on the mountains, and prevailing northwest winds. Were any of these conditions indeed con- tributory, this is still exactly the kind of situation in which special precautionary measures should be observed. Seri- ously aggravated circumstances can be created when such factors coincide with perigean spring tides and/or the aug- mented tidal currents produced during the same period (al- though generally not exactly coincident in time with, the maximized tides).] Again, as reported in the New York Times on the follow- ing day, February 5 (p. 7, col. 2) : "Passenger liners sailed from North River pier yesterday with 4,000 passengers . . . The first to leave at 1 1 a.m. was the French liner De Grasse for the West Indies — followed at 11 :30 a.m. by the Conte di Savoia, which was supposed to be on a slackwater. She moved out from a pier at W. 52nd St. — the tide got her and she started downstream broadside with 5 tugboats to prevent her hitting the end of the next pier, where the Aquitania was berthed. Three liners sailed at 5 p.m. ... the Aquitania which lost seven hours in docking Friday [2/3] because of the strong ebb tide . . . lost another six hours yesterday [2/4] and left at 6 p.m. instead of noon . . ." EXTREME TIDE AND CURRENT IMPACT ON OFFSHORE PLATFORMS IN SHAL- LOW OCEAN AREAS The further potential danger to offshore oil rigs im- planted on the ocean floor with foundations at depths at which tidal currents are still strong should not be over- looked. Erosion and weakening of the base of support by such strong tidal currents at the same time that the surface platform is being battered by strong winds and storm surges may cause an oscillating action of the entire structure which, through resonance, may work toward its final collapse. Whatever the ultimate cause, it should not be ignored that the destruction of an Air Force's radar tower located 80 miles off the mid-Atlantic coast on January 14, 1961 oc- curred on the same day as perigean spring tides which caused active coastal flooding in New Jersey. At this same time, strong subsurface currents were present and — at the surface — intense overwater winds. [Descriptions of the elab- orate oceanographic engineering measures designed to pro- tect a proposed nuclear-powered electric generating plant in a planned location 3 mi off Great Bay, N.J. — and simul- taneously to safeguard the coastal environment — are con- tained in: Public Service Electric and Gas Company, Atlan- tic Generating Station, Units 1 and 2 — Preliminary Site Description Report, vols. 1-2. (Cf., especially, vol. 1, pp. 2.2-5, 2.2-6 for storm tide effects. ) ] INFLUENCE OF PERIGEAN SPRING TIDES UPON THE ECOLOGY OF THE COASTAL ZONE In connection with the dynamic effects of perigean spring tides, their associated strengthened currents, and the possibil- ity for the production of active storm surges when these heightened tides are accompanied by strong, persistent, on- shore winds, there must be mentioned the further aspect of potential ecological damage to the coastal environment. Among appropriate considerations are the upstream in- trusion of saltwater far beyond the usual boundary of saline mixing, and saltwater penetration into freshwater ponds or pools consequent upon wind-blown storm surges and severe tidal flooding. Both of these actions are made physi- cally possible by the existence of perigean spring tides. The first-mentioned expansion of the semidiurnal salt- water intrusions may modify estuarine circulation and flush- ing patterns, result in a temporary but recurring diversion of freshwater bound downstream toward coastal estuarine destinations, and upset the usual chemical, physical, and biological exchange relationships with the freshwater run- off. The latter storm-surge effects also may be accompanied by the destruction of wildlife habitats, nests, and rookeries. Actions taken to offset these detrimental changes may, in themselves, be deleterious to the coastal environment. For example, the construction of seawalls, dikes, and break- waters to prevent tidal flooding, and barriers to prevent salinity intrusion, may, in turn, exert an ecological influence. Many of the ramifications of such manmade changes are dis- cussed in the publication series: U.S. Department of the Interior, Fish and Wildlife Service, National Estuary Study, vols. 1-7, Washington, D.C. 1970. [Cf., especially, vol. 2, pp. 1-39; vol. 4, pp. 1-16.] These factors need not, there- fore, be repeated here. References to certain other matters of ecological import which can be specifically affected by perigean spring tides are given in paragraph 10 of the sum- mary listing following section D, in succeeding pages. C. Unproven Geophysical Relationships With the Phenomenon of Perigee-Syzygy Thirdly, there are certain events of geophysical nature whose seemingly plausible associations with the alignment of perigee-syzygy must be better substantiated before any correlation can be scientifically accepted. As has happened in the case of the many suggested nonphysical attributions to sunspots, one of the most common unscientific actions ■186 Strategic Role of Perigean Spring Tides, 1635-1976 perpetrated is to attribute observed phenomena to oppor- tune physical causes simply because a time-coincidence between apparent cause and adduced effect exists between them. The lay literature all too frequently abounds with such efforts to establish possible causal connections be- tween two factors based upon their coexistence in time, or apparent repetition in cycles. Such imagined relation- ships involve a severe contravention of the principles of scientific method, since almost any two complex and com- prehensive sets of data can — subject to sufficient degrees of freedom — be made to show some individual correla- tions, if the right combinations of parameters are chosen. There is neither intention nor desire in the present work indiscriminately to amass various possible factors which might conceivably be affected by increased lunisolar grav- itational influences. However, scientific method dictates that an impartial and open mind be maintained toward any rationally es- tablished, empirically verifiable factor of causality. It further prescribes that no deductively or inductively de- rived, hypothetical causal relationship which is supported by a reliable body of evidence, be rejected until it fails completely under a sufficient number of analytic tests. Because such tests for acceptance are both rigorous and comprehensive, there is insufficient space in the conclud- ing pages of this work to more than list a few such po- tential relationships under various degrees of scientific investigation. Although each of these unquestionably re- quires further and broader evaluation, all are of a caliber of seriousness sufficient to warrant mention in terms of the possible additional test grounds afforded by perigean spring tides. No one case is to be regarded as any more than speculative at the present stage of research. 1. Wholly Conjectural Relationships Between Meteorological Factors and Perigee-Syzygy Statistically considered, a more than random number of cases of major tidal flooding exists involving a coincidence between perigean spring tides and the presence of strong onshore coastal winds which are a necessary contribution to tidal flooding. Among these are frequent instances of such flooding : ( 1 ) spaced one synodic-anomalistic month apart ; ( 2 ) joined in interrelated sets of 1 and either 6.5 or 7.5 periods of 29.5 days (see chapter 6 for explanation) ; (3) bridged in exact long-term multiples of these same periods; and, perhaps most significantly, (4) which have occurred simultaneously on both the east and west coasts of North America. (See table 1.) These circumstances lead logically to the academic question : Is there any pos- sible situation resulting from the extra gravitational forces produced by the alignment of Sun and Moon at ordinary syzygy — and particularly the additional forces created at perigee-syzygy — which, in known meteorological theory, could have an effect upon inducing, reinforcing, or sus- taining strong surface wind movements? More particu- larly, are there any induced meteorological effects result- ing from the enhanced gravitational forces at perigee- syzygy and capable of producing the very winds which, acting upon the perigean spring tides coincidentally raised, in turn create tidal flooding? In considering these questions, one closely relevant fac- tor which must not be overlooked is the statistical proba- bility of a simultaneous combination of the following events, considered as a meteorological circumstance only : That ( 1 ) a sufficiently deep, intense, atmospheric low pressure system (2) will be in exactly the right position close offshore ( 3 ) with wind movement directed onshore toward a vulnerable lowland portion of the coast; (4) such winds having blown over the water for a sufficient length of time to establish a long fetch and (5) having attained a sustained maximum velocity precisely within one of the few periods of several days in each year in which perigean spring tides reach their peak (6) coincidently with the short interval of a few hours corresponding to one or both of the daily high water phases of the tides. At this point in time, there seems to be no known physi- cal mechanism relating lunisolar gravitational force and barometric fluctuations except those same forces which cause the very small tides detectable in the Earth's atmos- phere. (See section 3, below.) If some parameter were present relating such external gravitational influences and dynamic convergence in the atmosphere — the latter factor being that creating low pressure systems and the associated steep barometric gradients responsible for strong winds — some more positive connection might be assumed. A considerable amount of research is underway cover- ing possible relationships between the tidal forces created at various lunisolar configurations (those consequent upon the phase of the Moon) and the observed amount of at- mospheric cloudiness and precipitation [see bibliography, category (33)]. Further statistical correlations with the Moon being simultaneously at perigee 1 and the lunar node have been detected. Such research might ultimately also lead to a possible association between lunar influence and those offshore storms, accompanied by winds, which con- tribute to coastal flooding at times of perigean spring tides. From many years of record, an above-average frequency of cloudiness has been observed at times of full moon. Regions of cloudiness are, almost without exception, repre- sented by regions of convergence and low atmospheric Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 487 pressure, which are also accompanied by strong winds. Any effect of the reduced parallax and increased gravita- tional force of the Moon on the Earth's atmosphere at times of perigee-syzygy is, however, opposed by the con- verse necessity — if any such augmented cloudiness rela- tionship holds true — for a statistical increase in clear skies at time of apogee, a circumstance which is not discernible among the records. The entire question of some possible meaningful corre- lation between the full phase of the Moon and precipita- tion factors, if real, is a challenging one deserving of fur- ther attention and should be rigorously investigated. By analogy with the qualification previously imposed, neces- sitating a decrease in cloudiness at apogee, if a connection between precipitation and full moon does exist (without requiring that the cause be luminosity-related ) a match- ing statistical decrease in precipitation over sublunar regions of the Earth should be noted between full moon and new moon. 2. Other Possible Geophysical Influences The known geophysical influences the Moon exerts upon ocean tides through enhanced gravitational forces at times of perigee-syzygy leads, in turn, to the possibility of: (a) increased influences upon tides in the solid Earth as a result of these same circumstances; (b) a small increase in the established lunar-induced component of the Earth's external magnetic field. a. Potential Connections Between Perigee-Syzygy, Earth Crustal Movement, and Seismic Activity The first of the preceding two conjectures also raises the closely related issue whether any role is played by the increased gravitational tide-raising forces at times of peri- gee-syzygy as a triggering mechanism for earthquakes. The necessary initiation of this action would be provided by earth-tidally induced ancillary stresses on opposite sides of a geological fault plane, of sufficient magnitude to cause shearing and sudden differential slippage along the plane — setting off an earthquake. Again, any correlative attempts to establish a causal connection between seismic events and the coincidence of perigee-syzygy are marked by many possible pitfalls and uncertain factors such as : ( 1 ) the existence of a fault plane whose contiguous faces are already near the rupture point as the result of built-up differential crustal deforma- tions — and along which a jarring dislocation and release of strain would likely have occurred anyway; (2) other factors of dynamic control in dislodgement of the fault- surfaces such as changes in lubrication between the oppos- ing faces, or in rock tensile-strength when strained to the ultimate fracture point; and (3) a triggering action im- posed by the mechanical jostling of other small earth- quakes or microseisms. However, the existence of a physical connection be- tween earthquakes and lunar syzygy with its coalignment of lunar and solar gravitational forces has been explored by many reliable scientists, and specific instances of cor- relation with times of perigee-syzygy also have been cited [see the references following section D, below, and in the bibliography, category (32)]. It must be emphasized that any possible relationships assignable between earthquakes and increased gravitational forces present at ordinary syzygy would be enhanced by the alignment of perigee and syzygy. Accordingly, any promising line of investigation should be comprehensively pursued to give adequate con- sideration to the latter cases. The possibility exists that the wide range of lunisolar forces imposed on the Earth throughout the complete half-cycle of lunar positions from perigee-syzygy to apogee- syzygy may result (to whatever small degree) in an al- ternate compression and resilient expansion of the Earth's ellipsoidal figure. The consequent maximum rate of de- formation of the crust at both perigee-syzygy and apogee- syzygy could well account for the failure of a large number of major earthquakes to coincide with times of perigee- syzygy alone. The only requirement under this expansion and contraction hypothesis ( if any connection with earth- quakes exists) would be that earthquakes would occur statistically with greater frequency within those anoma- listic months which contain perigee-syzygy alignments, since in these months the alternate compression and ex- pansion would be the greatest at perigee and apogee. In any dynamic correlation between lunitidal forces and earthquakes, greater emphasis also should be placed on vertical rather than horizontal tide-raising forces (see Geotimes, 19, 30, 1974). Inertial reaction times for any such gravitationally in- duced movement of the crust to take place, and corre- sponding relaxation times for the slightly deformed Earth to recover its figure must also be considered in any such investigation. This factor of indeterminancy for so many types of rock materials again points to the difficulty of establishing a meaningful correlation. Research in this field has gone forward in a progressive manner and, with equal consideration to opposing opin- ions, numerous representative examples may be cited. These examples are grouped in a supplemental commen- tary at the end of section D. Other citations to the scien- Strategic Role of Perigean Spring Tides, 1635-1976 tific literature on this topic are given in the bibliography, categories (26)-(29) and (32). c One final comment is germane in this connection. A rather controversial work was published in 1974. 2 This related to the possibility that a "supercon junction" of all of the planets of the solar system in 1982 might cause devastating earthquakes along the great San Andreas fault rift in California between 1980 and 1984. The earthquake catastrophe would come about, it is stated, by a triggering action induced by the mutual alignment of the planets. The gravitational effects of this alignment are assumed to proceed through a complex series of natural events, involving tidal disturbance and the production of huge sunspots in the solar photosphere, the generation of additional corpuscular streams of high-energy particles, a saturation of the Earth's upper atmosphere thereby, exci- tation of the motion of large air masses and turbulence, the imposition of an extremely minute but quick-acting deceleration of the Earth's rotation, a resulting deforma- tion of the crust, and the production of the earthquakes. Although this hypothesis is conceived upon tides raised in the Sun by this gravitational alignment, the Moon is at all times the principal tide-raising body in connection with earth tides. Despite the great mass of Jupiter, at even its least distance from the Earth it is still some 1,500 times farther away than the Moon. Since the tide-raising force on the Earth varies inversely as the cube of the distance of the attracting body, the tide-raising force of Jupiter is less than 0.00001 that of the Moon. Likewise, Venus, the closest planet to the Earth, exerts a tide-raising force only about 0.0001 that of the Moon. Astronomically considered, no instance of maximum proxigee-syzygy alignment — nor even a case of proxigee- syzygy (as both configurations are defined in chapter 7 ) — occurs during the period 1980 to 1984. c A pertinent newspaper summation of conflicting scientific opin- ions with regard to a possible lunar triggering action in connection with the Seattle earthquake of April 13, 1949, was contained on the front page of the Los Angeles Examiner for April 15, 1949. The effect was supposed by some seismologists to accompany a lunar eclipse occurring on April 12, without mention of the closer approach of the Moon to the Earth caused by the associated perigee-syzygy align- ment. This alignment (P— S = — 20", •„, =61'11.1") had a mean epoch of 1949 April 12, 1000" (P.s.t.)- Perhaps more significantly, in terms of a possible alternate, minute compression and expansion of the Earth's crust suggested in the text above as taking place during the succession of a close perigee, a remote apogee, and a second close perigee, the earthquake occurred one anomalistic month after a very close alignment (P— S=2", '„, = 61'28.2") having a mean epoch of 1949 March 14, 1200' 1 (P.s.t.). At the subsequent and intervening apogce-syzygy, the Moon's apogee distance was correspondingly greater, followed by a close perigee approach again at the April 12 perigee-syzygy alignment. By contrast, on March 8, 1993, the Moon will reach one of its closest possible approaches to the Earth (tt=61' 30.0"). It will then possess a very large Aw-coefficient, and the Sun will be at 8= —4.8° (close to the plane of the Moon, (8=0.4° ) at a time of maximum proxigee-syzygy. The mean epoch of the event (P~ S= — 2 h ) occurs at 0400 h (e.s.t.). Astronomically induced ocean tides, at least, will certainly be very high and susceptible to wind- supported flooding conditions along lowland coastlines of the Earth within several days on either side of this date. b. Geomagnetic Fluctuations of Tidal Nature Geomagnetic variations of measurable degree are related to the constantly changing gravitational effects associated with the actual and the apparent revolutions of the Moon and Sun around the Earth — as well as the Earth's rotation with respect to these objects. Such fluc- tuations are relatively long-period ones compared with the short-period variations which produce magnetic transients. ( 1 ) Atmospheric Tides as the Basis for Geomag- netic Variations Just as the Moon and Sun produce tides in the oceans of the Earth, tides are created in the Earth's atmosphere as a function of the changing positions and proximities of these bodies with respect to the Earth. Such atmospheric tides, and the influences they exert in expanding or con- tracting the electrical conducting portions of the iono- sphere, make themselves felt through detectable variations in the observed intensity of the external geomagnetic field. These variations comprise periodic functions similar to those produced within the oceanic tides. The Moon's gravitational influence results in a clear-cut semidiurnal effect, as well as a lunar declination effect which is super- imposed upon it. A semimonthly lunar variation evident in magnetometer records also corresponds to the semi- monthly ocean tidal height variations associated with spring and neap tides. A part of the Sun's gravitational influence in producing atmospheric tides is masked by its expansional heating effects and by the ionization phe- nomena which its ultraviolet radiation produces. These several lunar and solar effects on the total exter- nal magnetic field of the Earth, and the variations they produce through tidal action, are described in detail below. (2) The Solar Diurnal and Semidiurnal Variations During each 24-hour period, various components of the Earth's magnetic field exhibit patterns of magnetic influence associated with the overhead ionospheric cur- rents. However, all magnetic observing stations are not Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena similarly affected — a definite latitude dependence being exhibited. The observed changes in intensity of the ter- restrial magnetic field — although not following an iden- tical pattern — ostensibly, through what might be called an "induction process," are related to barometric fluctu- ations in atmospheric tides. The latter phenomenon involves a small observed rise and fall in atmospheric pressure at the ground surface caused by corresponding adjustments in the pressure of the air in the high atmos- phere above the observing station. These particular tidal fluctuations in the upper atmosphere, although produced in their main influence by causes other than gravity, nev- ertheless act in a manner similar to tides in the ocean waters. Minute but detectable incremental adjustments in sea-level atmospheric pressure are created, on the average, each 24 hours, with secondary maxima and minima at 12-hour intervals in between. Although the Moon's gravitational influence plays the predominant role in the production of the Earth's oceanic tides, the combination of solar heating and expansion of the atmosphere makes the Sun of greater influence in pro- ducing atmospheric tides. Both the 24-hour and 1 2-hour tidally induced maxima in atmospheric pressure observed are attributable to this solar influence. A harmonic analysis of barograph data recorded at sea level around the world indicates that, in the 1 2-hour solar cycle between the primary and secondary tidal maxima, barometric pressures may increase, due to atmospheric tides, as much as 1.3 millibars (0.98 millimeter of mer- cury) at the Equator. This variation is independent of either the presence or the nature of local topography, but the magnitude of the increase in barometric pressure caused by atmospheric tides decreases directly with in- creasing latitude. The 24-hour component in barometric pressure, averaging approximately 0.7 millibar (0.52 mil- limeter of mercury) is considerably more dependent upon altitude and geographic effects. (3) Corresponding Geomagnetic Variations (a) Solar Variation Suggestively similar maxima are locally observed in the intensity of the Earth's magnetic field, although actu- ally no midnight peak and no midday peak are observed at many latitudes. It is theorized that distortions of the ionosphere resulting from these tidal atmospheric pressure changes produce fluctuations both in the electric current flow in the ionosphere and in the associated external mag- netic field. At the Equator, the observed magnetic fluctuations roughly parallel the barometric fluctuations — a common maximum being recorded at about 1 1 a.m., local time. The disturbing influences on the ionosphere in general tend to follow the Sun, but are affected by latitudinal influences and other causes, including the elasticity of the atmosphere. Thus, especially at high latitudes, the magnetic effects may vary considerably, and either a max- imum or a minimum may be observed at 1 1 a.m. (b) Lunar Variation A much smaller, though similar magnetic variation, amounting to less than 1 / 1 0th the solar influence, is pro- duced by the tidal action of the Moon upon the upper atmospheric layers, and is observable with the changing phases of the Moon. The corresponding atmospheric tidal influence at the Equator and sea level, in the same terms as the preceding comparisons, results in a fluctuation of about 0.08 millibar (0.06 millimeter of mercury) in baro- metric pressure at each 12 h 25.5 m interval (a period equal to one-half that between two successive transits of the Moon across the local meridian of any place, on the average). As an academic matter, the reinforcing geomagnetic influences of Moon and Sun should be greater in their maximum tide-raising tendency at perigee-syzygy, if these effects are also combined with, rather than negated by, the radiational effects of the Sun. D. Geomagnetic Illustration of the Increase in Velocity of Tidal Currents at Times of Perigee-Syzygy A slightly different verification of the increase of gravi- tational force on the Earth's tidal waters resulting from the alignment of the Moon with the Sun at perigee-syzygy is made possible by the use of geophysical measurements. These involve the fact that the seawater itself (acting as a conductor of electricity) can generate its own electrical current flow when caused to pass through the Earth's lines of geomagnetic force. The minute electrical potential gradient thus estab- lished can be accurately measured between two electrodes floating on the surface of the water and moored to the ocean floor. The small increment in electrical voltage built up as the flow of water between the electrodes increases will be a determinable function of the water velocity. (This same relationship comprises the working principle of the von Arx electromagnetic current meter. See Wil- liam S. von Arx, An Introduction to Physical Oceanog- raphy, Reading, Mass., 1962, pp. 260-279.) In the case of tidal currents, these velocities will, in turn, increase in proportion to the tide and current gen- erating forces of the Moon and Sun — forces significantly amplified at the times of perigee-syzygy. 400 Strategic Role of Perigean Spring Tides, 1635-1976 Since the effect of perigee-syzygy on the Earth's external magnetic field is real but minuscule, the resulting varia- tion in electrical potential (of the magnitude observed) is due to the increase in water velocity subject to the rein- forcing gravitational action of the Moon and Sun at syzygy — together with the proximity of the Moon to the Earth at perigee. [The mean epoch of perigee-syzygy is 1918 September 20, 2100 h (G.c.t.), in the actual circum- stance illustrated in figure 166, which is redrawn from an article by F. B. Young, H. Gerrard, and W. Jevons, "On Electrical Disturbances Due to Tides and Waves," Philo- sophical Magazine and Journal of Science (London, Edinburgh, and Dublin), vol. XL (6th series, July-De- cember 1920), pp. 149-159, fig. 5.] The very definite reduction in positive amplitude of successive curve crests from near the time of perigee-syzygy on September 20 (accompanied by perigean spring tides) to lunar quadrature (neap tides) on September 27 is clearly revealed in this diagram. These individual curve crests correspond to the instants of greatest tidal current flow near the times of low water in each successive day. Complementing figure 153b, this diagram provides a real- istic illustration of the increase in the velocity of tidal cur- rents — just as the former shows the increase in the rate of tide rise subject to the influence of perigee-syzygy. SUPPLEMENTARY COMMENTS, SPECIFIC LIT- ERATURE CITATIONS, AND CASE EXAMPLES IN CONNECTION WITH THE INFLUENCES OF PERIGEE-SYZYGY ALIGNMENTS AND PERIGEAN SPRING TIDES /. Storm Surge Models and Tidal Flooding In addition to the wide range of papers on storm surges and their damage to the coastline listed in category (18) of the bibliography, numerous specific studies have been con- ducted and, in some cases, hypothetical models of the asso- ciated hydraulic actions have been established, covering various local harbors or estuaries. Illustrative of the reports on such projects are: Robert L. Miller, et al., "Preliminary Study of Tidal Erosion in Great Harbor at Woods Hole, Mass.," U.S. National Technical Information Service, Gov- ernment Reports Announcements (abstract only), 72, 89 (1972) ; Harry L. Bixby, Jr., Storms Causing Harbor and Shoreline Damage Through Winds and Waves Near Mon- terey, Calif., (master's thesis), Naval Postgraduate School, Monterey, Calif. (1962) 186 pp.; B. W. Wilson, et al., Feasibility Study for a Surge-Action Model of Monterey Harbor, Calif., Science Engineering Associates, San Ma- rino, Calif., Contract Report No. 2-136 for U.S. Army Engineer Waterways Experiment Station, Corps of Engi- neers, Vicksburg, Miss. (1965) 199 pp.; and Abraham S. Kussman, "The Storm Surge Problem in New York City, Transactions of the New York Academy of Sciences, series II, vol. 19, No. 8, pp. 751-763 (1957). 2. Engineering Protection Against Storm Surges and Tidal Flooding Aspects of protection against the ravages of storm surges have been discussed in such articles as: C. A. Evans, et al., "DuPont Tide and Storm Warning Service," American Meteorological Society Proceedings, 1st National Conference on Applied Meteorology, Hartford, Conn., October 28-29, 1957, Boston, Mass., pp. A-8 to A-18 (1958) ; P. C. Hyzer, "Hurricane Tidal Flood Protection, Narragansett Bay Area, Rhode Island and Massachusetts," Shore and Beach, 3, 16- 19 (1965) ; George M. Mayfield, "Surveying and Mapping Aspects, Storm Tide Protection," Surveying and Mapping, 92, 1-10 (1966) ; and Basil W. Wilson, "Design Sea and Wind Conditions for Offshore Structures," Proceedings, Offshore Exploration Conference (OECON) Long Beach, Calif., 1966, M. J. Richardson, Inc., Palos Verdes Estates, Calif., pp. 665-708 (1966). 3. Possible Coincidence of Tsunamis and Perigean Spring Tides The especially severe threat to Pacific coastal regions in the possible coincidence of perigean spring tides and earthquake-produced seismic sea waves or tsunamis is in- cluded in a report by Charles Petrauskas, et al., in Frequen- cies of Crest Heights for Random Combinations of Astro- nomical Tides and Tsunamis Recorded at Crescent City, Calif., University of California, College of Engineering Laboratory, Technical Report No. HEL. 16-18, Berkeley, Calif. (1971) 70 pp. (See also fig. 167, relating to a similar event on the east coast.) 4. Concepts of Earthquake Triggering A tide-enhancing astronomical alignment of perigee- syzygy, with a separation-interval of only — 14 h , occurred at 0000 h (P.s.t.) on November 21, 1976. With a higher high water of 7.1 ft occurring at 0805 on November 21, the resulting maximum daily range of the perigean spring tide predicted for Los Angeles (Outer Harbor) on November 21 was 8.6 ft, or 3.2 ft in excess of the diurnal range (differ- ence in height between mean higher high water and mean lower low water) which is 5.4 ft. at this station. At 0955 on November 22, an earthquake of magnitude 3.8 on the Richter scale occurred below the sea floor some 24 miles west of Los Angeles, Calif. The epicenter was situated 7 miles south of Malibu, among a maze of offshore faults in Santa Monica Bay which are related to the San Andreas fault. This was succeeded at 0320 (P.s.t.) on November 26 by another earthquake of magnitude 6.3, with epicenter in the Gorda Basin, north of Ferndale, Calif., at a point near to that at which the principally offshore Mendocino fracture zone intersects the San Andreas fault. Maximum perigean spring tides were predicted for nearby Eureka, Calif., at 1204 (P.s.t.) on November 22, with the maximum daily range of 7.8 ft on November 25 (subject to the continuing influence of the perigee-syzygy alignment) being still 1.1 ft above the [mean] diurnal range of 6.7 ft at this location. The time of higher high water at Eureka on November 25 was predicted for 1429 (P.s.t.). No severe weather systems or co 20 Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena MOORED ELECTRODES M, AND M 2 200 YARDS APART SEA VERY ROUGH SEA MODERATE -. SEA CALM > 3 ° ^T^jfflfi 14.8mv ' L ' i ^ -10^12 W 3 6 NOON 21-9-18 491 1 9 i I 12 3 I I I L I 6 9 12IW3 l I 6 „ 9 I 1? I ?! I 6 l I 9 12 H L H NOON H I H NOON L W W W 22-9-18 W W W 23-9-18 W w 20r- SEA CALM 6 io|- > SEA MODERATE SEA CALM _l -10 _ l I _12 3 I 6 I 9 l 12 l 3 I 6 i I i i 9 12 3 6 I l 9 12 l 1 3 6 1 l 9 12 NOON L H L H NOON L H L H NOON 23-9-18 W W W W 24-9-1 8 W W W W 25-9-18 SEA CALM SEA CALM 4.0mv H NOON L w 25-9-1 8 w H NOON L W 26-9-1 8 W 1.6mv i i l ~^- 6 9 12 L H NOON W W 27-9-1 8 SEA CALM 10 1- H W-1.6mv 2 - 4mv -101- 12 3 6 NOON L 27-9-18 W -0.8mv SEA SLIGHT H W I l II 6 9 12 3 L NOON W 28-9-18 6 9 L W 12 3 6 9 12 H L NOON H W W 29-9-1 8 w Resistance of Circuit 235 ohms. Deflections | indicate M 2 +ve with respect to Mi Figure 166. — (Discussed in text.) .102 Strategic Role of Perigean Spring Tides, 1635-1976 The New York Times Tues., Nov. 19, 1929 Page 20, Cols. 2, 3 QUAKE FELT HERE; TIDE FLOODS SHORES Seismograph Needle Breaks at Fordham— Father Lynch Sees Fault in Sea as the Cause. High Water Sweeps Bridge Away . . . New York City and vicinity distinctly felt the tremor that followed the earth- quake off the coast of Nova Scotia yester- day afternoon. High tides preceded and followed the shock, sending a high surf pounding up the beaches all along the northern shore of Long Island Sound, along the north shore of Queens and on the coast of Northern New Jersey. Queens communities suffered considerable damage as a result of the flood tides. Father Joseph Lynch, who has charge of the seismograph at Fordham University, said it was quite possible that the extreme- ly high tides and the disturbance in the ocean were related . . . . . . Father Lynch said that the seismo- graph at Fordham registered the first shock of the quake at 3:31 P. M. The tremors continued for several hours after that, with particularly severe disturbances recorded at 3:35:7 and 3:37.37. Three minutes later another sharp shock was shown by the needle . . . Shock Dislodged Needle. "One of the shocks was so violent that the needle was dislodged from its posi- tion," Father Lynch declared. "I do not think this quake was greater than the one that was felt in the New England States and in New York about three years ago." Checking up with the man in charge of the seismograph at St. Louis University, which is located about 1,712 miles from the supposed centre of the shock, Father Lynch reached the conclusion last night that the disturbance was caused by a fault in the ocean or in the Gulf of St. Lawrence. "We cannot place the centre definitely until we have taken a more accurate check-up," he declared. "I believe the dis- turbance today was the end of the fault that occurred in the St. Lawrence Valley, somewhere near the Saguenay River, three years ago, but I cannot say definitely whether it is the end of the fault until we have located the centre within a mile or so." The authorities in the American Museum of Natural History said they believed the shock was one of the most violent recorded on their seismograph within the past twelve years. According to their figures it began at 3 :31 P. M. and lasted one hour. They estimated that the centre of the dis- turbance was approximately 465 miles from New York, while Father Lynch said he estimated its distance from New York at 880 miles . . . ... A sand barge owned by the Hugh McGeeney Company, Inc., of Manhattan was caught by the swift-rising tide and was swept against a bulkhead at the Long Island Railroad drawbridge in Flushing Creek . . . . . . Gasoline stations along Northern Bou- levard, west of the Flushing Bridge, were under several feet of water when the tide was at its maximum height and at Sands Boathouse, near the Flushing Bridge, a flotilla of dories was put into service to remove people from the inundated areas . . . The Coast Guards at Sandy Hook sta- tion said that an unusually heavy tide began running at 8 A. M. and heavy seas came up . . . . . . They agreed that it was an extremely high tide even for "full moon tide." . . . ALL WARNED FROM PELEE. Flares From Martinique Volcano and Rumblings Cause Fear of Eruption. FORT DE FRANCE, Martinique, Nov. 18 (AP). — The government of Martinique today warned all persons to evacuate the zone at the foot of Mont Pelee owing to the increasing activity of the volcano. For the first time since the activity began flares of light were constantly noticed dur- ing the night from Saturday to Sunday. They seemed to come through a split in the upper part of the volcano's cone on the slope toward St. Pierre, which was destroyed with great loss of life in 1902. The split was almost vertical and about 240 feet high. The flashes of light were acompanied by underground rumblings, which were undoubtedly of volcanic origin 7929 NOV. 17 22h e.s.t. (+54) 54 Figure 167. strong onshore winds prevailed during this period to pro- vide any further tidal amplification. The November 22 earthquake followed by almost exactly one anomalistic month (27.528 d compared with 27.555 d ) the first of a series of 12 minor earthquakes which occurred in north Orange County, Calif, (near Fullerton) beginning at 2115 (P.s.t.) on October 24, and persisting intermittently until early on October 26. The largest was of magnitude 2.0. This series of small earthquakes occurred some 2-3 days after a close perigee-syzygy alignment whose mean epoch was 1976 October 23 0100" (P.s.t.), P~S=+8 h . A series of some 60 minor earthquakes also had occurred in the area of Brawley, Calif., on November 4 (i.e., within two days of apogee-syzygy, having a mean epoch of 1976 November 6 1100" P.s.t.). The dual perigee-apogee occur- rence of these multiple earthquake events, however meager in terms of the total number and variety of earthquakes, gives interesting grounds for speculation as to the possibility, previously suggested, of a contractional-expansional cycle based upon an increased amplification and reduction of the earth-tide raising forces caused by the near-coincidence of perigee-syzygy and apogee-syzygy, respectively. A similar relationship has been identified in the production of moon- quakes at both perigee and apogee. [See G. Latham, et al., Science, 174, 687-692 (1971).] Other positive correlations have been detected between such periods of gravitational maxima and both earthquake swarms and aftershocks. [See Geophysical Research Letters, 2, 506-509 (1975).] Conversely, in an article by L. Knopff on "Earth Tides as a Triggering Mechanism for Earthquakes," Bulletin Seis- mological Society of America, 54, 1865 ( 1964) , and another by J. S. Simpson having the same title in Earth and Plane- tary Science Letters (Amsterdam, The Netherlands) , 2, 473 (1976), these authors refute any major triggering of earth- quakes by the lunar gravitationl influences producing oceanic and earth tides. Another conceivable mechanism for earthquake trigger- ing exists in the concept of tidal loading, which itself is a Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena ■193 function of enhanced gravitational tide-raising forces. This permits a similar question to be raised : Were all four of the multiple earthquake events above cited, having epicenters offshore or close onshore, but additional earth tremors among the many resulting from California's very active fault zones — or are there contributing ocean tide-loading factors which further enhance the earthquake potential of these and other seismic-prone areas peripheral to the Pacific? (See also the recorded Atlantic coast effects in fig. 168.) In his paper "Triggering of the Alaskan Earthquake of March 28, 1964, and Major Aftershocks by Low Ocean Tide Loads," Nature, 210, 893 ( 1964) , Eduard Berg attrib- utes the triggering action in the case of this 1964 earthquake to tidal loading. As early as 1929 in a contribution titled "Tilting Motion of the Earthf's] Crust Caused by Tidal Loading," Bulletin of the Earthquake Research Institute (Tokyo, Japan), 6, 85 (1929), R. Takahasi points out that, near the shore, a crustal deformation caused by the tidal load produced by high ocean waters can amount to nearly 50 times the deformations associated with tides in the solid Earth. He cites a specific example where the maximum of such crustal deformations occurred accompanying an ordinary spring tide on August 15-17, 1928. However, the possible triggering of earthquakes by such deformations in the crust caused by tidal loading is still a matter of open speculation, together with the question of shear enhancement along fault planes induced by the effects of earth tides. E. Groten and J. Brennecke in a paper on "Global Inter- actions Between Earth and Sea Tides," Journal of Geo- physical Research, 78, 8519-26 (1973) point up the need for further knowledge relating to both the lateral attraction and vertical loading influences upon earth tides caused by unusually high ocean tides. G. P. Tanrazyan in an article "Tide-Forming Forces and Earthquakes," Icarus, 7, 59-65 (1967) substantiates a strong positive correlation between the lunar alignment at perigee-syzygy and earthquakes observed in the U.S.S.R. He also extends an earthquake-tidal force relationship to deep- focus and suboceanic-floor earthquakes in his article "On the Seismic Activity in the Area of the North-western Pa- cific Ocean Margin," Akademiya Nauk SSSR, Izuestiya, Seriya Geofizicheskaya (Moscow, U.S.S.R.) (1958) pp. 664- 668. Numerous papers have been published establishing a re- lationship between lunar phase relationships, earth tides, and earthquake microseisms. Typical examples are in : Jour- nal of Geophysical Research, 81, 2543-55 (1967); Geo- physical Research Letters, 2, 506-9 (1975) ; and Bulletin of the Seismological Society of America, 64, 2005-6 (1974). F. W. Klein in a comprehensive article in Geophysical Journal, Royal Astronomical Society, 45, 245-295 (1976) tabulates the results of a computerized analysis to show a significant positive correlation between the occurrence of earthquake swarms in the Imperial Valley of California and astronomically induced earth tides. He identifies both ocean loading and shear enhancement as probable trigger- ing mechanisms. The present state of knowledge in this elusive field of in- vestigation involving the search for a possible correlation between changing distances and aspects of the Moon and earthquakes would, with any degree of consistency, only allow for the following general precepts : ( 1 ) the existence of a possible correlation between either of the positions of lunar syzygy and the production of microseisms; (2) the absence, at present, of any definitive correlation between the occurrences of lunar syzygy or perigee-syzygy and seismic events of intermediate to large magnitudes on the Richter scale — although some acceptable correlations have been found with earthquakes of magnitude > 5, occurring at depths < 30 km, with fault motion (slip-dip) at least 30 percent in the vertical [Geotimes, 19, 30 ( 1974)]; (3) among those seismic events in which an acceptable correlation with syzygy or perigee-syzygy has been established, all are of shal- low-focus origin, but those in which fault motion (strike- slip) is parallel to the Earth's surface are generally excluded. 5. Tidal Loading The effects of vertical movement of the crust produced by tidal loading are summarized in a report by A. Waale- wijn, "Hydrostatic Measurement of Vertical Movement of the Coast Dependent on the Tides," in: Contributions to IAG Special Study Group 2.22 by the Permanent Service for Mean Sea Level, J. R. Rossiter, ed., presented at the 1970 Coastal Geodesy Symposium held in Munich, Ger- many, pp. 239-247 (1970). 6. Earth Tides A significant summary of the varying values of earth tides has been presented in an article by J. T. Kuo, et al., "Transcontinental Tidal Gravity Profile Across the U.S.," Science, 168, 968-971 (1970). This survey also reveals the futility of attempting to apply the theoretically derived data of corange and cotidal charts to determine the indirect effects produced by ocean tides upon tides in the solid Earth. The New York Times Tues., March 10, 1931 Page 1, Col. 2 Earth Shivers Are Linked To the World-Wide Storms Special to The New York Times. CAMBRIDGE, Mass., March 8.— On the heels of the storm and record tide which swept the New England coast Wednesday and Thursday, leaving a trail of damage and ruin in and around Boston, the Har- vard seismograph station today came for- ward with additional documentary evi- dence of the destructive forces at work coincidental with the flood tide, but defy- ing scientific explanation. The seismograms of the two days of the storm and yesterday give a record which even a layman can readily distinguish from normal oscillations and from the characteristic records of earthquakes. Microseisms, as explained by Lewis Don i^eet, instructor in seismology, who is in charge of the station, are microscopic shakings or rhythmic motions of the ground which continue for hours and, as in this case, for days. They have puzzled seismologists for many years . . . 7937 Mar. 4 5.5e.s.t. (0) D-57 Figure 168. 494 Strategic Role of Perigean Spring Tides, 1635-1976 7. CrustalTilt The further importance of tidally induced crustal tilt in the case of precise geodetic leveling measurement is obvious. The effects on both gravity measurements and land tilt pro- duced by a large mass of tidal water which piles up in an embayment or landlocked estuary have been well demon- strated in such investigations as "The Response of the Earth to Loading by the Ocean Tides Around Nova Scotia," by A. Lambert, Geophysical Journal, Royal Astronomical So- ciety, 19, 449-77 (1970). 8. Deflection of the Vertical The deflection of the vertical as the result of high ocean tides and its importance to geodesy have been discussed in such articles as that by G. W. Lennon, "The Deviation of the Vertical at Bidston in Response to the Attraction of Ocean Tides," The Geophysical Journal of the Royal Astro- nomical Society, 6, 64-84 ( 1962) . 9. Geomagnetic Effects Examples of the influence of lunar tides upon geomagne- tism and aeronomy are instanced by: E. S. Batten, Com- parison of Tidal Theory with Lower Thermospheric Wind Observations, Rand Corporation Papers No. P-4655 (May 1971 ) 16 pp., and Tidal Winds in the Mesosphere and Iono- sphere, (Ph. D. Thesis), University of California, Los An- geles, Calif. (1970) 137 pp.; P. Amayene, "Simultaneous Neutral Wind and Temperature Oscillations Near Tidal Periods in the F-Region Over St. Santin," Journal of At- mospheric and Terrestrial Physics (Oxford, England), 35, 1499-1505 (1973) ; Jagdish Chandra Gupta, "Special Anal- ysis of Geomagnetic Variations to Study the Tidal and the Storm Modulation Effects," Planetary and Space Science (Oxford, England), 20, 1613-1625 (1972); R. D. Harris and R. Taur, "Influence of the Tidal Wind System in the Frequency of Sporadic E Occurrence," Radio Science, Washington, D.C., 7, 405-410 (1972) ; and Windele, et al., "Sea Tidally Induced Variations of the Earth's Magnetic Field (Leakage of Current from the Atlantic)," Nature, 230,296,317-318 (1971). 10. Ecological Aspects Important environmental influences of exceptionally high tides are described in such papers as that by N. M. Ridge- way, "Directions of Drift of Surface Oil with Wind and Tides," New Zealand Journal of Marine and Freshwater Research, 6, 178-184 (1972); B. Johns, "Mass Transport in Rotatory Tidal Currents," Pure and Applied Geophysics, 60, 107-116 (1965) ; and J. Sherman Bleakney, "Ecological Implications of Annual Variations in Tidal Extremes, Ecol- ogy, 53,933-938 (1972). //. Internal Waves Recurrent evidences have shown up in the scientific lit- erature relating the phenomenon of internal waves to the syzygy position of the Moon — with the most significant correlation appearing to exist in connection with the extra strong subsurface currents running in narrow straits or chan- nels at times of perigee-syzygy. A typical instance of this relationship was the detection of large-amplitude internal waves in the Great Channel between Great Nicobar Island and Sumatra during the Indian Ocean Expedition of the U.S. Coast and Geodetic Survey ship Pioneer in 1964. The internal waves were first discovered on June 12 (G.c.t), within 2 days of an alignment of perigee-syzygy having a mean epoch of June 10 0300 h (G.c.t.) and a separation be- tween components of —2 hours. The presence of the in- ternal waves was manifest at the sea surface by a phenome- non resembling tide rips. [See bibliography, category (11), Perry, R. B., and Schimke, G. R. (1965).] In a direct followup to this earlier sighted occurrence, a letter dated March 4, 1977, from the chief scientist of the Exxon Production Research Co., pursuing offshore drill- ship operations in the Andaman Sea, indicated "with fair assurance that internal wave activity in the Andaman Sea corresponds very well with spring tide activity . . . the max- imal internal wave activity occurring within a four-day period centered around the spring tides." Occasional internal wave activity noted during other times of the month "is much reduced from that occurring near the spring tides." 12. Turbidity Currents The possibility that strong underwater currents produced at the times of perigean spring tides might also be associated with subsurface turbidity currents is raised by the report of a NOAA two-man submarine diving operation at the head of Oceanographer Canyon off the east coast of North America on July 17, 1974. A perigee-syzygy alignment oc- curred on July 19, 1974, with the mean epoch of perigee- syzygy at 1000 h (e.s.t.) . The report reads, in part, as follows. "Dive #14. Head of Oceanographer Canyon . . . head- ing 180° . . . 7/17/74 . . . Gamma Dive #441. 0846 ... on bottom 565' . . . Savoy silt with a few erratic boulders . . . started down slope between the two major tributaries ... At 600' we started picking up a slight westerly current (possibly coming out of the N.E. head) . . . This current became stronger with time and depth . . . Visibility was 30-40' . . . Temperature 49.5° F. at 600' . . . Continuing down to 700' the current be- came quite strong . . . water temperature at 700' was 51°! . . . Suddenly we were enveloped in a cloud of sediment . . . Visibility <2' . . . The sub started moving sideways (to the west) quite rapidly ([velocity] at least 2 knots — hard to estimate, but the bottom was going by very fast . . . observer thought 4 or 5 knots) ... I got the sub turned around and started upslope (to the north) while still drifting rapidly to the west . . . the bottom here was silty with many pebbles and 3-5" ripples (orientation un- known) . . . upon reaching the 650' level we suddenly came into still clear water . . . visibility 30' ... no cur- rent . . . turning around I could see the turbid area be- low us. All very strange and exciting ... the whole thing took only 5 (?) minutes. . . ." 13. Fish Migration In an earlier technical paper by Otto Pettersson on "The Connection Between Hydrographical and Meteorological Phenomena," Quarterly Journal of the Royal Meteorologi- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena ■lf). r ) cal Society, 38, 173-191 (1912), the author discusses cer- tain tidal and tidal-current phenomena in connection with climatology. He relates the undercurrent of the Skagerak and Kattegat to the declination of the Moon and its chang- ing distance from the Earth (thus indicating a deep-water tidal movement of the tropical and parallactic type) . These deep-water movements are, in turn, associated with the migration of herring shoals into the Kattegat in winter. Oscillatory movements occurring in the deep waters pro- duce large, long-period submarine waves of differing densi- ties and possessing a distinct correlation with the phase and position of the Moon. The subsurface waves produced in this phenomenon are termed "the Moon waves of the Gull- mar fjord." The peaking of these waves (i.e., attainment of their shallowest depths beneath the sea surface) near the times of syzygy is clearly shown in the article. 14. Biological Rhythms Technical discussions of many aspects of biological rhythms as they relate to tides are contained in John D. Balmer, et al., An Introduction to Biological Rhythms, New York (1976) 392 pp. In this work, the various contributors describe (chapter I) the responses to tidal rhythms by fiddler, penultimate-hour, and green shore crabs, as well as sand hoppers and even unicelled diatoms. They also subse- quently evaluate the evidence for external timing of bio- logical clocks, certain geophysically dependent rhythms, and the observed propensities among various life forms toward lunar periodisms. 15. Breakup of River Ice A classic and interesting example of the effect of perigean spring tides in breaking up river ice is contained in a record of natural events which occurred in the colonial period of America. In an article on "Some Old-Fashioned Winters in Boston," Fitz-Henry Smith, Jr. d notes (p. 275) an episode that occurred in the winter of 1 766 : "The harbor remained frozen from Sunday, Jan. 5 [N.S.] until the following Saturday [Jan. 1 1] when an extraordinary thaw and south wind dissipated the ice." He further states that "Tudor e commented that it was 'very remarkable for the Harbor to frees [sic] up so strong and be so clear again in 6 Days'." Table 16 shows that syzygy (new moon) occurred on 1766 January 10 at 2000" (75° W.-meridian time) and perigee at 1400 h on the same date, giving the mean epoch of perigee-syzygy as 1766 January 10, 1700" (75° W.- meridian time ) preceding by just a day [together with the effects of phase- and parallax-age] that on which the ice breakup occurred. The perigean spring tides and their associated strong currents undoubtedly provided an active contributing cause to dissipation of the ice. d Fitz-Henry Smith, Jr., "Some Old-Fashioned Winters in Boston, with Particular Reference to Times When the Harbor Froze," vol. 65, Proceedings of the Massachusetts Historical Society, Boston, 1940. e William Tudor, ed., Deacon Tudor' s Diary, Boston, 1896. The Challenge of Geophysical Dis- covery: An Advocacy of Interdisci- plinary Cooperation It is obvious from the preceding sections and chapters that many complex geophysical and biophysical problems exist that are dependent upon both regular variations and irregular extremes in gravitational force, and which, ulti- mately, only the application of a multidisciplinary scien- tific approach can solve. Such cooperative effort as that which motivated the joint National Academy of Sciences-Government agency- academic institution-private research corporation studies of the Great Alaskan Earthquake of 1964 [and which was set down for the record in the prefaces to the 3-volume ESSA (NOAA) publication series on that earthquake] has been demonstrated as both feasible and productive. In the predominantly empirical, case-study approach of several chapters of the present volume, the large amount of data tabulated giving special attention to de- tails of time and position has been included with a direct purpose in mind — that of providing a suitable base for coordinated use in other related disciplines of science. This plan of presentation is occasioned by a strong feel- ing that the innovative approaches resulting from overlap and feedback between various related sciences can best serve to reveal and confirm exact new causal connections not previously known — or at least to crystallize knowl- edge in many of the propositions and concepts earlier enumerated in theoretical form only. As has been several times remarked in connection with various suggested relationships throughout the immedi- ately preceding pages, available theories are presented which are often not yet fully supported by substantiating data. Further confirmatory evidence is definitely needed to establish such supposed relationships on a firm basis and, at the same time, to determine and verify the exact method of operation of the forces involved. In direct am- plification of the latter statement in terms of the ease of its misinterpretation, this work will be concluded on a purely academic note. Theories are inventions rather than discoveries. Some- what anomalously, therefore, from a pure research point of view, they may sometimes serve to limit progress to a certain degree rather than to accelerate it — since, after a theory is created, valuable time is often consumed in striv- ing to make data conform to it as a purely mechanistic artifice, instead of this same time being devoted to investi- gation of the cause of the impelling action itself. 496 Strategic Role of Perigean Spring Tides, 1635-1976 Thus, as a hypothetical example in the field of gravi- tation presently under discussion, in the days before Sir Isaac Newton a physical law might conceivably have been deduced to explain how an object gets from a point A to a point B under free-fall without bothering to explain how the motivating force originated, or even how the moving object got underway. Yet, the newly derived law of motion under free-fall, if self-sufficient, would be fully accepted as describing this motion and its effect in getting an object from point A to point B. To satisfy the physical cause of this action, the assumption might simply have been made that some arbitrary force of attraction exists between A and B. This assumption would be deemed ade- quate to fulfill the immediate need. But science, fortunately, does not work in this "closed- door" environment, satisfied to ignore the cause of any force or action until the need arises to ascertain the cause. Although over 300 years have elapsed since Newton first propounded his descriptive law of gravitation and numerous generations of scientists have sought, unsuc- cessfully, physically to define the interacting force, the search still goes on in laboratories and research institutions to find a clue to the exact nature of this force. Nor is this the only gap in fundamental geophysical knowledge. Examples from other fields are equally famil- iar. Even assuming the validity of the theories propounded for describing various types of motions, the scientist is still at a loss today in endeavoring to define the basic forces which, as single examples : ( 1 ) started electrons revolving around the nuclei of atoms; (2) initiated ring currents in the body of the Earth to produce an electromagnetic field ; or ( 3 ) caused the Sun to rotate on its axis and the planets to revolve around it. In the realm of other intangible physical entities, such as electromagnetic radiation, neither can he directly an- swer the question why rays of certain colors of light travel faster than rays of other colors through a medium of the same optical density, nor why rays of short wavelength carry with them more energy than long waves. As yet un- answered also are the reasons why a moving or rotating electron possesses an electrical field, and why a particle of mass exerts a gravitational force. Confronted by such basic questions as these, the depth of our knowledge and understanding of the forces, fields, and physical phenom- ena of the universe remains grossly inadequate. Perhaps one of the great benefits which may come out of interdisciplinary research in the geophysical sciences is a reappraisal of our whole scientific thinking — over- coming any Aristotelian-like, conditioned sense of satis- faction with classic theories. With the continuously growing trend in basic research may come a realization that there may be other new and as yet totally undiscov- ered laws, principles, or factors of physical causation at work — or fundamental modifications required in our ex- isting scientific laws — even including those of gravitation and geomagnetism. As an example, with respect to gravitation, there is presently no way of knowing whether the gravitational force field averaged for the entire universe might not actu- ally be effective in permeating and altering the local gravity field of the Earth — assuming that this universal, smoothed force field might be of such a small magnitude that its differential effects could not be detected across the relatively short distance comprising the diameter of the Earth. The extension of the available baseline to outer space through the use of artificial satellites, and the con- duct of experiments in deep space to evaluate more pre- cisely the gravitational constant — which provides a common denominator for gravitational action through the known universe — should provide important strides forward in this connection. Appendix The Basic Theory of the Tides Introduction The word "tides" is a generic term used to define the alternating rise and fall in sea level with respect to the land, produced by the gravitational attraction of the Moon and Sun. To a much smaller extent, tides also occur in large lakes, in the atmosphere, and within the solid crust of the Earth, acted upon by these same gravitational forces of the Moon and Sun. Additional nonastronomical factors such as configuration of the coastline, local depth of the water, ocean-floor topography, and other hydro- graphic and meteorological influences may play an im- portant role in altering the range, interval between high and low water, and times of arrival of the tides. The most familiar evidence of the tides along our shores is the observed recurrence of high and low water — usually, but not always, twice daily. The term tide correctly refers only to such a relatively short-period, astronomically in- duced vertical change in the height of the sea surface (exclusive of wind-actuated waves and swell); the ex- pression tidal current relates to accompanying periodic horizontal movements of the ocean water, both near the coast and offshore (hut as distinct from the continuous, stream-flow type of ocean current). Knowledge of the times, heights, and extent of inflow and outflow of tidal waters is of importance in a wide range of practical applications such as the following: Navigation through intracoastal waterways and within estuaries, bays, and harbors; work on harbor engineer- ing projects, such as the construction of bridges, docks, breakwaters, and deep-water channels; the establishment of standard chart datums for hydrography and for de- marcating the seaward extension of shoreline property boundaries; the determination of a base line or "legal coastline" for fixing offshore territorial limits, both on the sea surface and on the submerged lands of the Continental Shelf; provision of information necessary for underwater demolition activities and other military engineering uses; and the furnishing of data indispensable to fishing, boat- ing, surfing, and a considerable variety of related water sports activities. The Astronomical Tide-Producing Forces: General Considerations At the surface of the Earth, the Earth's force of gravi- tational attraction acts in a direction inward toward its center of mass, and thus holds the ocean waters confined to this surface. However, the gravitational forces of Moon and Sun also act externally upon the Earth's ocean waters. These external forces are exerted as tide-producing, or so-called "tractive" forces. Their effects are superimposed upon the Earth's gravitational force and act to draw the ocean waters to positions on the Earth's surface directly beneath these respective celestial bodies (i.e., toward the "sublunar" and "subsolar" points). High tides are produced in the ocean waters by the "heaping" action resulting from the horizontal flow of water toward two regions on the Earth representing the positions of maximum attraction of the combined lunar and solar gravitational forces. Low tides are created by a compensating maximum withdrawal of water from regions around the Earth midway between these two tidal humps. The alternation of high and low tides is caused by the daily (or diurnal) rotation of the solid body of the Earth with respect to these two tidal humps and two tidal de- pressions. The changing arrival times of any two succes- sive high or low tides at any one location is the result of numerous factors later to be discussed. Origin of the Tide-Raising Forces To all outward appearances, the Moon revolves around the Earth, but in actuality, the Moon and the Earth re- volve together around their common center of mass, or gravity. The two astronomical bodies are held together by gravitational attraction, but are simultaneously kept apart by an equal and opposite centrifugal force produced by their individual revolutions around the center-of-mass of the Earth-Moon system. This balance of forces in orbital revolution applies to the centers-of-mass of the individual bodies only. At the Earth's surface, an imbal- 202-509 0-78-34 497 w, Strategic Role of Perigean Spring Tides, 1635-1976 ance between these two forces results in the fact that there exists, on the hemisphere of the Earth turned toward the Moon, a net (or differential) tide-producing force which acts in the direction of the Moon's gravitational attrac- tion, or toward the center of the Moon. On the side of the Earth directly opposite the Moon, the net tide-producing force is in the direction of the greater centrifugal force, or away from the Moon. Similar differential forces exist as the result of the revo- lution of the center-of-mass of the Earth around the cen- ter-of-mass of the Earth-Sun system. Detailed Explanation of the Differential Tide-Producing Forces The tide-raising forces at the Earth's surface thus result from a combination of basic forces: (1) the force of gravitation exerted by the Moon (and Sun) upon the Earth ; and ( 2 ) centrifugal forces produced by the revolu- tions of the Earth and Moon (and Earth and Sun) around their common centers-of-gravity (mass). The effects of those forces acting in the Earth-Moon system will here be discussed, with the recognition that a similar force .com- plex exists in the Earth-Sun system. With respect to this center-of-mass of the Earth-Moon system (known as the barycenter) the above two forces always remain in balance (i.e., equal and opposite). In consequence, the Moon revolves in a closed orbit around the Earth, without either escaping from, or falling into the Earth — and the Earth likewise does not collide with the Moon. However, at local points on, above, or within the Earth, these two forces are not in equilibrium, and oceanic, atmospheric, and earth tides are the result. The center of revolution of this motion of the Earth and Moon around their common center-of-mass lies at a point approximately 1,718 km (1,068 mi) beneath the Earth's surface, on the side toward the Moon, and along a line connecting the individual centers-of-mass of the Earth and Moon. (See G, figure 1.) The center-of-mass of the Earth describes an orbit (Ei, E?, E 3 . .) around the center-of-mass of the Earth-Moon system (G) just as the center-of-mass of the Moon describes its own monthly orbit (Mi, Mi, M?, . .) around this same point. 1. The Effect of Centrifugal Force It is this little-known aspect of the Moon's orbital mo- tion which is responsible for one of the two force com- ponents creating the tides. As the Earth and Moon gravitate around this common center-of-mass, the cen- trifugal force produced is always directed away from the center of revolution in the same manner that an object whirled on a string around one's head exerts a tug upon the restraining hand. All points in or on the surface of the Earth acting as a coherent body acquire this com- ponent of centrifugal force, just as all points on an object whirled around the head tend to fly outward under the action of centrifugal force. And, since the center-of-mass of the Earth is always on the opposite side of this common center of revolution from the position of the Moon, the centrifugal force produced at any point in or on the Earth will always be directed away from the Moon. This fact is indicated by the common direction of the arrows ( repre- senting the centrifugal force F c ) at points A, C, and B in figure 1, and the thin arrows at these same points in figure 2. It is important to note that the centrifugal force pro- duced by the daily rotation of the Earth on its axis must be completely disregarded in tidal theory. This element plays no part in the establishment of the differential tide- producing forces. It may be graphically demonstrated that, for such a case of revolution without accompanying rotation as above enumerated, any point on the Earth will describe a circle around the Earth's center-of-mass which will have the same radius as the radius of revolution of the center-of- mass of the Earth around the barycenter. Thus, in figure 1 , the magnitude of the centrifugal force produced by the revolution of the Earth and Moon around their common center-of-mass ( G) is the same at point A or B or at any other point on or beneath the Earth's surface. Any of these values is also equal to the centrifugal force produced at the Earth's center-of-mass (C) by its revolution around the barycenter. This fact is indicated in figure 2 by the equal lengths of the thin arrows (representing the cen- trifugal force Fc) at points A, C, and B, respectively. 2. The Effect of Gravitational Force While the effect of this centrifugal force is constant for all positions on the Earth, the effect of an external gravita- tional force produced by another astronomical body may be different at different positions on the Earth because the magnitude of the gravitational force exerted varies with the distance of the attracting body. According to Newton's Universal Law of Gravitation, the force value decreases as the second power of the distance from the attracting body. As a special case, the tide-raising force varies in- versely as the third power of the distance of the center-of- mass of the attracting body from the surface of the Earth. Thus, in the theory of tides, a variable influence is intro- duced based upon the different distances of various posi- tions on the Earth's surface from the Moon's center-of- mass. The relative gravitational attraction (F p ) exerted by the Moon at various positions on the Earth is indicated Appendix 490 The solid and dashed circles represent near equatorial cross sections through the earth, containing the plane of the moon's orbit around the barycenter (G) Points Ej, E 2 . E3. and M ] M- 1 3 . are corresponding positions centers of mass of the earth and moon, respect Earth Moon Figure 1. — The monthly revolution of the Earth and Moon around the Barycenter of the Earth-Moon System. This revo- lution is responsible for a centrifugal force component (F c ) necessary to the production of the tides. in figure 2 by arrows heavier than those representing the centrifugal force components. 3. The Net or Differential Tide-Raising Forces: Direct and Opposite Tides It has been emphasized above that the centrifugal force under consideration results from the revolution of the cen- ter-of-mass of the Earth around the center-of-mass of the Earth-Moon system, and that this centrifugal force is the same anywhere on the Earth. Since the individual centers- of-mass of the Earth and Moon remain in equilibrium at constant distances from the barycenter, the centrifugal force acting upon the center of the Earth (C) as the result of their common revolutions must be equal and opposite to the gravitational force exerted by the Moon on the center of the Earth. This fact is indicated at point C in figure 2 by the thin and heavy arrows of equal length, pointing in opposite directions. The net result of this cir- cumstance is that the tide-producing force (Ft) at the Earth's center is zero. At point A in figure 2, approximately 6,378 km (3,963 mi ) nearer to the Moon than is point C, the force produced by the Moon's gravitational pull is considerably larger than the gravitational force at C due to the Moon (the Earth's own gravity is, of course, zero at point C). The smaller lunar gravitational force at C just balances the centrifugal force at C. Since the centrifugal force at A is equal to that at C, the greater gravitational force at A must also be larger than the centrifugal force there. The net tide-producing force at A obtained by taking the dif- ference between the gravitational and centrifugal forces is in favor of the gravitational component — or outward toward the Moon. The tide-raising force at point A is indicated in figure 2 by the double-shafted arrow extend- ing vertically from the Earth's surface toward the Moon. JIJO Strategic Role of Perigean Spring Tides, 1635-1976 Type of Force Designation Fc = centrifugal force due to earth's revolut around the barycenter on Thin arrow Fg = gravitational force due to the moon Heavy arrow Ft = the resultant tide-raising force due to the moon Double shafted arrow Moon Relative Magnitude of the Forces Present Fg > F c > F, Fg = F c > F e < F r > F t A north-south cross-section through the earth's center in the plane of the moon's hour angle, the dashed ellipse represents a profile through the spheroid composing the tidal force envelope, the solid ellipse shows the resulting effect on the earth's waters. Figure 2. — The combination of forces of lunar origin producing the tides. (A similar complex of forces exists in the Earth-Sun system.) The resulting tide produced on the side of the Earth toward the Moon is known as the direct tide. At point B, on the opposite side of the Earth from the Moon and about 6,378 km farther away from the Moon than is point C, the Moon's gravitational force is consid- erably less than at C. At point C, the centrifugal force is in balance with a gravitational force which is greater than at B. The centrifugal force at B is the same as that at C. Since gravitational force is less at B than at C, it follows that the centrifugal force exerted at B must be greater than the gravitational force exerted by the Moon at B. The resultant tide-producing force at this point is, therefore, directed away from the Earth's center and opposite to the position of the Moon. This force is indicated by the dou- ble-shafted arrow at point B. The tide produced in this location halfway around the Earth from the sublunar point, coincidentally with the direct tide, is known as the opposite tide. 4. The Tractive Force It is significant that the influence of the Moon's gravita- tional attraction superimposes its effects upon, but does not overcome, the effects of the Earth's own gravity. Earth-gravity, although always present, plays no direct part in the tide-producing action. The tide-raising force exerted at a point on the Earth's surface by the Moon at its average distance from the Earth (384,318 km or 238,855 mi) is only about one 9-millionth part of the force of Earth-gravity exerted toward its center (6,378 km from the surface) . The tide-raising force of the Moon, is, therefore, entirely insufficient to "lift" the waters of the Earth physically against this far greater pull of the Earth's gravity. Instead, the tides are produced by that component of the tide-raising force of the Moon which acts to draw the waters of the Earth horizontally over its surface toward the sublunar and antipodal points. Since the horizontal component is not opposed in any way to gravity and can, therefore, act to draw particles of water freely over the Earth's surface, it becomes the effective force in generat- ing tides. At any point on the Earth's surface, the tidal force produced by the Moon's gravitational attraction may be separated or "resolved" into two components of force — the one in the vertical, or perpendicular to the Earth's surface — the other horizontal or tangent to the Earth's Appendix 501 surface. This second component, known as the tractive ( "drawing" ) component of force is the actual mechanism for producing tides. The force is zero at points on the Earth's surface directly beneath and on the opposite side of the Earth from the Moon (since, in these positions, the lunar gravitational force is exerted in the vertical — i.e., opposed to, and in the direction of Earth-gravity, respec- tively) . Any water accumulated in these locations by trac- tive flow from other points on the Earth's surface tends to remain in a stable configuration, or tidal "bulge." Thus, there exists an active tendency for water to be drawn from other points on the Earth's surface toward the sublunar point {A, in fig. 2) and its antipodal point (B, in fig. 2) and to be heaped at these points in two tidal bulges. Within a band around the Earth at all points 90° from the sublunar point, the horizontal or tractive force of the Moon's gravitation is also zero, since the entire tide-producing force is directed vertically inward. There is, therefore, a tendency for the formation of a stable depression here. The words "tend to" and "tendency for" employed in several usages above in connection with tide- producing forces are deliberately chosen since, as will be seen below, the actual representation of the tidal forces at work is that of an idealized "force envelope" within which the rise and fall of the tides are influenced by many factors. 5. The Tidal Force Envelope If the ocean waters were completely to respond to the directions and magnitudes of these tractive forces at vari- ous points on the surface of the Earth, a mathematical figure would be formed having the shape of an oblate spheroid. The longest (major) axis of the spheroid extends toward and directly away from the Moon, and the short- er (minor) axes are centered, and mutually orthogonal to, the major axis. The two tidal humps and two tidal depres- sions are represented in this force envelope by the direc- tions of the major axis and rotated minor axis of the spheroid, respectively. From a purely theoretical point of view, the daily rotation of the solid Earth with respect to these two tidal humps and two depressions may be con- ceived to be the cause of the tides. As the Earth rotates once in each 24 hours, one would ideally expect to find a high tide followed by a low tide at the same place 6 hours later; then a second high tide after 12 hours, a second low tide 18 hours later, and finally a return to high water at the expiration of 24 hours. Such would nearly be the case if a smooth, continent -free Earth were covered to a uniform depth with water, if the tidal force envelope of the Moon alone were being considered, if the positions of the Moon and Sun were fixed and in- variable in distance and relative orientation with respect to the Earth, and if there were no other accelerating or retarding influences affecting the motions of the waters of the Earth. Such, in actuality, is far from the situation which exists. First, the tidal force envelope produced by the Moon's gravitational attraction is accompanied by a tidal force envelope of considerably smaller amplitude produced by the Sun. The tidal force exerted by the Sun is a composite of the Sun's gravitational attraction and a centrifugal force component created by the revolution of the Earth's center-of-mass around the center-of-mass of the Earth-Sun system, in an exactly analogous manner to the Earth- Moon relationship. The position of this force envelope shifts with the relative orbital position of the Earth in respect to the Sun. Because of the great difference between the average distances of the Moon (384,400 km or 239,000 mi) and Sun (149,500,000 km or 92,900,000 mi) from the Earth, the tide-raising force of the Moon is approximately 2j4 times that of the Sun. Second, there exists a wide range of astronomical vari- ables in the production of the tides caused by the changing distances of the Moon from the Earth, the Earth from the Sun, the angle which the Moon in its orbit makes with the Earth's Equator, the superposition of the Sun's tidal en- velope of forces upon that caused by the Moon, the vari- able phase relationships of the Moon, etc. Some of the principal types of tides resulting from these purely astro- nomical influences are described below. Variations in the Range of the Tides : Tidal Inequalities As will be shown in figure 6, the difference in height, in meters or feet, between consecutive high and low tides occurring at a given place is known as the range. The range of tides at any one location is subject to many variable factors. Those influences of astronomical origin will first be described. 1. Lunar Phase Effects: Spring and Neap Tides It has been noted above that the gravitational forces of both the Moon and Sun act upon the waters of the Earth. It is also obvious that, because of the Moon's changing position with respect to the Earth and Sun (figure 3) during its monthly cycle of phases ( 29.53 days) , the gravi- tational attraction of Moon and Sun may variously act along a common line or at changing angles relative to each other. When the Moon is at new phase and full phase (both positions being called syzygy) the gravitational attractions of Moon and Sun act to reinforce each other. Since the 302 Strategic Role of Perigean Spring Tides, 1635-1976 First Quarter Looking down on the north pole of the earth's figure (central solid circle). The two solid ellipses represent the tidal force envelopes produced by the moon in the positions of syzygy (new or full moon) and quadrature (first or third tidal force envelope produced by the sun To Sun Third Quarter The gravitational attractions (and resultant tidal force envelopes) produced by the moon and sun reinforce each other at times of new and full moon to increase the range of the tides, and counteract each other at first and third quarters to reduce the tidal range. Figure 3. — The phase inequality; spring and neap tides. resultant or combined tidal force is also increased, the observed high tides are higher and low tides are lower than average. This means that the tidal range is greater at all locations which display a consecutive high and low water. Such greater-than-average tides resulting at the syzygy positions of the Moon are known as spring tides — a term which merely implies a "welling up" of the water and bears no relationship to the season of the year. At first- and third-quarter phases (quadratures) of the Moon, the gravitational attractions of the Moon and Sun upon the waters of the Earth are exerted at right angles to each other. Each force tends in part fo counteract the other. In the tidal force envelope representing these com- bined forces, both the maximum and minimum force values are reduced. High tides are lower and low tides are higher than average. Such tides of diminished range are called neap tides, from a Greek word meaning "scanty." 2. Parallax Effects (Moon and Sun) Since the Moon follows an elliptical path ( figure 4 ) , the distance between the Earth and Moon will vary through- out the month by about 49,900 km (31,000 mi). The Moon's gravitational attraction for the Earth's water will change in inverse proportion to the third power of the dis- tance between Earth and Moon, in accordance with the previously mentioned extension of Newton's Law of Grav- itation. Once each month, when the Moon is closest to the Earth (perigee), the tide-generating forces will be higher than usual, thus producing above-average ranges in the tides. Approximately 2 weeks later, when the Moon (at apogee) is farthest from the Earth, the lunar tide-raising force will be smaller, and the tidal ranges will be less than average. Similarly, in the Sun-Earth system, when the Earth is closest to the Sun (perihelion), about January 2 of each year, the tidal ranges will be enhanced, and when the Earth is farthest from the Sun (aphelion), around July 2, the tidal ranges will be reduced. When perigee, perihelion, and either the new or full moon occur at approximately the same time, considerably increased tidal ranges result. When apogee, aphelion, and the first- or third-quarter moon coincide at approximately the same time, considerably reduced tidal ranges will normally occur. Appendv rm Aphelion (July 2) Common projection of the earth's orbital plane around the sun (the ecliptic) and the moon's orbital plane around the earth S =Sun E, = Earth at perihelion (Jan 2) E 2 = Earth at aphelion (July 2) M[ = Moon at perigee M 2 =Moon at apogee Earth's Orbit Perihelion (Jan. 2) Figure 4. — The lunar parallax and solar parallax inequalities. Both the Moon and the Earth revolve in elliptical orbits and the distances from their centers of attraction vary. Increased gravitational influences and tide-raising forces are produced when the Moon is at a position of perigee, its closest approach to the Earth (once each month) or the Earth is at its perihelion, its closest approach to the Sun (once each year) . This diagram also shows the possible coincidence of perigee with perihelion to produce tides of augmented range. 3. Lunar Declination Effects: The Diurnal In- equality The plane of the Moon's orbit is inclined only about 5° to the plane of the Earth's orbit (the ecliptic) and thus the Moon in its monthly revolution around the Earth remains within 28.5° of the Earth's Equator, north and south of which the Sun moves once each half year to produce the seasons. In a similar fashion, the Moon in making a revo- lution around the Earth once each month, passes from a position of maximum angular distance north of the Equa- tor to a position of maximum angular distance south of the Equator during each half month. (Angular distance perpendicularly north or south of the celestial equator is termed declination. ) Twice each month, the Moon crosses the Equator. In figure 5, this situation is shown by the dashed outline of the Moon. The corresponding tidal force envelope due to the Moon is depicted, in profile, by the dashed ellipse. Since the points A and A' lie along the major axis of this ellipse, the height of the high tide represented at A is the same as that which occurs as this point rotates to position A' some 12 hours later. When the Moon is over the Equator — or at certain other force-equalizing declina- tions — the two high tides and two low tides on a given day are similar in height at any location. Successive high tides and low tides are then also nearly equally spaced in time, and occur uniformly twice daily. (See top diagram in fig. 6. ) This is known as the semidiurnal type of tides. Factors Influencing the Local Heights and Times of Arrival of the Tides It is noteworthy in figure 6 that any one cycle of the tides is characterized by a definite time regularity as well as the recurrence of the cyclical pattern. However, con- tinuing observations at coastal stations will reveal — in addition to the previously explained variations in the heights of successive tides of the same phase — noticeable differences in their successive times of occurrence. The aspects of regularity in the tidal curves are introduced by the harmonic motions of the Earth and Moon. The varia- tions noted both in the observed heights of the tides and in their times of occurrence are the result of many factors, some of which have been discussed in the preceding sec- tion. Other influences will now be considered. The Earth rotates on its axis (from one meridian transit of the "mean sun" until the next) in 24 hours. But as the Earth rotates beneath the envelope of tidal forces pro- duced by the Moon, another astronomical factor causes the time between two successive upper transits of the Moon across the local meridian of the place (a period ',04 o Moon (at high declination) Strategic Role of Perigean Spring Tides, 1635-1976 A north-south cross-section through the earth's center; the ellipse represents a meridian section through the tidal force envelope pro duced by the moon -JVC (Diurnal Tide) Moon (directly over the equator) (Mixed Tide) j (Semidiurnal Tide - Equatorial Type) Earth Figure 5. — The Moon's declination effect (change in angle with respect to the Equator) and the diurnal inequality. The effects of the diurnal inequality in introducing semidiurnal, mixed, and diurnal harmonic constituents in the tides are also shown. (Compare with fig. 6.) known as the lunar or "tidal" day) to exceed the 24 hours of the Earth's rotation period — the mean solar day. The Moon revolves in its orbit around the Earth with an angular velocity of approximately 12.2° per day, in the same direction in which the Earth is rotating on its axis with an angular velocity of 360° per day. In each day, therefore, a point on the rotating Earth must com- plete a rotation of 360° plus 12.2°, or 372.2°, in order to "catch up" with the Moon. Since 15° is equal to one hour of time, this extra amount of rotation equal to 12.2° each day would require an extra period of time equal to 1 2.2 7 1 5 ° X 60 m/h , or 48.8 minutes— if the Moon revolved in a circular orbit, and its speed of revolution did not vary. On the average it requires about 50.415 minutes addi- tional each day for a sublunar point on the rotating Earth to regain this position directly along the major axis of the Moon's tidal force envelope, where the tide-raising influ- ence is a maximum. In consequence, the recurrence of a tide of the same phase and similar height (see middle diagram of figure 6) would take place at an interval of 24 hours 50 minutes after the preceding occurrence, if this single astronomical factor known as lunar retardation were considered. This average period of 24 hours 50 min- utes has been established as the tidal day, but its wide variations form an important aspect of the present monograph. A second astronomical factor influencing the time of arrival of tides of a given phase at any location results from the interaction between the tidal force envelopes of the Moon and Sun. Between new moon and first-quarter phase, and between full moon and third-quarter phase, this phenomenon can cause a displacement of force com- ponents and acceleration in tidal arrival times (known as priming of the tides) resulting in the occurrence of high tides before the Moon itself reaches the local meridian of the place. Between first-quarter phase and full moon, and between third-quarter phase and new moon, an opposite displacement of force components and a delaying action (known as lagging of the tides) can occur, as the result of which the arrival of high tides may take place several hours after the Moon has reached the meridian. These are the two principal astronomical causes for variation in the times of arrival of the tides. In addition to these astronomically induced variations, the tides are subject to other accelerating and retarding influences of hydraulic, hydrodynamic, hydrographic, and topographic origin — and may further be modified by meteorological conditions. The first factor of consequence in this regard arises from the fact that the crests and troughs of the large-scale, gravity-type, traveling wave formations comprising the tides strive to sweep continuously around the Earth, fol- lowing the position of the Moon (and Sun). In the open ocean, the actual rise (see middle diagram, figure 6 ) of the tidally induced wave crest is only one to a few feet. It is only when the tidal crests and troughs move into shallow water, against land masses, and into confining channels, that noticeable variations in the height of the water level can be detected. Possessing the physical properties of a fluid, the ocean waters follow all of the hydraulic laws of fluids. This means that since the ocean waters possess inertia and a Appendix Distribution of Tidal Phases . r )0:> Tida Day Tidal Period Tidal Period 3 2 1 1 2 3 A \ \ / Dal um \ \ V SEMIDIURNAL TIDE Tidal Period Tidal Day ^Higher \Hieh Lower High Wator f Tic Ri \ Water ial\ se \ f, \ \ 1 i \ \ Datum / Tidal L_ Range ^ Rar ial \ Hig her Vater lge Tidal \ Low \ Amplitude \^ \^ / Lower Low Water MIXED TIDE Tidal Day Tidal Period N S \ / Datum / \ — ' ^/ ^ — DIURNAL TIDE Figure 6. — The Principal types of tides. ■m Strategic Role of Perigean Spring Tides, 1635-1976 definite, small internal viscosity, both properties prevent their absolutely free flow, and somewhat retard the over- all movement of the tides. Secondly, the ocean waters follow the principles of traveling waves in a fluid. As the depth of the water shallows, the speed of forward movement of a traveling wave is retarded, as deduced from dynamic considera- tions. In shoaling situations, therefore, the advance of tidal waters is slowed. Thirdly, a certain relatively small amount of friction exists between the water and the ocean floor over which it moves — again slightly slowing the movement of the tides, particularly as they move inshore. Further internal friction (or viscosity) exists between tidally induced cur- rents and contiguous currents in the ocean — especially where they are flowing in opposite directions. The presence of land masses imposes a barrier to prog- ress of the tidal waters. Where continents interpose, tidal movements are confined to separate, nearly closed oceanic basins and the sweep of the tides around the world is not continuous. Topography on the ocean floor can also provide a re- straint to the forward movement of tidal waters — or may create sources of local-basin response to the tides. Restric- tions to the advance of tidal waters imposed both by shoaling depths and the sidewalls of the channel as these waters enter confined bays, estuaries, and harbors can further considerably alter the speed of their onshore passage. In such partially confined bodies of water, so-called '"resonance effects" between the free-period of oscillation of the traveling, tidally induced wave and that of the confining basin may cause a surging rise of the water in a phenomenon basically similar to the action of water caused to "slosh" over the sides of a washbasin by re- peatedly tilting the basin and matching the wave crests reflected from opposite sides of the basin. All of the above, and other less important influences, can combine to create a considerable variety in the ob- served range and phase sequence of the tides — as well as variations in the times of their arrival at any location. Of a more local and sporadic nature, important meteor- ological contributions to the tides known as "storm surges," caused by a continuous strong flow of winds either onshore or offshore, may superimpose their effects upon those of tidal action to cause either heightened or dimin- ished tides, or active coastal flooding. High pressure at- mospheric systems may also depress the tides, and deep low pressure systems may cause them to increase in height. Prediction of the Tides In the preceding discussions of the tide-generating forces, the theoretical equilibrium tide produced, and fac- tors causing variations, it has been emphasized that the tides actually observed differ appreciably from the ideal- ized, equilibrium tide. Nevertheless, because the tides are produced essentially by astronomical forces of harmonic nature, a definite relationship exists between the tide- generating forces and the observed tides, and a factor of predictability is possible. Because of the numerous uncertain and, in some cases, completely unknown factors of local control mentioned above, it is not feasible to predict tides purely from a knowledge of the positions and movements of the Moon and Sun obtained from astronomical tables. A partially empirical approach based upon actual observations of tides in many areas over an extended period of time is necessary. To achieve maximum accuracy in predictions, a series of tidal observations at any one location ranging over at least a full 18.6-year tidal cycle is required. Within this period, all significant astronomical modifications of tides will occur. Responsibility for computing and tabulating — for any day in the year — the times, heights, and ranges of the tides — as well as the movement of tidal currents in various parts of the world is vested in appropriate governmental agencies which devote both theoretical and practical effort to this task. The resulting predictions are based in large part upon actual observations of tidal heights made throughout a network of selected observing stations. The National Ocean Survey, a component of the Na- tional Oceanic and Atmospheric Administration of the U.S. Department of Commerce, maintains for this pur- pose a continuous control network of approximately 140 tide gages at fixed stations as illustrated in figure 7. These are located along the coasts and within the major embay- ments of the United States, its possessions, and United Nations Trust Territories under its jurisdiction. Tempo- rary secondary stations are also occupied in order to increase the effective coverage of the control network. Tital data are recorded on chart rolls (figure 8), on punched tape (figure 9) , and are translated onto punched cards or magnetic tape (figure 10) for electronic com- puter processing, tabular printout, and analysis. Predictions of the times and heights of high and low water are published by the National Ocean Survey for a large number of stations in the United States and its possessions as well as in foreign countries and United Nations Trust Territories. These predictions are published Appendix 507 each year (approximately 6 months or more in advance) in four volumes. The titles are : Tide Tables — High and Low Water Predictions ( 1 ) East Coast of North and South America, Including Greenland; (2) Europe and West Coast of Africa, Including the Mediterranean Sea; ( 3 ) West Coast of North and South America, Including the Hawaiian Islands; and (4) Central and Western Pacific Ocean, and Indian Ocean. Predictions of tidal currents are published annually in two volumes, titled: Tidal Current Tables (1) Atlantic Coast of North America; and (2) Pacific Coast of North America and Asia. Although for many years tidal data were calculated by the use of a special harmonic-constant tide-predicting machine developed within the National Ocean Survey, the daily predictions published in these tide tables and tidal current tables are now handled through high-speed auto- matic data-processing equipment, especially programmed to handle the mathematical evaluation of tidal information. Figure 7. — The NOS tide station on Padre Island, near Port Isabel, Tex. -)im Strategic Role of Perigean Spring Tides, 1635-1976 Figure 8. — A pressure-recording tide-gage system consisting of: (A) a gas bubbler (background) which senses the tide level by variation of hydrostatic pressure with changing height of the water above the remote, submerged orifice of the tide gage, and (B) a chart recorder or marigraph (center) which traces the water height against time. The resulting marigram trace is run through a marigram scanner, which yields a printout tabulation of hourly tidal heights. Appendix 50"'; Figure 9, — Tidal heights sensed by the float in a tide well are punched on a paper tape in a standard digital (binary-coded decimal) form by the instrument in the center foreground. -509 O - 78 - 35 510 Strategic Role of Perigean Spring Tides, 1635-1976 Figure 10. — By means of the converter unit (center) the tidal data already punched on tape (right) are transferred onto punched cards (left) which are then fed into an electronic computer for printout, tabulation, and subsequent analysis. Reference Sources and Notes Part I CHAPTER 1 1. William Bradford, Of Plymouth Plantation, 1620-1647, the complete text, with notes and introduction by Samuel Eliot Morison, new ed., New York, 1952, pp. 279-80. 2. Nathaniel Morton, New-Englands memoriall: or, A Brief relation of the most memorable and remarkable passages of the provi- dence of God, manifested to the planters of New-England in America; with special reference to the first Colony thereof, called New-Plimouth. Cambridge, Mass., 1669, pp. 102-3. 3. John Winthrop, The History of New England from 1630 to 1649 . . . From his original manuscripts . . . With notes . . . by James Savage. A new edition (2 vols.) . . . Boston, Mass., 1853, vol. I, pp. 195-8. Also: Winthrop' s Journal, "History of New England," 1630-1649, edited by James Kendall Hosmer, 2 vols., New York, 1908 [entry for August 16, 1635]. Sidney Perley, Historic Storms of New England, Salem, Mass., 1891, pp. 3-10. Edward Rowe Snow, Great Storms and Famous Shipwrecks of the New England Coast, Boston, Mass., 1943, pp. 34-6. 4. Gordon E. Dunn and Banner I. Miller, Atlantic Hurricanes (rev. ed.) Baton Rouge, La., 1964, p. 308; also pp. 308-362. 5. David M. Ludlum, Early American Hurricanes, 1492-1870, Boston, Mass., 1963, pp. 10-13. Also: Dunn and Miller, op. cit., pp. 204, 272-3. 6. Edward Rowe Snow, op. cit., pp. 59-60. [Quoting a letter titled "Tide and Storm of Uncommon Circumstances," from the Reverend Cotton Mather in Boston to Dr. John Woodward of the Royal Society in London.] 7. Boston News-Letter (New England weekly) of February 21-28, 1723 (O.S.), p. 2, col. 2. [See also under this date in table 5.] 8. The Boston Gazette and Country Journal of December 11, 1786 (N.S.), No. 1690, p. 3, col. 1. [See also under this date in table 5.] 9. Edward Rowe Snow, op. cit., pp. 81-6. Also: Sidney Perley, op. cit., pp. 124—8. David M. Ludlum, Early American Winters I, 1604-1820, Boston, Mass., 1966, pp. 70-1. 10. The New Hampshire Gazette, Portsmouth, N.H., March 30, 1830, p. 2, col. 2. Also: Sidney Perley, op. cit., pp. 249-51. 11. Sidney Perley, op. cit., pp. 302-10. 12. Edward Rowe Snow, op. cit., pp. 128-38. 13. U.S. Weather Bureau [now the National Weather Service, NOAA], Monthly Weather Review, vol. 38, No. 1 (January 1910), Washington, D.C., p. 4. 14. Ivan Ray Tannehill, Hurricanes (9th ed.) Princeton, N.J., 1956, pp. 141-263, 283-295E. CHAPTER 2 1. Howard I. Chappelle, The History of the American Sailing Navy, The Ships and Their Development, New York, 1949, p. 74. Louis F. Middlebrook, History of Maritime Connecticut During the American Revolution, 1775-1783, Salem, Mass., 1925, vol. 1, p. 204. M. V. Brewington, "The Designs of Our First Frigates," in The American Neptune, vol. VIII, No. 1 (January 1948), p. 20. 2. William James Morgan, ed., Naval Documents of the American Revolution, Washington, D.C., vol. 6, 1972, p. 654. Louis F. Middlebrook, op. cit., vol. II, p. 265. M. V. Brewington, op. cit., p. 24. Pennsylvania Evening Post, September 7, 1776. 3. M. V. Brewington, op. cit., pp. 15, 20. 4. Charles J. Hoadly, ed., The Public Records of the Colony of Connecticut, vol. XIII, May 1768 to May 1772, Hartford, Conn., 1885. [Map opposite p. 503: a reduced heliotype copy of a tracing of Capt. Parker's Chart of Saybrook Barr, prepared by Charles Burdette, 1885. The original map is in the possession of the Connecticut Historical Society.] 5. Lawrence J. Wroth, Abel Buell of Connecticut, Middletown, Conn., 1958, p. 62. 6. Thomas R. Harlow, "Connecticut Engravers, 1774-1820," in quarterly Bulletin of the Connecticut Historical Society, vol. 36, No. 4 (October 1971), p. 101. 7. Refer to the first paragraph of the resolution ordered by the Governor and Council of Safety of the State of Connecticut in response to an authorization by the Congress of the United States, as quoted in the present text (reference No. 16). 8. Compare the activities of John Deshon (member of the Eastern Navy Board) in this regard, as quoted from the Colonial Records of Connecticut in the present text (reference No. 14); see also the extract from a letter written by William Vernon, a member of the same Navy Board, on March 25, 1778, quoted in Gardner W. Allen, A Naval History of the American Revolution (reprint of 1913 ed.) 2 vols., New York, 1962, vol. I, p. 307. 511 512 Strategic Role of Perigean Spring Tides, 1635-1976 9. Gardner W. Allen, op. cit., vol. I, p. 362. William Bell Clark, ed., Naval Documents of the American Revolution, Washington, D.C., vol. 2, 1966, p. 498. 10. Entry for the date August 1 1, 1779, in the diary of Samuel Tully of Saybrook Point, Conn., excerpted in History of Middlesex County, Connecticut, with Biographical Sketches of Its Prominent Men, New York, 1884, p. 468. Also, Gardner W. Allen, op. cit., vol. II, p. 498. 1 1. Letter to the author from Thomas A. Stevens, historian of the Connecticut River, dated January 30, 1975. [The following information was added in press, with the issuance of volume 7 of Naval Documents of the American Revolution. William James Morgan, editor, Naval History Division, Department of the Navy, Washington, D.C., 1976.] Precise contemporary documentation of the Revolutionary War period newly available in this volume confirms several stated opinions with regard to: (1) the date of the TrumbulFs passage down the Connecticut River; (2) the necessity of an extraordinarily high tide to permit the Trumbull to clear the rivermouth bar; and (3) other tactical circumstances associated with the British attack on the Colonies which could well have prevented the Trumbull's use of intervening perigean spring tides between November 1776 and August 1779 to good advantage. John Cotton, shipbuilder of the Trumbull (launched near Middletown, Conn.) wrote to Barnabas Deane, the Continental Navy's designated authority for supervision of ship construction (himself resident at Wethersfield, Conn.) under the date November 18, 1776. In this letter, the former asks for disposition of shipbuilding stores not used, and concludes with a statement of the ship's imminent readiness to make the trip down the Connecticut River: "Sir/ Middletown Novbr 18th 1776 — When Capn. [Dudley] Saltonstall went away to Wethersfield I had forgott that you had pork Stored with Tewels Butt Desired him to a Quaint you that that pork left with Cooper was taken away, I shall take outt of Tewels Store two Barrels and putt on Board the Ship — I would be Glad if you Could hire and Send Down a Vessell to Take our Matters from the Ship yd Before we Go a way with the Ship as I Dont Like to Leave them there for fear of a Loss in Some Things that is Much Wanted Especialy Pitch — Nothing further, the Ship Will be Ready to Goe Down Tomorrow Or Next Day Yr[&c] John Cotton." [Morgan, op. cit., p. 197] In a footnote to a second communication sent on the following day, Cotton notes that the ship has not left yet, and indicates a dependence on high tides in the tidewater river. [Full moon and spring tides would have occurred around the date November 23, which is within the proposed week for "going down" to which Cotton refers. A close perigee-syzygy alignment (P — S = — 5 h ) already had occurred on September 27, 1776, with a mean epoch of 8:30 a.m., 75°W. -meridian time.] "Sir/ Middletown Novbr 19th 1776 I Wrote to Aquaint you that I have Taken to blls of Your Pork for the Ship Which was in Tewels Store Capn [Dudley] Saltonstall Desires that I would have You Send Down Some Coffee and Sugar and Chocolate if you have Any for the Ships Stores Round to New london What Other he wants I shall Endeavor to Gett here, and the above if they are to be Gott here if they Are they [are] Extravagant the prices Being high, as people are So Exceeding high in their prices they Know well Nott to ask if you have any Spare Bags I Could wish you Would Send Down V 2 Dozen as the Ship Wants them and the Capn Mentioned itt To Me I am Sir With Regards [Ac] John Cotton" yrsJ-C." [Morgan, op. cit., p. 209] N B The Ship Must Goe away this Week if the Tides Rises In a letter from Barnabas Deane to John Hancock datelined "Wethersfield 25th Jany 1777" Deane wrote to the chair- man of the Continental Marine Committee as follows: "Sir The Trumbull Frigate under my Direction Proceeded down Connecticut River the Last of Novr and when She had got within a few miles of the Rivers mouth Two of the Enemys Frigates Appear'd of[f] the River & kept that Station untill the River Froze, I Advisd with Govr Trumbull & his Opinion was to Lay the Frigate up in Some Safe Creek which I did about Twenty miles from the Rivers mouth — Capt Manly CalPd on me with a Letter from Govr Trumbull (a Copy of which you have on the Other Side) And Agreeable to his Advice I have Supply'd Capt Manly with the Trumbulls Cannon which I hope will be Agreeable to the Honble Congress; Govr Trumbull has Engaged that the First Cannon made After the Furnace in this State begins Again to Cast Shall be for to Replace those Supply'd Capt Manly with I am Respectfully [&c. ] Bar 8 Deane" [Morgan, op. cit., p. 1036] Reference Sources and Notes 513 It is significant in terms of the draft of the Trumbull at the time she cleared Saybrook Bar that the ship's cannon were still lacking on September 7, 1779, a month after the vessel left the river mouth. [Cf., Charles O. Paullin, ed. Out-Letters to the Continental Marine Committee and Board of Admiralty, August 1776-September 1780, New York, 1924, vol. 2, pp. 106-115.] The Trumbull therefore was not encumbered with this extra load of armament on crossing the bar. A further meaningful letter was transmitted from Nathaniel Shaw, Jr., Continental agent at New London, Conn., to Robert Morris, Chairman of the Secret Committee of the Continental Congress in Philadelphia, datelined "New London Feb 4 1777." This contains the following confirmatory information regarding the situation of unusually high tide required to permit clearance of Saybrook Bar by the frigate Trumbull: "... I have and shall Continue to supply Capt [Dudley] Saltonstall with what money he may want to get his ship out, at present she is in Connecticut River and am fearful we shall meet with Difficulty in getting her out as she draws so much water, it must be a very extraordinary tide to get her over the Barr, and in case she lies any time on the barr, as the British Ships are Continually passing they may take that opportunity to Destroy her, however you may depend that the greatest prudence will be observed — the Sale of the prize Ship Clarendon taken by the Cabot is not compleated soon as it can be effected shall send the Accot . . ." [Morgan, op. cit., p. 1103] 12. Henry P. Johnson, ed., The Record of Connecticut Men in the Military and Naval Service During the War of the Revolution, 1775-1783, Hartford, Conn., 1889, pp. 598-9. 13. Charles Oscar Paullin, The Navy of the American Revolution, Cleveland, Ohio, 1906. p. 526. 14. Charles J. Hoadly, ed., The Public Records of the State of Connecticut, vol. I, October 1776 to February 1778, Hartford, Conn., 1894, p. 113. 15. Ibid., pp. 517-18. 16. Ibid., pp. 567-8. 17. Ibid., p. 569. 18. Charles J. Hoadly, op. cit., vol. II, May 1778 to April 1780, Hartford, Conn., 1895, p. 499. 19. William James Morgan, ed., op. cit., vol. 6, 1972, pp. 322, 350, 360, 706, 759, 763, 892, 949, 1178, 1218-19, and especially p. 1220. 20. Ibid., p. 323. History of Middlesex County, Conn., loc. cit. 21. Samuel Adams Drake, Nooks and Corners of the New England Coast, New York, 1875, pp. 447-8. 22. Gardner W. Allen, op. cit., vol. II, p. 498. 23. Henry Steele Commager and Richard B. Morris, eds., The Spirit of 'Seventy-Six — The Story of the American Revolution as Told by Participants, New York, 1967, p. 956. 24. Charles J. Hoadly, op. cit., vol. XV, p. 206. 25. Ibid., pp. 238-9. 26. John Hamilton Moore, The New Practical Navigator, Being an Epitome of Navigation . . ., 12th ed., London, 1796, p. 133. 27. Howard I. Chappelle, loc. cit. Cf., also: M. V. Brewington, op. cit., pp. 15, 20. 28. Gardner W. Allen, op. cit., vol. II, p. 494 29. Frank Moore, compiler, and John Anthony Scott, ed., The Diary of the American Revolution, 1775-1781, New York, 1967, p. 412. 30. Loc. cit. 31. Letter from A. W. H. Pearsall, Historian, National Maritime Museum, Greenwich, England, to the author, dated November 4, 1974. 32. U.S. Navy Department, Official Records of the Union and Confederate Navies in the War of the Rebellion, series I, vol. 12, Washington, D.C., 1901, pp. 259-261. Virgil Carrington James, The Civil War at Sea, 3 vols., New York, 1960, vol. I, pp. 266-73. 33. Report of Assistant C. O. Boutelle, aboard U.S. Coast Survey Steamer Vixen at Port Royal Bay, S.C., November 8, 1861, in Appendix No. 31 of the annual Report if the Superintendent of the Coast Survey for 1861, Washington, D.C., 1862, p. 267. 34. Virgil Carrington James, op. cit., vol. I, p. 274. 35. Ibid., pp. 274-5. 36. Verified by Ships' Histories Branch, Naval History Division, U.S. Navy Department, Washington, D.C. 37. U.S. Navy Department, op. cit., series II, vol. 1, Washington, D.C, 1921, p. 234. 38. Annual Report of the Superintendent of the Coast Survey for 1847, Washington, D.C, 1847, p. 37; also Appendix No. 13, p. 77. 39. Ibid., in Appendix No. 13, pp. 76-7. 40. Ben Dixon McNeill, The Hatterasman, Winston-Salem, N.C, 1958, pp. 138, 282. 41. Virgil Carrington James, op. cit., vol. I, pp. 197-8. 42. Gary S. Dunbar, Historical Geography of the North Carolina Outer Banks (Louisiana State University, coastal studies series No. 3), Baton Rouge, La., 1958, pp. 28, 139. 43. Frank M. Bennet, The Steam Navy of the United States, Pittsburgh, Pa., 1896, p. 242. 514 Strategic Role of Perigean Spring Tides, 1635-1976 CHAPTER 3 1. Hubert Shirley Smith, The World's Great Bridges, 1st. ed.. New York, 1953, pp. 79-80. 2. David B. Steinman and Sara R. Watson, Bridges and Their Builders (reprint of 1941 ed.), New York, 1957, pp. 255-6. [Note: In connection with the perigean spring tide incident involving the Firth of Forth Bridge mentioned in the text of the present work, an explanatory detail is desirable. An obvious discrepancy occurs between the date of this happening ("New Year's Day of 1884") specified in the above-cited reference source and the date (May 26, 1884) given as that of the first actual constructional work, including caisson launching and implanting, in the immediately preceding paragraph of this same source. This inconsistency must also be considered against the confirmatory mention of an unusually high and low tide on the day of the accident — and the date (October 19, 1885) of subsequent surfacing of the caisson for the northwest corner of the Queensferry pier after its plunge to the bottom. Together, these evidences clearly indicate that the printed date for the accident should read "New Year's Day of 1885" instead of 1884.] 3. Ibid., p. 152. 4. F. D. Bickel. "Demolition of Ripple Rock," in The Military Engineer, vol. 51, No. 341 (May-June 1959), pp. 173-7. Jim Gibbs, Disaster Log of Ships, New York, 1971, pp. 105-114. [For April 7, 1958 in this article read April 5, 1958, and for Maude Island and Maude Inlet, read Maud Island and Maud Inlet, respectively.] Business Week, "Tunneling Under Sea to Blast Channel Clear," March 29, 1958, pp. 78-80; "The Big Bang at Ripple Rock," April 19, 1958, p. 42. 5. Will F. Thompson and Julia Bell Thompson, "The Spawning of the Grunion," State of California Fish and Game Commission, Fish Bulletin No. 3, Sacramento, Calif., July 15, 1919, pp. 1-29. CHAPTER 4 1 . Johann Kepler, Astronomia Nova seu de Motu Stellae Martis, in Joannis Kepleri Astronomi Opera Omnia, edited by Dr. Christian Frisch, vol. II, Frankfurt, Germany, 1859, p. 313. 2. Francis S. Benjamin, Jr. and G. J. Toomer, eds., Campanus of Novara [Campano Novarese] and Medieval Planetary Theory: Theorica planetarum, Madison, Wis., 1971, pp. 44-5, 175-7, 181, 377. 3. Royal Society Letter Book, C. 1, No. 4, "A Letter of Mr. Joseph Childrey to the Right Reverend Seth Lord [Bishop of Sarum] concerning some Animadversions upon the Reverend Dr. John Wallis's Hypothesis about the Flux and Reflux of the Sea, publish't No. 16 of these Tracts"; letter dated March 31, 1669/1770, Philosophical Transactions of the Royal Society, vol. 5, No. 64 (October 1670), pp. 2061-8. Also: Joshua Childrey, Syzygiasticon Instauratum. Or, An Ephemeris of the Places and Aspects of the Planets, as they respect the Sun as Center of their Orbes, Calculated for the Tear of the Incarnation of God, 1653, London, 1653. 4. Florian Cajori, ed., Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World. Translated from the Latin by Andrew Motte in 1729 [from the 3d ed. of Newton's Philosophiae natural is principia mathematica, etc. of 1726]. The translations revised, and supplied with an historical and explanatory appendix by Florian Cajori (2d printing) Berkeley, Calif., 1946, p. 479. 5. The Mathematical Principles of Natural Philosophy, by Sir Isaac Newton, translated into English by Andrew Motte, etc., care- fully revised and corrected by W. Davis, in three volumes, vol. Ill, London, 1803, pp. 241, 243. Also: Sir Isaac Newton's Principia (original Latin edition) reprinted for Sir William Thomson and Hugh Blackburn, Glasgow, 1861, pp. 465, 467. 6. Encyclopaedia Britannica, or a Dictionary of Arts and Sciences Compiled Upon a New Plan, etc., by a Society of Gentlemen in Scodand in three volumes, vol. I, Edinburgh, Scotland, 1771, p. 474. 7. John Hamilton Moore, The New Practical Navigator, etc., being an Epitome of Navigation, 12th edition, London, 1796, p. 133. 8. John Hamilton Moore, loc. cit. 9. D. L. Hutchinson, "The Saxby Gale," in Transactions of the Canadian Institute, vol. IX (1911), Toronto, 1913, p. 256. 10. David M. Ludlow, Early American Hurricanes, 1492-1870, Boston, 1963, pp. 108-111. 11. D. L. Hutchinson, op. cit., pp. 253-5. 12. Ibid., p. 259. 13. William Ferrell, "Report of Meteorological Effects on Tides," in the annual Report of the Superintendent of the Coast Survey for 1871, Appendix No. 6, Washington, D.C., 1874, p. 98. [Note: The sketch No. 38 referred to in the passage here quoted directly from the text of the article is a typographical error in the original publication and should read "Sketch No. 34."] 14. Horace Lamb, Hydrodynamics, 1st American printing of British 6th ed. (1932), New York, 1945, pp. 353-355. 15. William Thomson Kelvin and Peter G. Tait, Treatise on Natural Philosophy, 2 vols., Cambridge, England, 1923, article 60 [reprinted as Principles of Mechanics and Dynamics, New York, 1962]. 16. George B. Airy, Treatise "On Tides and Waves," in Encyclopaedia of Astronomy, London, 1848, vol. 5, p. 362, article 459 [re- printed from Encyclopaedia Metropolitana, London, 1845, vol. 5, p. 362]. 17. Hermann L. F. von Helmholtz, Lehre von den Tonemfindungen, 2d ed., Braunschwerg, Germany, 1870, p. 622. Reference Sources and Notes 515 Part II CHAPTER 3 1. Paul Schureman, Manual of Harmonic Analysis and Prediction of Tides. National Ocean Survey (formerly U.S. Coast and Geodetic Survey) Special Publication No. 98, rev. (1940) ed., reprinted 1958 with corrections; 2d printing 1971. U.S. Government Printing Office, Washington, D.C., 1971, pp. 170-171. 2. Hugh Godfray, An Elementary Treatise on the Lunar Theory (3d ed., revised) Macmillan and Co., New York, 1871, p. 64. The historical development of the theories of lunar evection, variation, and other solar-induced perturbational terms since the time of Newton can be traced through the following sources: (a) Sir Isaac Newton, Mathematical Principles of Natural Philosophy and His System of the World, translated (from Latin) into English by Andrew Motte in 1729 (from the 3d ed. of 1726); the translations revised, and supplied with an historical and explanatory appendix by Florian Cajori. University of California Press, Berkeley, Calif. (2d printing), 1946. Book I : The Motions of Bodies, Proposition LXVI, Theorem XXVI, pp. 173-182; also Book III: The System of the World, Proposition XXII, Theorem XVIII, pp. 433-434. (b) Roger Long, Astronomy, in Five Books, Cambridge, England, 1764. Book 4, volume II, chapter 4: The Irregularities of the Moon's Motion Caused by the Attraction of the Sun, pp. 620-629, sections 1441-1458. (c) Ferdinand R. Hassler, A Popular Exposition of the System of the Universe, G. & C. Carvill, New York, 1828. Part III, chapter III, pp. 88-94. (d) John Gummere, An Elementary Treatise on Astronomy, in Two Parts, revised by E. Otis Kendall (4th ed.) E.C. &J. Biddle, Philadelphia, Pa., 1851. Chapter XXII, pp. 209-214, sections 404-407. (e) Ernest W. Brown, An Introductory Treatise on the Lunar Theory, Cambridge University Press, London, England, 1896 (reprinted by Dover Publications, New York, 1960), pp. 124-130. (f) Carnegie Institution of Washington (Publication No. 9), The Collected Mathematical Works of George William Hill, in four volumes, Carnegie Institution of Washington, Washington, D.C. 1905-1907. Volume I, memoir No. 29 — On the Part of the Motion of the Lunar Perigee Which Is a Function of the Mean Motions of the Sun and Moon, pp. 243-270; volume I, memoir No. 32 — Researches in the Lunar Theory, chapter II: Determination of the Inequalities Which Depend Only on the Ratio of the Mean Motions of the Sun and Moon, pp. 305-335; volume IV, memoir No. 51 — The Secular Variation of the Motion of the Moon's Perigee, p. 105; volume IV, memoir No. 55 — Literal Expression for the Motion of the Moon's Perigee, pp. 41-50. (g) Forest Ray Moulton, An Introduction to Celestial Mechanics (2d rev. ed.), The Macmillan Co., New York, 1914. Chapter IX, section I: Effects of the Components of the Disturbing Force, pp. 325-332, and section II, The Lunar Theory, pp. 347-360. (h) Dirk Brouwer and Gerald M. Clemence, Methods of Celestial Mechanics, Academic Press, New York, 1961. Chapter XII, Lunar Theory, pp. 324-328, and pp. 360-366. CHAPTER 4 1. Rollin A. Harris, Manual of Tides, compiled from various technical appendixes to the annual Reports of the Superintendent of the U.S. Coast and Geodetic Survey, 1894-1907. U.S. Government Printing Office, Washington, D.C, 1895-1908. The pertinent reference appears in Appendix No. 9 of the annual report for 1897, Washington, D.C, 1898, part II, chapter IV, p. 525, equation 288. 2. Forest Ray Moulton, An Introduction to Celestial Mechanics (2d rev. ed.) The Macmillan Co., New York, 1914, p. 327. 3. U.S. Naval Observatory, Improved Lunar Ephemeris, 1952-1959, U.S. Government Printing Office, Washington, D.C, 1954, p. 317. The approximate equation given here contains only five of a series of 181 terms, the rest having very small coefficients. 4. This 1931 March 4 instance of an extremely small separation-interval between perigee and syzygy (P — S=+6 min.) ranks among the closest such alignments in the 400-year period 1600-1999. Its positive effects upon tidal flooding potential are amply demonstrated in the multiple descriptions of coastal inundation which accompanied the strong perigean spring tides produced (see Key No. D-57) as noted in tables 1 and 5 and in chapter 7 of the text. The extended astronomical influence of this very close agreement between the positions of perigee and syzygy is further emphasized by a chain of five interrelated tidal flooding events in the space of 23 consecutive months. These events are separated by periods of 2, 1, 7.5, and 1 anomalistic months, respectively (see table 1). Each interval between floodings is indicative of the mathematically commensurable relationships which govern successive perigee-syzygy alignments and their associated perigean spring tides. 5. Edgar W. Woolard and Gerald M. Clemence, Spherical Astronomy, Academic Press, New York, 1966, p. 161. 6. An exact coincidence between the ascending node of the lunar orbit and the vernal equinox would require that the Moon be crossing the ecliptic (i.e., the apparent celestial latitude of the Moon, 0(^ = 0°, and increasing from — to +) at the same time that the Sun is crossing the celestial equator from south to north (i.e., the apparent declination of the Sun, 8q = 0°). Although such an exact agreement is very rare, the attainment of the above conditions within a few days of each other is sufficient to produce the extreme lunar declinations noted in the text. See The American Ephemeris and Nautical Almanac for the year 1950, U.S. Government Printing Office, Washington, D.C, 1948, p. 4, pp. 60, 104, and pp. 134, 142. 516 Strategic Role of Perigean Spring Tides, 1635-1976 CHAPTER 5 1. Otto Pettersson, "The Connection Between Hydrographical and Meteorological Phenomena," Quarterly Journal of the Royal Meteorological Society, vol. XXXVIII, No. 163, July 1912, pp. 173-191 (especially pp. 190ff.). 2. Hans Pettersson, "Long Periodical Variations of the Tide-Generating Force," Conseil Permanent International pour l'Ex- ploration de la Mer, Publications de Circonstance No. 65, Copenhagen, Denmark, July 1913, pp. 3-23 (especially pp. 7ff.). 3. R. C. H. Russell and Commander D. H. Macmillan, Waves and Tides, (1st reprint ed.) Greenwood Press, Westport, Conn., 1970, p. 207. 4. Clyde Stacey, "Earth Motions," The Encyclopedia of Atmospheric Sciences and Astrogeology, vol. II, 1967, p. 337, col. 2. 5. U.S. Naval Observatory, Improved Lunar Ephemeris, 1952-59, U.S. Government Printing Office, Washington, D.C., 1954, pp. 286, 292; Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac, Her Majesty's Stationery Office, London, England, 1969, pp. 44, 107; Supplement to the A.E. 1968, U.S. Naval Observatory, Washington, D.C., 1966 (reprinted with footnote revisions, 1973), pp. 16s-18s. 6. H. F. Fliegel and T. C. Van Flandern, "A Machine Algorithm for Processing Calendar Dates," Communications of the Associatio n for Computing Machinery, vol. XI, No. 10, Oct. 1968, p. 657. CHAPTER 6 1. Cf., Hugh Godfray, An Elementary Treatise on the Lunar Theory, New York, Macmillan and Co., 1871, pp. 73-74. CHAPTER 7 1. George F. McEwen, "Destructive High Waves Along the Southern California Coast," Shore and Beach, vol. Ill, No. 2, April 1935, pp. 61-64 (especially p. 63). See also: Morrough P. O'Brien, "The Coast of California as a Beach Erosion Laboratory," Shore and Beach, vol. IV, No. 3, July 1936, pp. 74-79 (especially p. 74). 2. Dorothy Franklin, West Coast Disaster, Columbus Day, 1962, Gann Publishing Co., Portland, Oreg. (no publication or copy- right date). CHAPTER 8 1. Glenn W. Brier, "Diurnal and Semidiurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, vol. 93, No. 2, February 1965, pp. 93-100. 2. John R. Gribben and Stephen H. Plagemann, The Jupiter Effect, Walker and Co., New York, 1974; reprinted, 1975, revised, 1976, Vintage Books, New York. For technical reviews of the proposed theory, see: American Scientist, vol. 62, pp. 721-722, 1974; Annals of Science, vol. 32, pp. 601-603, 1975; Icarus, vol. 26, pp. 257-267, 270, 1975; Physics Today, April 1975, pp. 74-75; and Science, vol. 186, pp. 728- 729, 1974. Bibliography on Tides A selected list of reference sources, arranged by category, as follows: (1) CLASSIC WORKS AND TREATISES ON THE TIDES (See also category 8.) (2) TEXTBOOKS AND SURVEY WORKS ON PHYSICAL AND DYNAMICAL OCEANOGRAPHY (3) REFERENCE AND GENERAL SUMMARY ARTICLES ON THE TIDES (4) DESCRIPTIVE WORKS AND POPULAR PRESENTATIONS ON THE TIDES (5) THE EARTH-MOON SYSTEM; CLASSIC THREE-BODY PROBLEM; LUNAR THEORY AND PERTURBA- TIONS; EARTH TIDAL INFLUENCES ON THE MOON'S ORBIT (See also category 25.) (6) GRAVITATIONAL FIELDS OF THE EARTH, MOON, AND SUN; TIDE-GENERATING FORCES AND THE GRAVITATIONAL POTENTIAL (See also category 7.) (7) TIDAL THEORY AND TIDAL DYNAMICS (See also categories 12, 13, 14, 15, 16.) (8) HARMONIC ANALYSIS OF TIDES: TIDAL CONSTANTS AND CONSTITUENTS (9) NUMERICAL INTEGRATION, MODELS, AND SOLUTIONS OF SPECIAL TIDAL PROBLEMS (10) DEEP-SEA TIDES (See also category 24.) (11) INTERNAL TIDAL WAVES; SURFACE MANIFESTATION AS TIDE RIPS (12) TIDES IN A ZONAL OCEAN (13) TIDES IN SEAS AND BASINS, AND IN BAYS, HARBORS, AND GULFS; RESONANCE FACTORS (14) TIDES IN SHALLOW WATERS AND ESTUARIES; FRICTIONAL EFFECTS; TIDAL MIXING (15) SHORT-PERIOD TIDES: CLASSIFICATION, THEORY, AND CHARACTERISTICS (16) LONG-PERIOD TIDES AND WAVES; SECULAR TIDAL INFLUENCES (17) SPECIAL STUDIES OF TIDAL PHENOMENA BY TYPES AND REGIONS (OBSERVATIONS AND ANALYSES) (18) METEOROLOGICALLY INDUCED WAVES AND SWELL EFFECTS ON HIGH TIDES; WIND COUPLING AND WIND STRESS; STORM SURGES (19) TIDAL HYDRAULICS; COASTAL PROCESSES (See also category 24.) (20) SEASONAL EFFECTS ON TIDES AND SEA LEVEL (21) TIDE GAGES AND OTHER TIDE-RECORDING INSTRUMENTATION; RADAR DETECTION OF EXTREME TIDAL HEIGHTS; FREQUENCY ANALYSIS OF THE HIGHEST TIDES OF RECORD (22) LONG- AND SHORT-PERIOD FLUCTUATIONS IN MEAN SEA LEVEL; INFLUENCES ON GEODETIC SURVEYS (23) TIDAL PREDICTIONS, COMPUTATIONS, AND TABLES; ANALYSIS OF OBSERVATIONS, INCLUDING DIGITAL COMPUTER PROCESSING (See also category 8.) (24) TIDE AND TIDAL CURRENT RESPONSES ON THE OCEAN FLOOR; DEEP-SEA CURRENTS (25) TIDAL FRICTION ON THE ROTATING EARTH; ENERGY TRANSFER AND DISSIPATION; VARIATION IN THE LENGTH OF THE DAY (26) EARTH TIDES: TIDAL VARIATION IN THE FORCE OF GRAVITY (27) TIDAL LOADING; ELASTIC STRAIN; DEFORMATION; TILT; AND DEFLECTION OF THE VERTICAL (28) EARTH TIDES: GROUND- WATER RESPONSES IN WELLS AND RESERVOIRS (29) EARTH TIDES: DETERMINED FROM ANALYSIS OF ORBITAL PERTURBATIONS OF ARTIFICIAL SATELLITES (30) HYDRODYNAMICS; FIGURES OF THE EARTH AND MOON (31) TIDE EFFECTS ON THE ORBITS OF ARTIFICIAL SATELLITES (32) CORRELATION OF EARTHQUAKES WITH EARTH TIDES AND OTHER LUNISOLAR INFLUENCES; TIDAL INTERRELATIONS WITH MOONQUAKES (33) ATMOSPHERIC TIDES; POSSIBLE LUNITIDAL CORRELATIONS WITH ATMOSPHERIC PRECIPITATION (34) TIDAL CURRENTS: OBSERVATION, MEASUREMENT, AND PREDICTION TABLES (35) SALINITY EFFECTS OF TIDAL AND CURRENT MOVEMENTS (36) WATER TEMPERATURE VARIATIONS RESULTING FROM TIDAL AND CURRENT MOVEMENTS; DEN- SITY STRATIFICATION AND ENTRAINMENT (37) ELECTROMAGNETIC EFFECTS ASSOCIATED WITH VELOCITY OF TIDAL CURRENTS (38) PRACTICAL EFFECTS OF TIDES AND CURRENTS (39) TIDAL POWER (40) HISTORY OF TIDAL AND TIDE-RELATED ASTRONOMICAL OBSERVATIONS, MEASUREMENTS, THEORIES, AND PREDICTIONS (41) LUNAR INFLUENCES IN GEOMAGNETISM (CORRELARY TO INCREASED TIDAL EFFECTS) (42) BIBLIOGRAPHIES, SOURCE BOOKS, GLOSSARIES, AND STATE-OF-THE-ART LITERATURE RELATIVE TO TIDES AND TIDAL CURRENTS 517 ■)lf>, Strategic Role of Perigean Spring Tides, 1635-1976 (1) CLASSIC WORKS AND TREATISES ON THE TIDES (See also category 8.) Darwin, George H., 1879: On the bodily tides of viscous and semi- elastic spheroids, and on the ocean tides upon a yielding nucleus. Royal Society of London, Philosophical Transactions, part I, 1-35. , 1879: On the precession of a viscous spheroid, and on the remote history of the Earth. Royal Society of London, Philo- ophical Transactions, part II, 447-538. , 1880: Problems connected with the tides of a viscous spheroid. Royal Society of London, Philosophical Transactions, part II, 539-593. , 1880: On the secular changes in the elements of the orbit of a satellite revolving about a tidally distorted planet. Royal So- ciety of London, Philosophical Transactions, part II, 713-891. , 1881 : On the tidal friction of a planet attended by several satellites, and on the evolution of the solar system. Royal Society of London, Philosophical Transactions, part II, 491-535. , 1882: On the stresses caused in the interior of the Earth by the weight of continents and mountains. Royal Society of Lon- don, Philosophical Transactions, part I, 187-230. , 1962: The Tides (reprint ed.) Freeman, San Francisco, 342 pp. Ferrel, William, 1874: "Tidal researches," reprinted Appendix from the annual Report of the Superintendent of the U.S. Coast Survey for 1874, U.S. Government Printing Office, Washington, D.C. 268 pp. Harris, Rollin A., 1898: Manual of Tides, part I, Introduction and Historical Treatment of the Subject, as Appendix No. 8, pp. 319— 469; part II, Tidal Observation, Equilibrium Theory and the Harmonic Analysis, as Appendix No. 9, pp. 471-575, plus aux- iliary tables for the reduction and prediction of tides, pp. 577- 699, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1897. U.S. Government Printing Office, Washington, D.C. , 1895: Manual of Tides, part III, Some Connections be- tween Harmonic and Nonharmonic Quantities, including Appli- cations to the Reduction and Prediction of Tides, as Appendix No. 7, pp. 125-187, plus auxiliary tables for the reduction and prediction of tides, pp. 189-262, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1894. U.S. Government Printing Office, Washington, D.C. , 1901: Manual of Tides, part IV-A, Outlines of Tidal Theory, as Appendix 7, pp. 535-693, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1900. U.S. Government Printing Office, Washington, D.C. , 1904: Manual of Tides, part IV-B, Cotidal Lines for the World, as Appendix 5, pp. 315-400, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1904, U.S. Government Printing Office, Washington, D.C. , 1908: Manual of Tides, part V, Currents, Shallow-Water Tides, Meteorological Tides, and Miscellaneous Matters, as Ap- pendix 6, pp. 231-545, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1907, U.S. Govern- ment Printing Office, Washington, D.C. Levy, Maurice, 1898: Lecons sur la theorie des maries (Studies on the theory of the tides). Gauthier-Villars et Fils, Paris, France, 298 pp. Whewell, W., 1834: On the empirical laws of the tides in the Port of London: Some reflexions on the theory. Royal Society of London, Philosophical Transactions, series A, 133, 15-45. , 1836: Researches on the tides; Fourth series: On the empir- ical laws of the tides in the Port of Liverpool. Royal Society of London, Philosophical Transactions, .series A, 135, 1-15. Whewell, W., 1836: Researches on the tides; Fifth series: On the solar inequality and the diurnal inequality of the tides at Liver- pool. Royal Society of London, Philosophical Transactions, Series A, 135, 131-147. , 1837: Researches on the tides; Seventh series: On the diurnal inequality of the height of the tides, especially at Ply- mouth and Singapore; and on the mean level of the sea. Royal Society of London, Philosophical Transactions, series A, 136, 75- 85. , 1838: Researches on the tides; Ninth series: On the de- termination of the laws of the tides from short series of observa- tions. Royal Society of London, Philosophical Transactions, series A, 137, 231-247. , 1839: Researches on the tides; Tenth series: On the laws of the low water at the Port of Plymouth and on the permanency of mean water. Royal Society of London, Philosophical Trans- actions, series A, 138, 151-161. (See also part I, chapter 4, of the present work.) (2) TEXTBOOKS AND SURVEY WORKS ON PHYSICAL AND DYNAMICAL OCEANOGRAPHY Arx, William S. von, 1962: An Introduction to Physical Ocean- ography. Addison- Wesley, Reading, Mass., 422 pp. Defant, Albert, 1961 : Physical Oceanography. In 2 vols., Pergamon, Oxford, 1327 pp. Dietrich, Gunter, 1963: General Oceanography. Wiley-Interscience, New York, 588 pp. Gross, M. Grant, 1972: Oceanography: A View of Earth. Prentice- Hall, Englewood Cliffs, N.J., 560 pp. Neumann, Gerhard and Pierson, Willard J., Jr., 1966: Principles of Physical Oceanography. Prentice-Hall, Englewood Cliffs, N.J., 545 pp. Neumann, Gerhard, 1968: Ocean Currents. Elsevier, Amsterdam, The Netherlands, 352 pp. Officer, Charles B., 1976: Physical Oceanography of Estuaries and Associated Coastal Waters. Wiley-Interscience, New York, 465 pp. Phillips, Owen M. 5 1966: The Dynamics of the Upper Ocean. Cambridge University Press, London, 261 pp. Proudman, Joseph, 1953: Dynamical Oceanography. Wiley, New York, 409 pp. Sverdrup, Harald U., Johnson, Martin W., and Fleming, Richard H., 1959: The Oceans: Their Physics, Chemistry and General Biology. Prentice-Hall, Englewood Cliffs, N.J., 1087 pp. Turekian, Karl, 1976: Oceans. Prentice-Hall, Englewood Cliffs, N.J., 160 pp. (3) REFERENCE AND GENERAL SUMMARY ARTICLES ON THE TIDES Doodson, A. T., 1958: "Oceanic tides," in: Advances in Geophys- ics, vol. 5. Academic Press, New York, 118-153. Groves, Gordon W., 1971: "Tides," in: McGraw-Hill Encyclopedia of Science and Technology, vol. 13, McGraw-Hill, New York, 650-657. Hansen, Walter, 1962: "Tides," in: The Sea, vol. 1. Wiley-Inter- science, New York, 764-780. Henderschott, M. C. and Munk, W., 1970: Tides. Annual Review of Fluid Mechanics, 2, 205-224. Henderschott, M. C, 1973: Ocean tides. Eos (American Geophys- ical Union Transactions), 54, 76-86. National Academy of Sciences, 1932: "Tides and tidal currents," in: Physics of the Earth — Oceanography, vol. 5, ch. 7. Na- tional Research Council Bulletin No. 85, Washington, D.C, 581 pp. Bibliography on Tides 519 ossiter, J. R., 1963: "Tides," in: Oceanography and Marine Biology: An Annual Review, 1, 11-25. , 1967: "Tides," in: International Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1539-1543. , 1967: "Tides in oceans," in: International Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1547-1549. Rouch, Jules Alfred Pierre, 1961: Les marees {The Tides). Paris Payot, Paris, France, 230 pp. Rudaux, Lucien and de Vaucouleurs, G., 1967: "The tides," in: Larousse Encyclopedia of Astronomy. Prometheus Press, New York, 169-174. Swanson, R. L., 1976: Tides. Marine EcoSystems Analysis (MESA) Program, MESA New York Bight Atlas Monograph 4. New York Sea Grant Institute, Albany, N.Y., 34 pp. U.S. Navy Hydrographic Office (now the U.S. Naval Oceano- graphic Office), 1966: "Tides and tidal currents," in Nathanial Bowditch's American Practical Navigator, ch. XXXI. U.S. Navy Department Hydrographic (Oceanographic) Office, Publication No. 9, 1966 Corrected Print. U.S. Government Printing 'Office, Washington, D.C., 1524 pp. Wood, Fergus J., 1950- : "Tides," in: Collier's Encyclopedia. P. F. Collier, New York, vol. 22, 308-312. , 1957-67: "Tides," in: Encyclopedia Americana. Ameri- cana Corp., New York, vol. 26, 61 1-619. , 1979: "Tides," and "Proxigean Spring Tides," in: Ency- clopedia of Beaches and Coastal Environments. Western Wash- ington State College, Bellingham, Wash. Zetler, Bernard D., 1968- : "Tides," in: Encyclopedia Ameri- cana. Americana Corp., New York, vol. 26, 731-735. (4) DESCRIPTIVE WORKS AND POPULAR PRESENTA- TIONS ON THE TIDES Conoon, C. R., 1971: Principal features of tidal phenomena. Mari- ners Weather Log, 15, 337-340. Cummings, W. C, 1969: Tides: The longest waves in the ocean. Oceans Magazine, 1 } 50-51. MacMillan, D H., 1966: The Tides. C. R. Books, London, 240 pp. Marmer, Harry Aaron, 1926: The Tide. D. Appleton and Com- pany, New York, 282 pp. Russell, R. C. H. and Macmillan, D. H., 1970: Waves and Tides (1st reprinting). Greenwood Press, Westport, Conn., 348 pp. Sager, Giinther, 1959: Gezeiten und Schiffahrt {Tides and Navi- gation). Fachbuchverlag, Leipzig, East Germany, 172 pp. Smith, Frederick George Walton, 1968: Tidal vagaries. Sea Fron- tiers, 14, 263-271. , 1969: Ebb and flow. Sea Frontiers, 15, 86-89. , 1969: Man and tides. Sea Frontiers, 15, 142-151. , 1973: The Seas in Motion. T. Y. Crowell, New York, 248 pp. Stewart, John Q., 1945: Coasts, Waves, and Weather, chapters 13-14. Ginn and Co., New York, pp. 183-210. Tricker, R. A. R., 1964: Bores, Breakers, Waves and Wakes. Mills and Boon, London, 250 pp. Voit, S. S., 1956: What Are the Tides? Izdatel'stvo Akademiya Nauk SSSR (Moscow, USSR), 102 pp. (5) THE EARTH-MOON SYSTEM; CLASSIC THREE-BODY PROBLEM; LUNAR THEORY AND PERTURBA- TIONS; EARTH TIDAL INFLUENCES ON THE MOON'S ORBIT (See also category 25.) Alfven, H., 1963: The early history of the Moon and Earth. Icarus, 1, 357-363. Brouwer, Dirk and Clemence, Gerald M., 1961: Methods of Celes- tial Mechanics, ch. XII. Academic Press, New York, 308-375. Brown, Ernest W., 1960: An Introductory Treatise on the Lunar Theory. Reprint of original 1896 ed. published by Cambridge University Press. Dover, New York, 292 pp. (with the assistance of Hedrick, Henry B.), 1919: Tables of the Motion of the Moon, in 3 vols, and 6 sections. Yale Univer- sity Press, New Haven, Conn. , 1926: Complement to the Tables of the Motion of the Moon. Transactions of the Astronomical Observatory of Yale University, vol. 3, pt. 5, The Observatory, New Haven, Conn. Ferrel, William, 1871 : On the Moon's mass as deduced from a dis- cussion of the tides of Boston Harbor. Appendix No. 20 in the annual Report of the Superintendent of the U.S. Coast Survey for 1870. U.S. Government Printing Office, 1873, Washington, D.C., pp. 190-199. Gerstenkorn, Horst, 1967: On the controversy over the effect of tidal friction upon the history of the Earth-Moon System. Icarus, 7, 160-167. , 1969: The earliest past of the Earth-Moon System. Icarus, 11, 189-207. Godfray, Hugh, 1871: An Elementary Treatise on the Lunar Theory, 3d ed., rev. Macmillan and Co., New York, 123 pp. Goldreich, P., 1966: History of the lunar orbit. Review of Geo- ' physics and Space Physics, 4, 41 1-439. Groves, G. W. ; 1962: "Dynamics of the Earth-Moon system," in: Physics and Astronomy of the Moon, edited by Zdenek Kopal. Academic Press, New York, 538 pp. Jeffreys, H., 1930: The resonance theory of the origin of the Moon. Royal Astronomical Society, Monthly Notices, 91 , 169-173. Kaula, W. M., 1971 : Dynamical aspects of lunar origin. Review of Geophysics and Space Physics, 9, 217-238. Koziel, K., 1967: Difference in the Moon's moments of inertia. Royal Society of London, Proceedings, series A, 296", 248-253. Lambeck, Kurt, 1975: Effects of tidal dissipation in the oceans on the Moon's orbit and the Earth's rotation. Journal of Geophysical Research, 80, 2917-2925. Lambert, Walter D., 1927 : The variation of latitude and the fluctu- ations in the motion of the Moon. Journal of the Washington Academy of Sciences, 17, 133-139. Michael, W. H., Jr., 1970: Moments of inertia of the Moon. The Moon: An International Journal of Lunar Studies (Dordrecht, The Netherlands), /, 484-485. Michael, W. H., Jr., Blackshear, W. T., and Gapcynski, J. P., 1969: Dynamics of satellites, 1969. Proceedings of the Prague 12th Plenary of COSPAR and 10th International Space Science Sym- posium, May 11-24, 1969, edited by Bruno Morando (Prague, Czechoslovakia), 42-56. Moulton, Forest Ray, 1914: An Introduction to Celestial Mechan- ics (2d rev. ed.), chs. VIII, IX. Macmillan, New York, 277- 365. Oesterwinter, C. and Cohen, C. J., 1972: New orbital elements for Moon and planets. Celestial Mechanics, 5, 317-395. O'Keefe, J. A., 1969: Origin of the Moon. Journal of Geophysical Research, 74, 2758-2767. , 1972: Inclination of the Moon's orbit: The early history. Irish Astronomical Journal, 10, 241-250. Oppolzer, Theodor Ritter von, 1962: Canon der Finsternisse (Canon of Eclipses), translation of original 1887 ed. by Owen Gingerich. Dover, New York, 376 pp. Rubincam, David Parry, 1975: Tidal friction and the early history of the Moon's orbit. Journal of Geophysical Research, 80 } 1537- 1548. Schindler, Gerhard, 1959: Die Vollmondatten der letzten 110 Jahre (Full moon data for the last 100 years). Meteorologische Rundschau, 12, 132-133. -)'J(> Strategic Role of Perigean Spring Tides, 1635-1976 Schubart, J., 1961: Der Umlauf von Knoten und Perigaum des Mondes (The revolution of the nodes and the perigee of the Moon). Die Sterne (Leipzig, East Germany), 37, 7-9. Singer, S. F., 1968: The origin of the Moon and geophysical conse- quences. Geophysical Journal, 15, 205-226. Van Flandern, T. L., 1970: The secular acceleration of the Moon. Astronomical Journal, 75, 657—658. (6) GRAVITATIONAL FIELDS OF THE EARTH, MOON, AND SUN; TIDE-GENERATING FORCES AND THE GRAVITATIONAL POTENTIAL (See also category 7.) Akim, E. L., 1966: Determination of the gravitational field of the Moon by the motion of AMS Luna 10. Akademiya Nauk SSSR, Doklady (Moscow-Leningrad, USSR), 171, 799-802. Cartwright, D. E. and Tayler, R. J., 1971: New computations of the tide-generating potential. Royal Astronomical Society, Geo- physical Journal, 23, 45-74. Cook, A. H., 1961 : Resonant orbits of artificial satellites and longi- tude terms in the Earth's external gravitational potential. Royal Astronomical Society, Geophysical Journal, 4, 53-72. Doodson, A. I., 1921 : Harmonic development of the tide-generating potential. Royal Society of London, Proceedings, series A, 100, 305-329. Garland, G. D., 1965: The Earth's Shape and Gravity. Pergamon, London, 175 pp. Heiskanen, W. A. and Vening Meinesz, F. A., 1958: The Earth and its Gravity Field. McGraw-Hill, New York, 470 pp. Kaula, W. M., 1959: Statistical and harmonic analysis of gravity. Journal of Geophysical Research, 64, 2401-2421. , 1967: Geophysical implications of satellite determination of the Earth's gravitational field. Space Science Review, 7, 769— 794. , 1969: The gravitational field of the Moon. Science, 166, 1581-1588. Koch, K. R. and Morrison, F., 1970: A simple layer model of the geopotential from a combination of satellite and gravity data. Journal of Geophysical Research, 75, 1483-1492. Koch, K. R., 1971: Errors of quadrature connected with the sim- ple layer model of the geopotential. NOAA Technical Memoran- dum NOS 11, National Ocean Survey, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, Washington, D.C., 1-10. Longman, I. M., 1959: Formulas for computing the tidal accelera- tions due to the Sun. Journal of Geophysical Research, 64, 2351— 2355. MacMillan, W. D., 1958: The Theory of the Potential. Dover, New York, 343, 405. Melchior, P., 1971: Precession-nutation and tidal potential. Celes- tial Mechanics, 4, 190-212. Munk, W. H. and MacDonald, G. J. F., 1960: Continentality and gravitational field of the Earth. Journal of Geophysical Research, 65, 2169-2172. O'Keefe, J. A., 1960: "Determination of the Earth's gravitational field," in: Space Research, vol. 1, edited by H. Kallmann. North- Holland, Amsterdam, The Netherlands, 448-457. Pollack, Henry N., 1973: Longman tidal formulas: Resolution of horizontal components. Journal of Geophysical Research, 78. 2598-2600. Suess, Steven T., 1970: Some effects of gravitational tides on a model Earth's core. Journal of Geophysical Research, 75, 6650- 6661. Vinti, J. P., 1971: Representation of the Earth's gravitational po- tential. Celestial Mechanics, 4, 348-367. (7) TIDAL THEORY AND TIDAL DYNAMICS (See also cate- gories 12, 13, 14, 15, 16) Bouasse, Henri, P. M., 1924: Houle, rides, seiches, et marees (Swells, Ripples, Seiches and Tides). Librairie Delagrave, Paris, France, 516 pp. Eckart, C, 1952: "The propagation of gravity waves from deep to shallow water," in: Gravity Waves, National Bureau of Stand- ards Circular 521, Washington, D.C., 165-174. , 1962: "The equations of motion of sea water," in: The Sea, vol. 1, edited by M. N. Hill. Interscience, New York, 31-40. , 1963 : Some transformations of the hydrodynamic equations. Physics of Fluids, 6, 1037-1041. Godin, Gabriel, 1972: The Analysis of Tides. University of Toronto Press, Toronto, Canada, 264 pp. Haubrich, R. and Munk, W. H., 1959: The pole tide. Journal of Geophysical Research, 64, 2373-2388. Longman, I. M., 1959: Formulas for computing the tidal accelera- tions due to the Moon and Sun. Journal of Geophysical Research, 64, 2351-2360. Michelson, Irving, 1965: Resolution of tidal high water anomaly. Pure and Applied Geophysics (Basel, Switzerland), 61, 149-151. Mosetti, F. and Manca, B., 1972: Some methods of tidal analysis. International Hydrographic Review (Monaco), 49, 107-120. Munk, W. H., 1962: "Long ocean waves," in: The Sea, vol. 1, edited by M. N. Hill. Interscience, New York, 647-663. Munk, W. H. and Bullard, E. C, 1963: Patching the long-wave spectrum across the tides. Journal of Geophysical Research, 68, 3627-3634. Munk, W. H. and Hasselman, K., 1964: "Super resolution of tides," in: Studies on Oceanography, Tokyo Geophysical Insti- tute, University of Tokyo, Japan, 339-344. Proudman, J., 1925: A theorem in tidal dynamics. Philosophical Magazine, 49, 570-579. (8) HARMONIC ANALYSIS OF TIDES: TIDAL CON- STANTS AND CONSTITUENTS British Admiralty, 1959: The Admiralty Semi-Graphic Method of Harmonic Tidal Analysis. Admiralty Tidal Handbook No. 1 (H.D.505). Hydrographic Department, Admiralty, London, 74 pp. Darwin, G. H., 1883: Report of a committee for the harmonic analysis of tidal observation. British Association for the Advance- ment of Science, Reports, 48-118. Doodson, A. T., 1921 : The harmonic development of the tide gen- erating potential. Royal Society of London, Proceedings, series A, 100, 305-329. Doodson, A. T. and Warburg, H. D. (Admiralty, Hydrography De- partment), 1941: Admiralty Manual of Tides. His Majesty's Stationery Office, London, 270 pp. Hough, S. S., 1897: On the application of harmonic analysis to the dynamical theory of the tides. Royal Society of London, Philo- sophical Transactions, series A, 189, 201. , 1899: On the application of harmonic analysis to the dy- namical theory of tides. II. On the general integration of Lap- lace's tidal equations. Royal Society of London, Philosophical Transactions, series A, 191, 139-185. Pekeris, C. L. and A—ad, Y., 1969: Solution of Laplace's equations for the M 2 tide in the world oceans. Royal Society of London, Philosophical Transactions, series A, 265, 413-436. Rossiter, J. R., 1967: "Harmonic constituents of tides," in: Inter- national Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1545-1547. Bibliography on Tides 521 Schureman, Paul, 1971 : Manual of Harmonic Analysis and Predic- tion of Tides. National Ocean Survey (formerly U.S. Coast and Geodetic Survey) Special Publication No. 98, rev. (1940) ed., reprinted 1958 with corrections; 2d reprinting, 1971. U.S. Gov- ernment Printing Office, Washington, D.C., 317 pp. (9) NUMERICAL INTEGRATION, MODELS, AND SOLU- TIONS OF SPECIAL TIDAL PROBLEMS Bogdanov, K. T., Kim., K. V., and Magharik, V. A., 1964: Numeri- cal solution of tide hydrodynamic equations by means of BESMA-2 electronic computer for the Pacific area. Akademiya Nauk SSSR, Institut Okeanologii, Trudy (Moscow, USSR), 75, 73-98. Bogdanov, K. T. and Magharik, V. A., 1967: Numerical solutions of the distribution problem for the semidiurnal tidal waves (M 2 and S 2 ) in the world ocean. Akademiya Nauk SSSR, Doklady (Mos- cow-Leningrad, USSR), 172, 1315-1317. Grant, H. L., Stewart, R. W., and Moilliet, A., 1962: Turbulence spectra from a tidal channel. Journal of Fluid Mechanics, 12, 241-268. Groves, G. W., 1955: Numerical filters for discrimination against tidal periodicities. American Geophysical Union, Transactions, 36, 1073-1084. Lennon, G. W., 1967: Some numerical methods of tidal prediction [Abstract]. Royal Astronomical Society, Geophysical Journal, 13, 297-312. Pagenkopf, James R. and Pearce, Bryan R., 1975: Evaluation of Techniques for Numerical Calculation of Storm Surges. Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Report No. 199. School of Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 120 pp. Wilson, B. W., Hendrickson, J. A., and Kilmer, R. E., 1965: Feasibility Study for a Surge-Action Model of Monterey Harbor, California. Contract Report No. 2—136 prepared for U.S. Army Engineer Waterways Experiment Station, Corps of Engineers, Vicksburg, Miss., by Science Engineering Associates, San Marino, Calif., 166 pp. Zerbe, W. B., 1949: The tide in the David Taylor Model Basin. American Geophysical Union, Transactions, 30, 357—368. (10) DEEP-SEA TIDES (See also category 24.) Cartwright, D. E., 1969: Deep-sea tides. Science Journal, 5> 60-67. Cartwright, D., Munk, W., and Zetler, B., 1969: Pelagic tidal meas- urements. Eos (American Geophysical Union, Transactions), 50, 472-477. Heaps, N. S., 1969: Some notes on tidal theory and its possible relevance to a program of deep-sea tidal measurement. Deutsche Hydrographische Zeitschrift (Hamburg, West Germany), 22, 11-25. Lambert, Walter D., 1928: The Importance from a Geophysical Point of View of a Knowledge of the Tides in the Open Sea. Bulletin No. 1 1 of the Section on Oceanography of the Interna- tional Council of Research. Venice, Italy, 1 1 pp. Munk, Walter, 1957: Deep Sea Tides. National Research Council Publication No. 473, Washington, D.C., 28-31. Munk, W., Snodgrass, F., and Wimbush, M., 1970: Tides offshore: Transition from California coastal to deep-sea water. Geophysical Fluid Dynamics, 1, 161-235. Nowroozi, A. A., Kuo, J., and Ewing, M., 1969: Solid Earth and oceanic tides recorded on the ocean floor off the coast of northern California. Journal of Geophysical Research, 74, 605- 614. Vantroys, L., 1957: La determination des marees au dessus des fonds oceaniques (Determination of the tides above oceanic beds). Academie des Sciences, Comptes Rendu (Paris, France), 245, 340-343. (11) INTERNAL TIDAL WAVES; SURFACE MANIFESTA- TION AS TIDE RIPS Davis, F. A. and Patterson, A. M., 1956: The creation and propaga- tion of internal waves, a literature survey. Pacific Naval Labora- tory Technical Memorandum 56-2, Defense Research Board, Canada, 15 pp. Defant, A., 1950: On the origin of internal tide waves in open sea. Journal of Marine Research, 9, 1 1 1-1 19. Emery, K. O., 1956: Deep standing internal waves in California basins. Limnology and Oceanography, 1, 35—41. Gaul, R. D., 1961: Observations of internal waves near Hudson Canyon. Journal of Geophysical Research, 66, 3821-3830. Haurwitz, B., 1950: Internal waves of tidal character. American Geophysical Union, Transactions, 31 , 47-52. LaFond, E. C, 1961: Internal wave motion in shallow water. Program of the Pacific Science Congress, Honolulu, August 23, 1961, 149. Lee, O. S., 1961: Observations on internal waves in shallow water. Limnology and Oceanography, 6, 312-321. Mooers, C. N. K, 1970: The Interaction of an Internal Tide with the Frontal Zone of a Coastal Upwelling Region. Ph. D. Dissertation, Oregon State University, Corvallis, Oreg., 480 pp. Perry, Richard B., and Schimke, Gerald, R., 1965: Large-amplitude internal waves observed off the northwest coast of Sumatra. Journal of Geophysical Research, 70, 2319-2324. Rattray, Maurice, Jr., 1957: Propagation and dissipation of long internal waves. American Geophysical Union, Transactions, 38, 495-500. , 1960: On the coastal generation of internal tides. Tellus (Stockholm, Sweden), 12, 54-62. Reid, J. L., Jr., 1956: Observations of internal tides in October 1950. American Geophysical Union, Transactions, 37, 278-286. Summers, H. J. and Emery, K. O., 1963: Internal waves of tidal period off southern California. Journal of Geophysical Research, 68, 827-839. Uda, M., 1938: Researches on "siome" or current rip in the seas and oceans. Geophysical Magazine (Tokyo, Japan), 11, 307-372. (12) TIDES IN A ZONAL OCEAN Doodson, A. T., 1935: Tides in oceans bounded by meridians. II: Ocean bounded by complete meridian. Diurnal tides. Royal Society of London, Philosophical Transactions, series A, 235, 290-333. , 1937: Tides in oceans bounded by meridians. Ill: Ocean bounded by complete meridian. Semi-diurnal t : des. Royal Society of London, Philosophical Transactions, series A, 237, 311—373. Longuet-Higgins, M. S., 1966: Planetary waves on a hemisphere bounded by meridians of longitude. Royal Society of London, Proceedings, series A, 260, 317-350. Longuet-Higgins, M. S. and Pond, G. S., 1970: The free oscilla- tions of a fluid on a hemisphere bounded by meridians of longi- tude. Royal Society of London, Proceedings, series A, 266, 193— 223. Proudman, J., 1935: Tides in oceans bounded by meridians. I. Oceans bounded by complete meridian: General equation. Royal Society of London, Philosophical Transactions, series A, 235, 273-289. vn Strategic Role of Perigean Spring Tides, 1635-1976 (13) TIDES IN SEAS AND BASINS, AND IN BAYS, HAR- BORS, AND GULFS; RESONANCE FACTORS Garrett, Christopher, 1972: Tidal resonance in the Bay of Fundy and Gulf of Maine. Nature, 238, 441-443. , 1975: Tides in gulfs. Deep-Sea Research, 22, 23-35. Godin, Gabriel, 1965: Some remarks on the tidal motion in a narrow rectangular sea of constant depth. Deep-Sea Research, 12, 461-468. Hendershott, M. and Speranza, A., 1971 : Co-oscillating tides in long, narrow bays: The Taylor problem revisited. Deep-Sea Research, 18, 959-980. Hilgard, J. E., 1874: On the tides and tidal action in harbors. Smith- sonian Institution, Annual Report, 207-226. Parsons, H. deB., 1913: Tidal phenomena in the harbor of New York. American Society of Civil Engineers, Proceedings, 39, 653- 767. • , 1913: Tidal phenomena of New York. American Society of Civil Engineers, Transactions, 76, 1979-2108. Rattray, M. and Charnell, R. L., 1966: Quasi-geostrophic free oscil- lations in enclosed basins. Journal of Marine Research, 24, 82-102. Redfield, A. C, 1950: The analysis of tidal phenomena in narrow embayments. Papers in Physical Oceanography and Meteorology, 11, 1-36. Rossiter, J. R., 1967: "Tides in seas and gulfs," in: International Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1549-1551. (14) TIDES IN SHALLOW WATERS AND ESTUARIES; FRICTIONAL EFFECTS; TIDAL MIXING Blanton, Jackson, 1969: Energy dissipation in a tidal estuary. Journal of Geophysical Research, 74, 5460-5466. Hunt, J. N., 1964: Tidal oscillations in estuaries. Royal Astronomi- cal Society, Geophysical Journal, 8, 440-445. Johns, B., 1966: Vertical structure of tidal flow in river estuaries. Royal Astronomical Society, Geophysical Journal, 12, 103-110. , 1967: Tidal flow and mass transport in a slowly converg- ing estuary. Royal Astronomical Society, Geophysical Journal, 13, 377-386. McGregor, R. C, 1971: The influence of topography and pressure gradients on shoaling in a tidal estuary. Royal Astronomical Society, Geophysical Journal, 25, 469-480. Munk, W. H. and Gallagher, B. S., 1971: Tides in shallow water: Spectroscopy. Tellus (Stockholm, Sweden), 23, 343-363. Proudman, J., 1925: On the tidal features of local coastal origin and on sea-seiches. Royal Astronomical Society, Monthly Notices, Geophysical Supplement, 1, 247-270. , 1941: The effect of coastal friction on the tides. Royal Astronomical Society, Monthly Notices, Geophysical Supplement, 5, 23-26. , 1958: On the series that represent tides and surges in an estuary. Journal of Fluid Mechanics, 3, 411-417. Rossiter, J. R., 1967: "Tides in shallow water," in: International Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1551-1553. Rossiter, J. R. and Lennon, G. W., 1968: An intensive analysis of shallow-water tides. Royal Astronomical Society, Geophysical Journal, 76,275-293. Zetler, B. D. and Cummings, R. A., 1967: A harmonic method for predicting shallow-water tides. Journal of Marine Research, 24, 103-114. (15) SHORT-PERIOD TIDES: CLASSIFICATION, THEORY AND CHARACTERISTICS Dietrich, G., 1973: The tides of the oceans — a new presentation of the principal lunar tide M 2 . (In a special publication dedicated to N. K. Dannikar), Marine Biology Association, Madras, India, 60, 241-249. Garrett, C. J. R., and Munk, W. H, 1971 : The age of the tide and the "Q" of the oceans. Deep-Sea Research, 18, 493-503. Lindzen, R. S., 1966: On the theory of the diurnal tide. Monthly Weather Review, 94, 298. Marmer, Harry Aaron, 1934: The variety in tides. Smithsonian In- stitution Annual Report, 181-191. Munk, W., and Hasselmann, K., 1964: "Super-resolution of tides," in: Studies on Oceanography. Tokyo Geophysical Institute, Uni- versity of Tokyo, Japan, 339-344. Munk, W., and Cartwright, D. E., 1966: Tidal spectroscopy and prediction. Royal Society of London, Philosophical Transactions, series A, 259, 533-581. Sager, Giinther, 1959: Eine kritische Betrachtung zur Einteilung des Ablaufs der halbtagigen Meeresgezeiten in Spring-Nip-und Mittzeit (Critical comments on the division of semidiurnal ocean tides into spring, neap and mean tides). Zeitschrift fur Meteor- ologie,13 (7/8), 184-189. (16) LONG-PERIOD TIDES AND WAVES; SECULAR TIDAL INFLUENCES Cartwright, D. E., 1972: Secular changes in the oceanic tides at Brest, 1711-1936. Royal Astronomical Society, Geophysical Jour- nal, 30, 433-449. De Rop, W., 1971: A tidal period of 1800 years. Tellus (Stockholm. Sweden), 23, 261-262. Maximov, I. V., 1954: On the long period tidal phenomena in the sea and the atmosphere of the Earth. Akademiya Nauk SSSR, Institut Okeanologii, Trudy (Moscow, USSR), 8, 18-40. , 1958: The long period luni-solar tide in the world oceans. Akademiya Nauk SSSR, Doklady (Moscow-Leningrad, USSR), 778,888-890. , 1965: The solar semi-annual tide in the oceans. Akademiya Nauk SSSR, Doklady (Moscow-Leningrad, USSR) 767, 347- 350. , 1966: Long period lunar and solar tides in the ocean. Okeanologiya (Moscow, USSR), 6, 26-37. Munk, W. H. and Bullard, E. C, 1963: Patching the long-wave spectrum across the tides. Journal of Geophysical Research, 68, 3627-3634. Proudman, J., 1960: The condition that a long period tide shall follow the equilibrium law. Royal Astronomical Society, Geo- physical Journal, 3, 244-249. Wunsch, C, 1967: The long-period tides. Reviews of Geophysics, 5, 447-475. Zetler, Bernard D., 1967: Tides and other long period waves. Amer- ican Geophysical Union, Transactions, 48, 591-595. (17) SPECIAL STUDIES OF TIDAL PHENOMENA BY TYPES AND REGIONS (OBSERVATIONS AND ANALYSES) Doodson, A. T. and Corkan, R. H, 1932: The principal constitu- ent of the tides in the English and Irish Channels. Royal Society of London, Philosophical Transactions, series A, 257, 29-53. Godin, Gabriel, 1965: The M 2 tide in the Labrador Sea, Davis Strait and Baffin Bay. Deep-Sea Research, 12, 469-477. Gordon, R. B. and Pilbeam, C, 1973: Tides and circulation in central Long Island Sound. Eos (American Geophysical Union Transactions) , 54, 301-302. Hicks, S., Goodheart, A. J., and Iseley, C. W., 1965: Observations of the tide on the Atlantic continental shelf. Journal of Geophysi- cal Research, 70, 1827-1830. LeLacheur, E. A., 1931: Tidal phenomena of Long Island Sound. Washington Academy of Science, Journal, 21, 239-242. Maximov, I. V., 1960: The long period luni-solar tide at the coasts of the Arctic. Problemy Arktiki i Antarktiki (Leningrad, USSR), 3, 17-20. Bibliography on Tides 52:i Maximov, I. V., 1965: The results of the studies of the nine day lunar tide in the Arctic, Problemy Arktiki i Antarktiki (Leningrad, USSR), 21, 93-96. , 1967: On the study of the nine day lunar tide in the Arctic Ocean. Okeanologiya (Moscow, USSR), 7, 307-313. Proudman, J., 1944: The tides of the Atlantic Ocean. Royal As- tronomical Society, Monthly Notices, 104, 244-256. Redfield, A. C, 1958: The influence of the continental shelf on the tides of the Atlantic coast. Journal of Marine Research, 17, 442-448. Sager, Giinther, 1962: Die Variation der Hochwassereintrittszeiten in der Nordsee, dem Kanal und der Irishchen S" ; "i n w ^uf einer Tiderperiode (Variations in the times of the beginnings of high tides in the North Sea, the Channel and tiie insh Sea during a single tidal period). Beitrage zur Meereskunde (Ber- lin, West Germany), No. 5, 17-28. (18) METEOROLOGICALLY INDUCED WAVES AND SWELL EFFECTS ON HIGH TIDES; WIND COU- PLING AND WIND STRESS; STORM SURGES Barnett, T. P., 1968: On the generation, dissipation, and predic- tion of ocean wind waves. Journal of Geophysical Research, 73, 513-529. Bretschneider, Charles L., 1966: Steady-state wind tides over a sloping continental shelf caused by winds blowing at an angle to the coastline. Shore and Beach, 34, 8-11. , 1967: "Storm surges," in: Advances in Hydroscience, edited by Ven te Chow. Academic Press, New York, vol. 4, 341— 418. Bryan, K., 1963: A numerical investigation of a nonlinear model of wind-driven ocean. Journal of Atmospheric Science, 20, 594- 606. Burling, R. W., 1959: Wind Generation of Waves on Water. Ph. D. Dissertation, Imperial College, London, 181 pp. Charnock, H, and Crease, J., 1957: North Sea surges. Science Progress (London), 45, 494-511. Collins, G. F., 1957: Du Pont tide and storm warning service. Weatherwise, 10, 164-167. Dines, J. S., 1929: Meteorological conditions associated with high tides in the Thames. Geophysical Memoirs (London), 47, 27-39. Donn, W. L., 1958: An empirical basis for forecasting storm tides. Weatherwise, 39, 640-647. Environmental Science Services Administration (now the National Oceanic and Atmospheric Administration), 1970: Coastal Flood- ing, Long Beach Island and Adjoining Mainland, Ocean County, New Jersey. A study for the Federal Insurance Administration, Department of Housing and Urban Development, under the National Flood Insurance Act of 1968 in compliance with Agree- ment IAA-H-19-69, dated May 16, 1969, 43 pp. Evans, G. A., Collins, G. F., 1958: Du Pont tide and storm warning service. Proceedings of the First National Conference on Applied Meteorology, Hartford, Conn., Oct. 28-29, 1957, American Meteorological Society, Boston, Mass., A-8 to A-18. Harris, D. Lee, 1956: Some problems involved in the study of storm surges. Pacific Tropical Cyclone Symposium, Brisbane, 1956, Bureau of Meteorology, Melbourne, Australia, 365-411. , 1963: Characteristics of the hurricane storm surge. U.S. Weather Bureau Technical Paper No. 48, U.S. Government Printing Office, Washington, D.C., 139 pp. Jelesnianski, Chester P., 1966: Numerical computations of storm surges without bottom stress. Monthly Weather Review, 94, 379- 394. , 1967: Numerical computation of storm surges with bottom stress. Monthly Weather Review, 95, 740-756. Kajura, K., 1959: Theoretical and Empirical Study of Storm In- duced Water Level Anomalies. Final Technical Report, Contract CWB-9559, Texas A&M, Department of Oceanography and Meteorology, Texas A&M University, College Station, 97 pp. Keers, J. F., 1968: Empirical investigation of the interaction between storm surge and astronomical tide on the east coast of Great Britain. Deutsche Hydrographische Zeitschrift (Hamburg, West Germany), 2/ (3) : 118-125. Lacey, J. M., 1937: Ocean swells and abnormal tides. Engineering (London), 744,406-408. Lighthill, M. J., 1962: Physical interpretation of the mathematical theory of wave generation by wind. Journal of Fluid Mechanics, 14, 385-398. Miller, Arthur R., 1957: The effect of steady winds on sea level at Atlantic City. Meteorological Monographs, 2(10) : 24-31. , 1958: The effects of winds on water levels on the New England coast. Limnology and Oceanography, 3, 1-14. Myers, Vance A., 1970: Joint probability method of [storm] tide frequency analysis applied to Atlantic City and Long Beach Island, New Jersey. NOAA Technical Memorandum WBTM Hydro 11, Office of Hydrology, Environmental Science Services Administration (now the National Oceanic and Atmospheric Administration), Silver Spring, Md., 109 pp. , 1975: Storm tide frequencies on the South Carolina coast. NOAA Technical Report NWS- 16, National Weather Service, National Oceanic and Atmospheric Administration, Silver Spring, Md. ,79 pp. Nickerson, J. W., 1971 : Storm-surge forecasting. U.S. Navy Weather Research Facility (NAVEARSCHFAC) Technical Paper 10-71, Norfolk, Va., 44 pp. Phillips, Owen M., 1957: On the generation of waves by turbulent wind. Journal of Fluid Mechanics, 2, 417-445. , 1967: "The theory of wind-generated waves," in: Ad- vances in Hydroscience, edited by Ven te Chow, Academic Press, New York, vol.4, 119-149. Pierson, W. J. and Moskowitz, L., 1964: A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. Journal of Geophysical Research, 69, 5181- 5190. Pore, N. Arthur, 1961 : The storm surge. Mariners Weather Log, 5, 151-156. Proudman, J., 1955: The propagation of the tide and surge in an estuary. Royal Society of London, Proceedings, series A, 231, 8-24. Reid, R. O., 1957: On the classification of hurricanes by storm tide and wave energy indices. Meteorological Monographs, 2(10): 58-66. Reynolds, G., 1953: Storm-surge research. Weather, 8, 101-107. Rossiter, J. R., 1954: The North Sea storm surge of January 31, and February 1, 1953. Royal Society of London, Philosophical Transactions, series A, 246, 371-400. , 1962: Tides and storm surges. Royal Society of London, Proceedings, series A, 265, 328-330. Thomasell, A. and Welsh, J. G., 1963: Studies of the Specification of Surface Winds Over the Ocean. Travelers Research Center Report 7049-88. Hartford, Conn. 44 pp. Veronis, G. and Stommel, H, 1956: The action of variable wind stresses on a stratified ocean. Journal of Marine Research, 15, 43- 75. Williams, G. G., Jr., 1968: Microwave radiometry of the ocean and the possibility of marine wind velocity determination from satel- lite observations. Journal of Geophysical Research, 74, 4591-4594. 324 Strategic Role of Perigean Spring Tides, 1635-1976 (19) TIDAL HYDRAULICS; COASTAL PROCESSES (See also category 24.) Bascora, Willard, 1964: Waves and Beaches. Anchor Books, New York, 257 pp. Bauer, H. A., 1960: The margins of the restless ocean: The tides. Natural History, 69, 470-477. Darwin, G. H., 1882: On the geological importance of the tides. Nature, 25, 213-214. Hubbard, Dennis K. and Finley, Robert J., 1973: Tidal Inlet Mor- phology and Hydrodynamics of Merrimack Inlet, Massachusetts, and North Inlet, South Carolina. Coastal Research Division, De- partment of Geology, University of South Carolina, Columbia, S.C. ,260 pp. Hull, E., 1881: Ancient tidal action and planes of marine denuda- tion. Nature, 23, 177-178. Ippen, Arthur T., 1966: Waves and tides in coastal processes. Journal of the Boston Society of Civil Engineers, 53, 158-181. , 1966: Estuary and Coastline Hydrodynamics. McGraw- Hill, New York, 744 pp. Jeffreys, Sir Harold, 1968: Waves and tides near the shore. Royal Astronomical Society, Geophysical Journal, 16, 253-257. Johnson, D. W., 1919: Shore Processes and Shoreline Development. John Wiley, New York, 584 pp. Pillsbury, George B., 1939: Tidal Hydraulics. U.S. Army Corps of Engineers, Washington, D.C., 247 pp. Shepard, Francis P. and Wanless, Harold R., 1971: Our Changing Coastlines, McGraw-Hill, New York, 579 pp. Van Straaten, L. M. J. U., 1950: Giant ripples in tidal channels. Nederlandsch Aardrijkskundig Genootschap, Tijdschrift (Am- sterdam, The Netherlands), 67, 336-341. Wiegel, Robert L., 1965: Oceanographical Engineering, 2d print- ing Prentice-Hall, Englewood Cliffs, N.J., 532 pp. (20) SEASONAL EFFECTS ON TIDES AND SEA LEVEL Brunson, B. A. and Elliott, W. P., 1974: Steric contribution to the seasonal oscillation of sea level off Oregon. Journal of Physical Oceanography, 4(3), 304-309. Gill, A. E. and Niiler, P. P., 1973: The theory of seasonal variability in the ocean. Deep-Sea Research, 20, 141-177. Huyer, A., Pillsbury, R. D., and Smith, R. L., 1975: Seasonal variation of the alongshore velocity field over the continental shelf off Oregon. Limnology and Oceanography, 20, 90-95. Liese, Rudolf, 1969: Uber das jahreszeitliche Wandern schwerer Strumfluten und tiefer Luftdruckwerte und iiber eine Deutung dieser Erscheinung aus Planetenbewegungen (On hte seasonal shifting of the heavy high tides and low pressure values and the possibility of finding an explanation in planetary movements). Deutsche Gewdsserkundliche Mitteilungen (Koblenz, West Ger- many, 13, 132-137. Lisitzin, Eugenie and Pattullo, June G, 1961: The principal fac- tors influencing the seasonal oscillation in sea level. Journal of Geophysical Research, 66, 845-852. Pattullo, J., Munk, W., Revelle, R., and Strong, E., 1955: The seasonal oscillation in sea level. Journal of Marine Research, 14, 88-155. (21) TIDE GAGES AND OTHER TIDE-RECORDING IN- STRUMENTATION; RADAR DETECTION OF EX- TREME TIDAL HEIGHTS; FREQUENCY ANALYSIS OF THE HIGHEST TIDES OF RECORD Harris, D. L. and Lindsay, C. V., 1957: An index of tide gages and tide gage records for the Atlantic and Gulf coasts of the United States. National Hurricane Research Project Report No. 7, U.S. Weather Bureau (now the U.S. Weather Service, NOAA), Washington, D.C., 104 pp. Johnson, E. P., 1967: An example of radar as a tool in forecasting tidal flooding. Environmental Science Services Administration (now the National Oceanic and Atmospheric Administration) Technical Memorandum WBTM-ER-24, Eastern Region Head- quarters, Scientific Services Division, U.S. Weather Service, Gar- den City, N.Y., 7 pp. Lennon, G. W., 1963: A frequency investigation of abnormally high tidal levels at certain west coast ports. Proceedings of the Institute of Civil Engineers, 25, 451-484. Matthaus, W., 1972: On the history of recording tide gauges. Royal Society of Edinburgh, Proceedings, section B, 73, 25-34. Sneyers, Raymond, 1961: Etude des proprietes statistique des plus fortes marees a Ostende [Belgique] (Study of the statistical prop- erties of the highest tides at Ostend [Belgium]), del et Terre (Brussels, Belgium), 77 (4/6), 202-212. (22) LONG- AND SHORT-PERIOD FLUCTUATIONS IN MEAN SEA LEVEL; INFLUENCES ON GEODETIC SURVEYS Disney, L. P., 1955: Tide heights along the coasts of the United States. Proceedings of the American Society of Civil Engineers, 81, 1-9. Doodson, A. T., 1960: Mean sea level and geodesy. Bulletin Geo- desique (Paris, France) , 55, 69-88. Guttenberg, B., 1941: Changes in sea level, postglacial uplift and mobility of the Earth's interior. Geological Society of America, Bulletin, 52, 721-772. Groves, Gordon W., 1956: Periodic variation of sea level induced by equatorial waves in the Easterlies. Deep-Sea Research, 3, 248- 252. Karklin, V. P., 1967: The semi-annual variations in sea level in the Atlantic Ocean. Okeanologiya (Moscow, USSR), 7, 987-996. Kaye, C. A. and Stuckey, G. W., 1973: Nodal tidal cycle of 18.6 yr. : Its importance in sea-level curves of the east coast of the United States and its value in explaining long-term sea-level changes. Geology, I, 141-144. Lafond, E. C, 1939: Variations of sea level on the Pacific coast of the United States. Journal of Marine Research, 2, 17-29. Lisitzin, Eugenie, 1959: The frequency of extreme heights of sea level along the Finnish coast. Merentukinuslaitoksew Julkaisu- Hausforsknings Institutets Skrift, 190, 37 pp. Marmer, H. A., 1925: Sea level along the Atlantic coast of the United States and its fluctuations. Geographical Review, 15, 438-448. , 1951 : Tidal Datum Planes. U.S. Coast and Geodetic Sur- vey Special Publication 135, Washington, D.C., 142 pp. Munk, W. and Revelle, R., 1952: Sea level and the rotation of the Earth. American Journal of Science, 250, 829-833. Namias, Jerome and Huang, J. C. K., 1972: Sea level at southern California: A decadal fluctuation. Science, 177, 351-353. Roden, G. I., 1960: On the nonseasonal variations in sea level along the west coast of North America. Journal of Geophysical Research, 65, 2809-2826. , 1966: Low frequency sea level oscillations along the Pa- cific coast of North America. Journal of Geophysical Research, 71, 4755-4776. Rossiter, J. R., 1967 : An analysis of sea level variations in European waters. Royal Astronomical Society, Geophysical Journal, 12, 259-299. Wunsch, G, 1972: Bermuda sea level in relation to tides, weather and baroclinic fluctuations. Reviews of Geophysics and Space Physics, 10, 1-49. Bibliography on Tides :->2 r > Yamaguti, Seiti, 1965: On the changes in the heights of mean sea- levels, before and after the great Niigata earthquake on June 16, 1964. Tokyo University Earthquake Research Institute, Bulletin, (Tokyo, Japan), 43, 167-172. (23) TIDAL PREDICTIONS, COMPUTATIONS, AND TABLES; ANALYSIS OF OBSERVATIONS, INCLUD- ING DIGITAL COMPUTER PROCESSING (See also category 8.) Doodson, A. T. and Warburg, H. D. (Admiralty, Hydrography De- partment), 1941: Admiralty Manual of Tides. His Majesty's Stationery Office, London, 270 pp. Dos Santos, Franco A., 1966: The semi-graphic method of analysis for seven days of tidal observations. International Hydrographic Review, 43, 75-88. , 1968: The Munk-Cartwright method for tidal prediction and analysis. International Hydrographic Review, 45, 115-165. Dronkers, J. J., 1964: Tidal Computations in Rivers and Coastal Waters. Wiley-Interscience, New York, 518 pp. Harris, D. L., Pore, N. A., and Cummings, R. A., 1965: Tidal and tidal current prediction by high speed digital computer. Inter- national Hydrographic Review, 42, 95-103. Hendershott, M. C, Munk, W. H., and Zetler, B. D., 1974: "Ocean tides from Seasat-A," in: Seasat-A Scientific Contributions. Na- tional Aeronautics and Space Administration, Washington, D.C., 54 pp. National Oceanic and Atmospheric Administration, National Ocean Survey (published annually) : Tide Tables — High and Low Water Predictions ( 1 ) East Coast of North and South America, Including Greenland; (2) Europe and West Coast of Africa, In- cluding the Mediterranean Sea; (3) West Coast of North and South America, Including the Hawaiian Islands; and (4) Central and Western Pacific Ocean, and Indian Ocean (four vols.). National Ocean Survey, Rockville, Md. Rossiter, J. R., 1967: "Analysis and prediction of tides," in: Inter- national Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1543-1545. Schureman, Paul, 1971: Manual of Harmonic Analysis and Predic- tion of Tides. National Ocean Survey (formerly U.S. Coast and Geodetic Survey) Special Publication No. 98, rev. (1940) ed., reprinted 1958 with corrections; 2d reprinting, 1971. U.S. Gov- ernment Printing Office, Washington, D.C., 317 pp. Webb, D. J., 1974: Green's function and tidal prediction. Reviews of Geophysics and Space Physics, 12, 103-1 16. Zetler, B. D., 1967: Shallow-water tide predictions. Proceedings of Symposium on Oceanographical Fish Resources of Tropical At- lantic, 20-28 October 1966. UNESCO, 163-166. (24) TIDE AND TIDAL CURRENT RESPONSES ON THE OCEAN FLOOR; DEEP-SEA CURRENTS Belderson, R. H. and Stride, A. H., 1966: Tidal current fashioning of a basal bed. Marine Geology (Amsterdam, The Netherlands), 4,237-257. Bowden, K. F., 1962: "Measurements of turbulence near the sea bed in a tidal current," in: Turbulence in Geophysics. American Geophysical Union, Washington, D.C., 3181-3186. Cornish, V., 1901 : Sand waves in tidal currents. Geographical Jour- nal, 18. 170-202. Heezen, B. C. and Hollister, C, 1964: Deep-sea current evidence from abyssal sediments. Marine Geology (Amsterdam, The Netherlands),/, 141-174. McAllister, R. F., 1962: "Deep current measurements near Ber- muda," in: Marine Sciences Instrumentation, edited by R. D. Gaul, D. D. Ketchum, J. T. Shaw, and J. M. Snodgrass. Plenum, New York, 210-222. Nowroozi, A. A., Ewing, M., Nafe, J. E., and Fleigel, M., 1968: Deep-ocean current and its correlation with the ocean tide off the coast of northern California. Journal of Geophysical Research, 73, 1921-1932. Nowroozi, A. A., Kuo, J. T., and Ewing, M., 1968: Solid earth and oceanic tides recorded on the ocean floor off the coast of northern California (abstract only). American Geophysical Union Trans- actions, 49, 211-212. (25) TIDAL FRICTION ON THE ROTATING EARTH; ENERGY TRANSFER AND DISSIPATION; VARIA- TION IN THE LENGTH OF THE DAY Curott, D. R., 1966: Earth deceleration from ancient solar eclipses. Astronomical Journal, 71, 264-269. Groves, Gordon W. and Munk, Walter, 1958: A note on tidal friction. Journal of Marine Research, 17, 199-214. Jeffreys, H., 1967: "Tidal friction," in: International Dictionary of Geophysics. Pergamon, Oxford, vol. 2, 1535—1536. Kaula, W. M., 1964: Tidal dissipation by solid friction and the resulting orbital evolution. Reviews of Geophysics and Space Physics, 2, 661-685. , 1969: Tidal friction with latitude dependent amplitude and phase angle. Astronomical Journal, 74, 1108-1114. Lagus, P. L. and Anderson, D. L., 1968: Tidal dissipation in the Earth and planets. Physics of the Earth and Planetary Interiors (Amsterdam, The Netherlands), 1, 505-510. MacDonald, G. J. F., 1964: Tidal friction. Reviews of Geophysics and Space Physics, 2, 467-541. Miller, G. R., 1966: The flux of tidal energy out of the deep oceans. Journal of Geophysical Research, 71, 2485-2489. Minz, Yale and Munk, W., 1951: The effect of winds and tides on the length of day. Tellus (Stockholm, Sweden), 3, 117-121. Munk, W. H., 1968: Once again — tidal friction. Royal Astronomi- cal Society, Quarterly Journal, 9, 352—375. Newton, R. R., 1968: A satellite determination of tidal parameters and Earth deceleration. Royal Astronomical Society Geophysical Journal, 14, 505-539. Ward, W. R., 1975: Tidal friction and generalized Cassini's laws in the solar system. Astronomical Journal, 80, 64-70. (26) EARTH TIDES: TIDAL VARIATION IN THE FORCE OF GRAVITY Clarkson, H. N. and La Coste, L. J. B., 1956: An improved instrument for measurement of tidal variations in gravity. Ameri- can Geophysical Union, Transactions, 37, 266-272. Groten, E. and Brennecke, J., 1973: Global interaction between earth and sea tides. Journal of Geophysical Research, 78, 8519- 8526. Hendershott, M., 1973: Solid earth and ocean tides. Eos (American Geophysical Union, Transactions) , 54, 76-86. Jackson, B. V. and Slichter, L. B., 1974: The residual daily earth tides at the South Pole. Journal of Geophysical Research, 79, 1711-1715. Lambert, W. D., ed., 1940: Report on Earth Tides. U. S. Coast and Geodetic Survey (now National Ocean Survey) Special Publication 223, U.S. Government Printing Office, Washington, D.C., 24 pp. Longman, I. M., 1960: The interpolation of earth tide records. Journal of Geophysical Research, 65, 3801-3804. Marchal, Anatole F., 1960: Les marees terrestes (Earth tides). Industrie (Brussels, Belgium), 74,864-873. Melchior, P., 1964: "Earth tides," in: Research in Geophysics, vol. 2, edited by H. Odishaw. Massachusetts Institute of Technology Press, Cambridge, Mass., 183-193. , 1966: The Earth Tides. Pergamon, Oxford, 458 pp. 202-509 0-78-36 526 Strategic Role of Perigean Spring Tides, 1635-1976 Melchior, P., 1966: Diurnal earth tides and the Earth's liquid core. Royal Astronomical Society, Geophysical Journal, 12, 15-21. Melchior, P. and Georis, B., 1968: Earth tides, precession- nutation and the secular retardation of the Earth's rotation. Physics of the Earth and Planetary Interiors (Amsterdam, The Netherlands), 7,267-287. Molodensky, M. S., 1961: The theory of nutation and diurnal earth tides. Communications de VObservatoire Royal de Belgique, Serie Geophysique, 172, 25-56. Nishimura, E., 1950: On earth tides. American Geophysical Union, Transactions, 31, 357-376. Prothero, W. A. and Goodkind, J. M., 1972: Earth tide measure- ments with the superconducting gravimeter. Journal of Geo- physical Research, 77, 926-937. Stacey, Frank D., 1969: Physics of the Earth (1st ed.), section 3.4. Wiley, New York, 59-64. (27) TIDAL LOADING; ELASTIC STRAIN; DEFORMA- TION; TILT; AND DEFLECTION OF THE VERTI- CAL Farrell, W. E., 1972: Deformation of the Earth by surface loads. Reviews of Geophysics and Space Physics, 10, 761-797. , 1972: Global calculations of tidal loading. Nature, 238, 43-47. • , 1973: Earth tides, ocean tides and tidal loading. Royal So- ciety of London, Philosophical Transactions, series A, 274, 253- 254. Lambert, A., 1970: The response of the Earth to loading by the ocean tides around Nova Scotia. Royal Astronomical Society, Geophysical Journal, 19, 449-477. Lennon, G. W., 1961: The deviation of the vertical in response to the attraction of the ocean tides. Royal Astronomical Society, Geophysical Journal, 6, 64-84. Longman, I. M., 1966: Computation of Love numbers and load deformation coefficients for a model Earth. Royal Astronomical Society, Geophysical Journal, 11, 133-149. Takeuchi, H., 1950: On the earth tide of the compressible Earth of variable density and elasticity. American Geophysical Union, Transactions, 31, 651-689. Warburton, R. J., Beaumont, C, and Goodkind, J. M., 1975: The effect of ocean tide loading on tides of the solid Earth observed with the superconducting gravimeter. Royal Astronomical So- ciety, Geophysical Journal, 43, 707-720. Zadro, M. B., 1972: Earth tides and ocean load effects recorded at Trieste. Bollettino di Geofisica Teorica ed Applicata (Trieste, Italy), 14(5), 192-202. (28) EARTH TIDES: GROUND-WATER RESPONSES IN WELLS AND RESERVOIRS Bredehoeft, J. D., 1967: Well-aquifer systems and earth tides. Journal of Geophysical Research, 72, 3075-3087. George, W. O. and Romberg, F. E., 1951: Tide producing forces and artesian pressures. American Geophysical Union, Transac- tions, 32, 369-371. Pekeris, C. L., 1940: "Note on tides in wells," in: Report on Earth Tides, edited by W. D. Lambert. U.S. Coast and Geodetic Survey (now National Ocean Survey) Special Publication 223, U.S. Government Printing Office, Washington, D.C., 23-24. Rinehart, J. S., 1972: Fluctuations in geyser activity caused by variations in earth tidal forces, barometric pressure and tectonic stresses. Journal of Geophysical Research, 77, 342-350. Robinson, T. W., 1939: Earth-tides shown by fluctuations of water level in wells in New Mexico and Iowa. American Geophysical Union, Transactions, 20, 656-666. (29) EARTH TIDES: DETERMINED FROM ANALYSIS OF ORBITAL PERTURBATIONS OF ARTIFICIAL SATELLITES Lambeck, Kurt, Cazenave, Anny, and Balmino, Georges, 1974: Solid earth and ocean tides estimated from satellite orbit analyses. Review of Geophysics and Space Physics, 12 ( 3 ) , 42 1 , 434. Smith, D. E., Kolenkiewicz, R., and Dunn, P. J., 1973: A deter- mination of the earth tidal amplitude and phase from the orbital perturbations of the Beacon Explorer C spacecraft. Nature, 244, 498-499. (30) HYDRODYNAMICS; FIGURES OF THE EARTH AND MOON Benjamin, T. B. and Ursell, F., 1954: The stability of the plane free surface of a liquid in vertical periodic motion. Royal Society of London, Proceedings, series A, 225, 505-515. Bullard, E. C, 1948: The figure of the Earth. Royal Astronomical Society, Monthly Notices, Geophysical Supplement, 5, 186—192. Darwin, G. H., 1887: On Jacobi's figure of equilibrium for a rotating mass of fluid. Royal Society of London, Proceedings, series A, 47,319-336. , 1899-1900: The theory of the figure of the Earth carried to the second order of small quantities. Royal Astronomical Society, Monthly Notices, 60, 82-124. , 1906: On the figure and stabil'ty of a liquid satellite. Royal Society of London, Philosophical Transactions, series A, 206, 161-248. Jeffreys, H., 1948: The figures of the Earth and the Moon. Royal Astronomical Society, Monthly Notices, Geophysical Sup- plement, 5, 219-247. , 1953: The figures of rotating planets. Royal Astronomical Society, Monthly Notices, 113, 97-105. , 1964: On the hydrostatic theory of the figure of the Earth. Geophysical Journal, 8, 196-202. Khan, Mohammad Asadullah, 1967: Some parameters of a hydro- static Earth. American Geophysical Union, Transactions, 48, 56. , 1968: A re-evaluation of the theory for the hydrostatic figure of the Earth. Journal of Geophysical Research, 73, 5335- 5342. (31) TIDE EFFECTS ON THE ORBITS OF ARTIFICIAL SATELLITES Douglas, B. C, Klosko, S. M., Marsh, J. G, and Williamson, R. G, 1974: Tidal perturbations on the orbits of Geos-1 and Geos-2. Celestial Mechanics, 10, 165-178. Felsentreger, T. L., Marsh, J. G., and Agreen, R. W., 1976: Anal- yses of the solid earth and ocean tidal perturbations on the orbits of the Geos 1 and Geos 2 satellites. Journal of Geophysical Re- search, 81 ,2557-2563. Groves, Gordon V., 1960: On tidal torque and eccentricity of a satellite's orbit. Royal Astronomical Society, Monthly Notices, 727,497-502. Kozai, Y., 1965: Effects of the tidal deformation of the Earth on close Earth satellites. Publications of the Astronomical Society of Japan, 77,395-402. Musen, P. and Estes, R., 1972: On the tidal effects in the motion of artificial satellites. Celestial Mechanics, 6, 4—21. Musen, P. and Felsentreger, T., 1973: On the determination of long period tidal perturbations in the elements of artificial Earth satellites. Celestial Mechanics, 7, 256-279. Newton, R. R., 1965: An observation of the satellite perturbation produced by the solar tide. Journal of Geophysical Research, 70, 5983-5989. Bibliography on Tides 527 Newton, R. R., 1968: A satellite determination of tidal parameters and Earth deceleration. Royal Astronomical Society. Geophysical Journal, 14, 505-539. (32) CORRELATION OF EARTHQUAKES WITH EARTH TIDES AND OTHER LUNISOLAR INFLUENCES; TIDAL INTERRELATIONS WITH MOONQUAKES Allen, M. W., 1936: The lunar triggering of earthquakes in south- ern California. Seismological Society of America, Bulletin, 26, 147-157. Chapman, W. B. and Middlehurst, B. M., 1974: Moonquake pre- determination and tides. Icarus, 21 , 427—436. Heaton, T. H., 1975: Tidal triggering of earthquakes. Royal Astro- nomical Society, Geophysical Journal, 43, 307-326. Klein, Fred W., 1976: Earthquake swarms and the semidiurnal, solid earth tide. Royal Astronomical Society, Geophysical Journal, 45, 245-295. Knopoff, L., 1964: Earth tides as a triggering mechanism for earth- quakes. Seismological Society of America, Bulletin, 54, 1865- 1870. ■ 1970: Correlation of earthquakes with lunar orbital mo- tions. The Moon: An International Journal of Lunar Studies (Dordrecht, The Netherlands) , / , 484-485. Ryall, A., Van Wormer, J. D., and Jones, A. E., 1968: Triggering of microearthquakes by earth tides, and other features of the Truckee, California, earthquake sequence of September, 1966. Seismological Society of America, Bulletin, 58, 215-248. Sadeh, D. S. and Meidav, M., 1973: Search for sidereal periodicity in earthquake occurrences. Journal of Geophysical Research, 78, 7709-7716. 1975: Possible solar effects on earthquake occurrences. Journal of Geophysical Research, 80, 3378-3380. Shlien, S., 1972: Earthquake-tide correlation. Royal Astronomical Society, Geophysical Journal, 28, 27-34. Tamrazyan, G. P., 1967: Tide-forming forces and earthquakes. Icarus, 7, 59-65. 1968: Principal regularities in the distribution of major earthquakes relative to solar and lunar tides and other cosmic sources. Icarus, 9, 574-592. (33) ATMOSPHERIC TIDES; POSSIBLE LUNITIDAL COR- RELATIONS WITH ATMOSPHERIC PRECIPITA- TION Adderley, E. E. and Bowen, E. C, 1962: Lunar component in pre- cipitation data. Science, 137, 749-750. Bradley, D. A., Woodbury, M. A., and Brier, G. W., 1962: Lunar synodical period and widespread precipitation. Science, 137, 748- 749. Brier, G. W., 1965: Lunar tides, precipitation variations and rain- fall calendaricities. New York Academy of Sciences, Transactions, 27,676-688. Chapman, S. and Lindzem, R. S., 1970: Atmospheric Tides: Ther- mal and Gravitational. Gordon and Breach, New York, 200 pp. Fedorov, K. N., 1959: The causes of the semi-annual periodicity in atmospheric and oceanic processes. Akademiya Nauk SSSR, Izvestiya, Seriya Geograficheskaya (Moscow, USSR), 4, 17-25. Hines, C. O., 1966: Diurnal tide in the upper atmosphere. Journal of Geophysical Research, 71 , 1453. Hollingsworth, A., 1971 : The effect of ocean and earth tides on the semidiurnal lunar air tide. Journal of Atmospheric Science, 28, 1021-1044. Lindzen, R. S. and Chapman, S., 1969: Atmospheric tides. Space Science Review, 10, 1-188. Muller, H. G., 1966: Atmospheric tides in the meteor zone. Planetary and Space Science, 14, 1253-1272. O'Mahony, G., 1965: Rainfall and Moon phase. Royal Meteorologi- cal Society, Quarterly Journal, 91, 196-208. Woodrum, Arthur and Justus, C. G., 1968: Atmospheric tides in the height region 90 to 120 kilometers. Journal of Geophysical Research, 73, 467-478. (34) TIDAL CURRENTS: OBSERVATION, MEASURE- MENT, AND PREDICTION TABLES Bowden, K. F. and Howe, M. R., 1963: Observations of turbulence in a tidal current. Journal of Fluid Mechanics, 17, 271-284. Dyer, K. R., 1970: Current velocity profiles in a tidal channel. Royal Astronomical Society, Geophysical Journal, 22, 153—161. Hughes, P., 1969: Submarine cable measurements of tidal cur- rents in the Irish Sea. Limnology and Oceanography, 13, 269-278. Marmer, H. A., 1923: Flood and ebb in New York Harbor. Geo- graphical Review, 13, 413-444. National Oceanic and Atmospheric Administration, National Ocean Survey (published annually) : Tidal Current Tables (1) Atlantic Coast of North America; and (2) Pacific Coast of North America and Asia (2 vols.). National Ocean Survey, Rockville, Md. Pritchard, D. W., 1955: Estuarine circulation patterns. American Society of Civil Engineers, Proceedings, 81 (Separate 717), 1—11. Richardson, W. S., Stimson, P. B., and Wilkins, C. H., 1963: Cur- rent measurements from moored buoys. Deep-Sea Research, 10, 369-388. Sager, Giinther, 1968: Maximal Geschwindigkeit des Gezeiten- stroms zur mittleren Springzeit in der Nordsee, dem Kanal und der Irischen See (Maximum velocity of tidal currents in the sea- son of the mean springtides in the North Sea, the English Chan- nel and the Irish Sea). Beitrage zur Meerskunde (Berlin, West Germany), No. 22, 53-59. Shepard, F. P. and Marshall, N. F., 1969: Currents in La Jolla and Scripps submarine canyons. Science, 165, 177-178. U.S. Naval Oceanographic Office, 1965 : Oceanographic Atlas of the North Atlantic Ocean; Section I — Tides and Currents (Publica- tion No. 700). U.S. Naval Oceanographic Office, Washington, D.C., 75 pp. (35) SALINITY EFFECTS OF TIDAL AND CURRENT MOVEMENTS Garvine, R. W., 1975: The distribution of salinity and temperature in the Connecticut River estuary. Journal of Geophysical Re- search, 80, 1176-1183. Ippen, Arthur, T. and Harleman, Donald R. F., 1961: One-dimen- sional analysis of salinity intrusion in estuaries. U.S. Army Corps of Engineers, Committee on Tidal Hydraulics, Technical Bul- letin 5, Vicksburg, Mississippi, 7-48. Keulegan, G. H., 1966: "The mechanism of an arrested saline wedge," in: Estuary and Coastline Hydrodynamics. McGraw-Hill, New York, 546-574. Meade, R. H, 1966: Salinity variation in the Connecticut River. Water Resources Research, 2, 567-579. Turner, J. S., 1965: The coupled turbulent transports of salt and heat across a sharp density interface. International Journal of Heat and Mass Transfer, 8, 759-767. , 1967: Salt fingers across a density interface, Deep-Sea Re- search, /f, 599-611. Wright, L. D. and Coleman, J. M., 1971: Effluent expansion and interfacial mixing in the presence of a salt wedge, Mississippi River delta. Journal of Geophysical Research, 76, 8649-8661. -;2H Strategic Role of Perigean Spring Tides, 1635-1976 (36) WATER TEMPERATURE VARIATIONS RESULTING FROM TIDAL AND CURRENT MOVEMENTS; DENSITY STRATIFICATION AND ENTRAINMENT Bryan, K., 1962: Measurements of meridional heat transport by ocean currents. Journal of Geophysical Research, 67, 3403-3414. Cairns, J. L., 1968: Thermocline strength fluctuations in coastal waters. Journal of Geophysical Research, 73, 2591-2959. Ingram, R. Grant, 1976: Characteristics of a tide-induced estuarine front. Journal of Geophysical Research, 81, 1951-1959. LaFond, E. C, 1961: The isotherm follower. Journal of Marine Research, 19, 33-39. Munk, Walter and Anderson, Ernest R., 1948: Notes on a theory of the thermocline. Journal of Marine Research, 7, 276-295. Skogsberg, T., 1936: Hydrography of Monterey Bay, California. Thermal conditions, 1929-1933. American Philosophical Society, Transactions, 29, 1-152. (37) ELECTROMAGNETIC EFFECTS ASSOCIATED WITH VELOCITY OF TIDAL CURRENTS Arx, W. S. von, 1950: An electromagnetic method for measuring the velocities of ocean currents from a ship under way. Papers in Physical Oceanography and Meteorology, 1 1 (3), 1-62. Cox, C, Teramoto, T., and Filloux, J., 1964: "On coherent electric and magnetic fluctuations in the sea," in Studies on Ocean- ography, edited by Kozo Yoshida. University of Washington Press, Seattle, 449-451. Longuet-Higgins, M. S., Stern, M. E., and Stommel, H., 1954: The electric field induced by ocean currents and waves, with applications to the methods of towed electrodes. Papers in Physi- cal Oceanography and Meteorology, 13 (1), 1-37. Olsson, B. H., 1955: The electrical effects of tidal streams in Cook Strait, New Zealand. Beep-Sea Research, 2, 204-212. Sanford, T. B., 1971: Motionally induced electric and magnetic fields in the sea. Journal of Geophysical Research 76, 3476- 3492. Young, R. B., Gerrard, H., and Jevons, W., 1920: On electrical disturbances due to tides and waves. Philosophical Magazine, series 6, 40, 149-159. (38) PRACTICAL EFFECTS OF TIDES AND CURRENTS Bleakney, J. S., 1972: Ecological implications of annual variations in tidal extremes. Ecology, 53, 933-938. Hay, J. and Farb, P., 1969: The Atlantic Shore: Human and Natu- ral History from Long Island to Labrador. Harper & Row, New York, 246 pp. Heaney, F. L., 1960: Design, construction and operation of sewer outfalls in estuarine and tidal waters. The Journal of Water Pollution Control Federation, 32, 610-621. Jensen, H. A. P., 1953: Tidal inundations, past and present, parts I, II. Weather, 8, 108-113. Markert, Robert E., Markert, Betsy J., and Vertress, Nancy J., 1961 : Lunar periodicity in spawning and luminescence in Odon- tosyllis enopla. Ecology, 42, 414-415. National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1975: Ocean Dumping in the New York Bight. NOAA Technical Report ERL 321-MESA 2, Boulder, Colo., 78 pp. , 1976: Evaluation of Proposed Sewage Sludge Dumpsite Areas in the New York Bight. NOAA Technical Memorandum ERL MESA-1 1 , Boulder, Colo., 2 1 2 pp. National Oceanic and Atmospheric Administration, Office of Coastal Zone Management, 1976: Natural Hazard Management in Coastal Areas. Prepared under contract for the U.S. Depart- ment of Commerce at the Institute of Behavioral Science, Pro- gram of Research on Technology, Environment and Man, the University of Colorado. Office of Coastal Zone Management, NOAA, Washington, D.C., 295 pp. Niles, T. M., 1957: Dispersal of pollution by tidal movements. American Society of Civil Engineers, Proceedings, 83-SA5, Paper No. 1408, 18 pp. Sager, Gunther, 1959: Gezeiten und Schiffahrt (Tides and Navi- gation). Fachbuchverlag, Leipzig, East Germany, 173 pp. Steers, J. A., 1971: "The east coast floods [England] 31 January- 1 February 1953," in: Applied Coastal Geomorphology, edited by J. A. Steers, Macmillan, New York, 198-223. (39) TIDAL POWER Bernshtein, L. B., 1965: Tidal Energy for Electric Power Plants (translated from the Russian 1961 ed.) U.S. Department of Commerce, Clearinghouse for Federal Scientific and Technical Information (now National Technical Information Service), Springfield, Va., 378 pp. Clancy, Edward P., 1970: "The power plant at La Ranee," in: Man and the Sea, edited by Bernard L. Gordon. Natural History Press, Garden City, N.Y., 443-449. Davey, Norman, 1923: Studies in Tidal Power. Constable and Co., London, 255 pp. Ericson, David B. and Wollin, Goesta, 1967: The Ever-Changing Sea. Knopf, New York, 342-343. Gray, T. J. and Gashus, O. K., eds., 1972: Tidal Power. Plenum Press, New York, 6.30 pp. International Passamaquoddy Engineering Board, 1959: Investi- gation of the International Passamaquoddy Tidal Power Project; Report to the International Joint Commission by the Interna- tional Passamaquoddy Engineering Board, Ottawa, Ontario, Canada, and Washington, D.C., 271 pp. Ippen, Arthur T. and Harleman, Donald R. F., 1958: Investigation on Influence of Proposed International Passamaquoddy Tidal Power Project on Tides in the Bay of Fundy. Massachusetts In- stitute of Technology, Cambridge, 31 pp. Laba, Jan T., 1964: Potentials of Tidal Power on the North At- lantic Coast in Canada and United States. American Society of Civil Engineers, Proceedings, of Ninth Conference on Coastal Engineering, Lisbon, Portugal, June, 1964, 832-857. Wilson, E. M., 1973: Energy from the sea — tidal power. Under- water Journal and Information Bulletin, 5(4), 175-186. (40) HISTORY OF TIDAL AND TIDE-RELATED ASTRO- NOMICAL OBSERVATIONS, MEASUREMENTS, THEORIES, AND PREDICTIONS Aleem, A. A., 1967: Concepts of currents, tides and winds among medieval Arab geographers in the Indian Ocean. Deep-Sea Research, 14, 459-463. Deacon, Margaret, 1971: Scientists and the Sea, 1650-1900; A Study of Marine Science, chapter 5 "Theories and Observations of Tides," and chapter 12 "Wild-Meeting Oceans: The Study of Tides." Academic Press, New York, 445 pp. Muller, P. M. and Stephenson, F. R., 1975: "The acceleration of the Earth and Moon from early astronomical observations," in: Growth Rhythms and History of the Earth's Rotation, edited by S. K. Runcorn and G. D. Rosenberg. Wiley-Interscience, New York, 560 pp. Bibliography on Tides r )L") Newton, R. R., 1970: Ancient astronomical observations and the accelerations of the Earth and Moon. Johns Hopkins Press, Balti- more, 749 pp. Rossiter, J. R., 1972: The history of tidal predictions in the United Kingdom before the twentieth century. Royal Society of Edinburgh, Proceedings, section B, 73, 13-23. (41) LUNAR INFLUENCES IN GEOMAGNETISM (COR- RELARY TO INCREASED TIDAL EFFECTS) Bell, Barbara and Defouw, Richard J., 1964: Concerning a lunar modulation of geomagnetic activity. Journal of Geophysical Re- search, 69, 3169-3174. , 1966: On the lunar modulation of geomagnetic activity. 1884-1931 and 1932-1959. Journal of Geophysical Research, 71, 4599-4603. Bigg, E. K., 1963: The influence of the Moon on geomagnetic disturbances. Journal of Geophysical Research, 68, 1909-1913. , 1963: Lunar and planetary influences on geomagnetic dis- turbances. Journal of Geophysical Research, 68, 4099-4104. Cochrane, N. A. and Srivastava, S. P., 1974: Tidal influence on electric and magnetic fields recorded at coastal sites in Nova Scotia, Canada. Journal of Atmospheric and Terrestrial Physics, 36, 49-59. Jackson, J. S., 1971: Diurnal variation of the geomagnetic field, 2. The lunar variation. Journal of Geophysical Research, 76, 6909-6914. Michel, F. C, Dessler, A. J., and Walters, G. K., 1964: A search for correlation between K P and the lunar phase. Journal of Geophysical Research, 69,4177-4181. Rassabach, M. E., Dessler, A. J., and Cameron, A. G. W., 1966: The lunar period, the solar period, and K p . Journal of Geophysical Research, 71, 4141-4146. Stolov, Harold L. and Cameron, A. G. W., 1964: Variations of geomagnetic activity with lunar phase. Journal of Geophysical Research, 69, 4975-4982. Stolov, H. L., 1965: Further investigations of a variation of geo- magnetic activity with lunar phase. Journal of Geophysical Re- search, 70,4921-4926. (42) BIBLIOGRAPHIES, SOURCE BOOKS, GLOSSARIES, AND STATE-OF-THE-ART LITERATURE RELATIVE TO TIDES AND TIDAL CURRENTS American Meteorological Society, 1965: Meteorological and Geo- astrophysical Abstracts. Collected Bibliographies on Physical Oceanography (1953-1964), Malcolm Rigby, ed., part IV, An- notated Bibliography on Storm Surges, by M. P. Kramer, pp. 370- 392. American Meteorological Society, Washington, D.C., 807 pp. Association d'Oceanographique Physique, Union Geodesique et Geophysique Internationale, 1955: Bibliography on tides 1665— 1939. Publications in Science, 15, 220 pp. , 1957: Bibliography on tides 1940-1954. Publications in Science, 17, 63 pp. , 1971: Bibliography on tides 1955-1969. Publications in Science, 29, 19-40. Baker, B. B., Jr., Deebel, W. R., and Geisenderfer, R. D., 1966: Glossary of Oceanographic Terms, 2d ed. (S.P.-35). Department of the Navy, U.S. Naval Oceanographic Office and U.S. Govern- ment Printing Office, Washington, D.C., 240 pp. Bretschneider, C. L. and Pick, G S., 1966: A Bibliography on Storm Surges and Related Subjects, Sponsored by Office of Naval Re- search (unclassified). Clearinghouse for Federal Scientific and Technical Information (now National Technical Information Service) , Springfield, Va., 48 pp. Pore, N. A., 1970: Summary of Selected Reference Material on the Oceanographic Phenomena of Tides, Storm Surges, Waves, and Breakers. Weather Bureau Technical Memorandum WBTM TDL 30, Environmental Science Services Administration (now the National Oceanic and Atmospheric Administration), Silver Spring, Md., 103 pp. Schureman, Paul, 1975: Tide and Current Glossary. Revised by Steacey D. Hicks. (Formerly U.S. Coast and Geodetic Survey Special Publication No. 228), U.S. Government Printing Office, Washington, D.C., 25 pp. Wiegel, Robert L., 1953: Waves, Tides, Currents and Beaches: Glossary of Terms and List of Standard Symbols. Council on Wave Research, The Engineering Foundation, University of California, Berkeley, Calif., 113 pp. Index Accelerate currents at perigee-syzygy 95, 98,105,106,485,489 Aeronomy: tidal winds 494 Age of parallax inequality 298 Age of phase inequality 297 Almucantars 123 Angle of eccentricity 127 Annual equation 165,270,292,435 Annual variation 159 Anomalistic month 130, 275, 288, 318, 436 gain in length perigee-syzygy 288 length variations 287, 288, 290 mean value 287 relation to synodic month 284-290 Anomalistic tides 115 Apparent motion 125 Aphelion 130 Apogee 130 figure of lunar obit at 208 Apogee-syzygy : lunar parallax 207 new moon at 216 Apse 142 Astronomical positions : methods of defining 121 Astronomical tidal forces 497 Atmospheric tides 488, 489 geomagnetic fluctations caused by 488, 489 Augmented tide-raising forces 11, 203, 218, 313 Autumnal equinox 122, 190 Azimuth 123 Baguio 25 Barycenter : Earth-Moon system 498 Earth-Sun system 501 Beach flooding 102 Biological rhythms 495 Bridge construction — influence of perigean spring tides : explosive decompression of caissons 94 Firth of Forth caisson 94 hydrostatic pressure changes caused by tides 94 effects of accelerated currents 96 Calendar styles: conversion 1 Camel (buoyancy device) 60, 70 Page Carbon dioxide variations in seawater 100 Catch-up motions: duration of tide-raising forces. 269, 271 Celestial equator 121 Celestial latitude 123 Celestial longitude 7, 123 lunar motion in 192 Celestial meridian 122, 123 Center-of-mass : Earth-Moon system 498 Centrifugal force: Earth-Moon system 498 in lunar orbit 498 Charleston Harbor, S.C., effects of perigean spring tides on Second Battle of 70-78 Coastal processes: foreshore undercutting 84, 424 historical aspects of 85 perigean spring tides in relation to 84 Computational sources 13 Conjunction 7 Coplanar lunisolar alignment 199-203, 218, 313, 435 Coplanar lunisolar declinations 198, 201-202, 218, 435 Crustal tilt 494 Daily lunar retardation 137, 271 Data source selection 327 Declination 121 maximization in 18.6-year nodical cycle 189 Deflection of the vertical 494 Delta omega-syzygy coefficient 435, 436, 440, 475 Differential tide-producing forces 498 Direct tides 500 Diurnal inequality 152, 198, 475, 503 nullified 204 Docking, effect of perigean spring tides on 96 Draconitic month 126 Duration of tide-raising forces 192, 271, 306 Earth astronomical motions 124 Earth-Moon system: center of mass 498 centrifugal force 498 Earth's rotation: catch-up on Moon at perigee-syzygy 270 catch-up on Moon's orbital motions 126, 272 diurnal 124, 198 Earth tides 492, 493 531 532 Index Earthquake triggering potential : Page at apogee-syzygy 487 at perigee-syzygy 487 East Coast (North America) : Connecticut River hydrographic data 69 Connecticut River, navigation problems 70 Connecticut River, perigee-syzygy high water 69 Connecticut River, phase and parallax ages 69 Connecticut River, tidal response 69 Connecticut River, tide heights 69 Connecticut River, water depth over sandbars 65, 70 Connecticut River, water depths 60, 64 Connecticut River, 1771 chart 60 North Carolina, Bodie's Island inundated 85 North Carolina, Hatteras Inlet, Civil War 87, 89 North Carolina, Hatteras Inlet formation 85-88 North Carolina, Pamlico Sound 85, 86 Nova Scotia, Saxby Tide 112 South Carolina, Charleston Harbor 70-74 South Carolina, Port Royal Entrance 79, 80, 83, 84 South Carolina, Port Royal Sound, Civil War 78 Ebb Currents 96, 98, 485 duration of 96 Eccentricity 127, 173, 176, 179, 216, 217 Echo-sounding 97 Eclipses 7 Ecliptic 1, 2, 7, 198, 199, 202 Ecliptic system 7, 122 coordinate transformation to equatorial system- _ 124 Ecology : extreme high and low tides, effect on 98, 485, 494 Ellipse 127 Elliptic terms: lunar orbit 175 Elliptic variation (inequality) 159, 179 Entrainment 99 Ephemeris time 13 Epoch of osculation 216 Epoch: tidal constituent 297 Equatorial horizontal parallax 174 Equatorial system 121 coordinate transformation to ecliptic system 124 coordinate transformation to horizon system 124 Equinoctial colure 122 Equinoctial tides 150 Erosion 31, 36, 84, 424, 481 Estuarine environment 99, 482, 485 Estuarine pollution 100, 483 flushing by tides 98, 102 Euryhaline organisms 99 Evaporation basins 99 Evection term: lunar parallax 175 Exogee 316 Extreme low water 31, 33, 34, 93, 426 Extreme proxigean spring tides 316 Page Fetch 6,437 First point of Aries 122 Fish migration: tidal currents 495 Flattening of Earth's poles 148 Flood tide currents 96 Flounder — behavior in accelerated currents 102 Full moon: parallax near apogee-syzygy 215 parallax near perigee-syzygy 214 increased cloudiness at perigee 486 Gaussian gravitational constant 187 Geocentric distance: at time of perigean spring tides 25-28, 481 Earth from Sun 144 Moon from Earth 143 relation to geocentric horizontal parallax 142 Geocentric parallax 134, 148, 224 Geoid 124 Geomagnetic fluctuations due to atmospheric tides — 488 Geomagnetism: lunar tides 494 Geophysical investigations : tidal effects 107, 485 Gravitational force: Earth-Moon system 498 Gravitational force potential 187 Greenwich hour angle 122 Greenwich mean astronomical time 13 Greenwich mean time 13 Grunion : avoidance of peak of perigean spring tides 101, 102 biological clock 101 Gulf Coast: smaller tidal ranges 96, 300, 406, 408 Harmonic analysis: methods 294-296, 475 High water springs: mean range 297 Highest astronomical tide 31 Horizon 123 Horizon system 123 coordinate transformation to equatorial system 124 Hour angle subsystem 122, 134 Hour angles 122 Hour circles 122 Hurricanes 3,6,481 examples 25 frequency 321 intensity classification 25 nomenclature 28 Hydrological runoff 102 blocked by tides 31, 35, 482 Interdisciplinary cooperation 495 Internal waves: lunar syzygy 494 "Inverted barometer" effect 6, 408, 420 Julian Day 229 Kepler's laws of planetary motion 127, 129, 130 Lagging of the tides 303, 504 Latus rectum 217 Page Line of apsides 142 forward motion 179 Low tides extreme: adverse effects 105 beneficial effects 105 caisson blowouts 94, 105 deep-draft vessel strandings 95, 105, 483 exposure of seafloor 105 extreme at perigee-syzygy 31, 33, 34, 93, 426 fixed marine structure repair 105 gangplank adjustment 95, 105 moored vessel groundings 105 offloading belt adjustment 105 offshore winds accompanying 6, 12, 105 Lower branch of meridian 122 Lower transit 122 Lunar apsides cycle 292, 293 Lunar ascending node: vernal equinox coinci- dence 190, 193, 196 Lunar augmentation 147, 202 Lunar day 137, 139, 269, 271, 272, 504 duration 7 relation to solar day 271 variations in length 272 Lunar declination 218, 503 effect on motion in right ascension 193 regional effects on tides 148 relation to right ascension 149 Lunar descending node : vernal equinox coincidence. 1 90 Lunar eclipses 1 ; 2, 7, 198 Lunar evection 153, 154, 175, 302 analysis of equation for 173 effect of solar gravitation 214 perigee-syzygy, at 174 Lunar evection effects 162, 163, 170, 175 diurnal tidal analysis 172 fortnightly tide analysis 172 semidiurnal tide analysis 172 Lunar months, lengths: anomalistic 131 draconitic 126 sidereal 126 sinodic 126 tropical 126 Lunar motion: in celestial longitude. _ 146, 192, 309, 310 Lunar orbital relationships : alternate solar acceleration and deceleration of Moon in orbit 156 alternate solar acceleration and deceleration of Moon with respect to Earth 157 angular velocity 214, 309, 310, 504 apogee-quadrature 175, 207 Index 533 Lunar orbital relationships — Continued Page apparent daily motion 197 centrifugal force component 498 declination angle 272 eccentricities 155, 169, 205, 272 eccentricity at perigee-syzygy 174, 179, 217 effect of maximum declination on motion in right ascension 192, 268 elliptic inequality 175 evection 5, 216, 272 figure 127, 128, 207 figure at apogee-quadrature 207 figure at quadrature 208 figure at syzygy 208 figure, interpretation of 205 figure, variations in 214 geocentric inclination 196, 272 in right ascension 132-135, 196-226 in true anomaly 266 increased daily motion in longitude 196 long-term perturbation effects 272 maximum inclination to ecliptic 123 maximum motion in right ascension 196 mean daily motion 127 mean eccentricity 173 mean inclination to ecliptic 123 osculation, epoch of 216 parallax increase 197 perigee-quadrature 175 perturbation equations 217 proxigee-syzygy 218 radius of curvature 158, 205, 207 relative motion in declination 192 relative motion in right ascension 192 seasonal influences 219 semimajor axis 128, 173, 218 solar gravitational effects 214 solar perturbation component at apogee 207 solar-produced eccentricities 209 Sun at apsides 175 syzygy-apse orientation 197 tangential forces 173 topocentric inclination 193, 196 variation increases eccentricity 219 velocity and perturbations 173 velocity at large parallax 192 velocity at perigee 216 velocity at small parallax 192 velocity decrease at perihelion 271 velocity in anomalistic month 192 velocity variations 157, 158, 192 Lunar nodes: coincidence with equinoxes 199 Lunar nodical cycle 189, 291 declination maximization 189 534 Index Lunar parallactic inequality 159, 435, 502 summary analysis 176 Lunar parallax: absolute maximum 159, 203, 219, 220 absolute minimum 159, 219 angle to linear distance conversion 212 apogee value of 212 apogee-syzygy value of 207 decrease toward apogee-quadrature 208 effect of solar gravitation 214 evection effects on 219 maximum winter values 218 perigee-apogee comparison 210 perigee-quadrature value of 208 perigee-syzygy value of 174, 205, 210, 211, 213 solar perigee (perihelion) value of 199,218 syzygy value of 175, 208 variation effects on 219 Lunar parallax age: local variation in tide arrival 273 Lunar perigee : motion of 177-184 Lunar period : modified by lunar apsides cycle 292 Lunar phase age: local variation in tide arrival 273 Lunar reduction 159 Lunar retardation 137, 272, 504 Lunar right ascension: motion decrease in 196 motion increase in 196 velocity in, and catch-up time 196 Lunar variation 155,301 Lunar variation effects : analysis of equations for 173 diurnal tidal analysis 172 fortnightly tidal analysis 173 perturbative 156, 160, 162, 165, 175 semidiurnal tidal analysis 172 Lunisolar declinational constituent 298 Lunitidal intervals 139 Major axis 127 Marconi's tower 93 Marine ecobiology 100 Marine engineering 96 Marine technology 93 Marine temperature variations 100 Maritime technology 93 Marshlands 99 Maximum perigean spring tide 313 Maximum perigee springs 203 Mean anomaly: lunar parallax 175 Mean daily lunar retardation 138, 272 Mean distance 127 Mean high-water lunitidal interval 297 Page Mean longitude : sinusoidal variation with true longi- tude 184 Mean lunar day 138, 272, 273 derivation of length and mean solar days 272 Mean vs. true motions 164, 176, 177 Mean parallax 212 Mean sidereal month 138 Mean sidereal time 125 Mean solar day 125 Mean solar time 13, 125 Mean Sun 125 Mean tidal day 138, 273 Metonic cycles 296 Minor axis 127 Mixed tides 298 diurnal inequality__I 474 Moon: angular velocity at apogee-quadrature 143 angular velocity at apogee-syzygy 143 angular velocity at perigee-quadrature 143 angular velocity at perigee-syzygy 143 apparent motion in right ascension 140 celestial latitude, limits of 123 conditions for closest approach 219 daily angular velocities 130 effect of parallax on apparent motion 133 geomagnetic variations 489 local meridian transit 272 maximum declinations 190 mean anomalistic period of revolution 131 mean daily motion 127 mean daily synodic motion 138 mean diurnal geocentric motion 134 mean diurnal topocentric motion 134 mean sidereal rate of revolution 130 motion calculated in geocentric coordinates 133 motion calculated in topocentric coordinates 133 motion in declination 132 relative angular speed of revolution 127 revolution around Earth 125 true parallax 175 National Ocean Survey: tide gages 506 Navigation : perigean spring tides, effects on 96, 483 tides in shallow harbors, effects on 68 Neap tides 501 New Moon: parallax near apogee-syzygy 216 parallax near perigee-syzygy 216 Newton's Universal Law of Gravitation 498 Nodal alignment 218 Nodes 7 Index 535 Page Nodical month 126 Obliquity of ecliptic 190 Offshore platforms: tidal and current impact 485 Offshore winds 3, 6, 12, 105, 408, 420 Onshore winds 3, 6, 78, 79, 96, 97, 218, 302, 326, 481 Opposite tides 500 Opposition 7 Ordinary spring tides 301, 311, 318 Parallactic inequality 142, 143 Parallax age 6, 11, 68, 297 Perigean neap tides: conditions 31 Perigean spring tides 5, 7, 317 adverse effects 103 amplitude control factors 153 astronomical factors 169 buoyancy increase and mast clearance 103 buoyancy increase and small craft 103 classification 312-317 coastal ecology 482, 485 coastal erosion 31, 36, 84 coincidence with hurricanes 25-28, 481 concealment of navigational hazards 103 deep-water layer isohaline undulations 104 deflection of the vertical 104 dive times and decompression 94, 104 earliest references to 110, 111 ecological effects 98-102, 482 environmental effects 102, 482 height variations 214 historical impact 59 historical survey 109 hydrological runoff impaired 31, 35, 482 international terminology 203 lunar proxigee, effects on 169 lunisolar augmentation of 169 maximization conditions 11, 203, 218, 313 meteorological reinforcement of 326 negating conditions 3, 6, 105, 408, 420 new inlets and channels breached 104 ocean environment studies 104 offshore winds, and 3, 6, 105, 408, 420 onshore winds, and 2 onshore wind lacking (calm) 196 origin of concepts 109 perigee-syzygy separation-interval 266 periodicity 177, 189, 285, 318-326 physical oceanography studies 104 pollutant flushing enhanced 97, 98, 102, 104 pollution runoff 103 practical influences 103 systematic quantitative designation 312-317 winter storms, and 320 18th century knowledge 68 Pago Perigee 5, 128, 130 equation for motion of 180 full moon accompanying 214 increased duration 176 mean and true motions of 179, 182 mean daily motion of 177 mean progression of 178, 179, 289 new moon accompanying 216 retrograde motion of 179, 435 true motions of 177, 179, 184 Perigee-quadrature: figure of lunar orbit at 209 Perigee-syzygy 2,4,7 coincidence with perihelion 271 conjectural meteorological relationships 486 cycles of alternation 285 extreme high and low water effects 486 extreme lunar declination 195, 196 figure of lunar orbit 210 lunar angular velocity 131 lunar declination 196 lunar motion in right ascension 196 lunar node and equinox coincidence 194 lunar node at equinoxes 193 lunar parallax value 174 mean period 318 node-apse-perihelion coincidence 219 periodic relationships 177, 189, 285, 318-326 relation to cloud conditions, study of 486 seismic activity, potential relation to 486 separation-interval 203, 266, 286, 287, 289, 290 tidal current effects 482 unproven geophysical relationships 485 31-year cycle 321 Perihelion 127, 130 winter solstice 271 Phase age 6, 68, 297 Pi factor 438, 439 Plimsoll marks: saltwater intrusions 102 Potential tidal flooding: astronomical-meteorological index 437 Precipitation: potential lunar syzygy relationship__ 486, 487 Principal declinational constituent 298 Progression of lunar apsides 184 Proxigean spring tides 5, 203, 313, 316 future occurrences 480 Proxigee 5, 116, 316 Proxigee-syzygy : lunar angular velocity 176 lunar orbital velocity 131 Pseudo-perigean spring tides 8, 69, 71, 317, 481 Quadrature: ordinary 208 Radius vector 142, 158, 217 536 Index Page Recreational beaches, tidal flooding of 102 Reference tide stations 69 Right ascension 7 Salinity: corrosion 99 green algae 99 irrigation 100 Salt flats 99 Saltwater intrusions: high buoyancy 102 prevention of ice formation 102, 498 Saltwater wedges 99 Saxby tide 112, 113 Scotland: Firth of Forth bridge 94 SCUBA diving operations 94, 104 Sediment transport 85 Semidiurnal tides 298, 448, 503 Separation-interval 266 Ship groundings : low water phase_ 95, 96, 482, 483, 484, 485 Sidereal day: average value 125 Sidereal month 126, 138 Solar day 271 Solar declination effect on lunar orbital velocity 271 Solar diurnal variation 488, 489 Solar eclipses 2, 7, 198, 199, 202 effect on lunar parallaxes 199 Solar parallactic inequality 131,288,435,502 Solar perigee 143,199,218 motion of line of apsides 270 Solar semidiurnal variation 488, 489 Solstitial tidal peaks 132 Solstitial tides 149 Spring tides 5,501 onshore winds 481 syzygy 502 Stars: individual motions 125 Station differences 69 Stenohaline organisms 99 Stern chase motions: lunar acceleration at perigee effect on 269 lunisolar declination angles effect on 269 Storm surges 15,490,506 Sun: angular velocity in right ascension 270 apparent annual motion 199 apparent daily motions 199 daily angular velocities 131 daily motions at aphelion and perihelion 131 daily motions at equinoxes 131 daily motions at solstices 131 declinational effects on solar motion 132, 148, 198 geomagnetic variations 489 Sun — Continued gravitational force mass maximum declination- mean anomaly Page 214 214 132 166 Synodic month__. ._ 126, 138, 177, 272, 284, 288, 290, 318 conditions for duration 275 influence of perigee-syzygy 275 relation to anomalistic month 284-290 Syzygean spring tides : onshore winds 28 Syzygy 501 Tangential forces 173 Temperature variations: effect on marine ecobi- ology 100 Tidal acceleration 296 Tidal amplification: lunar parallactic inequality 269 lunisolar declinations 270 Tidal amplitudes: semidiurnal lunar constituents 297 semidiurnal solar constituents 297 Tidal analysis 68 Tidal bulge 497 Equator 198 maximum peak 198 Tidal currents 497 adverse effects 105 atmospheric tide reinforcement 106 basins with interconnecting channels 106 beneficial effects 106 collisions 105 deepwater diving 105 electrical potential 106,489 erosion intensified 106 hydrography alteration 105 ice flow drift accelerated 105 marine engineering hazards 105 navigational hazards 105,483,485 pollutant diffusion accelerated 97, 104, 105 sheet ice formation, deterrent to 106 thermohaline balance in estuaries 106 tide rip effect 105 Tidal day 139,302,504 changing parallax effects 150 conditions for lengthening 291 declinational influences 150, 290, 291 duration 7, 132, 150, 191,271 duration as indicator of flooding potential 440 duration at maximum lunar declination 270 duration at perihelion 270 duration decreased 196 duration increased 196, 197, 269 duration influences 273 Tidal day — Continued Page duration maximum 274 lunar orbital velocity increase 274 lunar orbit inclination 196 lunar velocity in right ascension 196 relation to lunar day 440 solar declinational effects 148, 150 systematic variations in duration 273, 440 Tidal depression 497 Tidal flood engineering 490 Tidal flooding: astronomical conditions 11,25 conditions 10 damage 408 effectiveness of advisories 406 examples 15 hypothesis tested 197 inaccurate documentation 12 local conditions 437 lunar declination 196 off- vs. on-shore winds 12 onshore winds 291 protective barriers 409 recurring short-range potential 117 research hiatus 117 wind function 117 1927 events 474 1931 event 331, 474 1933 event 474 1939 event 374 1959 event 383 1962 event 117, 386, 445 1974 event advisory 405, 406 1976 event 424 1978 events 429, 430, 431 Tidal flooding potential: numerical index of astronomical factors 434 tide rise rate 448 Tidal force envelope 303, 306, 501 produced by Moon 501 produced by Sun 501 Tidal height: equations 169 predicted 440 related to lunar positions 273 seasonal factors 151 semidiurnal component 173 Tidal lag 303 Tidal literature: 18th century HI early 19th century 112 late 19th century 114 20th century 115 Index 537 Page Tidal loading: earthquakes 492,493 Tidal prediction 14, 506 lunar augmentation 147 Tidal priming 302 Tidal priming and lag: analysis 306 Tidal range 82,84,95,96,298 at aphelion 502 at perihelion 502 increase at perigee-syzygy 6 lunar declination 503 lunar phase 501 physical retardation 504 variations 501 Tidal retardation : climatological factors 273 hydrological factors 273 Tidal types 298,448,474,475,505 Tide amplitude 59 Tide growth: rates 290 Tide-raising forces 6 apogee 502 augmentation of 147, 198, 202 compensating influences 204 counterproductive influences 185, 204 declination effects 186-191 duration 176, 192, 271, 306 harmonic constituents 296 intensification factors 197 limiting conditions 199 lunar declination equations 187 lunar parallax effect 193, 502 lunisolar declinations 271 magnitude and duration 137 maximum 11,199,202,203,218,313 Moon vs. Sun 204, 501 parallax effects 502 perigee 502 semidiurnal solar constituent 502 time related factors 296 Tide-raising potential 197, 498 augmentation of 197, 433 duration of augmented forces 296, 306 seasonal factors 198 Tidelands 99 Tide-reducing forces 204 Tide rips 105 Tide tables 14, 449-452 Tides : atmospheric systems 506 accelerating factors 504 arrival time 503 basic theory 497 causes 121 538 Index Tides— Continued Page control factors 497 lagging of 302,303,504 local height 503 military engineering 497 navigation 497 offshore territorial limits 497 priming of 302, 303, 504 resonance effects 506 retarding factors 502 shoreline property boundaries, importance for 497 standard chart datums 497 strong wind effects 506 types of 298,448,474,475,505 unique local timing response 69 water sports, effect on 497 Topocentric parallax 148 Tractive forces 500 Tropic tides 149 Tropical cyclones 25 Tropical depressions 25 Tropical month 126 True anomaly 184,217 True longitude: sinusoidal variation with mean longitude 184 True parallax: perigee-syzygy value 176 True perigee longitude 217 True tidal day: tide curves 303 Trumbull, American frigate 59-70 Tsunamis 490 Turbidity currents 105,494 Typhoons 25 Ultimate-maximum proxigean spring tides 313 Universal time 13 Upper branch of meridian 122 Upper transit 122 Vernal equinox 122, 190 Vertical circles 123 Wales: 1849 floods 96 Water pollution 99 Weather maps 14,328,329 West Coast (North America) : British Columbia, Ripple Rock 97, 98 California 408 Wind damage 481 Wind symbols, synoptic map 330,331 "Windows" of tidal flooding 474 Zenith 123 ' •• 1. 1 'VI h'NMENT PRINTING OFFICE : 1978-O-202-509 7961 'L-y t/MOJV 1° duipoojf ppy kq pgyovnq I • / \- 'puvjsj §uuj 'uorfuwyjnos wju 'fog xoupy Jo yjnos qmaq mixvq fo uoijuoj y %*&£& J it \