CSS.ZZ'^ U.S. DEPARTMENT OF COMMERCE WEATHER BUREAU HYDROMETEOROLOGICAL REPORT NO. 36 INTERIM REPORT PROBABLE MAXIMUM PRECIPITATION IN CALIFORNIA REPRINTED WITH REVISIONS OF OCTOBER 1.969 Washington October 1961 *No. 1. *No. 2. *No. 3. *No. 4. *No. 5. *No. 6. *No. 7. HYDROMETEOROLOGICAL REPORTS (Nos. 6-22 Numbered Retroactively) Maximum possible precipitation over the Ompompanoosuc Basin above Union Village, Vt. 1943. Maximum possible precipitation over the Ohio River Basin above Pittsburgh, Pa. 1942. Maximum possible precipitation over the Sacramento Basin of California. 1943. Maximum possible precipitation over the Panama Canal Basin. 1943. Thunderstorm rainfall. 1947. A preliminary report on the probable occurrence of excessive precipitation over Fort Supply Basin, Okla. 1938. Worst probable meteorological condition on Mill Creek, Butler and Hamilton Counties, Ohio. 1937. (Unpub- lished.) Supplement, 1938. *No. 8. A hydrometeorological analysis of possible maximum precipitation over St. Francis River Basin above Wappa- pello, Mo. 1938. *No. 9. A report on the possible occurrence of maximum precipitation over White River Basin above Mud Mountain Dam site, Wash. 1939. *No. 10. Maximum possible rainfall over the Arkansas River Basin above Caddoa, Colo. 1939. Supplement, 1939. *No. 11. A preliminary report on the maximum possible precipitation over the Dorena, Cottage Grove, and Fern Ridge Basins in the Willamette Basin, Oreg. 1939. *No. 12. Maximum possible precipitation over the Red River Basin above Denison, Tex. 1939. *No. 13. A report on the maximum possible precipitation over Cherry Creek Basin in Colorado. 1940. *No. 14. The frequency of flood-producing rainfall over the Pajaro River Basin in California. 1940. *No. 15. A report on depth-frequency relations of thunderstorm rainfall on the Sevier Basin, Utah. 1941. *No. 16. A preliminary report on the maximum possible precipitation over the Potomac and Rappahannock River Basins. 1943. *No. 17. Maximum possible precipitation over the Pecos Basin of New Mexico. 1944. (Unpublished.) *No. 18. Tentative estimates of maximum possible flood-producing meteorological conditions in the Columbia River Basin. 1945. *No. 19. Preliminary report on depth-duration-frequency characteristics of precipitation over the Muskingum Basin for 1- to 9-week periods. 1945. *No. 20. An estimate of maximum possible flood-producing meteorological conditions in the Missouri River Basin above Garrison Dam site. 1945. *No. 21. A hydrometeorological study of the Los Angeles area. 1939. *No. 21A. Preliminary report on maximum possible precipitation, Los Angeles area, California. 1944. *No. 2 IB. Revised report on maximum possible precipitation, Los Angeles area, California. 1945. *No. 22. An estimate of maximum possible flood-producing meteorological conditions in the Missouri River Basin between Garrison and Fort Randall. 1946. *No. 23. Generalized estimates of maximum possible precipitation over the United States east of the 105th meridian, for areas of 10, 200, and 500 square miles. 1947. *No. 24. Maximum possible precipitation over the San Joaquin Basin, Calif. 1947. *No. 25. Representative 12-hour dewpoints in major United States storms east of the Continental Divide. 1947. *No. 25A. Representative 12-hour dewpoints in major United States storms east of the Continental Divide. 2d edition. 1949. *No. 26. Analysis of winds over Lake Okeechobee during tropical storm of August 26-27, 1949. 1951. *No. 27. Estimate of maximum possible precipitation, Rio Grande Basin, Fort Quitman to Zapata. 1951. *No. 28. Generalized estimate of maximum possible precipitation over New England and New York. 1952. *No. 29. Seasonal variation of the standard project storm for areas of 200 and 1,000 square miles east of 105th meridian. 1953. No. 30. Meteorology of floods at St. Louis. 1953. (Unpublished.) No. 31. Analysis and synthesis of hurricane wind patterns over Lake Okeechobee, Florida. 1954. No. 32. Characteristics of United States hurricanes pertinent to levee design for Lake Okeechobee, Florida. 1954. No. 33. Seasonal variation of the probable maximum precipitation east of the 105th meridian for areas from 10 to 1,000 square miles and durations of 6, 12, 24, and 48 hours. 1956. No. 34. Meteorology of flood-producing storms in the Mississippi River Basin. 1956. No. 35. Meteorology of hypothetical flood sequences in the Mississippi River Basin. 1959. No. 36. Interim report — Probable maximum precipitation in California. No. 37. Meteorology of hydrologically critical storms in California. (In preparation.) No. 38. Meteorology of flood-producing storms in the Ohio River Basin. 1961. * Out of print. U.S. Department of Commerce U.S. Department of Army Weather Bureau Corps of Engineers HYDROMETEOROLOGICAL REPORT NO. 36 INTERIM REPORT PROBABLE MAXIMUM PRECIPITATION IN CALIFORNIA REPRINTED WITH REVISIONS OF OCTOBER 1969 Prepared by Hydrometeorological Section Hydrologic Services Division U.S. Weather Bureau U. S. Depository Copy Washington, D.C. October 1961 TABLE OF CONTENTS CHAPTER I. AUTHORIZATION AND PURPOSE CHAPTER II. APPRAISAL OF PROBABLE MAXIMUM PRECIPITATION PROBLEM CHAPTER III. TYPES AND CHARACTERISTICS OF MAJOR CALIFORNIA PRECIPI- TATION STORMS CHAPTER IV. CONVERGENCE PROBABLE MAXIMUM PRECIPITATION CRITERIA CHAPTER V. CRITERIA FOR PROBABLE MAXIMUM OROGRAPHIC PRECIPITATION ON WINDWARD SLOPES CHAPTER VI. CRITERIA FOR PROBABLE MAXIMUM SPILLOVER PRECIPITATION CHAPTER VII. COMBINATION OF CONVERGENCE AND OROGRAPHIC PROBABLE MAXIMUM PRECIPITATION CHAPTER VIII. CHECKS ON PROBABLE MAXIMUM PRECIPITATION CHAPTER IX. SUMMARY OF STEPS IN OBTAINING PROBABLE MAXIMUM PRECIPE TAT ION FOR A BASIN CHAPTER X. TEMPERATURE AND WIND CRITERIA FOR SNOWMELT ACKNOWLEDGMENTS REFERENCES FIGURES Page 1 3 12 25 40 87 93 102 117 126 133 134 137- 202 in 139 29 140 29 141 29 142 29 FIGURES Page Refer to text, page 3-1. Low- latitude -type major orographic storm (northern and central California) 137 14 3-2. High-latitude-type (southern California) 137 15 3-3. Mid-latitude-type, southwesterly approach (northern and central California) 138 16 3-4. Cool-season convergence storm centered at Sacramento, April 20-21, 1880 138 18 4-la. Seasonal envelope of maximum observed dew points b. Seasonal envelope of maximum observed dew points c. Seasonal envelope of maximum observed dew points d. Seasonal envelope of maximum observed dew points 4-2. Highest 12-hour persisting 1000-mb dew points November 18-20, 1950 and December 10-11, 1937 143 27 4-3. Maximum annual October 12-hour persisting dew point, Fresno 4-4. Comparison of observed and adopted moisture decays 4-5a. Enveloping 12-hour persisting 1000-mb dew point maps b. Enveloping 12-hour persisting 1000-mb dew point maps 4-6. Enveloping precipitable water in percent of January 4-7. Maximum P/M ratios (with orographic storm) 4-8. Maximum P/M ratios (convergence -only storm) 4-9. Ratio of 6- to 24 -hour precipitation 4-10. Ratio of 72- to 24-hour precipitation 4-11. Effective elevations and barrier heights 4-12. Convergence PMP index 4-13a. Variation of convergence PMP with basin size and duration b. Variation of convergence PMP with basin size and duration c. Variation of convergence PMP with basin size and duration 5-1. Schematic inflow and outflow wind profiles over mountain barrier 154 43 5-2. Average ratio of observed, V , to geostrophic wind component, V gc y Oakland, California 155 44 iv 144 28 144 32 145 29 146 29 147 29 148 33 149 35 150 34 150 35 after 150 37 after 150 38 151 38 152 38 153 38 FIGURES (Cont'd) Page Refer to 5-3. Coastal V /V profiles c gc 5-4, Central Valley V /V profiles c gc 5-5. Central Valley areal variations of V /V , (a) 1000 mb, (b) 950 mb, (c) 900 mb C gC 5-6. Schematic air streamlines in orographic storm 5-7. Schematic plot of temperatures and pressures in oro- graphic storm on thermodynamic diagram 5-8. Central Valley degree-of -saturation for PMP conditions 5-9. San Joaquin Valley dew-point variations 5-10. Central Valley surface -relative -humidity for PMP conditions 5-11. Schematic diagram of orographic model 5-12. Storm calibration areas 5-13. Model coefficient, X, (a) Coastal Range, (b) Sierras 5-14. Average model coefficient, X 5-15. Precipitation-distribution test areas 5-16. Comparative precipitation profiles 5-17. Maximum sea-level geostrophic winds 5-18. Ratio of 500 -mb to surface geostrophic wind 5-19. Geostrophically -derived maximum winds, Coastal 5-20. Maximum winds aloft, Oakland, California 5-21. Maximum winds aloft, Santa Maria, California 5-22. Comparison of statistical with geostrophically- derived maximum winds, Coastal 171 74 5-23. Adopted maximum 1-hour winds and supporting data, Coastal, (A) composite, (B) geostrophically-derived, (C) adopted, (D) 50 -year, Oakland 5-24. Variation of 900 -mb windspeed, Oakland 5-25. Adopted variation of windspeed with duration 5-26. Adopted maximum winds normal to Coast Range 5-27. Adopted maximum winds normal to Sierras text, page 156 44 156 44 157 45 158 47 158 48 159 51 159 52 160 52 161 54 162 56 163 67 164 68 164 69 165 69 166 71 167 72 168 73 169 74 170 74 171 75 172 76 172 77 173 77 174 77 FIGURES (Cont'd.) Page 5-34. 5-35. 5-28. Maximum 4000- foot windspeed comparison, Coastal 5-29. Model-coefficient-variation tests, (a) \ vs. rank of computed precipitation, (b) \ vs. rank of average of computed and observed precipitation 5-30. Orographic PMP computation areas 5-31. Adopted ground profiles (PMP areas numbered, see figure 5-30) 5-32. Latitudinal variation of maximum winds 5-33a. 10-year 3-day point precipitation map b. Convergence component of 10-year 3-day point precipitation map c. Orographic component of 10-year 3-day point precipitation map Ratio of 6- hour January orographic PMP to orographic component of 10-year 3-day precipitation Orographic PMP index 5-36. Variation of orographic PMP with duration 5-37. Seasonal variation of maximum winds 5-38. Seasonal variation of orographic PMP 5-39. Basin-width variation 6-1. Orographic plateau spillover 6-2. Orographic plateau spillover (Cont'd.) 6-3. Leeward evaporation 6-4. Spillover comparison - Coastal (see figure 5-15) 6-5. Spillover comparison - Sierra (see figure 5-15) 6-6. Spillover comparison - PMP and maximum observed precipitation 7-1. Schematic comparison of some features of orographic storm and combined storm 7-2. Sequences of observed precipitation 7-3. Sample PMP time- sequences *Please see the revision dated October 1969 of figure 5-35 that is included at the end of this publication. 175 Refer to text, page 78 176 78 after 176 79 177 79 177 80 after 177 81 after 177 81 after 177 81 178 81 after 178 81 179 83 179 84 180 84 180 85 181 88 182 88 183 90 183 91 184 91 184 91 185 98 186 99 187 100 vi FIGURES (Cont f d.) Page Refer to text, page 8-1. Test areas for comparison of storm values with PMP 188 107 8-2. Comparison of PMP from Hydrometeorological Report No. 33 with statistical PMP for 24 hours and 10 square miles 8-3. Statistical PMP for 24 hours at a point, California 8-4. Comparison of statistical PMP with PMP from this report for 24 hours and 10 square miles 8-5. Comparison of SPS and PMP for 6 hours and 10 square miles 8-6. Comparison of SPS and PMP for 6 hours and 200 square miles 8-7. Comparison of SPS and PMP for 24 hours and 200 square miles 8-8. Comparison of SPS and PMP for 24 hours and 1000 square miles 8-9. Comparison of SPS and PMP for 72 hours and 1000 square miles 8-10. Ratio of 2-year and 100-year 24-hour precipitation to 10 -square -mile 24 -hour PMP 8-11. Ratio of 10-year 72-hour precipitation to 10-square- mile 72-hour PMP 8-12. Comparison of PMP from W.B. Technical Paper No. 38 with PMP from this report and Standard Project Storm (SPS), for selected basins 8-13. Comparison of PMP from W.B. Technical Paper No. 38 with this report for 24 hours and 200 square miles 8-14. Comparison of PMP from W.B. Technical Paper No. 38 with this report for 6 hours and 10 square miles 10-1. Variation of precipitable water with 1000-mb dew point temperature 10-2. Decrease of temperature with elevation 10-3. Temperatures prior to a PMP storm 10-4. Pressure-height relation 188 114 189 114 190 114 191 114 192 114 193 114 194 114 195 114 196 115 197 115 198 115 199 115 200 115 201 126 201 127 202 127 202 131 vi i Chapter I AUTHORIZATION AND PURPOSE Purpose of report 1.01. The purpose of this report is to present criteria for estimating probable maximum precipitation over basins above prospective flood-control structures in the Pacific drainage of California. Similar generalized cri- teria were previously prepared by the Hydrometeorological Section for the area of the United States east of the 105th meridian in Hydrometeorological Reports Nos. 23 and 33, (1) and (2), for the Corps of Engineers and by the Cooperative Studies Section of the Weather Bureau for the United States west of the 105th meridian in Weather Bureau Technical Paper No. 38 (3) for the Soil Conservation Service. The latter report includes California, but of necessity covers that area in less detail than the present report. Authorization 1.02. The authorization for this study is contained in a memorandum from the Office of Chief of Engineers dated August 13, 1956, which states: "Work should be initiated in the immediate future as follows: (1) The Hy- drometeorological Section will study orographic precipitation for the entire Pacific Coast area, applying the latest meteorological techniques and utiliz- ing data from the latest storms, especially those of 1950 and 1955. The probable maximum precipitation studies by the Hydrometeorological Section will be concentrated primarily in the Sacramento- San Joaquin River Basin. Probable maximum precipitation, coincidental snow cover, and the tempera- tures and winds throughout the storm period will be furnished by the Hydrometeorological Section." In later conferences between representatives of the Corps of Engineers and the Weather Bureau it was agreed that the studies should be extended to all of the Pacific drainage of California as the area of first priority, with a view to eventual further extension to derive consistent patterns of probable maximum precipitation values along the Pacific Coast from the Co- lumbia Basin south to Los Angeles. It was also agreed that studies had progressed to the point where this volume should be published as an interim report. It was intended that a final report later would encompass refinements of certain procedures. There were no apparent reasons for anticipating major changes in over-all results in the final report. Scope of this report 1.03. Criteria are developed for obtaining estimates of probable maxi- mum precipitation for storm durations up to 72 hours, for basin areas up to several thousand square miles throughout the Pacific drainage, by months through the primary precipitation season of October through April. The ques- tion of intense local storms outside the primary precipitation season exceed- ing these criteria is discussed in chapter II. The more general topographic features are taken into account to the extent feasible. The possible effects of lesser topographic variations on individual basins are discussed in chapter II. Snowmelt is an important contributor to floods at some seasons over some basins in California. Values of wind and temperature that may be ex- pected preceding and during probable maximum storm conditions at various elevations are derived for the purpose, of computing snowmelt. The possible depth of the antecedent snow cover is not covered. Organization of this report 1.04. Those problems incident to estimating probable maximum precipita- tion (PMP) in California which the user should take into account in evalua- ting the final PMP values are reviewed in chapter II. The meteorological characteristics of California storms that are most indicative of PMP condi- tions are summarized in chapter III and are analyzed in more detail in a separate report (see below). Those characteristics are applied to developing specific criteria for PMP storms of the two primary types, convergence and orographic (chapters IV and V) and are followed by the criteria for their combination into one storm event (chapter VII) . A collection of checks on the PMP (chapter VIII) and comparison with other data give the user further aid in appraising the values. These include a discussion of the maximization steps as a whole, comparison with maximum observed values, statistical checks, relation to Standard Project values, and comparison with other PMP estimates. For convenience in computing PMP values for a specific basin from the various charts and nomograms, the requisite steps, discussed in detail at various places in the report, are collected together in a working list in chapter IX. The special problems associated with spillover, the drift of precipita- tion with the wind across the crest of a mountain, are treated in chapter VI. The final chapter covers dew point and wind criteria for snowmelt. Relation to Hydrometeorological Report No. 37 1.05. Development of the California PMP required extensive analysis of the nature of precipitation storms that have affected the state in the past. Much of the results of this part of the investigation have been placed in a separate volume, Hydrometeorological Report No. 37, under the title "Meteoro- logical Characteristics of Hydrologically-Critical Storms in California" (4). The frequent references to that report in the present volume are abbreviated "HMR 37." Chapter II APPRAISAL OF PROBABLE MAXIMUM PRECIPITATION PROBLEM 2.01. The purpose of this chapter is to point out the special charac- teristics of the PMP problem in California as compared with that in other areas, to indicate the physical, synoptic, and statistical facts and analy- ses that have been made and to give some perspective as to how these facts and analyses influence the estimates. Elements of PMP estimates 2.02. Maximum precipitation data in region . The first basic data for probable maximum precipitation estimates in any region at any season are the greatest depths of precipitation that have been observed in that region or a climatologically and topographically similar region at that season. These values are sometimes viewed by the casual investigator as approaching the upper limit of precipitation potential for the region. In reality these data are an unequivocal lower bound to the estimate of the probable maximum precipitation. 2.03. Maximum precipitation data in adjacent regions . Maximum observed depths of precipitation in one place are not only obvious clues to the cli- mate at that place but also are clues to the climate of adjacent regions. In estimates of probable maximum precipitation considerable reliance is placed on increasing the data applicable to a particular basin by trans- position of observed maximum precipitation depths from one location or season to another location or season, with appropriate adjustments for topo- graphic and meteorological differences. The limitation on this technique is the reliability with which the adjustment factors can be devised. In large quasi -homogeneous regions such as the Central Mississippi Valley simple ad- justment factors suffice. More complex procedures are required in regions of rugged topography, such as most of California. In the development of criteria for Standard Project Storms, the Sacramento District of the Corps of Engineers transposed orographic storms by use of adjustment factors de- rived from a map of 3 -day point precipitation depths with a mean recurrence interval of ten years (5) (6). The pattern of isopleths on this map is similar to that on a chart of mean annual precipitation. Transposition of orographic storms is indirect in the present report but nontheless is an inherent part of the procedure. Orographic PMP is hypothesized from a model which incorporates seasonal, latitudinal, and topographic variations. The model is then calibrated against selected major orographic storms. This procedure has the effect of transposing the selected storms to other areas with appropriate adjustments for latitude, season, and topography. In a statistical approach referred to in chapter VIII the transposed factor is a statistical parameter related to rainfall variation. 2.04. Maximization . The storms are extended to probable maximum values after investigation has devised both a "how" and "how far." The "how" consists of a storm model which relates extreme precipitation to measurable variables which may be regarded as causes of the precipitation. Present knowledge does not yet account for all aspects of precipitation for- mation in a quantitative way, therefore the model is a combination of estab- lished physical or statistical laws and judicious hypotheses. Development of the appropriate storm model for maximization is the most complex aspect of estimating probable maximum precipitation. The same basic model is used for storm transposition as for maximization. In application, parallel parts of both adjustments can be combined into a single computation. The "how far" is the specification of the maximum values of the vari- ables to which precipitation is related by the model. These limits are al- ways based ultimately on observations of climatological parameters, appro- priately organized and analyzed, and are therefore empirical. There are no purely theoretical limits. An example of an appropriate observed climato- logical parameter of a statistical character is the standard deviation of the series of the maximum annual point 24-hour depths at a station. Examples of parameters of a more physical character as employed in this report are maximum surface dew points and maximum wind speeds at various levels. Ex- amples of other physical parameters not employed explicitly in this report that might be used with a different physical model are sea-surface tempera- ture, length of wind fetch over water, and elevations of tops of cumulonim- bus clouds. The limiting values of each parameter must be set with due regard for compatibility with other parameters. This is discussed in paragraph 2.08. 2.05. Relation of storm sample to maximization . The number of precipi- tation storms that give useful clues to the precipitation potential over a particular basin is limited by several factors. These are the frequency and areal extent of severe storms, the density and length of record of precipi- tation gages, and the size of geographical areas and duration of season from which reliable transpositions can be made. Severe limitation of storm sample pertain to intense local precipi- tation in California, both local storms and intense-precipitation centers of large-area storms. Insolation and low-level moisture are at a maximum during the summer but storm mechanisms (convergent, wiudclows r two hours, during the summer season. These storms have not been assessed in this report in order to concentrate on other problems. The user of this report should obtain separate estimates of short -duration small -area summer MP for watersheds where such storms might produce more critical floods than the generalized cool-season estimates of this report. Characteristics of California storms and application to PMP 2.15. Large California storms require properly oriented pressure gradients, adequate moisture, and lifting mechanisms, both topographic and those inherent in the storm circulation itself. 2.16. Pressure gradient and wind. A large California storm requires a strong persisting pressure gradient of favorable orientation for rapid lift- ing of air over mountain barriers. The primary guides to onshore wind com- ponents in a probable maximum storm are maximum observed winds at various levels and maximum pressure gradients. The latter are related to wind by the theoretical geostrophic relationship and also by empirical studies of the interrelationship at California stations where the influence of the moun- tains extends to considerable height. Development of maximum wind criteria is covered in chapter V. 2.17. Moisture . Large California storms require an adequate supply of moisture. The primary guides to maximum moisture content of the air in as- sociation with maximum winds are maximum observed surface dew points. Maxi- mum coastal dew points are applied to the Coast Range and Southern Califor- nia. The maximum moisture criteria for the Central Valley and Sierras are defined by Central Valley dew points. The development, use, and reasoning behind the dew point criteria are covered in chapter IV. 2.18. Lifting mechanisms . Heavy precipitation requires that near- saturated air be lifted on a vast scale. The lifted air cools adiabatically, thus lowering its capacity to contain water vapor. This lifting can be as- cribed to three causes: orographic, horizontal convergence including frontal lifting, and instability. All are found in major California cool-season storms. 1. Orographic lifting. The influence of topography as a lifting me- chanism is obvious from a glance at charts of the geographical distribution of mean annual precipitation; a similar effect is noted in most storms. Esti- mates of maximum orographic effect are related to estimates of both maximum component of wind normal to barriers and to moisture. The many complicating factors are treated in chapter V. 2. Horizontal convergence. Stated in simple terms, when horizontal air streams converge, vertical motion is required to carry off the air. Such convergence takes place primarily in the vicinity of low pressure areas and troughs. Convergence mechanisms may be identified by hourly rainfall meas- urements at the ground as patterns moving more or less independent of to- pography. The primary guide to the magnitude of the precipitation possible from horizontal convergence is maximum observed point precipitation at stations in California where orographic influence is at a minimum and in storms where instability contribution (see next paragraph) is thought to be slight. Be- cause of the paucity of such data, that from other regions must be consider- ed also, especially with respect to variation of precipitation depth with size of basin. 3. Instability. The most impressive release of instability is in a thunderstorm. A lesser degree of instability facilitates moderate or heavy precipitation without thunder or lightning. Instability in California storms results primarily from offshore heating and moistening of air from below as it travels from a more northerly latitude over progressively warmer water. Lifting by horizontal convergence, fronts or orography may facilitate its release. Inflowing air in California storms from a more southerly latitude tends to be more stable as the trajectory is over progressively colder wa- ter. Thus the inflow direction favoring maximum moisture does not favor maximum instability. 2.19. Evaluation of orographic and convergence precipitation . In this report convergence PMP and orographic PMP are evaluated separately, then combined. It is intended that each of the separate evaluations be an index of processes existing in a combined storm. The definitions adopted to carry out this purpose are given in paragraph 3.01. Separate evaluation of the orographic and convergence PMP permits sep- arate definition of the respective variations with season, size of basin, geographical location, elevation, and storm duration. 2.20. Combination of orographic and convergence PMP. The two are com- bined by adding together. Care has been taken to minimize the contamination of the data used in the development of each by the opposite process. Storm types which illustrate the simultaneous occurrence of orographic and convergence precipitation are described in chapter III. Further dis- cussion of considerations for combination are contained in chapters IV and VII. Use of report 2.21. Use related to method of development . Use of the values given in this report should be consistent with the methods employed to derive 10 them. It is again necessary to refer to the distinction between "general level" and "internal consistency." The applicability of each to the partic- ular project should be considered separately. 2.22. Topographic detail . The design engineer would first assess the internal consistency as applied to his basin, that is, does the degree of detail in the report appear to adequately cover his basin in view of the real topographic variations and his requirements? The degree of topographic detail taken into account in this report is indicated by the orographic in- dex map, figure 5-35. Basins with more critical topography than the general topographic variations indicated by figure 5-35 would be expected to have higher values of PMP than the report indicates while more sheltered, even with due regard for spillover, might have lesser values. In other words, no geographical safety factor has been introduced into the report to take care of localities that are topographically more critical than a general- ized view of the topography would indicate and the user should consider this possibility, and whether further more detailed studies are needed. 2.23. General level . The designer would next consider the general level and its pertinence to his requirements. The meteorological aspect of the over-all PMP problem in California and the particular solutions pre- sented in this report are covered in some detail for the necessary purpose of permitting the design engineer user to acquire some feel for the meteor- ological judgment factors involved. He will then be in a position to de- cide, in view of the degree to which risk has been eliminated in the PMP values furnished in the report, and in view of the particular requirement of his project, whether the PMP values should be adopted for his design, should be adjusted one way or the other, or whether further studies are required. Relation to other PMP reports 2.24. This report is intended to serve purposes similar to those served by two previous Weather Bureau reports. These are Hydrometeorologi- cal Report No. 33, "Seasonal Variation of the Probable Maximum Precipitation East of the 105th Meridian for Areas from 10 to 1,000 Square Miles and Du- rations of 6, 12, 24 and 48 Hours" (2), and by Weather Bureau Technical Paper No. 38, "Generalized Estimates of Probable Maximum Precipitation West of the 105th Meridian for Areas to 400 Square Miles and Durations to 24 Hours" (3). Probable maximum precipitation is intended to be defined in the same way in the three reports. Technical Paper No. 38 and the early parts of the present report were in preparation at the same time, by different groups of meteorologists of the Weather Bureau but working in close con- sultation. Technical Paper No. 38 is restricted to maximum areas of 400 square miles and durations of 24 hours in accordance with the primary de- sign problems of the supporting agency, the Soil Conservation Service. The present report extends to larger areas and longer durations in accord- ance with the needs of the supporting agency, the Corps of Engineers. 11 Comparisons are given in this report between the PMP values here and those presented in Technical Paper No. 38 for the zone of geographical over- lap and corresponding storm areas and durations. Numerical accuracy 2.25. Precipitation depths, windspeeds, dew points, and other vari- ables are assigned numerical values to three significant figures throughout the report. Most of these numbers are indices of postulated natural con- ditions rather than measurements, and therefore no one of them has an abso- lute accuracy that is valid to three significant figures. The three signif- icant figures are the convenient and common-sense method of portraying smooth variations geographically and over season, storm duration, and storm area. 12 Chapter III TYPES AND CHARACTERISTICS OF MAJOR CALIFORNIA PRECIPITATION STORMS 3-A. INTRODUCTION Definitions of orographic and convergence precipitation 3.01. Orographic precipitation is defined as that falling as a result of the lifting effect of a topographic feature on a flow of air passing over it. The induced vertical motions in the flow are primarily due to the slope of the ground but may also be related to the narrowing of the terrain. The latter effect is significant where valleys become constricted, such as in the northern Sacramento Valley. Orographic precipitation includes, in addi- tion to that falling on upwind slopes, that blown across orographic barriers by the wind at the barrier, referred to in chapter VI as spillover. Convergence precipitation in this report includes all precipitation re- sulting from lifting induced by atmospheric processes other than orographic. These are mainly horizontal convergence, frontal lifting and instability. Convergence and orographic precipitation occur simultaneously in mountain areas. Condensation and precipitation 3.02. The lifting process, whether orographic or non-orographic, re- sults in cooling of the air at the rate of 5.4 F. degrees per 1000 feet change in elevation until saturation is reached, then at 3 to 4 F. degrees, depending on temperature and pressure. The condensation process begins to take place as soon as saturation is attained. Minute water droplets or ice crystals are formed on various types of nuclei. These droplets and crystals are sustained by the vertical motion of the air. A net transport of moisture from water drops to ice particles takes place due to difference in vapor pressure, and from small to larger drops through collision. Precipitation results from inability of the upward motion of the air to sustain the hydro- meteor (rain, snow, sleet, etc.) against the force of gravity. The size of hydrometeors is dependent on the magnitude of the vertical motions to which they are subjected. Their form on reaching the ground is largely dependent on air temperature. The subject of condensation and precipitation is discussed in more de- tail in chapter I of Hydrometeorological Report No. 34 (7). 13 3-B. OROGRAPHIC STORMS Definition 3.03. The term "major orographic storm" is used to denote storms which are important from the standpoint of sustained high intensity in orographic areas rather than in non-orographic areas. This definition serves to dis- tinguish such storms from storms in which convergence precipitation (related to the storm mechanisms alone) is the more important feature. It recognizes that convergence precipitation is present in orographic storms as a contrib- uting factor to total precipitation. Factors in major orographic precipitation storms 3.04. Season . Seasonal controls limit California orographic precipita- tion to the cool months, roughly October to May. With the shift of the pre- vailing westerlies north of the latitude of California during summer months, the Pacific anticyclone dominates California with stable dry air, except for infrequent invasion of moisture from the Gulf of Mexico which results in showers and thunderstorms over the southeast desert areas and the Sierras and Southern California mountains. Orographic storms similar to those of winter months do occur infrequent- ly in the northern part of the state during September and into early June. Although these storms may have precipitation intensity comparable to that during the cool months their duration is restricted in these months by the transitory nature of offshore Lows and their runoff potential by dryness of the soil. 3.05. Intensity . The intensity of orographic precipitation depends on the strength of the wind normal to the mountain range and the moisture con- tent of the air. California topography prescribes an optimum wind direction favorable to upslope motion varying from west- southwest to south. Optimum moisture content is contingent upon similar wind directions and upon storm trajectories from south of west, that is from a lower latitude. It follows that the storm of optimum orographic precipitation intensity in California is one in which the offshore trajectory of the airstream is south of west. This is the trajectory of the air during most of the storm duration in major orographic storms. It is also the trajectory of the storm center itself in most Northern California and some Southern California major orographic storms. Storms from a northerly latitude also may produce fairly heavy orographic precipitation in Southern California which are relatively less intense in Northern California because of the less favorable orientation of the flow and particularly because of more limited moisture. The intensity of convergence precipitation superimposed on the oro- graphic precipitation in mountain areas depends on moisture and strength of convergence mechanisms. These mechanisms may vary rapidly with time compared 14 to variations in upslope flow at a given location. Horizontal divergence may briefly decrease total precipitation in mountain areas. 3.06. Area . The areal extent of California orographic storms is usual- ly large in comparison to size of drainage basins except for the two main Central Valley drainage basins. Thus orographic PMP criteria derived from relations based on major California storms is adequate for California basin sizes. 3.07. Duration . The feature of lengthy duration in major orographic storms is dependent upon a pressure pattern of such stability as to assure prolongation of vigorous upslope flow of moist air. Such a pattern can be stated in general terms as one involving low pressure in the eastern Pacific Ocean and high pressure over the mid- continent. High pressure may also dom- inate the central Pacific Ocean. Basis for classification of major orographic storms 3.08. If more or less stationary anticyclones are of such strength as to interrupt the normal middle-latitude west -to -east flow or reroute it to low and/or high latitudes for a considerable period of time, the High is re- ferred to as a blocking High. The resulting meridional flow from low to high latitudes and vice versa in such patterns permits maximum abnormalities of temperature and moisture. The major California orographic storms of this century are classified on the basis of this feature of blocking in HMR 37 as an aid in assessing the relationships of over-all weather map patterns to California cool-season precipitation. A summary of the classification is given here. Storms are grouped under three main headings, Low, Middle or High-lati- tude types. This classification suggests the latitude relative to California from which storm centers move across the eastern Pacific, and depends on the longitude of blocking Highs which are effective prior to and/or during the course of the storm. Low- latitude type (figure 3-1) 3.09. Storms of the Low- latitude type are nearly all centered in the northern two thirds of the state. The type involves a north- south blocking High in mid-Pacific between 160W and 180W. This High joins an intense High over Alaska which extends southeastward into the central United States. This pattern surrounds a Low of varying intensity and position in the southern Gulf of Alaska which is maintained by outbreaks of cold air from the interior of Alaska or across the eastern part of the Aleutian chain. The main storm track from the western Pacific is diverted south of the block on its way to the Northern California coast. The storms following this trajectory, joined by a continuous frontal boundary, are forced to move rap- idly in the strong flow under the periphery of the large Gulf of Alaska Low, 15 and have little opportunity to become large storm entities. Just south of this frontal boundary a strong persistent flow of moist stable air from a near tropical latitude is established around the eastern Pacific anticyclone. The potential for orographic precipitation in this flow at the coast is ex- tremely high. Convergence patterns in this flow have been shown to contrib- ute significantly to rainfall totals at low elevations. Instability is min- imized by cooling of lower layers in transit from a distant low latitude. The duration of the above-described arrangement depends on the mainte- nance and stability of position of the Gulf of Alaska Low as well as the block to the west. The November 1950 and December 1955 flood storms are out- standing examples of this storm type. High-latitude type (figure 3-2) 3.10. Storms of the High-latitude type are more intense in Southern California than farther north, with minor exceptions, because of the storm trajectory. The Pacific block is east of 160W; it extends southward to low latitudes and joins the High over Alaska and western Canada to form a cres- cent-shaped ridge of shorter radius than in the Low- latitude type storms. In most cases Low centers form off the British Columbia or Washington coasts and deepen as they move southward. Off the Northern or Central California coast they change direction toward northeast or north, depending on the ori- entation of the crescent- shaped ridge. Offshore falling pressures on the trailing cold front extend the trough of low pressure southward along the Southern California coast, resulting in a strong flow from south and south- west into Central and Southern California. Because of its limited trajectory this air is not extremely moist. The orientation of the flow is particularly favorable for orographic rain in parts of Southern California. Examples of this storm type in which the Pacific block is complete and oriented north- northwest- south- southeast as shown in figure 3-2 are the storms of Jan- uary 16-19, 1916 and January 26-28, 1916. A variation of this type is found in the January 20-23, 1943 storm (not shown). Weakening of the Pacific block permitted breakthrough of a weak storm from the west. As it moved eastward toward the coast rapid deepening occurred when cold air flowing southward along the Washington coast entered its circulation. This sequence was repeated at a lower latitude a day later. This succession of deep Lows resulted in high pressure gradients over the en- tire state. Orographic precipitation was particularly high in Southern Cal- ifornia where dew points were fairly high. Mid-latitude type 3.11. This type is characterized by low pressure in the central and eastern Pacific with varying degrees of blocking over western North America. The direction of approach of Lows near the coast is influenced by both the general offshore circulation and the effectiveness of the continental block. 16 It is the basis for classing these storms as Southwest, Southerly or Westerly. The Southwest subtype is the most common of Mid-latitude type storms. It is illustrated in figure 3-3 for Northern California. (In Southern Cal- ifornia storms, the Low centers are shifted to the southeast.) Repeated en- try of Lows into the eastern Pacific and cyclonic rotation around a mean off- shore position in most storms brings weakening occluded frontal systems on- shore and maintains a strong southwest flow there. The trajectory of this flow, originally from a distant polar source, over a low latitude results in high moisture content. Examples of Southwest Mid-latitude type storms in Northern California are February 25-29, 1940 and January 30-February 2, 1945; in Southern California, examples are April 4-8, 1926 and February 28-March 3, 1938. The Southerly Mid- latitude type storms (not shown) are diverted north- ward by the continental block to a greater extent than are the Southwest type storms, permitting a more nearly southerly flow of very moist tropical air at the coast. An example in Northern California is the storm of Decem- ber 9-11, 1937 and in Southern California that of December 30, 1933- Jan- uary 1, 1934. Westerly Mid- latitude type storms undergo little blocking at the coast as frontal systems move from west to east at rather infrequent intervals. Moisture is relatively low in air whose trajectory is essentially from west. Hence storms are comparatively minor. An example in Northern California is the storm of March 29-April 5, 1958. 3-C. CONVERGENCE STORMS Factors in convergence precipitation 3.12. The three most important factors involved in convergence pre- cipitation in California are reviewed below and discussed in more detail in chapter IV, HMR 37. 3.13. Ageostrophic convergence . The term "ageos trophic convergence" is used in this report to refer to horizontal convergence resulting from im- balance between horizontal pressure gradient and wind. It results from the time lag in response of an air particle to adjust its speed and direction to changes in magnitude and direction of pressure gradient forces. Its magni- tude varies both with the pressure gradient changes encountered by the wind field and with the strength of the wind. It is the main cause of vertical motion not ascribed to orography in major winter California orographic storms. This motion is upward in that part of the air column which contains most of the moisture. The resulting precipitation may be noted on weather maps ahead ot fronts, troughs, and in advance or to the right of moving Lows. 17 3.14. Frontal lifting . Vertical motions due to lifting of air over frontal surfaces, also a form of horizontal convergence, combine with those due to ageostrophic convergence as described above. Usually a large portion of the convergence rain in California winter storms occurs near and partic- ularly in advance of the frontal systems; but most of this, particularly with warm fronts, is the result of the unbalanced wind-pressure gradient field associated with the frontal system rather than of lifting up the frontal slope. In most major California orographic storms frontal lifting is some- what limited by lack of significant change in windspeed and direction at the fronts . 3.15. Instability . The importance of instability as a convergence pre- cipitation mechanism lies in the capacity of unstable air to sustain large upward vertical motions over a limited area as a result of release of latent heat of condensation in ascending saturated air. Upward vertical motions due to instability, as observed in thunderstorms and large cumulus clouds, are large in comparison to possible values averaged over a larger area and re- sulting from ageostrophic convergence and frontal or orographic lifting. Yet they may combine, the latter causes of vertical motion tending to initiate the release of instability. Instability is released as a result of increase of vertical gradient (commonly called 'lapse rate') of temperature and/or moisture. Three causes for this increase are surface heating, advection, and lifting. Heating in lower layers by a warmer ocean surface while the air is moving toward a lower latitude offshore steepens temperature and moisture lapse rates. Surface heating by the land increases temperature lapse rate in spring and fall, es- pecially during the latter part of a storm during daylight hours when in- solational heating of the ground surface is permitted by a breakup of the cloud deck. Vertical difference in horizontal advection of temperature and/ or moisture can be an important factor in producing unstable lapse rates in major orographic storms. Lifting, either by orography or by convergence me- chanisms, provides a means of release of convective instability by increase of temperature lapse rate. Convective instability appears at the coast in major California oro- graphic storms mainly near trough lines associated with cold or occluded fronts. In advance of the front, differences in temperature advection at different levels and vertical motion due to convergence, may cause a steepen- ing of temperature lapse rate in the lower troposphere; behind the front a fairly steep temperature lapse rate may exist to the depth of the cooler air, especially if the front is the final one of the storm. However, the insta- bility is hardly comparable to that which may be realized in large conver- gence storms. Classification of large convergence storms 3.16. Large convergence storms are classified by season under the fol- lowing headings: 18 1. Large cool-season convergence storms (approximately October through April) involving unusually heavy local convergence precipitation during a general storm. In assessing the level of convergence precipitation in such storms for comparison purposes it is necessary to account for or avoid contamination by orographic effects. Thus the preferred area for source material is the central part of the Central Valley. The 24-hour amounts at a point, provide the best means of comparing convergence precipitation in these storms and the most complete use of historical storm data because of the lengthy record of 24-hour rainfall measurements. 2. Large late spring and early fall convective storms. These storms, though usually associated with a general storm from the Pacific, are of short dura- tion and very local. They depend primarily on instability and features of the nearby terrain for their intensity. 3. Large summer convective storms occurring in air from the Gulf of Mexico. These storms are also local short -duration storms depending primarily on in- stability and features of the nearby terrain. Examples of each class are described briefly below. Fuller description of these storms is given in chapter V, HMR 37. Examples of large cool- season convergence storms 3.17. In the first two storms discussed below, the offshore track (from northwest) favored instability as a factor in the heavy local rain but limit- ed storm moisture. The reverse situation was the case in the third storm. 3.18. The April 20-21 » 1880 storm at Sacramento . This storm is im- portant because the 22-hour rainfall of 7.24 inches at Sacramento is a record during a general cool-season storm in an area of California free of orograph- ic effects. A 1000-mb Low (figure 3-4) moved onshore from the northwest near Fort Bragg on the 20th and stagnated in the North Coastal area on the 21st before filling and then drifting southeastward on the 22d. Heavy rain was general over the northern half of California at low elevations; a low snow level resulted from the low temperatures prevailing in the recent polar air. The 7.24 inches at Sacramento occurred mostly in the 18 hours after noon of the 20th as almost continuous rain, with three distinct bursts of very heavy rain. Despite absence of thunderstorm reports, instability is believed to have been an important factor in this extremely heavy local rainfall. 3.19. The December 20-21, 1866 storm at San Francisco . Like the above storm, instability in recent polar air flowing around a stagnant Low con- tributed to a heavy local rainfall. Two Lows moved inland near Point Arena from northwest, on December 18 and December 20, respectively. The second center stagnated about 50 miles north of San Francisco before moving north- ward and filling rapidly on the afternoon of the 21st. The storm was severe 19 at low elevations over the northern half of California. Because of the Low track from northwest, cold temperatures restricted precipitation at higher elevations to snow. Between 1145 PST December 20 and 0815 PST December 21, 7.66 inches of rain was measured at one gage in San Francisco, a value substantiated by large amounts at several other locations within the city. The effect of in- stability as a factor in this heavy local rainfall is evident in the reports of many thunderstorms in and near the city on both days. (Local effect of topography added an orographic component to the above rainfall amount. Its magnitude in the average storm has been estimated at 237,, based on a compar- ison of rain at San Francisco and southeast Farallones.) 3.20. The Los Angeles area storm of January 25-26, 1956 . This general storm over the southern half of California centered in the Southwest Plains area of the Los Angeles Basin. It involved passage of two occlusions across California from the west on the afternoons of the 25th and 26th. But the main feature of the storm was a warm front off the Southern California coast on the morning of the 26th. It had formed offshore on the trailing end of the first occlusion. Ageostrophic convergence in connection with the warm front is believed to have accounted for most of the 24-hour rainfall near the storm center in the Los Angeles Basin. An example of this high 24-hour in- tensity is the 7.42 inches west of Gardena. (This amount is thought to con- tain a slight orographic component, estimated as 0.9 inch). During the peri- od of this rainfall, prior to approach of the second occlusion but including passage of the first occlusion, instability as indicated by raob data was not an important factor in rainfall intensity. Thus the convergence rainfall during this period is regarded as caused by factors compatible with those that might occur in the maximum orographic storm. Examples of late spring and early fall convective storms 3.21. Local thunderstorms have been observed in certain parts of Cali- fornia during the months of May and September, the short-period intensity of which was higher than in the 1956, 1866 or 1880 storms described above. In these storms there was an unknown but probably minor direct orographic com- ponent in the rain total. Topography apparently limits the location at which such storms may oc- cur; thus in the Central Valley, records of the more intense thunderstorms come only from the extreme north end of the valley, from Red Bluff northward. The combination of lifting of a southerly surface flow in the north end of the valley (both by rise in elevation and by constriction of the width of the valley) and lifting of a southwesterly flow over the high coastal range to the west, appears to be essential to the storms' occurrence to the lee of the coastal range in the foothills at the north end of the valley. The fact that these storms occurred in late spring and early fall months 20 partially explains their instability potential as the contribution of in- solational heating during these periods. Transposition of the instability features of the storm to the cool season is thus restricted. The first two of the three storms described briefly below developed in connection with, or as an aftermath of, a storm more or less typical of the winter season. The name of each refers to the area near which it is thought to have been centered. Kennet and Newton are located near Shasta Lake. 3.22. Kennet May 9. 1915 . The Kennet storm, occurring during the aft- ernoon, resulted in 8.25 inches in 8 hours. A Low moved from north of Hono- lulu east -northeastward into Southern British Columbia. Its frontal system did not become well occluded until it reached the Northern California coast; rainfall was general over Northern California and northeastward into northern Nevada and eastern Oregon, The intense thunderstorm development at Kennet was a very local feature, as no other thunderstorms were reported in Califor- nia on that date. Rain at nearby stations measured 1 to 2 inches for the storm. 3.23. Newton September 18, 1959 . In this thunderstorm an estimated 10.6 inches fell in 6 hours at Newton and 7 inches in the same period at Toyon, about 2-1/2 miles away. This happened some 12 hours after a vigorous winter-type storm, early for the season, moved in from west-northwest and passed across Northern and Central California during the morning, leaving a stationary trough offshore. Surface heating and lifting of the air in the low-level southerly flow in transit up the narrowing Sacramento Valley, along with cold advection in the upper- level flow superimposed on this southerly low-level flow after being destabilized by lifting over the high coastal mountains, apparently accounted for the instability release. During the aft- ernoon, thunderstorms developed over the mountains to the west, later drift- ing eastward over the foothills, where heaviest rain occurred. 3.24. Red Bluff September 14, 1918 . This storm occurred as the after- math of a general rain over the northern half of the state on the 12th and 13th from the circulation aloft about an old tropical storm. The latter had been carried from the Mexican coast northward offshore in an elongated north- south trough, moving inland aloft near Monterey and on up the Sacramento Val- ley. The unstable nature of the tropical circulation above the level of the stabilizing marine influence is evident in the 8.75-inch 24-hour rainfall at Wrights in the Santa Cruz Mountains (elevation 1600 feet), largely from a thunderstorm on the night of the 11th. It was not until a winter-type storm from north-northwest became involved with the warm moist air from the tropi- cal circulation, that the thunderstorm near Red Bluff developed on the night of the 13th. With a surface dew point of 63, 4.70 inches fell in 3 hours and 5.70 inches in 6 hours. Examples of summer-type convective storms 3.25. The following convective storms are typical of the summer season when air from the Gulf of Mexico is the moisture source. Such a storm is in- compatible with a winter-type orographic storm with moisture source from the Pacific Ocean. 21 A storm at Encinitas, on the coast 12 miles south of Oceanside on Octo- ber 12, 1889, resulted in 7.58 inches of rain in 8 hours. Seasonally it approaches the period of winter storms, but its origin was a typical summer- type flow of moist air from the Gulf of Mexico which moved unusually far to the west. It is apparent that the rainfall resulted from a very local in- tense thunderstorm, not evident at either San Diego or Los Angeles where 0.44 and 0.04 inches, respectively, were observed. Except for any upwind topo- graphic effect of the coastal mountains in developing the thunderstorm, the rainfall amount can be considered as relatively free of orographic effects because of its occurrence on fairly level terrain. The convective storm at Campo, in the coastal mountains near the Mexi- can border, in which 11.50 inches were reported in 80 minutes on August 12, 1891, involved a flow of air from the Gulf of Mexico westward over the coast- al mountains of Southern California. Reports indicate that two thunderstorms merged in the area to produce the extremely high intensity. Because of the moisture source, the influence of terrain on the storm's development and the orographic component in the rainfall amount, its areal transposition is lim- ited. A more detailed discussion of this storm is given in Weather Bureau Technical Paper No. 38, pp. 48-50.(3). 3-D. COMBINATION OF ELEMENTS OF OROGRAPHIC AND CONVERGENCE PRECIPITATION Combination in observed storms 3.26. The cyclonic circulation inherent in all large orographic storms involves horizontal convergence and assures widespread convergence precipi- tation. Cool- season storms which cause heavy precipitation in orographic areas are often observed to cause heavy convergence precipitation in non- orographic areas. Convergence bursts are observed to occur during periods of heavy orographic rain (chapter I V-A, HMR 37). Thus combination of large values of convergence and orographic precipitation in the same storm is an established fact. In storms in which each factor assumes comparable im- portance, the classification of the storm as a convergence or orographic storm is arbitrary; both might be suitable. Further, a storm may have little convergence precipitation in one area compared to another, in both of which the orographic precipitation may be large. The questions pertinent to PMP estimates is whether optimum values of convergence precipitation can occur in the optimum orographic storm and whether highest intensities can occur simultaneously. The following remarks draw on experience with past storms as a basis for combination of optimum values of most synoptic factors and for imposition of some restriction on the direct combination of other factors. Synoptic factors in optimum combination 3.27. Combination of elements of orographic precipitation . Simultane- ous occurrence of optimum values of moisture and favorably oriented pressure 22 gradient so as to cause optimum orographic precipitation is based on observed combination in large storms. Strong persisting gradients of an alignment most favorable to upslope flow over most California barriers have been ob- served to occur in storms whose general offshore circulation is conducive to a prolonged flow of moist air from a low latitude. Further, highest values of pressure gradient and dew point tend to occur simultaneously. 3.28. Combination of elements of orographic precipitation with ageo - s trophic convergence and frontal lifting . 1. Moisture. Optimum moisture logically combines simultaneously with optimum values of ageostrophic convergence and frontal lifting, just as op- timum moisture and upslope motion combine to produce optimum orographic pre- cipitation. 2. Pressure gradient. Strong winds and large values of horizontal con- vergence are natural companions. This is so, first, because the vigorous cyclones which produce the high winds require convergence and the associated rising of warm air to high levels to maintain their energy source. Second, the higher the winds the greater the opportunity for large horizontal spatial variations. The total horizontal convergence at any one level is the sum of the wind velocity gradients in two directions: c = . — * Y. bx by where V x is the component of velocity in the x- direction, V y the component in the y- direction, and C the convergence. A tendency for the simultaneous occurrence of high winds and high convergence (the latter is revealed by the rainfall) is illustrated by cyclonic storms throughout the world. The procedure followed in developing the PMP criteria was to combine optimum moisture values with the highest values of horizontal convergence estimated to have occurred in selected cool-season storms in which instabil- ity was not an important factor. These values are regarded as appropriate convergence rain values to combine with the optimum orographic storm. No account was taken of the effect of pressure gradient on horizontal conver- gence, other than that inherent in the observed extreme values. 3.29. Combination of elements of orographic precipitation with in - stability . 1. Moisture. The role of instability in California cool-season storms tends to vary inversely with moisture supply: If moisture supply is limited by recent offshore air trajectory from north of west, then instability as- sumes importance in convergence precipitation because of the increased prob- ability of an unstable lapse rate resulting from heating and addition of moisture to lower layers as air moves over warmer water toward the coast. 23 Thus instability precipitation may compensate for loss of convergence pre- cipitation from factors other than instability, as moisture is limited by trajectory. Larger cool-season convergence storms in California (measured by 24-hour point rainfall) do not necessarily require high moisture, as is the case in the eastern United States where high moisture and instability are compatible in the same storm (chapter IV 3-E, HMR 37), Since moisture requirements in the optimum orographic storm predicate an offshore air trajectory which favors stability, it follows that the opti - mum orographic storm cannot logically be combined with the optimum conver - gence storm in which instability is an important contributor, as a result of a recent offshore trajectory of the air from west or northwest. 2. Pressure gradient. Instability precipitation induced by orographic lifting tends to be spread over an area, in the case of extreme upslope winds, rather than concentrated at a point. Hence it is considered expedient to limit the instability contribution to convergence to that inherent in the highest observed values of convergence found in orographic storms, and max- imize only for moisture. In summary, optimum values of factors involved in combination of con- vergence and orographic PMP are considered suitable for simultaneous combina- tion, with the exception of moisture and instability. Combination of opti- mum values of factors involved in convergence PMP only, is not restricted. 3-E. TROPICAL STORMS History 3.30. Tropical storms originate off the coast of Central America or southern Mexico at 10-20 degrees N. latitude, mainly from June to October and particularly September. They frequently move northwestward along the coast of lower Baja California before veering to northeast. On rare occa- sions they move far enough north before veering to bring heavy rains to southern mountain and southeast desert regions of California. On one occa- sion, September 25, 1939, the center moved inland over Los Angeles with winds of 30 knots at San Diego. On September 12-14, 1918 the upper circulation of a former tropical storm brought heavy rains to Central and Northern Cali- fornia, a prelude to the Red Bluff convective storm described above. More detail on these two storms is found in HMR 37. Requisite synoptic pattern 3.31. Tropical storms approach the latitude of Southern or Central Cal- ifornia while still offshore only when a strong north-south trough is present just off the coast between an unusually strong warm High southward from Colo- rado and another north-south blocking High in the eastern Pacific. The 24 strength, orientation and persistence of this north-south trough influence the extent of northward penetration of the tropical storm before it moves onshore. Such a trough pattern is one which blocks wintertime Pacific storms from reaching the coast, except from a northwesterly direction. Factors limiting precipitation potential 3.32. There are several limitations on precipitation potential from tropical storms in California. Probable maximum coastal wind velocity in a tropical storm is limited by the distance of California from storm source region. The energy of the storm is depleted by its northward movement over cooler water, a loss reflected most in reduction of surface wind velocity. Although winds to 115 knots have been observed along the coast of Baja Cali- fornia south of 30 degrees N. latitude, the highest surface velocity recorded in California was 30 knots at San Diego in the September 1939 storm. Coastal surface winds were light in the September 1918 storm when it moved onshore in Central California, although winds were strong aloft. Surface friction resulting from the rough coastal mountain terrain rap- idly erodes lower- level wind velocity in a tropical storm as it moves on- shore. The small area of the circulation of the storm does not provide a continuing source of kinetic energy at lower levels. Duration of orographic precipitation at any location is seriously lim- ited by the rapid shift in wind direction as the storm moves by. With a movement of 200 miles per day (slow for a tropical storm at the latitude of Southern California) approximately a 90-degree change in wind direction at a local point would take place in that time. Rate of movement is not ham- pered by blocking Highs, as may occur in the eastern United States, since the arrival of the storm in California is dependent on the north-south trough ex- tending northward into middle latitudes. Instability release in coastal areas is restricted by environmental cool- ing of lowest layers. Instability may be an important factor in local con- vergence precipitation in inland areas or in the coastal mountains above the marine inversion. Past experience indicates that the season of occurrence of tropical storms in California is limited to months when extratropical storms are at a minimum and when hydrologic factors such as soil moisture limit runoff. The limitations on precipitation from tropical storms in California are such that the potential is estimated as less than that in some other storm types. The omission of these storms from the PMP criteria is discussed in paragraph 2.13. 25 Chapter IV CONVERGENCE PROBABLE MAXIMUM PRECIPITATION CRITERIA Purpose and procedure in maximizing convergence rain 4.01. The purpose of this chapter is to develop a method of estimating probable maximum convergence precipitation so as to provide: 1. Estimates of PMP for non-orographic areas. 2. Estimates of the convergence portion of PMP to be combined with amounts computed by the orographic model in orographic areas. The procedure employed is to develop, for durations through 72 hours: 1. Seasonal curves of enveloping precipitation/moisture ratios (ex- plained below) and 2. Similar seasonal enveloping moisture curves. These enveloping data are regarded as maximum values of the convergence pre- cipitation parameters suitable for combination. The next step is to combine corresponding values by multiplication: Precipitation ^ x Moisture = conv ergence PMP. Moisture J max 'max Values of convergence PMP are obtained for all months October through April and for all durations through 72 hours; these values are then distributed geographical ly . 4.02. The enveloping precipitation/moisture (called P/M) ratio curves are indices of the highest observed efficiency of the storm processes, ex- clusive of orographic, which convert water vapor to precipitation, as dis- cussed in chapter III. They are expressed in terms of precipitation in a given length of time per unit of moisture in the air (that is, inches of precipitation per inch of precipitable water, Wp). As a matter of con- venience, ratios for all durations are ratios of precipitation for the various durations to 12 -hour moisture values. The term P/M ratio is syn- onymous with the term C -factor used in Hydrometeorological Preliminary Esti- mate No. 5004 (8) and by Fletcher (9). 4.03. The enveloping moisture curves are based on envelopment of ob- served persisting 1000-mb dew points at low-level stations in California and the assumption of a moist -adiabatic lapse rate. 26 4 -A. DEVELOPMENT OF ENVELOPING DEW POINTS 4.04. Surface dew points are used in this study as an index of the moisture which is processed both in probable maximum precipitation and in storms of record. Studies have been made showing that the surface dew point is, in general, representative of the moisture through depth during storm situations. One of the more recent studies is described in U. S. Weather Bureau Technical Paper No. 38, "Generalized Estimates of Probable Maximum Precipitation for the United States West of the 105th Meridian" (3). In both the orographic and convergence PMP components, observed storm depths are essentially maximized for moisture by multiplying by the ratio of the maximum moisture to the observed storm-moisture where the maximum moisture is that which is consistent with the storm type, the season, and the geo- graphical location of the storm. The purpose of enveloping dew point charts is to provide these maximum moisture criteria. 4.05. The enveloping surface dew points provide other necessary in- formation to the over-all problem. The height of the freezing level, which affects the amount of spillover beyond the crest, is set by the surface dew points and an assumed saturated pseudoadiabatic lapse rate of the air. Tem- peratures during the PMP storm at any basin elevation necessary to evaluate the snow-melt contribution to the PMP flood, are similarly established. 4.06. Basic dew point data . The highest persisting dew points of rec- ord for 12 hours duration for each month at first-order Weather Bureau stations, adjusted for elevation to 1000 mb, were the basic data used. By persisting is meant the dew point which was equaled or exceeded throughout the indicated duration. Use of persisting dew points allows including the considerable dew point data from older records when only 2 or 3 observations were taken in a 24 -hour period. (For these early records, the concurrent minimum temperatures were also surveyed in order to take into account that the highest persisting dew point cannot be higher than the minimum tempera- ture recorded during the period). If time-averaged dew points were used in- stead of the persisting values, higher dew points would usually result. A 12 -hour duration was selected as being long enough to represent values which are consistent with a fairly broad general flow of warm moist air into a storm area. Dew points for a spectrum of durations are developed in para- graphs 4.21-4.25. The highest persisting dew points were adjusted to 1000 mb in order to have a common reference at which to compare the dew points observed at various elevations. This was done by reducing along the satu- rated pseudoadiabatic lapse rate. For the period 1905-1945 the highest per- sisting dew points are published in Weather Bureau Technical Paper No. 5, "Highest Persisting Dew Points in Western United States" (10). These pub- lished values are for midmonth and were taken from a seasonal envelope of observed values plotted at dates of occurrence. Durational consistency was obtained in these data by drawing a smooth dew point -duration curve. Changes were made in the published maximum 12 -hour persisting values that were ex- ceeded in the more recent years (1945-1959). For the Los Angeles area, 27 additional 12-hour persisting values were taken from a more complete survey made for Hydrometeorological Report No, 21B, "Revised Report on Maximum Possible Precipitation, Los Angeles Area, California" (11). 4.07. Rejection of unrepresentative dew point values . The procedure employed of simultaneous combination of maximum moisture with maximum pres- sure gradient in the maximum orographic storm imposes a slightly restricted definition of persisting dew point data, namely that they should come from a situation typical of a large cool-season storm and that they should occur during the storm rather than afterward. Therefore, some of the higher per- sisting 12-hour dew points were rejected. Examples of bases for rejection are described below. 4.08. In October, tropical or Gulf of Mexico air infrequently reaches Southern California and the Central Valley, resulting in high surface dew points. In October and April, high dew points occur along the Southern California coast with the approach of a weak cold front from the north down the east side of the Pacific High. High dew points are occasionally re- corded there with a summer-type stratus condition in October and April. In the November 1950 storm, dew points in the San Joaquin Valley increased at the end of the storm which was terminated by a northward shift of the ridge over Southern California and of the storm track into Northern California on the 20th. Surface heating and evaporation along with maintenance of the moist flow from the southwest at lower levels accounted for the higher sur- face dew points after the rain ended. A similar situation occurs in the northern Sacramento Valley in late spring and early fall when a light southerly surface flow continues after the storm ends so that moisture and heat are added from the ground surface. Envelope of maximum observed 12 -hour persisting dew points 4.09. Two fundamental restrictions to an envelope of observed dew points are that it should largely envelop data observed during storm situ- ations and that it should be smooth both seasonally and areally. The de- velopment of enveloping curves complying with these restrictions is de- scribed in the following paragraphs. 4.10. Maximum observed 12 -hour persisting dew points . On figures 4-la to 4-ld are plotted for first-order Weather Bureau stations the highest mid- month 12-hour persisting dew points taken from Technical Paper No. 5, (10) or any higher observed values, determined from hourly observations or more recent storms, which exceed those of Technical Paper No. 5. Those in paren- theses were determined to result from non-storm situations as explained in paragraph 4.07 and therefore were not considered in the envelope. It may be seen that the great storms of November 1950 and December 1937 contribute many of the controlling points. Figures 4-2a and 4-2b show the highest 12- hour persisting values reduced to 1000 mb from all of the observation sta- tions during these storms. (The highest average 12 -hour dew points for the same dates are about 1° higher than the highest 12-hour persisting value 28 shown.) For the November 1950 storm, those south of 37 °N latitude occurred after the intense rain and possibly are a degree or two too high to be representative of a storm situation. For example, the 64° at Fresno on the 20th was rejected and 63° dew point for the 19th used. These figures show that the first -order station dew points are representative of those in the general area and of large-scale flow of moisture. 4.11. Seasonal variation . Smooth seasonal variation from month to month is imposed by the gradual change in the meteorological parameters during the cool season. An envelope of highest observed storm dew points would therefore reasonably be an over -envelopment in some months which have not yet experienced the magnitude of storm that is potentially possible. For example, a close envelope of observed dew points constructed prior to November 1950 undoubtedly would have considerably undercut those attained in the storm of that month. 4.12. The shape of the seasonal curves of dew points at the key sta- tions were determined from several guides, two of a statistical nature. For each first -order Weather Bureau station in California and southern Oregon the highest 12 -hour persisting dew point for each month (October -April) was found for each of 25 years (1927-1945; 1950-1955). Dates of occurrence of the monthly maximum indicated little if any bias toward the beginning or ending of months; therefore each dew point was assigned to the mid-month day. Each set of dew points were then plotted on normal probability paper and a straight line of best fit drawn to the data. The fact that these data so plotted, quite readily fit a straight line indicates that they follow the normal probability distribution. The line of best fit then defines the 12-hour persisting dew point to be equaled or exceeded once in 2, 25, 50, etc. years. Figure 4-3 is an example of these plots of maximum 12-hour per- sisting values for Fresno for the month of October. 4.13. The dewpoints to be equaled or exceeded once in 2 years, termed the 2-year return period values, plotted for each station on figures 4-la to 4 -Id, show a fairly smooth progression through the season. The 100 -year return period values on the other hand are not as stable since more weight is given to the higher values observed. In defining the line of best fit by eye on probability paper some variation in the 100-year return value re- sults; therefore the 100-year return period dew points are indicated by vertical bars on the figures, representing the span of good fits of straight lines to the 25 years of data. 4.14. To serve its purpose as a guide, a smoothed 100-year return period curve was determined, shaped similar to the 2 -year return period curve. This was done by plottings (not shown) of the 2-year value against the 100-year for each station, which gave fairly good correlations for most stations, and then adjusting the 100-year value to the line of best fit through each station 1 s plot. The resulting smooth 100-year and 2 -year re- turn period values provide a guide to the shape of the enveloping dew point curve. (For comparison 10- and 50-year return period dew points are also 29 shown on figures 4-la to 4-ld. These are smoothed similar to the 100-year values. ) 4.15. Another guide is derived from mean sea-surface temperatures. Temperatures in the area of the source of moist flow to points along the California coast might be considered an index to the upper limit of moisture which is available to these points. Modifications in the air mass limit the amount of moisture that could reach the coast. However, the month-to-month variation in sea -surface temperatures upwind of the coast would appear to typify that of enveloping dew points. Such average monthly sea-surface temperatures are shown on figures 4-la to 4-ld for points 600 nautical miles southwest of each station. In general, their variation with season is quite similar to the smooth seasonal variations of 2 -year and 100 -year return peri od dew points. 4.16. Enveloping seasonal 12-hour persisting dew point curves . An en- velope for each station was drawn through the highest observed representa- tive 12-hour persisting values and shaped after the 2- and 100-year return- period curves and the sea-surface temperature curve. These envelopes, shown on figures 4-la to 4-ld by solid lines, include minor adjustments for geo- graphic smoothing which is described in the next paragraph. The 1950 and 1937 storms control the curves for most stations. 4.17. Monthly maps of enveloping 12 -hour persisting dew points . Seasonally smoothed enveloping dew points for each California and southern Oregon station were plotted on maps, month by month (figures 4 -5a and 4 -5b) and lines of enveloping dew points were drawn with some geographical smooth- ing. The maximum observed values for bordering states were also plotted to consider large-scale features over the Western States and to minimize dis- continuities. 4.18. Mean seasonal variation of 12-hour moisture . The shape of the seasonal dew point curves of figures 4-la to 4-ld differs somewhat from sta- tion to station. Therefore, the geographical variation of seasonal trend of 12 -hour moisture was studied in order to decide whether a mean seasonal variation is permissible for the entire state. The difference in seasonal variation can be seen on figure 4-6 which shows the ratio (as a percentage) of the precipitable water (to the top of the column, assuming a saturated pseudoadiabatic lapse rate) corresponding to the maximum 12 -hour persisting dew points for each month to the precipitable water for January at stations and grid points. Within the drainage areas of California with which this report is concerned Khe arsal range in percentages is: Oct. Nov. Dec. Feb. Mar. Apr 127. 57. 27. 37. 4% 67. The large October areal range is explained as follows: the latitudinal dew point gradient in October in Northern California is relaxed because of Octo- ber storm tracks being such as to bring warm moist air to the Pacific North- west. 30 4.19. Considering the relatively small areal range shown above, it is reasonable to adopt one seasonal variation of moisture for the California area of concern. Averaging the percentages at the stations and grid points, and expressing them in terms of percentages of February (month of lowest average moisture), the following percentages result: Oct. Nov. Dec. Jan. Feb. Mar. Apr 121 110 105 100+ 100 101 104 Smoothed values from a curve drawn to these data give: Table 4-1 SEASONAL VARIATION OF MAXIMUM MOISTURE. PERCENT OF FEBRUARY Oct. Nov. Dec. Jan. Feb. Mar. Apr. 121 111 104 100 100 101 104 These ratios, if applied to the precipitable water for the dew point on the February map at any location, will give the seasonal variation of moisture for that location. The mean seasonal variation when applied to January dew points at key stations results in the dotted curves in figures 4-la to 4-ld. It is seen that adjustment for the geographically-averaged seasonal trend makes changes of less than 1°F from the station envelope at most stations. Comparison of enveloping with 100-year return period dew points 4.20. Because 100-year return period dew points have been determined, it is of interest to see the effect on the PMP if they alone had been used to define the moisture criteria. The average difference between the en- veloping and 100-year return period dew points for the eight key stations for each month is a measure of the difference between the two over the whole area. These differences are given in table 4-2 for each month. Table 4-2 EXCEEDANCE OF ENVELOPING OVER 100 -YEAR RETURN PERIOD DEW POINTS ( °F) (Average of Eight Key Stations) Oct. Nov. Dec. Jan. Feb. Mar. Apr. 0.4 0.8 1.1 1.2 1.3 0.9 0.5 Individual 100-year return period values range from over 3°F lower at San Francisco to 2°F higher at Eureka than the enveloping criteria. A 1°F change in dew point affects convergence PMP by 5 to 6 percent and orographic PMP by 2-1/2 to 3 percent. 31 In assessing the exceedance of the enveloping curves over M 100-yr n values it should be taken into account that the 100 -yr values are for a month only. Thus, on the average over a span of 100 years, at each station the October value would be equaled or exceeded once, the November value once, etc. , that is seven exceedances for the October-April season. Moisture criteria for other durations 4.21. Thus far we have dealt only with 12-hour dew points. Variation of dew point with storm duration is useful in defining the moisture that is processed during the 72 -hour PMP storm. Such variations were obtained by plotting, for each station, the precipitable water Wp corresponding to the highest persisting California dew point values for the 12, 24, 36, 48,60 and 72 hours published in Weather Bureau Technical Paper No. 5 (10) and drawing a smooth curve, extrapolated to 1 hour. These curves, called 'de- cay 1 curves, permit expressing Wp for any duration in terms of the 12 -hour w p . 4.22. In order to determine if a composite or mean decay curve can be adopted for all areas and seasons, it is necessary to study the geographical and seasonal variation in the curves. 4.23. Geographical variation of decay rate . For each California sta- tion and each month (October-April) the ratios of the Wp for the 12 -hour dew point to that for the 24, 36, 48, 60 and 72 -hour dew point were computed. The largest range in these ratios, from station to station within each month, showed up in those for 12/72 hours, mainly because of high ratios (less decay) at Red Bluff, especially for winter months - about 10% less decay in moisture from 12 to 72 hours than at adjacent stations. This sin- gularity may be due to the trapping of the lower level inflow moisture at the head of the Sacramento Valley at the end of storms, resulting in an overestimate of the precipitable water for longer durations. Because this effect is restricted to lower level moisture and to a small area no geo- graphical variation of the decay rate of moisture has been introduced. 4.24. Seasonal variation of decay rate . The monthly decay rates were determined by averaging the decays at the California stations. These de- cays showed very little seasonal variation, the ratios of the Wp for 12 hours to that for 24, 36, and 48 hours varying by 0.02 and ratios of the W p for 12 hours to that for 60 and 72 hours by 0.03. 4.25. Composite decay rate . The above studies justify use of a com- posite variation of moisture with duration for all areas and months. In terms of the precipitable water for a saturated pseudoadiabatic column it is given in the following table. 32 Table 4-3 DURATIONAL VARIATION OF MAXIMUM MOISTURE Duration (hours) 1 3 6 12 18 24 30 36 42 48 54 60 66 72 Percent of 12-hour precipitable water 107 106 104 100 97 95 93 91 89 88 86 85 84 83 This average durational decay of persisting moisture has been compared with some observed decays in major storms and is shown in figure 4-4. The adopt- ed moisture decay for PMP computations is similar to that in observed storms. Enveloping moisture criteria as indices of maximum moisture 4.26. In the development of moisture criteria, a few observed values for some stations and months were used as key points on a general seasonal envelope of 12 -hour persisting moisture which in turn was extended to other durations by use of observed relations. The purpose of the enveloping mois- ture criteria thus developed is to provide an index of moisture suitable for combination with other maximized parameters involved in the PMP storm. Though not representative of absolute maximum values, the above enveloping criteria are regarded as adequate for use in combining with other maximized parameters in the PMP storm, in line with the presentation of maximization in chapter II. For this reason, a smoothed envelope of observed values of moisture are referred to as maximum moisture values. 4-B. DEVELOPMENT OF ENVELOPES OF PRECIPITATION/MOISTURE RATIOS 4.27. The precipitation/moisture ratio is defined in paragraph 4.02. 4.28. Limitations of P/M ratio data applicable to California 1. Areal restriction of P/M ratio evaluation, necessary to avoid orographic contamination in point rainfall by upslope or spillover effects, limits data selection in California mainly to stations in the central portion of the Central Valley, between Red Bluff and Bakersfield. 2. Length of record of observations in this area is very limited for du- tations other than 24 hours, except for a few stations, so that enveloping P/M ratios for other durations must be obtained mostly by indirect means. 3. Maximum P/M ratios from the non-orographic parts of the eastern United States are not directly transposable to California and are too high. In the East there is a positive correlation between P/M ratio and dew point, high moisture seeming to promote storm efficiency. In California this 33 correlation is absent because of differences in trajectories that favor high moisture and marked instability (paragraph 3.29). In other words, in Cali- fornia, winds with a southerly component generally are accompanied by less instability than at times prevails in the Eastern States. Classification of storms for development of P/M ratios 4.29. The minor contribution of instability toward convergence pre- cipitation in the orographic storm as compared to that in the pure con- vergence storm, discussed in chapter III, leads to classifying convergence storms into two groups on that basis for obtaining P/M ratios, namely: 1. Convergence storms in which instability is a minor factor. 2. Convergence storms in which instability is an important factor. Enveloping P/M ratios are developed from (1) for convergence PMP to be com- bined with orographic PMP and from (2) for convergence PMP not combined with orographic PMP. The largest P/M ratios come from Group 2. Enveloping P/M ratios to combine with the maximum orographic storm 4.30. Applicable data . Only storms in Group 1 of paragraph 4.29 are used to develop P/M ratios for the convergence part of orographic storms. Group 2 storms, as well as local convective storms which are seasonally un- suitable, are eliminated. For short durations, such as 1 hour, the in- stability restriction on data in Group 1 is relaxed since short period in- stability is not uncommon in major storms. Storm values were found from three sources: (a) The extensive pre- cipitation compilations during major orographic storms; (b) the published extreme 24-hour station values in Weather Bureau Technical Paper No. 16 (12) for Central Valley stations; (c) high 2-day totals from Climatological Data (13). Storms from the last two sources were subjected to a qualitative syn- optic appraisal intended to insure that they fell in the required Group 1. For the two-day totals, maximum values for 24 consecutive hours were esti- mated by constructing mass curves for stations in the vicinity. Two of the daily values were reduced to durations of less than 24 hours, also on the basis of comparative mass curves. The larger P/M ratios are listed with pertinent data on figure 4-7. 4.31. All-season envelope of 24-hour P/M ratio . Envelopment of the Central Valley P/M ratios on figure 4-7 yields a 24-hour maximum of 6.4. A computed ratio of 7.4 at Colusa for 24 hours is undercut by the en- velope. This was done because original records leave some possibility that the reported 24-hour precipitation may have occurred in a longer period of time. 34 The next highest effective value is at Willows, during a storm in- volving a deep occluding Low from the southwest with an apparently minor instability effect. The 22 -hour assigned duration is an estimate supported by the Red Bluff recorder and several other mass curves. The third highest effective value comes from the Southern California storm of January 25-27, 1956. This storm is discussed in detail in HMR 37. 4.32. Seasonal variation of 24-hour P/M ratio . There are insufficient values to define the seasonal variation of maximum 24-hour P/M ratios di- rectly. Extensive seasonal plots of maximum values of 24-hour precipitation for numerous stations in general indicate no trend in any region of Cali- fornia at non-orographic stations for higher values in one month than an- other, within the October-May cool season. The 24 -hour duration is the approximate "cross-over" point. For shorter durations, the higher values occur in spring and fall. For longer durations the mid-winter maxima are the largest. This variation is indicated by figures 4-9 and 4-10, dis- cussed in subsequent paragraphs. 4.33. The conclusion from the precipitation plots is that for the 24- hour duration the seasonal trends of maximum moisture and P/M ratio must counteract each other. The seasonal variation of the maximum P/M ratio is then the reciprocal of the seasonal trend of maximum moisture (table 4-1). Applying this concept, the enveloping value of 6.4 of 24 -hour P/M ratio is assigned to the driest month, February, in figure 4-7. The enveloping 24- hour P/M ratios for the other months are calculated from the indicated re- ciprocals. 4.34. P/M ratios for other durations . The durational variations of the P/M ratio, like the seasonal variation, is based primarily on the observed variation of precipitation. Since the denominator of the P/M ratio, for convenience, is always the 12-hour moisture, in this report (paragraph 4.02), the durational variation of P/M is the same as the durational variation of precipitation, P. The 24-hour enveloping P/M ratios for the various months in figure 4-7 are extended to other durations by use of 1/6- , 6/24-, and 72/24-hour precipitation ratios in large storms. The resulting P/M ratio curves envelop satisfactorily the highest P/M ratios found for durations other than 24 hours. 4.35. Enveloping P/M ratios for 6 hours . A seasonal variation of 6/24- hour precipitation ratios was obtained by averaging the ratios from the highest monthly 6-hour and 24-hour storms for 21 Central Valley recorder stations, most of them with short records. This seasonal trend is similar to that for eastern data, as shown in figure 4-9. An average mid-winter ratio of 0.55 was assigned to February and fall value of 0.70 to October; intermediate ratios were interpolated. Use of a California seasonal trend of 6/24-hour precipitation in this way distributes enveloping 6-hour P/M ratios in a symmetrical manner. 35 4.36. Enveloping ratios for 1 hour . A seasonal variation of 1/6-hour rain ratio was obtained by study of highest monthly 1- and 6-hour rainfall values for 30 Central Valley stations for approximately 14 years. It in- dicates 1-hour to 6 -hour ratios ranging from .40 in midwinter to .48 in October. These values were used in extending the 6 -hour P/M ratios to 1 hour. 4.37. Enveloping values for 72 hours . A seasonal variation of 72/24- hour rain ratios was obtained by averaging ratios of 7 2/ 24 -hour rain from the 10 highest 24-hour rains and 10 highest 7 2 -hour rains for each month from 50 representative stations, mostly in the Central Valley. This season- al 72/24 -hour rain ratio curve is shown in figure 4-10. For each month the ratio from this curve was multiplied by the 24-hour P/M ratio for the corre- sponding month to obtain monthly 7 2 -hour P/M ratios. Monthly P/M-ratio enveloping curves for to 72 hours were drawn through the 1-, 6-, 24-, and 72-hour values (figure 4-7). The approximate envelop- ment of the highest observed 24-hour values by the February curve results in approximate envelopment of values for all durations in any month of occur- rence. Enveloping P/M ratios for the maximum convergence storm 4.38. The purpose of the curves in figure 4-8 is to provide enveloping P/M ratios which, when combined with maximum moisture, will yield pure con- vergence PMP for non-orographic areas. (It also yields pure convergence PMP for foothill areas if it is greater than the total PMP obtained by combi- nation of orographic PMP and convergence PMP based on the P/M ratio curve developed for orographic storms, figure 4-7.) 4.39. Storm data applicable to this envelopment are from storms ex- cluded from the curves in figure 4-7, namely those with a storm trajectory from north of west or those with high instability precipitation due to cold air intrusion from northwest during much of the storm. The two storms used in the 24 -hour envelopment are those at Sacramento in April, 1880 and at San Francisco in December, 1866. Not used in the envelopment but plotted for reference purposes only were a summer -type storm in a moist flow from the Gulf of Mexico (Encinitas, October 12, 1889) and spring and fall local con- vective storms peculiar to the foothills in the north end of the Sacramento Valley (Red Bluff, September 14, 1918; Newton, September 18, 1959; Kennet, May 9, 1915). Storms entered in figure 4-8 are described in some detail in chapter V of HMR 37. 4.40. The procedure in constructing these curves is the same as that for the curves in figure 4-7. The highest observed P/M ratio near 24 -hours is enveloped and assigned to February. The same seasonal variation of 24- hour values as in figure 4-7 was assumed. The same 1/6- , 6/24-, and 72/24- hour precipitation ratios were used to obtain 1-, 6-, and 72-hour seasonal P/M ratios since those ratios were determined without regard to the off- shore trajectory of the storm. 36 4.41. The seasonal envelopes drawn to these 1-, 6-, 24-, and 72 -hour computed values (figure 4-8) slightly undercut the highest observed 24 -hour value in month of occurrence. However, envelopment in month of occurrence in the case of the 1880 storm is not considered necessary inasmuch as it was in most respects typical of a cold midwinter storm. The enveloping P/M ratios for non-orographic storms, figure 4-8, have a constant ratio of 1.33 to the P/M ratio values for convergence rain in orographic storms, figure 4-7. Enveloping P/M ratios as maximum ratios 4.42. The enveloping P/M ratios are regarded as maximum values in the same sense as enveloping moisture values are regarded as maximum values, namely, suitable values for combination with other maximized variables. Oc- currence of higher values of P/M ratio than those enveloped is probable in view of the extremely limited sampling area for non-orographic rain in Cal- ifornia and the short period of record at most stations. 4.43. The convergence part of the PMP is directly proportional to the adopted P/M ratios. Different assumptions as to enveloping P/M ratios would make corresponding changes in the convergence PMP. 4-C GENERALIZED CONVERGENCE PMP CHARTS Combination of parameters of convergence PMP 4.44. Multiplication of the enveloping P/M ratios (derived in 4-B) by the enveloping moisture criteria (derived in 4-A) gives convergence PMP. Since the P/M ratio curves of figures 4-7 and 4-8 are in terms of 12-hour persisting moisture, the convergence PMP for any duration is the product of P/M for that duration and the 12-hour persisting moisture. Two sets of values of convergence PMP result from this combination of the two sets of P/M ratio curves with moisture. Since the P/M ratios are based on precipitation at a point, the convergence PMP values are referred to as point values. Reduction of convergence PMP for elevation and coastal barrier 4.45. Reduction for effective elevation . For slopes not affected by an upwind barrier, the reduction in convergence PMP with elevation is assumed to be proportional to the reduction of W p in a saturated column. Thus no ac- count is taken of variation with elevation of the convergence mechanisms such as release of instability precipitation by orographic lifting. The effective elevation is taken as the height of the ground 5 miles upwind of a given lo- cation because raindrops or snowf lakes are carried forward in the wind stream. 37 4.46. Reduction for effective coastal barrier . The convergence mecha- nisms that produce the heaviest point rainfalls in California in winter storms approaching probable maximum proportions require the interplay of vigorous horizontal wind systems and horizontal pressure gradient forces that are not in balance with these wind systems. Thus, in the sense of con- tributing to convergence precipitation, air lying below the crest of the Coast Range in the southernmost part of the Central Valley is considered as virtually dead air since the strength of horizontal wind components in this layer is limited. On this basis the effective elevation for computing con- vergence PMP in that region is taken as the minimum elevation of the coastal barrier over which wind might be expected to flow. East of San Francisco Bay there is an opportunity for low-level winds to penetrate into the north- ern end of the Sacramento Valley, and contribute to a convergence mechanism. Taking these factors into account, effective barriers have been estimated for reducing (by moisture depletion) the above convergence PMP values for the floor of the Central Valley, slopes to the lee of the coastal mountains and the Sierra foothills. In the southern San Joaquin Basin the effective barri- er is equal to the actual barrier; in the Sacramento Basin the effective barrier is much less than the actual barrier. A map of estimated effective barrier heights (figure 4-11) was constructed for basin sizes of 200 square miles and greater. Local topographic features that would affect very small basins were necessarily smoothed out. 4.47. Reduction of convergence PMP for elevation and coastal barrier is accomplished by the same elevation and barrier profiles in both the combined convergence and orographic storm and the pure convergence storm. The greater relative role of instability in the pure convergence storm, not reduced to the same extent by the shadow effect of the Coastal Range as is the effect of unbalanced pressure fields, suggests a less stringent barrier reduction. Since this difference does not lend itself to evaluation, it was not taken into account. Reduction of 10 -square -mile convergence PMP for basin size 4.48. The variation of California convergence PMP with basin size was made similar to that in selected areas of the eastern United States from Hydrometeorological Report No. 33 (2). Zones were selected on the basis of latitude and season. This procedure eliminated the most southerly zones (5, 8 and 9) and the east coastal zones during the hurricane season. For each month (October -April) in each of the remaining zones, the 6 -hour incremental maximum precipitation for standard-sized areas was expressed as a percent of the 10 -square -mile value. Then an average of the areal variation (percents of 10 -square -mile values) was obtained for each month in the selected zones for each 6-hour increment to 72 hours. Since the relations in Hydrometeoro- logical Report No. 33 extend only to 1000 square miles, values to 5000 square miles were obtained by smooth-line extrapolation. The percents showed little areal variation beyond the third 6 -hour increment. This eastern United States basin size reduction relation was used to convert California 10 -square -mile values of convergence PMP to other basin sizes. 38 Construction of a 6-hour 200-square-mile January-February probable maximum convergence precipitation index map 4.49. The steps taken in combining the factors involved in an index map of probable maximum convergence precipitation for the first 6 hours for January or February for a 200-square-mile basin size are outlined in 1 to 5 below. 1. The 6 -hour increments of P/M ratio (for a point or 10 square miles) were read from figure 4-7 for each month and plotted for smoothing. 2. These 6 -hour smoothed values were expressed as percentages of the 1st 6 -hour February value. They refer to a point or 10 square miles. This gives combined seasonal and durational variation of P/M ratio. 3. The barrier and elevation reduction map (figure 4-11) was used to reduce geographically the moisture criteria for mid-February (month of lowest dew point) on figure 4-4b, expressed as precipitable water. 4. These reduced values of Wp were multiplied by the first 6-hour 10- square-miles February P/M ratio from figure 4-7 to give 6 -hour 10 -square - mile February probable maximum convergence precipitation . 5. From the eastern United States basin-size reduction relation, described in paragraph 4.48, a factor 0.80 was applied to the 10-square mile probable maximum convergence precipitation values in step (4), to reduce to a basin size of 200 square miles. Figure 4-12 shows the resulting 1st 6 -hour 200- square-mile February probable maximum convergence precipitation index map for California areas of concern in this report. As the differences are in- significant, the map also applies to January. 4.50. This map, referred to as the probable maximum convergence pre- cipitation index map , gives values from which may be derived values of con- vergence PMP for different sizes of areas and durations for combination with corresponding values of orographic PMP to obtain the total PMP. Values of convergence PMP for the maximum convergence storm are obtained by multiply- ing by 1.33 and are applicable to non-orographic areas and to foothill areas where total PMP values obtained by the above combination are smaller. Monthly charts of variation of convergence index with basin size and du- ration 4.51. The variation of convergence PMP for basin size and duration was incorporated into monthly charts of percentage of index (figures 4-13a to 4-13c). These relations are derived by combining (a) Seasonal variation of moisture, table 4-1, (b) Seasonal and durational variation of P/M ratio, figure 4-7, and (c) Basin-size reduction relation described in paragraph 4.48. 39 Convergence PMP for 1 and 3 hours 4.52. For small basins it may be necessary to define the PMP for du- rations less than 6 hours, therefore the convergence PMP for one hour for areas up to 100 sq. mi. and for 3 hours for areas up to 500 sq. mi. have been included in this report. 4.53. The areal variations of rainfall for these durations were based on all convergence type storms contained in "Storm Rainfall" (14) for which the 1- and 3-hr maximum depths had been determined. The depths for standard sized areas were expressed in percent of the depth at 10 sq. mi. for each storm. Averaging the percentage decrease of depth with area for all the available storms and smoothing with area resulted in the following per- centages. Table 4-3 AREAL VARIATION OF SHORT -DURATION CONVERGENCE PMP Duration Area rs) (sq. mi.) 10 30 50 100 Percentage of 10 sq 1 100 90 84 76 3 100 94 90 84 78 71 This defined the basin-size reduction for 1 and 3 hours (similar to that described in paragraph 4.49 step 5 for 6-hour increments) and enabled com- bining with the seasonal variation of moisture and P/M ratios to obtain the depth-areal 1- and 3-hour duration curves of figures 4-13a to 4-13c. 40 Chapter V CRITERIA FOR PROBABLE MAXIMUM OROGRAPHIC PRECIPITATION ON WINDWARD SLOPES 5 -A. OROGRAPHIC PRECIPITATION Definition 5.01. Precipitation which results from the forced lift imparted to moist air by its motion over a solid barrier is called orographic precipita- tion. It does not include that component of the total precipitation which would have occurred had the barrier not been there (i.e., caused by the dy- namics of the general weather situation). Treatment 5.02. The orographic component of the total precipitation, its forma- tion, path of descent, distribution on windward slopes including loss to lee- ward by spillover, variation with time, and finally its maximization are the subjects of this chapter. 5-B. THE OROGRAPHIC MODEL Introduction Basic characteristics 5.03. The 2-dimensional orographic model used in the Los Angeles and San Joaquin Reports (11) and (15) is also applied in this report, but with some modifications. There are different formulations of this basic model, but the following features are common to each: 1. The 2-dimensional model (length along the current and height) is ex- panded to 3 dimensions by averaging the parameters across the current, i.e., wind, moisture, topography, etc. 2. Precipitation is conceived of as the difference between inflow and outflow moisture in a specified volume. 3. There is no convergence or divergence of the air. Except for the water vapor precipitated, which amounts to a few percent at most, con- servation of mass is realized. 4. As a closely associated condition, laminar flow is assumed, i.e., the air moves smoothly in nearly parallel streamlines, with no turbulent motion. 41 5. At some great height (low pressure) above the mountain called the nodal surface the atmospheric flow is horizontal. 6. The air is saturated. 7. A steady state is assumed, i.e., velocities at all points are inde- pendent of time. Formulas 5.04. The basic condensation model formulas, derived in the Los Angeles Report (11), are: (1) (2) r -4 v, q^- •* v 2 q 2 af 2 t Y and v (w - — - w ) fi V l < W pl AP 2 W p2 ; t = Y Since from mass continuity considerations: V~ AP~ = V- AP- (3) (1) may be written: R .4 W l g x AP X - ^AP^ .4 V 1 AP 1 (q^ - q £ ) (4) t = Y = Y Equation (4) is the form used most in the report. Symbols 5.05. A list of symbols used in the above equations and in the rest of this chapter follows: R - precipitation (inches); also gas constant for air R - observed precipitation R - computed precipitation t - time (hours) V - windspeed (mph) V - speed of air at inflow V - speed of air at outflow 42 V - component of the wind V - component of the geostrophic wind V - geostrophic windspeed W . - precipitable water at inflow (inches) pi W 9 - precipitable water at outflow Y - distance, inflow to outflow (miles) X - distance, normal to Y _q - specific humidity q 1 - average specific humidity at inflow (gm/gm) q 9 - average specific humidity at outflow P - pressure (mb) AP-. - pressure difference at inflow AP 9 - pressure difference at outflow -2 g - acceleration of gravity (cm sec ) Z - height (geopotential meters) -?r- - slope of isobaric surface normal to contour lines on £P on pressure change per unit horizontal distance f - coriolis parameter (2o) sin*), a function of latitude a) - angular velocity of the earth - latitude X. - model coefficient C - temperature, °Centigrade F - temperature, °Fahrenheit T - temperature, °Absolute T - virtual temperature (°C) S - indicator for an air streamline A - area on thermodynamic diagram (figure 5-7) R.H. - relative humidity k - an arbitrary frictional coefficient, dimensionless p - air density n - subscript indicating nodal surface 1, 2, 3, 4, etc. Subscripts applied to other variables. All odd- numbered subscripts refer to values above the foot of a ridge or mountain (inflow) . All even numbered subscripts refer to values above the crest of the mountain (outflow). 43 The Inflow Wind (V ) The inflow wind profile 5.06. A reasonably accurate portrayal of the inflow wind profile is of great importance in the estimation of orographic precipitation. The inflow wind is one factor (and an important one) in determining the outflow wind. In combination these profiles determine the amount of air available to be processed and the degree to which it is lifted. Referring to the schematic diagram, figure 5-1, the inflow face is XAP. and the component of the windflow against this face is shown by the hatched area formed by connecting the surface, 500 mb and nodal surface wind vectors. It is seen that the more wind vectors used to construct the inflow wind pro- file, the better the approximation to the true rate of inflow. Winds at 100-mb intervals were used for construction of the inflow profiles, except for two 50-mb layers at the bottom of the atmosphere where the wind turns fastest with height. The geostrophic wind approximation 5.07. Because of an almost complete lack of upper air wind observations in storms over most of California an approximation to the real wind is made by the use of the geostrophic wind and empirical relations between the two. The geostrophic wind is defined as the theoretical horizontal wind ve- locity for which the coriolis acceleration would balance the horizontal pres- sure force. At sufficiently great heights above the ground the airflow is normally close to geostrophic. Thus the geostrophic formula has great util- ity in estimating winds. Its speed is given by: 1 Sp V = — — t— (for constant level chart, e.g., /cX g fp on i i \ (5) & sea- level map) v _ _ .& _ (f or constant pressure chart, (6) 8 r dn e.g., 500 mb) Its direction is parallel to the isobars or height lines. The formula which gives the geostrophic windspeed in mph when the pres- sure gradient is expressed in millibars per mile is: V g = (1.39 x Hf 4 ) ^ (7) -1 3 Here f and p are in the usual units of sec and gm/cm , respectively. 44 Relation of wind to geostrophic wind 5.08. On the average over land the wind and geostrophic wind approxi- mate each other above about 4000 feet with sub-geostrophic windspeeds and more or less cross-isobar flow toward lower pressure below 4000 feet. The rougher the terrain the deeper the friction layer. (Under certain weather conditions, e.g., rapidly changing pressure, the wind may depart significant- ly from the geostrophic at any level). In order to establish quantitatively the deviations from geostrophic conditions over the rough terrain of California a series of wind studies was undertaken. Pilot balloon and rawin (radio wind sounding) reporting stations used for these studies were: Bishop, Inyokern, Los Angeles, Merced, Oak- land, Red Bluff, Sacramento and Santa Maria, Calif.; Medford, Ore.; and Reno, Nev. At each of these stations 3 to 6 seasons (October through April, in- clusive) of data were processed. Cases were selected for study when a) the wind aloft observation extended to sufficient height and b) the direction of the geostrophic wind at the time was within a span typical of storms and the speed was in excess of certain minimum values. A sample comparative plot of actual and geostrophic wind for one sta- tion, Oakland, Calif., is presented in figure 5-2. This example is based on 5 seasons of record (1951-1955 inclusive). Each dot represents one ob- servation unless otherwise indicated. The figure shows the ratio of the actual wind component against the Coast Range, V , to the geostrophic com- ponent, V . (The component in all study cases was taken normal to the mountain range in the vicinity of the station.) It will be noted that the mean value of V /V rises from a very low value at the surface to near geo- strophic condition! at 500 mb. This result is fairly typical of all sta- tions. Similar data for other stations are shown in HMR 37. Figures 5-3 and 5-4 show the mean profiles of V /V„ c for the study sta- tions. The grouping of curves into Coastal and Central Valley was suggested by the generally higher values along the coast up to the 500-mb level. A single average V c /V gc curve was adopted for the Coast Range and is shown by the heavier line on figure 5-3. The coastal relation is based pri- marily on Oakland and Santa Maria and to a lesser extent on Long Beach.* *The curve for Long Beach appears to be low compared with Oakland and Santa Maria. A possible reason for this difference is a bias due to the small num- ber of cases suitable for study at Long Beach. Although 5 years of data were searched only 4 cases were found to meet selection specifications. At Oak- land and Santa Maria 25 and 12 cases respectively were found for an equal length of record. 45 The rapid rise to three fourths of the geostrophic at 900 mb shows the effect of sea proximity, since at this level approximately 907 o of the geostrophic speed is attained over the ocean. Full geostrophic windspeed is not attained till 500 mb, due to the impedance of the Coast Range. The Central Valley relation proved to be more complicated than the Coastal. Three stations were studied in the Valley; Red Bluff, Sacramento and Merced. The three curves at the higher levels were generalized to one valley prototype shown by the heavier line on figure 5-4. Below 800 mb Red Bluff and Merced were very similar and therefore combined. Results of the Sacramento wind study indicated that the lower elevation of the Coastal Range around the San Francisco region is responsible for higher V /V ratios be- low 850 mb. It is estimated that when the wind is from the southwesterly quadrant this influence is felt from about Stockton to Chico, with fullest effect near Sacramento. Figure 5-5 shows the adopted areal distribution of the V /V ratio at 1000, 950 and 900 mb. c gc Obtaining the inflow wind profile 5.09. In this report inflow wind profile in a storm is obtained from geostrophic winds and the V /V ratio. A short survey indicated that the vertical profile of the geostrophic wind could be approximated to a suffi- ciently accurate degree by only 2 measurements, the surface and 500-mb geo- strophic wind and the assumption of a linear relation between the two. The appropriate V /V ratio from figures 5-3, 5-4 or 5-5 is then applied to the geostrophic wind 8 profile to obtain the "real" wind profile. In some storm cases the 500-mb wind is not known. In these, the 500-mb wind is estimated by indirect means, discussed in paragraph 5.27. The 300-mb wind was derived by extrapolation from the 500-mb wind by the following re- lation: V 300 = l ' 30 V 500 (8) This relation was derived from an empirical study of observed winds in storm or near-storm situations. The Outflow Wind (V2) and Pressure (P2) Flow over slopes 5.10. The amount of orographic precipitation is related to the decrease in pressure experienced by each part of the flow. The windflow that would yield the maximum of orographic precipitation would be for the entire flow at each level to rise and fall parallel to the ground, so as to be lifted by an amount equal to the height of the barrier. Such a flow, however, is never obtained in the atmosphere. Rather there is a tendency for a leveling off of 46 the airflow at some great height above the ridge; thus the amount of lift de- creases upward from the ground. The lift is equal to the height of the ridge only at the ground and decreases to zero at the elevation where the flow es- sentially levels off. The nodal surface 5.11. The outflow pressures required for computing orographic precipi- tation are found in two steps. The first is the choice of the pressure at which the flow is level, called the nodal pressure . The other is determining the spacing of the streamlines on a pressure scale between the ground and this nodal surface . These pressures could be computed rather simply from re- quirements for continuity of mass if an observed vertical profile of the windspeed above the crest of the ridge were available. However, such observa- tions are non-existent and the entire flow above the slope and crest of the mountain must be estimated from the given inflow at the foot of the mountain by application of pertinent laws. The assumption of an upper level of near-horizontal flow derives from several considerations. Foremost is the analogy to flows that can be direct- ly observed. The flow of water in a river levels off above an obstacle on the bottom. Similar effects are observed in model experiments with fluids. Second is the stability of the stratosphere. The near- isothermal vertical distribution of temperature in the base of the stratosphere is an extremely stable stratification. Such stable layers are quite resistant to being lift- ed. There is much less resistance to lifting in the upper portion of the troposphere where a condition of near-neutral equilibrium in the vertical stratification is often approached. It would be expected that the winds a- bove a large ridge would exhibit some tendency to level off no higher than the lower portion of the stratosphere. These and other considerations suggest that the windflow in an orographic precipitation storm can be approximated by placing a nodal surface near the tropopause. In this study a nodal surface is considered to exist at 300 mb in observed storms, at the same level in a probable maximum storm over the Coast Range, and at 250 mb in a probable max- imum storm over the Sierra Range. Physical laws of airflow 5.12. In a frictionless, laminar- flow, two-dimensional model in which there is no transverse convergence of the airstream, four laws which govern the flow are: 1. Continuity equation. This is expressed by equation (3) or, in differential form, I S 3 VdP = constant (9) b l where the integration is vertically between any two streamlines, S and S« 47 2. Bernoulli's equation for motion along a streamline i dP + -|d(V 2 ) + gdZ = (10) 3. Hydrostatic equation. dP = -pgdZ (11) 4. Adiabatic laws. For air not reaching saturation the adiabatic law is T 2 V*V 286 (12) where the subscripts refer to successive values of the same air parcel along a streamline. The law describing the temperature variation of saturated air undergoing adiabatic expansion is not stated explicitly because of its com- plexity but is solved graphically on a thermodynamic diagram (pseudo- adiabatic chart) . Application of laws 5.13. How these four laws control the flow will be discussed with ref- erence to the schematic flow diagram of figure 5-6. Start with any assumed distribution of windspeeds. First the spacing between any two streamlines above B, in millibars, must represent a con- traction of the spacing between the same streamlines above A in relation to the increase in windspeed as given by the continuity equation. Thus the con- tinuity equation, for the particular windspeed field, and the known pressure at point 2, will yield the pressure on each streamline above B. Second, the temperature changes along a streamline are known from the adiabatic laws. The changes, subtracted from the initial temperatures above A, yield temperatures on each streamline at B. These temperatures in com- bination with the pressure in turn, through the hydrostatic equation, fix the height of each streamline above B. (The height of the various streamlines at designated pressure levels above A are also known through the hydrostatic equation.) But, the resulting differences in height and pressure from A to B along any streamline, through the Bernoulli equation, permit only a specific change in the square of the windspeed between the same two points. If this difference does not agree with the postulated windflow, the flow is dynamical- ly inconsistent. For a specified ground profile, nodal surface, and distribution of at- mospheric variables above A, there is a unique wind field that will satisfy the physical requirements when analyzed in the above fashion. 48 Computation of outflow pressure and winds 5.14. To compute the required outflow wind and pressure above a ridge the flow was divided into layers, bounded by streamlines, as in figure 5-6. The four laws were then combined into two equations. In the following dis- cussion subscripts are used that apply to the layer nearest the ground in figure 5-6. The equations also apply to any other layer by changing the sub- scripts. The continuity of mass equation, (9), may be written (V x + V 3 ) (P 1 - P 3 ) . (V 2 + V 4 )

»oooooooo CM ^-\ 00>trO No^fO --<0^ > js CN4ooir>tnoor-to\Or-» • < o • a r-l U-l • v£> a 4J w <5 •i X H !—» | • • 1 • m CO V0 s-/ s • o • r-4 m m 43 cs a 9* M 6 -tf^mvooNOoooo CMvOCMr^vOOOOOO c^f^o (< »a - q b > (17d) t " Y Total windward precipitation formed as snow, above freezing level from this layer: R * 4 V I00 > <% - V (17e) Total precipitation reaching ground between C and D from this layer; (17f) .4V a (100) (q c - q d ) The several formulas are used in this report as follows: The total windward orographic precipitation in storms is obtained for model coefficient determinations, by applying (17b) to each layer. (17f) is used for determina- tions of orographic precipitation for various segments of the windward slope, in a test of precipitation distribution, to be described. For the PMP, the rain formation and snow formations were computed separately, by (17d) and (17e) for reasons to be given later. Test of Trajectory Model on Storms The test 5.24. The orographic model was tested by 6-hour periods on a group of major California storms of predominantly orographic character. These storms were: December 21-23, 1955; November 17-20, 1950; January 31-February 2, 1945; January 20-23, 1943; February 24-29, 1940; and December 9-12, 1937. The tests were conducted for 8 areas covering a wide range of California orog- raphy (figure 5-12). Basically the test consisted of comparing observed oro- graphic precipitation (defined in paragraphs 5.01 and 3.01) on the 8 windward 56 slopes with the amount predicted by the model. The orographic spillover pre- cipitation could also be compared, but to a lesser degree of reliability ow- ing to the greater difficulty of judging the convergent rain component on the lee slopes. In addition, the observed precipitation on the lee side is not as well defined because of the sparse network of stations. The model can also be used to calculate the distribution of precipita- tion within upslope or downslope areas, but this degree of refinement did not seem justified because large differences in distribution could be due to small differences in wind direction. A limited test was conducted, however, on the distribution within two test strips, one on the Coast Range, the other on the Sierras. The results of this test are given in paragraph 5.30. Storm test areas 5.25. The test areas (figure 5-12) were chosen for their nearness to weather stations having hourly pressure records in the large storms of the region. The outflow side of the area was determined by the generalized topo- graphic ridge line, the sides by parallel lines that pass through weather re- porting stations. The inflow side was generally parallel to the outflow and about 5 miles upwind from the first significant rise in ground level (or the seacoast) . This distance was chosen to include any upwind effect. The in- flow or (outflow) side need not be one straight segment if the average dis- tance from inflow to outflow (Y) is used in the computations. - Storm moisture 5.26. The index of moisture for all tests (except tests of distribu- tion within areas) is the surface dew point. A saturated pseudoadiabatic atmosphere is assumed. At most times of heavy rainfall this index is prob- ably reasonably close to a true measure. During lulls in the storm when drier air may slip in above moist surface air, the surface dew point is an overestimate of moisture in depth. But since lower layers are usually the most important rain contributors, this situation is not very serious. A bias toward moisture underestimation comes about at times of a surface temperature inversion. This effect is apt to be most important in the earlier portion of a storm when, for example, residual polar air still covers the Central Valley. The model coefficient, discussed in paragraph 5.29 is an attempt to take care of these and other deficiencies. Storm winds 5.27. Inflow winds are, in all cases, estimated from geostrophic winds. The geostrophic winds are then converted to "real" winds by the wind-geo- strophic wind relation discussed in paragraph 5.08 and as applied in 5.09. In the storms prior to 1945, the upper air geostrophic wind could not be obtained for many storm periods. In these cases the 500 mb-geostrophic wind 57 had to be estimated from surface data only. A relation involving the surface pressure and temperature gradient was developed to do this. The surface tem- perature gradient is, in effect, substituted for the mean surface- to-500-mb temperature gradient which, if known, would give the 500-mb geostrophic wind exactly. It was found that the best relationships between the surface tem- perature gradient and upper air temperature gradient was obtained when the surface stations from which the gradient was measured were latitudinally far apart. For example, the Medford-Oakland surface temperature difference was used for the Northern California relation and San Diego-Oakland for Southern California. Storm outflow winds are entirely theoretical and are based upon mass continuity and energy balance considerations. Computational details of the energy balanced model for outflow winds were taken up in paragraph 5.14. Storm orographic rainfall 5.28. Average storm rainfall depths over the test areas were determined by the percent of normal annual rainfall (29) method. Six-hourly increments at each available rain reporting station were expressed in percent of the normal annual. The average percent of the normal annual for each six hours for each area was then determined, and multiplied by the normal annual over the area to obtain the 6-hour average storm rainfall depths. The observed storm rainfall is a combination of orographic and con- vergence types. The observed rainfall must therefore be depleted by an esti- mate of the convergence rainfall. The convergence rain in each storm period was estimated from observed rainfall values at nearby stations considered relatively free of orographic influence. The Sierra area estimates were based on average observed amounts at sta- tions near the zero orographic precipitation line in the Central Valley. This average convergence rainfall amount was then depleted for average storm test area effective elevation by a moisture reduction factor based on ratios of precipitable waters. For example, in an area whose average pressure is 900 mbs, the upwind precipitation average is reduced by a factor surface-to- 900-mb precipitable water over total column precipitable water. (A moist adiabatic lapse rate is assumed for reduction factor purposes.) On the coast, the same kind of elevation reduction procedure was applied, but more attention was given to orographic contamination of the index sta- tions. In some cases stations to the lee of the Coast Range were used in ad- dition to coastal stations to compensate for coastal orographic effect. The amount of compensation required depended on the moisture flow across the bar- rier. For Southern California areas, as well as some other coastal areas where no suitable inland stations are available, percentage reductions were made for orographic effect, depending on station and strength of upslope flow. 58 An attempt was made to compensate for precipitation bursts oriented parallel to the coast which were apparent at the coast during the last part of a 6-hour period but over most of the basin during the following period. In storms involving semi -stationary convergence patterns, such as ahead of slow-moving warm fronts, large geographical variation of convergence pre- cipitation over the area introduces errors in the use of upwind values for area values. Also in a few cases, low- level divergence occurred over large regions, resulting in negligible rain upwind of the area during the 6-hour period, which only partially reflects the depletion of orographic rain over the area. These effects, not compensated for, play a part in the poor com- puted-observed orographic precipitation relation in some periods. Table 5-2 contains the estimated convergence precipitation, estimated orographic and the total precipitation. The convergence precipitation, de- pleted for elevation appears in the table as a positive quantity additive to the orographic rain to equal the total observed precipitation. In a few storm periods the index stations showed short periods of no rain between intense precipitation bursts. In this situation it is logical to assume that these short no-rain periods were associated with divergence between regions of intense convergence. Further it is assumed that these divergence areas are operative over the nearby slopes causing the orographic rain to be less than what would occur without the divergence. A correction was therefore applied in these periods, analagous to the convergent correc- tion. The amount of the divergence correction was determined by a plot of the time-intensity bursts at the non-orographic index stations. The ampli- tude of the negative portion of the time-intensity profile was arbitrarily made one-third of the average amplitude of the preceding and following bursts. These corrections appear as negative numbers in the convergent precipitation column of table 5-2. This amount is subtracted from the orographic precipi- tation to give the observed total. A depletion for elevation was also ap- plied here. Test results 5.29. Table 5-2 contains the basic storm data that went into the model, the observed total rainfall, the adjustment to "observed orographic", the computed orographic, and the ratio observed to computed (X). The ratio of observed to computed rain (\) is a measure of the efficacy of the model in duplicating the rain. It is by the study of this ratio that the results are evaluated. A total of 111 cases in the eight test areas were computed. Not all storm periods within a given storm were done because of time limitations. The 1st, 2nd, 3rd, 4th, 6th, 8th and 12th period, in order of observed oro- graphic precipitation intensity, were chosen for computation. 59 CM I m ,0 to H M O M fa fa § U w 1 8 I r-4 Pn M O I o M 8 Z u CD 4J r CUT* •H CD o > CD M M CD * o . O -r4 CO . O -H o . S-5 o -H > o O M m > >N CD 43 •-I a > ct} W CD 03 CD C O »H (0 O <« a* CO CD Q £ 1 d" «4* oo\On\o r-l i-l O r-4 t-4 O O * O rH O r-l U0 vO UO CO CO N 00 o m m d , cM ©©omooomominm r-icor^cMvor^r^.r>»oovom^vOCM00^vOCM00 CM©rHr-4CMOr-«r-ICMOr-lT-4 CD CM CO O r-l CM CO CM CM CM CM CM CM r-iCMcoOr-4CM 60 & T3 O • •H O U 2 CO Oh n vomc odd d m m vo m i . • i o o CO o O mvON ^ = o • rH sO CO O • • . sO CM • • o CM • 00 < sO • 00 » CM -d- vO . in r-l m oo on m CM o r-4 o r-l cu u • /"*s U 0) O ♦ CO r-l CO CO CO o < ON CO CM o CO CO 0> m r-4 CM ON rl inMON S e •H r-t /-> o 1^ CO m CM SO on o m oo ^ cm VO T-4 CM 00 00 CM J o 6 • CO 4J O C o v-^ o CO 4J o m 2 r«. CO o CO CO ON o m m CM rH cu r-l ON in 1 CD M r-4 ON m > /■> t m m \D 00 00 r** r** r^ sO m < cu m -* vO m CO u sO in m rs. in SO CO rH r-l t> • 6 CO 6 rO cu ,0 (0 %-/ cu cu i rO (0 cu H o § H 0) cu > Q o 2 o cu Q 4J Ct4 o o o o o O O o m r-4 sO CO r*» r-l tf- r-l l i r* ^ d d ON d r^ r*«* on on CT\ VO >J H CO cu m m m m sO sO m m vO vO m sO m m m m m m m m cu cu /-N e H vO CM CO vf v£> CM 00 sO 00 ON CM CM CO CM rHCMrO^-msOr^COONOrHCM rH cm co cu ^ « O n-i CO . 4J C O -H O • o ^ > . (3 C > o o m 0) > W)T-t > « CU CO • oo oo v© • CM O N >t m Ov£>tOv£> o o cooo cooo c g O^fOOOvOMnNinOvOM O>t^rlN00NOOfr C d o o o o o oo on O r-* t M r^ N ^ N 00 00 CM CO 00 sO . oo cm o> ON co n^- O O r-l r-l O U0 O ON CO ON r-l U0 ON CM CO O O O rJ d sO m m .» O m UO m ON ON t-l r-4 u u CU cu rQ rQ 6 »>«. co m r-i CM ON r^. 6 o r-l OO ON ro CU rH CM r^ CM CM r-4 CU CO o o cu 25 Q 00 00 NO O CO CM CO ro m m m m r^ so m m m m m m m 00 O r-l r-l ro vO 00 N vO N m m m m m NOCM00 U Q) * 0) fl •H 4J fl o o CM l in •8 O • O *H CO . 4-> fl o -.-« O fl O >-H O -H > o o m > CD 00 r-4 I CO 0) CO » o 'ONNrINO u C o o o o I o o en 00 cm 3" en O r-4 r-l O CM O en r^» r-4 oo en vO o o> o on m m r-l O rH O O O o o fl fl en iw C •H • o o o en CM en r-* i • . i r-4 O • O O O CO C O r-4 oooenoomr-4»cMO Or-4r-40r-40000 . » O O r-l r-4 r-l O » O O O r-4 r-4 r-4 O o m CM r-l cm o en O r-4 CM CM en >fr O CO m m OvoinoNCMoooooNin oors.r»*cMCMONOCM* en en r*» o\ o 25 en r-4 (0 o\ cu r-4 u < U CD 4J ^ CO e r* so o vo m vo o CD CD r-i t N N ONM CM 00 nJ vO CM 00 r-4 r-l CM r-4 r-l CM CM CM CM —icMcn r-i cm en M CD cd . O -H o >~4 •i > O O N> m Q) > •N CD 43 00 r-< Q > I I CQ >*> 0) . • in .oo • • » co i-* vo m m m m COcOCMCMCMstvOO»mcoocMinoNr-i»>d - ONooo\incMONcOf-ivocMooOr-iooincor>» co»vocooooNvo^-cocMCMoNONOO »nin«ninininminin«ninmininind - o CM CM CO CM CM ^ SO r-l CO cm m m m CO in ^ vo n oo *vDCM00«NfvDCMCO»oooNO'- P. M C O -h CO . 4J d O -r^ o . O -H O -H 50 r-l > CO H 00 o o cu > CD I CO r-l • i • i O r-l vo m . oo cm Oooocjooooor^oooor^ r-J cd d d c 6 c d d d d d vO*vO'-tOr4HO\ OOOOOOOOOr-ir-ir-iO o o> • • ^ o • CM O o in m o o r-l 00 00 O 00 CO CM O • • • • o O i-l t-» vo co m ocor-ico o 53 oooNOOr^r^r^vomr-oor^^o •Nfooin^OOrvoocMr^cMr^. C/lHvOONvONlTIH r* vo • CO ON^> m nco rs oorx 0fr CO co "1 -1 CM cDcovOr^r^mmr^o m co CD CD CM O r-l H O CD CD Q Q oocMoocMoN^cocomvoooom r>»vOr-.ooO'-icoo mmvommmmmmvOvovovo ooOCMr^cocooooOCM oovONvorNoooor^^oo inininminininm«n«d' i-* co r-i \n vtvON00^vONCO*vOCM00»oooNO 65 0) J-l 04 W JO O d o u cm i m 00 ^ > CO H OO ■i o o m CO O • O -H CO . u d O -H O • O -H la O -H rd P4 I co o CO 3- m • r-l CM O O CM C «— I r- 1 o . cm m ONOOcnr*.mOvf'-« c>c>c>c5dc)«-^r-Jdd mso rlCJNHO--tNNOO d o o oooooooooo OONin^cMv^cjNcnoN. en ON r-4 vO u en a) 1 o ONooONvtovom 4JnnsoNNNvoo\omonfOooo vONNooooN^on^ wminstinNNvOin^ininvOvo^inm o m ON oooooocno-Nf^ONCN ^ m m m vo m en t— i cNCNcncMcnocoooom 0N cMoocncMmcMoOr-4vooovooooi^ONcn cMinooooro-ONOO inmmmmmvovo oo n o r-i cm m m m so vo vo vo -d- cm vO vO oo M00 CM r-l r-l CM r-l r-l VO CM 00 d-«nvo 66 CD o e tf Pd 13 o . H$ d o o o -H H ^1 0uT3 O • H C O -r-l 'rA oo r-l 00 o o m CD > 1-1 I cd CO jz % cd c co o c H -C I vO 2 O • •r< O CD ex. m in r«» o r»* f-< SO v£> fOfOrtN 1 . . 1 1 • . . . o r-i ,_< ,-| ,-» ,-4 on on en oo r*% »eoooor-icoinmoo OOr-li— IOCMr-li-li— I vOCMCMCMvfcnoOOl^ OOr-lr-IOr-lr-lr-lr-l stSvOrvHOO^^NvO *tfO00CMO*d"OOOO CO C r-f o oo m o *oooo O O O O r-4 oo vo r-< on on m VO cm r-i r** en oo cm r^ en O r-A oo no m o r* m r-« cm o r-l vo cm cm cm QrHOr-lOOOOOO sOCMOr^*'sfini^oooooN o m ON u CD ,a m rinNvOMTKl-nvO CM en CM m m ON u ^ ON 00 CM NfMrHQ > o 23 o CD a fOONCM^NlflNrl vor^vor^oNONOOvoen mmmminminmin moNCMcMr-ienenoNONOO cm cm m m vo cm o vOoooNf^r^r-ienencMCM inminminvovovOvovo r-i m oo oo oo r^ r-» m m m m m m m 00^vOCM00 s *■* ( V*,2 P s = (P /W ) (W ) . c p x p x,2 (4) The maximization- transposition relation, (4), is the same as the index relation, (1) when: the enveloping precipitation/moisture ratio, (P /W ) , c p X is for 10 square miles and 6 hours in January, is adjusted to 200 square miles by an average relationship, and (W ) 9 is for 6 hours in January. 7.05. Orographic PMP . The basic relationships for orographic PMP are: Index relation: V . /X? Q _ . /X/B X (V.) = (PMP) , (5) x, 6, Jan, 2 -- ^x, 6, Jan, 2 -- 2 6 av. o,i 96 Maximization relation at storm location: (PMP) oq (0 - u o,l 2J '...

s .. Q .. v -- B x (9) 97 Now substituting the definition of the model coefficient, (8), in (9), the coefficient-adjusted maximization-transposition relation is (PMP >0,2=V2^ 7V x,2^ B 2 X \v. ("> It is now apparent that where the values of Q and V in relation (10) are for 6 hours in January and A. is for 6 hours that (10) is the same as relation (5). This means that the orographic index map is by and large a composite of mois- ture-adjusted and wind-adjusted transposed orographic storm values. It is not an envelope of such values but rather an average of selected high values. The convergence PMP index was derived by enveloping storm values with one maximization adjustment. The orographic PMP index is derived by aver- aging storm values with two maximization adjustments. 7.06. Total PMP . Finally the total PMP for 6 hours and 200 square miles in January is obtained from < PMP) t,6,200,Jan = (PMP >c,i + (PMP) o,i. < ll > In anticipation of this combination, P , which enters into the orographic PMP, was derived from ' P = P„ - P . (12) o,s t,s c,s P , which enters into the convergence PMP through the precipitation/mois- ture ratio, was derived from P = P^ - P . (13) c,s t,s o,s Here values of P ^ were mostly obtained by restricting the selection to cases where P was equal to zero. o,s ' Safeguards 7.07. Steps were taken to minimize contamination of the basic oro- graphic storm precipitation data by convergence rain and conversely. The safeguards are explained in detail in chapters IV and V, respectively, and will be summarized here. In estimating the convergence PMP, the measure of intensity of the storm mechanism is the P/M ratio in outstanding past storms. The first safeguard was the separation of the controlling P/M ratios in two classes, those compatible with orographic precipitation, and those not, be- cause of characteristics of the individual storm. The two resulting en- velopes of P/M ratios are, respectively, indices of the maximum convergence mechanism that would be expected without restriction, and of the maximum that would be expected as part of an orographic storm. The other safeguard was in the location of storms selected to provide the P/M ratios. These were re- stricted to the Central Valley of California at some distance from either of the principal ranges. One exception was a San Francisco value, which was cor- rected for minor orographic influence by comparison with Farallon Islands. 98 In deriving the criteria for orographic PMP the following safeguards were applied. First, in calibrating the orographic precipitation model against observed storms, an estimate of the convergence precipitation was subtracted from the total observed precipitation over the mountain slopes in each storm period to yield an estimate of the orographic precipitation in the storm. The last was used in the calibration. The estimate of the con- vergence precipitation was based on observed rainfall catches at low-level stations relatively free of orographic influence. A similar refinement was introduced in use of the 3-day 10-year point precipitation map as an index for the distribution of orographic PMP with large blocks. The 3-day 10-year map was divided into an estimated conver- gence component and orographic component throughout region of the study, again by using values at low-lying stations as guided to the convergence rain on adjacent slopes. The orographic component was then used for the dis- tribution step. Airflow in combined storm 7.08. A clue as to the nature of the combined convergence and oro- graphic storm may be derived from figure 7-1, a schematic cross section through the Yuba Basin. Idealized air streamlines are shown for pure oro- graphic flow (solid curves) and for combined orographic and convergence flow. Also shown are the corresponding trajectories of fall of precipitation ele- ments. The air streamlines for the combined storm are derived by superim- posing convergence on the orographic flow. The rate of convergence is uni- form from the ground to the 750-mb streamline with compensating divergence between there and the nodal surface. The convergence value superimposed is that required to produce convergence rainfall throughout the area at a rate of 2 inches per 6 hours. This is comparable to the winter convergence PMP in the Sierras during the 2nd 6 -hour period of the PMP storm. The superimposed convergence is from an unspecified combination of longitudinal convergence, and transverse convergence. The net result, as can be seen from the dashed lines, is for greater lift of all air parcels and greater crowding of the streamlines toward the nodal surface. It should be emphasized that the dashed curves are average streamlines. It would be anticipated that in the storm more severe lifts would be experienced for shorter periods of time, averaged with lesser lifts at intervening times. The two inches in six hours is an average over a large area. It can be envisioned that more intense local cells would double the convergence com- ponent over small areas, thus yielding the convergence PMP values of this report. Sample trajectories of precipitation elements are shown schematically in figure 7-1. Those labeled "orographic storm" are constructed according to the criteria for orographic PMP in chapter V. The trajectories of pre- cipitation elements for the combined storm apply to the more severe condi- tions resulting from the more vigorous convergence activity, larger raindrops 99 and larger and wetter snowf lakes resulting in greater rates of fall. The ef- fective freezing level is placed higher to take greater cognizance of liquid condensation processes that occur at temperatures colder than 0°C. The steeper precipitation element trajectories yield more precipitation over a given area at the ground than the other set. Such differences are not esti- mated explicitly in this report. They are included in the convergence rain, which is defined as all effects other than the orographic rain. Summary of procedure for obtaining total PMP 7.09. The orographic PMP is computed for a project basin six-hour peri- od by six-hour period, for each month of interest, and the same for conver- gence PMP. The two are then combined by simple addition. The highest monthly total at each duration is then the all- season PMP. Thus, for exam- ple, the highest 6-hour value may occur in October, while the highest 24-hour value pertains to January. The January 24-hour value does not contain the 6-hour PMP, which was in October, but rather the somewhat smaller January 6-hour PMP. A list of the computational steps to derive the total PMP for a particular basin is given in chapter IX with examples. Time distribution 7.10. Requirements for time distribution . To compute a flood hydro- graph for the probable maximum storm it is necessary to specify the time se- quence of the precipitation. The estimate of PMP is derived by six-hour increments. In the text and figures of the report the "first" 6-hour period means the first in order of magnitude rather than the first in time sequence. Nomenclature for the other increments is similar. It is intended that the increments be arranged in a sequence that will result in a critical flood hydrograph and which is meteorologically reasonable. There are two meteorological factors to be taken into account in de- vising the time sequence for the PMP storm. First is the time sequence in observed storms. The PMP time sequence should be modeled somewhat after ob- served storms in order to simulate natural conditions. Samples of observed hyetographs both for points and for areal averages are depicted in figure 7-2. There is some tendency for the two or three highest 6-hour increments in a storm to bunch together, as that length of time is required for the influ- ence of a severe precipitation-producing situation to pass a given region. Otherwise the hyetographs for observed storms are quite varied. The second factor to take into account derives from the manner of de- veloping the theoretical PMP data. The maximum dew points by 6-hour incre- ments are derived from envelopes of persisting values. Thus in a series of dew points a second peak has no influence on the maximum value for various durations. The treatment of pressure gradients is identical. Maximum ob- served wind, P/M ratios, and storm rainfall data are analyzed on a basis of enveloping values of total accumulation or averages for consecutive 6-hour 100 periods. The foregoing method of developing the parameters from which the PMP is computed leads to the following principle: For consistency in main- taining critical PMP conditions for each duration, the 6-hour increments that make up the PMP for that duration must be adjacent to each other in time. For example, the second highest increment must be adjacent to the highest in order to provide the critical combination for 12 hours, the third highest should be immediately before or after this 12-hour sequence to pro- vide the maximum 18-hour total, and the fourth highest should be before or after the 18-hour sequence to give 24-hour PMP, etc. Sample pattern PMP time sequences that conform strictly to the foregoing principle are shown in fig- ures 7 -3a and b. Review of the observed hyetographs will show that 3-day storms typically have two or more peaks or bursts. Time sequence patterns which show this characteristic storm behavior and which conform to the sequential require- ment described in the preceding paragraph within practical limits, though not strictly adhering to it 6-hour period by 6 -hour period, are obtained by application of the following rules: (a) Group the four heaviest 6-hour increments of the 72-hour PMP in a 24-hour sequence, the middle four increments in a 24- hour sequence, and the smallest four increments in a 24-hour sequence. (b) Within each of these 24-hour sequences arrange the four in- crements in accordance with the sequential requirements. That is, the second highest next to the highest, the third highest adjacent to these, and the fourth highest at either end. (c) Arrange the three 24-hour sequences in accordance with the sequential requirement, that is, the second highest 24-hour period next to the highest with the third at either end. Any of the possible combinations to the three 24-hour periods is acceptable with the exception of placing the lightest 24-hour period in the middle. 7.11 Examples . Figure 7-3c, d, and e depict sequences arranged in ac- cordance with the foregoing rules. The 24-hour grouping is in accordance with a general practice of the Corps of Engineers. It is intended that the hydrologist experiment with different time sequences to uncover any factors that would make one more critical than another in his basin. Within the limits of the rules for time distribution the hydrologist may wish to give preference to patterns of distribution most similar to the hyetographs of one or more past major storms in the vicinity of his basin, this may be done provided other time distribution patterns do not yield ap- preciably more critical flood hydrographs. 101 7.12. Snowmelt winds and dew points . The time distribution of 6-hour dew points and windspeeds for snowmelt computations is explained in chapter X of this report. The arrangement of these is fixed by the adopted time distribution of the rain, that is the highest dew point and wind coincident with the highest period of rainfall, etc. The corresponding dew points have been entered on figure 7-3 to illustrate this point. 102 Chapter VIII CHECKS ON PROBABLE MAXIMUM PRECIPITATION 8.01. Checks on the magnitude of the derived PMP of this report are obtained in two ways; first, by a review of the maximization incorporated in each variable and secondly, by comparing the PMP with observed precipitation and statistically derived values. Maximization of meteorological factors 8.02. An important aspect in appraising an estimate of probable maxi- mum precipitation is to view the degree of maximization in the aggregate. It is necessary to choose degrees of maximization for each factor which, in combination, are representative of a probable maximum storm. General principles and guide lines on maximization were discussed in chapter II. 8.03. Maximization of the important meteorological factors used in this report are summarized below. In order to give some perspective, three degrees of maximization are listed. The "extreme" maximization might be used to estimate something comparable to a probable maximum value of that variable alone. The "intermediate" maximization in each instance is a de- scription of the procedure used in this report and is considered suitable for combination with the other maximizations to estimate probable maximum precipitation. The "minimal" assumption is a lesser criterion than used in this report and ranges between PMP and Standard Project conditions. 1. Surface dew point Extreme: Equate to offshore sea-surface temperature at a source lati- tude; or extrapolate past record for all stations to allow for future events that will exceed past record. Intermediate: Envelop long records at key stations but with some undercutting of higher values, especially those during periods of sluggish airflow. Smooth seasonally and areally to compensate for small sample of great storms. Minimal: Use highest values during selected major storms without search of long record. 2. Relation of upper-air moisture to surface dew point Extreme: Envelop relation of upper level moisture to surface dew point in storms for which upper-air data are available. Such an envelope would 103 show higher dew points aloft than at the surface on account of the surface inversion effect. Intermediate: Assume saturated pseudoadiabatic atmosphere. Minimal: Make some allowance for non-saturated layers aloft. (The model coefficient factors for later durations of the probable maximum pre- cipitation are in part due to this effect.) 3. Storm mechanism, convergence component of PMP Extreme: Envelop precipitation/moisture ratios throughout the United States; transpose precipitation/moisture ratios without adjustment through- out season. Intermediate: Restrict envelope of precipitation/moisture ratios pri- marily to storms in the Central Valley of California. Undercut Campo, Calif, storm considerably; undercut slightly P/M ratios of certain storms in northern Central Valley where there are special topographic effects. Have sufficient downward trend in precipitation/moisture ratios from winter toward summer to compensate for the upward trend in moisture at 24- hour duration. Determine separate sets of precipitation/moisture ratios; one set for combining with orographic precipitation, the other not so limited. Minimal: The "intermediate" degree of maximization approaches a "mini mal" character for point precipitation. There is some compensation toward higher values for areas larger than a point, covered in item 9. 4. Wind, orographic component of PMP Extreme: Wait for accumulation of 25 years of rawin observations (which are carried out regardless of cloudiness) at several California stations; extrapolate beyond the record to more severe future events by a Gumbel frequency analysis or equivalent. Determine maximum surface geostrophic winds from the long period of surface pressure observations and suitably extrapolate to upper levels in the atmosphere. Intermediate: Select wind values characteristic of the probable maxi mum precipitation storm intermediate between a and b that follow. a. Maximum observed geostrophic winds at the various levels corrected for mountain frictional effects by mean ratios of observed wind to geostrophic wind. .04 b. Frequency extrapolation of maximum winds found in the fragmentary record of upper wind observations, includ- ing those during cloudy weather, at Oakland and other stations. Restrict such winds to the southwest quad- rant. Minimal: Envelop the wind record. 5. Raindrop and snowflake terminal velocities Note: The higher the assumed terminal velocity the greater the col- lection of orographic precipitation on the windward slope. The smaller the terminal velocities the greater the total spillover; however optimum pre- cipitation a few miles beyond the crest is associated with fairly high ter- minal velocities. Extreme: Neglect spillover precipitation as a loss to the windward slopes in view of the various uncertainties. Intermediate: Adopt as terminal velocities values near the highest, but not the absolute largest values, of those observed in laboratory ex- periments. Assume a wet snow layer for a space extending a couple of thousand feet upward from the freezing level, in which the terminal velocity is intermedi- ate between rain and dry snow. Minimal: Assume dry snow above 34 °F level, and an average terminal velocity for all raindrop sizes below. 6. Orographic model coefficient Extreme: Envelop model coefficients determined from major storms, undercutting a few extreme values. Intermediate: Average model coefficients arrayed for each storm in decreasing order of precipitation intensity. Minimal: Set an arbitrary ceiling of 1.0 on model coefficient. Or use the over-all average model coefficient irrespective of storm duration. Introduce a characteristic decay of precipitation with duration over and above the moisture and wind decays in some other fashion. 7. Combination of orographic and convergence components of precipitation Extreme: In view of the predilection of thunderstorms to occur more frequently and possibly more severely in mountainous areas, superimpose the extreme convergence rain on the extreme orographic rain that might be ex- pected in any one season. 105 Intermediate: Add maximum values of a convergence PMP and an oro- graphic PMP, each derived for compatibility with the other, 6-hour period by 6 -hour period. Minimal: As a Standard Project type of approach, combine the above 6-hour increments in some other arrangement than maximum with maximum, etc. Or, base criteria on observed total precipitation only. 8. Upwind barrier depletion for Sierras Extreme: Neglect any upwind barrier effects. This would be supported by the facts that the air is nearly saturated during periods of precipi- tation at Merced and other valley stations, that maximum valley dew points are in general as high as coastal dew points at the corresponding latitudes > and that the mean annual precipitation increases rapidly at fairly low ele- vations in the foothills of the Sierras. Intermediate: Apply a fairly severe barrier depletion to convergence rain and a more moderate depletion to orographic rain as a balance. De- plete convergence PMP by ratio of precipitable water in column above ele- vation of crest of Coast Range to precipitable water in column above sea level. For orographic PMP make some allowance for recharge of valley air with moisture by evaporation of falling precipitation. (Per figure 5-8.) Minimal: Lesser recharge than assumed above. 9. Areal variations This item refers to adjustments to index map values for area of basin. Extreme: The precipitation/moisture ratios are for the most part based on point values. Use a flat relationship in going from point values of con- vergence rain to a 200-square-mile index. Such a relationship would be supported by the considerable scatter of the data and by the high probabili- ty that the observed point samples are not the largest values that actually occurred in each storm. For orographic PMP, do not correct for areal variation. Intermediate: Derive an average depth-area relationship from many storms to go from a point to a 200-square-mile index. Assume in general that point values of precipitation are representa- tive of 10 square miles, except for a few extreme events which may be under- cut by a 10 -square -mile enveloping curve. 106 For orographic PMP deplete the index for basins wider than 30 miles in proportion to the distribution of extreme pressure gradients. Minimal: The foregoing approaches minimal values. 10. Durational variations Extreme: Base durational variation of moisture on all -station envelope of observed decays since a flat decay is as reasonable at any one station as at any other. The same reasoning is apropos to the wind decay used for orographic precipitation. Intermediate: Use an average durational decay of moisture determined from envelopes of persisting dew points at key stations. For winds use an average of observed decays during strong wind situations. Minimal: The intermediate criterion approaches minimal standards. Comparison of PMP with maximum observed precipitation 8.04. The most obvious comparison of PMP estimates with other data is with the maximum observed storm precipitation depth of the region. Tables 8-1, 8-2, 8-3, and 8-4 list maximum known precipitation depths in the Cen- tral Valley, the Sierra slopes, the Coastal slopes, and Southern California respectively, together with the PMP derived from the criteria of this report at the corresponding locations. The PMP values are given both for the month of occurrence of the observed storm and the maximum for the October -April season. A few September and May storm values are compared with October and April PMP respectively. Point observed depths are compared with 10-square mile PMP unless indicated otherwise. 8.05. The closest approach of an observed value to PMP in the Central Valley is at Newton in the September 18, 1959, convective storm. The 3- hour and 6-hour point values were estimated from a mass rainfall curve re- constructed for Newton by use of observers' notes and surrounding measure- ments. The 3-hour estimated point value of 8.1 inches is slightly higher than the 3 -hour 10-square mile PMP for Newton. An isohyetal map was drawn for this period which gave a reduction of 17 percent from point to an area of 10 square miles. This results in a 10-square mile depth of 6.7 inches in 3 hours which is 85 percent of the PMP. Point values at three other stations, (Red Bluff, Fresno and Sacramento) are near or exceed 50 percent of the 10-square mile PMP at some duration (Reference table 8-1.) 8.06. In the Sierras, the March 1907 storm yielded 59 percent of the PMP over 1100 square miles of the Feather River and Yuba Basins and 56 per- cent over 90 square miles in the Feather River Basin. Other instances of storm precipitation reaching more than 50 percent of the probable maximum were the 24-hour point value at Cathay Bull Run Ranch in the November 1950 storm, and the December 19 13 -January 1914 storm over 419 square miles of the Feather River Basin. (Reference table 8-2) 107 8.07. In the coastal region, the November 22, 1874 point rain at Ft. Ross was over 80 percent of the 10-square mile PMP. This extreme rain was measured near the base of an abrupt slope of about 1500 feet elevation, and although the observer had only shortly prior to this storm started to take precipitation measurements he has a long history of accurate records and the extreme rain is quite probably correct. Other observed point amounts reaching 50 percent of the 10-square mile PMP occurred at Hobergs, December 10-11, 1937; San Francisco, December 20, 1866; Orick Prairie Creek, November 20, 1950; and Upper Matole, January 30, 1888. (Reference table 8-3) 8.08. In Southern California, the Campo measurement of 11.5 inches in 80 minutes on August 12, 1891 greatly exceeds the 10-square mile PMP for the October-April season as does the 7.1 inches of July 18, 1922 in 2 hours. Ex- clusion of storms of this type has been discussed in chapter II of this re- port. The very localized nature of such severe summer convective rains leads one to suspect that the 10-square mile average value was considerably less than the point value in each storm. However, if hydrologic problems in these areas arise in spite of the dry ground conditions, they must be dealt with individually. (Reference table 8-4) Significance of size of sampling area on ratio of observed precipitation to PMP 8.09. Two factors that must be given important weight when assessing PMP relative to maximum observed precipitation values are the length of pre- cipitation records and the size of region (sampling area) over which compari- sons are made. The larger the region, the more nearly will the biggest observed storms approach PMP proportions. The non-orographic Central Valley and few coastal regions of California are examples of small sampling areas for non-orographic rains. Thus, if observations were available for the ad- joining ocean region, it is most probable that ratios of maximum observed to PMP would be larger than those shown in table 8-1. Examples of large sampling areas are regions in the Central and Eastern States where a relatively few widely spaced storms, such as Thrall, Texas and Smethport, Pennsylvania of 1921 and 1942, respectively, are considered to come near to PMP proportions for certain durations and sizes of areas. Table 8-5 has been prepared to illustrate the sampling area effect and is somewhat analogous to the preceding tables (8-1, -2, -3, and -4) for Cal- ifornia. Table 8-5 compares PMP values as derived from Hydrometeorological Report No. 33 (2) with maximum observed values from "Storm Rainfall in the United States" (14) for six areas in the Central and Eastern States which are the size and shape of the San Joaquin and Sacramento drainage of California. The respective areas are depicted in figure 8-1. No attempt was made to place them either on or between major storms; therefore, they are randomly spaced. None of the observed/PMP ratios within the six test areas are as large as some that can be found outside these areas, illustrating that areas of this size can "miss" big values. The ratios of table 8-5 are of about the same order of 108 Q> d 3 O • • r-» (0 O CO C3 •H > 0) +J CO (Q . ■w C*5 co su H M •■> a d CO §8 «: o *o NNOCOH CN CM o •H 4J CO > lfl>tfOlOOflOCONNNO ^- m \o m m >d* m T-< z CO • CO o OS CO ■w M X» H ^ o pH < 2 S H 04 P-i CM M -.4 M-U4J4J4J4J4J4J 4-1 4J 6 1 /"\ u e CO £88888888 8 • cu d o 0) V-/ >»• N-^ S-/ V-/ >■• >»/ >«• N-/ v-' P* cr w i CO P4 4-1 CO o d «* o n m oMn omh o n co O . in m r-l r^. >• CM-vfOx^Ol-vCMr^CMvOr^ON m o cn r>» o\ oo a o n M <4-» •r-< r-l i-4 t-l r-l r-l r-l r-l r-» CM < 43 u . > 4J o & 1-1 •H t J & X d /-> > B 00 1 tf CO r-l u o CO o CM r-4 CM p» H 1 d CU JE Q o ♦r-l > 1 o U CO CO 73 /■S 3 -H C* r-l CO 0> CO =*{==£:** o ^ W CO r-l CO M-4 CU ,_4 > u d cu XI o mmm«-iT-4r-» r-l ITS 00 00 CN a\ cm cu MfMvOH\SWXXSXfn*W • ^->* 4J O CO CU ss»--t>soo CO CO coco n n tnv OOCT> vO o O r-l 4J CO Q COCOV,0\Hr-(HrH^HH rlNNNH CM CN 2 o 4J 4J vf^r-linOONCftOVONONO o\ a) nn m O >* sO CO o vX> r-i ON CO ON CO ON 00 00 ON 4J CO co «• • a* CO 43 O 3 04 VJ <^s o. C co 1 < 1 O a> CO 43 -i ^ >* co r*. CT» r^ r^ vO rH r-l CO o vO 00 CO 00 ON • Ok ■u cd o m r<* t-« CO O ON O r*. fO i-« O r>I ro d >tON CO cj CD C NNf-l CO CM >* r—i i— i CM -d- O co •<*/ m >* d- ON CM * r-l r-( CM -^ w 3 fa 31 • CO fa cd *H 4J 4J 4J 4J U . r»* r-l o o 1 ge •H -• 0U 0U cu a a r-4 r-l r-4 i-4 4-> M fr <-■ CN v£> CM 00 00 CM vO 00 vO 00 ^ ^* * CO -* O T3 >«■> 5 0) a> CO x r4 > c a> CO v© CO CM i-l r-. r>. 00 00 o r*. -* o r-l OvOCM 00 M (0 u CX 4= • >d & CD o u ON r-l SO CO » CO v.0 r-4 * ">^ r>. co . P*. 1^ O O o CO c NNOOON o r-l r-i r-l r-l r-l r-4 r-l r-l O co CO CO co m m m p-i •H cn co m m r-i ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON SI cd i *^.->*» ">•*. i r-l r-l r-i r-r r-l r-l r-l H r-l r-4 r-4 r-l r-l r-l r-l r-l r-l u r-4 r-l ON 00 00 i a) CM t-4 t-» i-4 r-l • u 4J |4 o c CJ c o c CJ c U O o o 6 > > > o C cd CM CM i-l r-4 r-l cd a> cd CU cd cu cd CU cd IS cu CU CU o O o u 1-4 04 Q S Q •-> Q •-> Q ^o Q •n Q Q Q 2 2 z >«• c 3 CU CO c •H CO S cd T3 73 § to (3 CO T3 C cd T3 sins Basins c cd CO 06 cd c C a c C3 cd cu cu CU cd CU cd G u h4 •H •r4 f-t t4 •r4 43 O O o PQ o PQ G CU cu •H §33 CO (0 CO CO CO to 3 U U M u 1-4 r-l r-4 CO > CU CU CU cu CU CU CO 3 3 cd >* 0> 3 u o 0Q PQ CQ PQ PQ a X 2 fl s G cd H H PQ C G Jw PQ o u A 3 1 * o cd o fa oo U M u U U r4 « *. M 3 «v M CO •H o >> (3 0) CU cu cu CU CU O o o r-l o r^ 43 43 43 00 4J 43 cd 4J i-l 43 4: 43 43 43 43 C c G o c O CO cd cd G cd 0) co J3 C 4J 4J 4-1 4J 4-1 4J 4J CO CO CO 3 CO 3 0) d) CD i-l o 3 3 4-» U cd • 05" CO J* o a I • CO 0) I CO O -H J3 0) U 43 S O "O -3 0) 0) U 4J cd co a a a ■* O T3 o g G En -H O O §~ co -G ^ C 5 co H33JI H C O <4-l -H G O /-s •H CO 4J U C 0) l-i 0,43 * CM fOd-vj'COCO>Cl'tf-»-d-cooocO'sOcovOOCMNCNHrHHCMCNNNCNr4HO "X* r-1 ^"^^'N^^^^-^-^^^^^^.^CO CNSNNHHrJHNNONNHNCNCNS l>» r>. r^ r>» CO CO CO CO ON o> OS a\ r-l 1-1 i-4 r-l . • • • o o o 0) 0) 0) d> Q Q Q Q CO CO _C -u H J3 C« 0) g r-l CC CO CO -O 4JObbOcoco p 3G (do G O O >-i » oo .o .£> 9 »-i4:3-u*Jcdi-ioor^ C t4 O »-i ■U -r< CO r-l Cd o s X u 0) o o CO f^ -r* O u SI O u J 2 G C cd cd CO CO "3 GO "O 0)5-10) U O) J-i p! 91 jQ 4) 0) 4-1 O -U a G £ c a, a> a) rO u a 00 T3 M 0) 0) U jO 0) O 4-» PC G 0) cd co 00 T? U 0) 0) H X) 0) O 4-» 33 G 0) o 00 5-i a> O Ill (O cn vOinvOCMlTKfNvO OOi^N - 2< C CO oj <: O r^ -> 10 • PC •H O H 5 OJ s M M 3 * * Ss 0) • • r-l B on HvOONCOr-IOOOO^O CO M> O CO O 00 ON o ^O * on m ro o o cM •j-n n r-l CO VO d- 00 m o r^ 00 CM J2S t-l (2 CM CM CM t-4 CM rH CO CM r-l CM ro m r-l r-l CM *> 1 o # •H u uuuuuuuu u u u u u u 00 2 •H co e 00000000 O o O o CM CM CM CM 2 6 0J •H •H «H t4 «H -r-l 'M t4 t4 •H «rW f-l •H «r-l «r-l O o O o O o O O OJ gfl i u • O OOOOOOOO O O O O O ro ro ro ro r*» r» r>» r««. 1-1 K < o a PuCkCuCXPuCuCuCu CU Q* CU O- Ou O- 43 H cr CO CO 0) (0 ^ u •H o a u 0) H O i C/> o • • T-l £2 Q /-> •H •■-• g 42 4J O CO 6 B en § i-l *J '.■ - ovo 42 4J •rl § I § CO (2 (!) CM COr-»r-imT-4vOvOUO m» m m vO m m 00 ro i-< r-l >d O J-i a<42 l^iTll^HOOONN fO N vO O CM CO in On r^ vf vJ 1 00 m' r-l T3 OJ u CO JgJ 1-4 (0 Pu £2 r-| r-l r-| ,-| CM r-l r-l CM r-l CM i-H 43 •H fa CO O V O *w 1 CJ g •H ro CO ro CO CO ro CO CO o CO CM CM rH ^-^ •H 4J r-l CMCOr-lr-ICOr-lr-lr-l CM CM CM CO *, **v "^ ^ ^ ->v. , "^^.^^ ^.•^"^ CO CO CO CO CO CO CO CO w P-, Q r-l r-lcOr-OOCMCMOcO ON r-l rH CM CO CO ►-J ■-> •n -> »"5 *-i *-> *-i OJ u cj w r-l r-l r-l • u u CO to oj aj E to oj 8 oj e* XJ 4J to J-I J-I Q 42 o 60 >* >. r-l o o s g g a § e § § r-H OJ ^ 4J V-i Q, Pu CO CO 3 CO cfl 42 M 32 -H CO (0 CO (0 CO to CO to CO to CO w CO CO CO to 43 O CO U (0 S Pw CO co (2 Ctf M M CO o o to CO o s X x OJ -o OJ T3 OJ T3 OJ TD OJ -d OJ •0 OJ TD OJ 4J O CO O 4J U 4J i - - CO 1-1 V OJ OJ 0J CO -H ,-4 4J co a> a) N AJ CO CO u 60 u 60 u 60 r-l 60 u 60 u 00 u 60 J-i 60 4J CO 0JCQOOC0CC0) QJ U OJ 0) P CO u u cu CU OJ OJ Or-l tU^co342O00 U 60 6042 AJ i-l r-l ■u o +J O ■u 4J ■p o ■U o 4J o u O 8 U o a» oj 32 32 32 32 c 32 32 32 X 3 CO ° o 0) •H -r-l OJ 0) OJ OJ OJ OJ OJ OJ ►J AflUUUUUb O 32 32 J en en CJ o o CJ CJ CJ CJ CJ 112 Table 8-5 COMPARISON OF MAXIMUM STORM VALUES WITH PMP FOR AREAS THE SIZE AND SHAPE OF SAN JOAQUIN AND SACRAMENTO DRAINAGE OF CALIFORNIA (Ref. fig. 8-1) Maximum Storm Ratio Duration Area Observed Assignment PMP (Obs./PMP) (hrs) (sq. mi.) (in.) No. (in.) Test Area No. 1 6 10 12.0 MR 4-3 22.9 .52 6 200 11.2 MR 4-3 18.2 .62 6 1000 8.7 MR 4-3 14.3 .61 24 10 12.3 MR 4-3 30.0 .41 24 200 11.5 MR 4-3 22.4 .51 24 1000 9.2 MR 4-3 18.4 .50 ' Test Area No. 2 6 10 8.5 UMV 1-22 23.8 .36 6 200 7.8 UMV 1-22 16.2 .48 6 1000 5.6 UMV 1-22 12.6 .44 24 10 12.4 GL 2-29 28.6 .43 24 200 11.3 GL 2-29 20.3 .56 24 1000 9.2 Test Area GL No. 3 2-29 16.2 .57 6 10 20.1 NA 2-4 26.9 .75 6 200 15.0 NA 2-4 19.5 .77 6 1000 8.8 NA 2-4 15.2 .58 24 10 22.7 NA 2-4 31.4 .72 24 200 16.5 NA 2-4 23.8 .69 24 1000 12.4 Test Area NA No. 4 2-22A 16.2 .77 6 10 17.3 SW 2-11 29.1 .59 6 200 13.3 SW 2-11 21.3 .62 6 1000 9.1 SW 2-11 17.7 .51 24 10 21.3 SW 2-11 34.3 .62 24 200 16.4 SW 2-11 26.5 .63 24 1000 11.1 Test Area SW No. 5 2-11 22.1 .50 6 10 7.9 GM 2-25 30.0 .26 6 200 6.4 UiV 2-5 22.2 .29 6 1000 5.5 LMV 2-5 17.9 .31 24 10 12.6 WV 2-5 37.9 .33 24 200 12.2 LMV 2-5 30.8 .40 24 1000 11.3 Test Area LMV No. 6 2-5 26.5 .43 6 10 8.4 SA 3-20 28.9 .29 6 200 7.9 SA 3-20 21.7 .36 6 1000 7.1 SA 3-20 17.5 .41 24 10 16.0 SA 3-20 37.0 .43 24 200 14.9 SA 2 -9 A 28.3 .53 24 1000 13.5 SA 2-9A 21.4 .60 113 magnitude (for six randomly -selected areas in the East) as the ratios in tables 8-1 through 8-4. The largest ratios are in California, not consider- ing the special -category storms at Newton and Campo. This comparison sug- gests that the California PMP in the present report is at a comparable general level to Report No. 33 for the East, or possibly that the California PMP is at a slightly lower level. Statistical approach to PMP 8.10. A statistical approach to estimating PMP has recently been de- vised. It is explained briefly in the following paragraphs and results from its application in California compared with this report. Further details of the method are in a paper by Hershfield (26). 8.11. There are two factors which at this time suggest a statistical approach to the PMP problem: the large quantity of available rainfall data and new statistical techniques . As a by-product of the many rainfall- frequency studies made by the Weather Bureau during the past decade, records from several thousand stations are in a form amenable to probability analy- sis; i.e., the annual maxima of daily rainfall have been extracted from climatological publications. 8.12. In 1951, Chow (27) demonstrated that the only difference between the theoretical distributions which lend themselves to the analysis of ex- treme-value hydrologic data is the value of the factor K in the following equation X T = x + K s N (1) where X T is the rainfall for return-period T, x is the sample mean of a series of annual maxima, sjq is the sample standard deviation, and N is the size of the sample. If the maximum observed rainfall, X M , is substituted for X T in equation (1) K becomes K^, the number of standard deviations that have to be added to the mean to obtain that maximum: *M - * + Si S N (2) Km's were determined for the series of annual maximum 24-hour rainfall depths for each of more than 2600 stations from several countries. An enveloping value of 15 for K^ was considered appropriate for estimating PMP. The parent paper (26) shows that K^ is both independent and random with respect to rain- fall magnitude, storm that produced the maxima, and geographical location. This is another way of saying the K^'s are transferable. Therefore, to de- termine a statistically derived PMP for a station, one need only calculate the x and sjj from the series of annual maxima at that station to solve equation (2). 114 8. 13. A statistical map with K^ = 15 is illustrated in figure 8-2 for eastern United States along with the Hydrometeorological Report No. 33 (2) isolines for 24 hours and 10 square miles. The statistical PMP isolines of this figure are based on the 100 long-record Weather Bureau First Order and 100 Cooperative stations shown on the chart. Agreement between the Report No. 33 and the statistical map is excellent along the Gulf of Mexico. They diverge rapidly to the north and west with the Report No. 33 map sometimes showing results twice as large as the statistical map. 8.14. A similar analysis was performed in California where orography has a great influence on the rainfall regime. The statistical map is shown in figure 8-3 along with the points (solid dots) from more than 400 stations which were used to define the position of the isolines. No consideration was given to orography in the construction of the isolines--just simple line- ar interpolation between the points with some degree of smoothing between closely-spaced points. 8.15. Statistical values for California are compared with 24-hour 10- square-mile PMP from this report in figure 8-4. The map shows values from both sources plotted on a grid. The upper number is interpolated from the lines of figure 8-3. The lower number is the highest of the monthly PMP's for October through April, by the steps in chapter IX. Some values are from the convergence-only criteria, others from orographic-plus convergence cri- teria. In each instance the higher value is used. 8.16. The relative level of the two methods may be compared in the scatter diagram of figure 8-4. The statistical value from the map for each grid point has been plotted against the corresponding PMP of this report. The position of the points with respect to a 45° line suggests that the gen- eral level of the physical - synoptic values is a little lower. 8.17. The level of the statistical method can be adjusted by changing %. A value of 15 was shown to yield results comparable to Hydrometeorologi- cal Report No. 33 (2) in the southern United States, but relatively lower values farther north. The inference is that, if there is any difference, the PMP values of this report for points are less conservative than Report No. 33L Comparison of PMP with SPS 8.18. The PMP of this report is compared with the Standard Project Storm values derived by the Sacramento District Corps of Engineers for the Sacra- mento-San Joaquin Valley (5). The comparison may extend the scope of the SPS report, however storms that were used in its derivation encompass the coastal drainage of California. The comparisons are shown on figures 8-5 through 8-9. For 6 hours, 10 and 200 square miles; 24 hours, 200 and 1000 square miles; and 72 hours, 1000 square miles the SPS and PMP values are plotted on a 1/2° grid and a separate map provided showing the computed ratio of SPS to PMP at each grid point for each of the duration and area combina- tions. It can be seen that in general the SPS runs from 40 to 60 percent of 115 the PMP. There is also a trend from relatively lower ratios of SPS to PMP in drier regions to higher ratios in regions of greater storm frequency. This is climatologically correct. Some scattered anomalous high or low ratios derive from differences in generalization of topographic influences in the respective reports. Comparison of SPS and PMP for certain selected basins is shown on fig- ure 8-12. 8.19. The values for different sizes of areas on figure 8-5 through 8-9 are obtained by applying the appropriate areal relationship to the index values at each respective grid point for both PMP and SPS and therefore will differ somewhat from the value that would be obtained for a basin of that size in that vicinity where the index values throughout the basin would be weighted. This difference is of no consequence for the comparisons. The SPS values and ratios on the charts that are in parentheses are derived from the "local" SPS criteria (5) for small areas and short durations. Comparison of PMP with precipitation for various return periods 8.20. The PMP in this report is derived primarily by generalizing from a few large storms in California on a synoptic, physical, and topographic basis. The long-term precipitation records of the individual stations also contain a measure of the synoptic, physical and topographic effects. Grid comparisons of 2-year 24-hour values (24-hour point depth with a mean re- currence interval of 2 years) , and 100-year 24-hour values with the PMP for 24-hour 10- square miles are shown in figure 8-10. Ten-year 72-hour values are compared with the 72-hour 10- square mile PMP in figure 8-11. At each grid point the ratio of the return period value to the PMP is plotted in per- cent. The 2-year and 100-year return period values were derived from Weather Bureau Technical Paper 40, (28) charts 44 and 49. The 10-year 72-hour values are from chart No. 6 of Technical Bulletin No. 4, "Ten Year Storm Precipita- tion in California and Oregon Coastal Basins", Sacramento District Corps of Engineers (6). Figures in the referenced studies show isolines drawn rather closely to a large number of station values. 8.21. The primary significance of these comparisons is of geographical consistency (see "internal consistency" in chapter II) rather than of the gen- eral level of the PMP. It can be seen that generally the percentages of PMP fall into reasonable patterns and that they are lower in dry regions than in regions of greater storm frequency. Comparison of PMP of this report with Weather Bureau Technical Paper No. 38, "Generalized Estimates of Probable Maximum Precipitation for the United States West of the 105th Meridian ." 71 8.22. Selected comparisons between the PMP values of this report and those from Weather Bureau Technical Paper No. 38 (3) are shown in figures 8-12 through 8-14, in a manner similar to the comparison with SPS values. 116 Figures 8-13 and 8-14 include differences at the high spots on the respective index maps (figure 5-35 of this report and figures 6-1 and 6-4 of Weather Bureau Technical Paper No. 38). The differences at these points, of course, are biased by the method of selection, while the grid point comparisons may be regarded as random. 8.23. Some differences between the two reports result from different but reasonable approaches to making PMP estimates and thus are a measure of the uncertainty in estimates of PMP. Other differences and reasons for them are as follows. In this paragraph the reports are referred to as "TP 38" and "HMR 36 n respectively, (a) On the San Joaquin Valley floor and in other arid regions HMR 36 values are lower than TP 38 because further studies have given more confidence in relying on the desiccating effects of downslope motions which inhibit rain, (b) TP 38 includes small-area intense local warm-season storms, while HMR 36 is restricted to cool-season storms, as discussed else- where. This accounts for the large differences on the charts in Southern California, (c) HMR 36 values exceed TP 38 along the crest of the Sierras at 24 hours. This results in part from closer drawing to topography on larger scale maps made possible by the more detailed study, (d) A single 6/24-hour duration ratio (for each size area) was adopted throughout the study-region of TP 38 that is characteristic of the intense local storms that control most of the PMP values. Somewhat lower 6/24-hour ratios were adopted for Cali- fornia in HMR 36, as characteristic of the cool-season storms of primary em- phasis. This accounts for the difference in shape of the comparative depth- duration curves in figure 8-12. 117 Chapter IX SUMMARY OF STEPS IN OBTAINING PROBABLE MAXIMUM PRECIPITATION FOR A BASIN 9.01. The steps necessary to obtain generalized values of PMP have been kept to a minimum. For computing the orographic component of PMP, the proba- ble maximum orographic precipitation index map (figure 5-35)'*, the orographic PMP computation areas (figure 5-30), the basin-width variation (figure 5-39) and the seasonal -duration variation (table 5-5)*are used. The restricted convergence PMP (to be combined with the orographic PMP) requires the proba- ble maximum convergence precipitation index map (figure 4-12), and the vari- ation of convergence PMP with basin size and duration (figures 4-13a, b, and c). The unrestricted convergence PMP (which is used if it exceeds the com- bined orographic and restricted convergence values) is 133 percent of the re- stricted convergence component of PMP. A detailed step-by-step procedure in determining PMP for a basin follows, after which several examples are given. 9 -A. PROCEDURE FOR COMPUTING PMP 9.02. Steps in determining orographic PMP 1. Determine average probable maximum precipitation index within basin out- line from figure 5-35. (A grid average is adequate.) 2. Determine the basin representative width perpendicular to the optimum in- flow direction. This is measured perpendicular to the sides of the orograph- ic PMP computation areas shown on figure 5-30. (Narrow extensions of the basin perpendicular to the inflow would not be considered in determining the basin representative width.) 3. Determine basin-width adjustment factor from figure 5-39. 4. Multiply the basin average probable maximum orographic precipitation in- dex from step 1, by the basin-width adjustment factor. This will give the January 6 -hour maximum orographic PMP. 5. To obtain all 6 -hourly increments of orographic PMP for each month use percentages given in table 5-5. If the basin is in the Sierra Range east of a line through the middle of Central Valley multiply the width-adjusted ba- sin-average probable maximum orographic precipitation index from step 4 by the Sierra Range percentages. For a basin in any other area, multiply the width-adjusted basin-average probable maximum orographic precipitation index from step 4 by the Coastal Range percentages. *Please see the revision dated October 1969 to the appropriate figure, table, and section that is included at the end of this publication. 118 6. For small basins, the 1- and 3 -hour duration orographic PMP values are 20 and 54 percent respectively (see paragraph 5.50) of the 1st (maximum) 6- hour orographic PMP. 9.03. Steps in determining convergence PMP A. Restricted convergence PMP to be combined with orographic PMP. 1. Determine average probable maximum convergence precipitation index within basin outline from figure 4-12. (A grid average is adequate.) 2. Tabulate the 6 -hour incremental percentages of convergence PMP index for the area of the basin for each month, October through April (figures 4-13a, b, and c). After the 3rd or 4th 6 -hour increment, there is no areal vari- ation so the percentages are given on the figures. For small basins, the 1- and 3 -hour duration percentages are obtained from the same figures. 3. Multiply the basin-average probable maximum convergence precipitation in- dex from step 1 by the percentages determined in step 2. The results are the 1- and 3 -hour duration and 6 -hourly incremental restricted convergence PMP values that are added to the orographic PMP month for month. B. Unrestricted convergence PMP for basins with zero or a relatively small probable maximum orographic precipitation index. 1. Multiply the restricted convergence PMP from 9.03 A3 by 1.33 to obtain the unrestricted convergence PMP increments. 2. Accumulate the 6-hour ly increments to obtain the 6-, 12-, 18-, etc. hour duration unrestricted convergence PMP. 9.04. Total PMP 1. Add the 6-hour ly increments of orographic PMP from 9.02.5 to the 6-hour ly increments of restricted convergence PMP from 9.03 A3 month for month; 1st 6- hour orographic to 1st 6 -hour convergence, 2nd 6 -hour orographic to 2nd 6- hour convergence, etc. For small basins also add the 1- and 3 -hour duration orographic and convergence values. 2. Accumulate the 6 -hourly incremental values of combined restricted con- vergence PMP and orographic PMP for each month to obtain the 6-, 12-, 18-, etc. hour duration values. 3. For pronounced orographic areas the combined orographic and restricted convergence PMP will exceed the unrestricted convergence PMP month for month. For basins in non-orographic regions, the unrestricted convergence is the 119 total PMP. For foothill areas, the combined orographic and restricted con- vergence PMP (9.04.2) and unrestricted convergence PMP (9.03 B2) may be com- pared and the most critical selected dependent upon critical duration and other hydrologic factors. For any basin the PMP values for the various months should be evaluated on the basis of snowmelt contribution, (ref. chapter X for snowmelt winds and temperatures) size of basin, etc. in order to select the most hydrologically critical precipitation. 9.05. Time distribution Arrange 6 -hour increments of selected PMP into a critical storm se- quence (ref. chapter VII paragraphs 7.10 to 7.12). Figure 7-3 gives ex- amples of such sequences. Winds and temperatures for computing snowmelt should be arranged in the same sequence. 9-B. EXAMPLES OF PMP COMPUTATIONS I. Large Sierra Slope Basin Tuolumne River above LaGrange, California. Basin Area: 1540 square miles 9.06. Orographic PMP for Tuolumne Basin 1. Basin average probable maximum orographic precipitation index (figure 5-35): 4.86 inches 2. Basin representative width (figure 5-30): 30 miles 3. Basin-width adjustment factor (figure 5-39): 1.00 4. Basin-width adjusted probable maximum precipitation index: 4.86 X 1.00 = 4.86 inches 5. All 6-hour ly increments of orographic PMP: 4.86 times Sierra Range percentages from table 5-5 6- Hour P eriod Mid- month 1 2 3 4 5 6 7 8 9 10 11 12 6 -hourly incremental orograph ic PMP in inches Oct. 4.71 3.69 2.96 2.43 2.09 1.75 1.46 1.21 1.02 .83 .68 .53 Nov. 4.76 3.69 3.01 2.48 2.09 1.75 1.46 1.21 1.07 .87 .68 .53 Dec. 4.81 3.74 3.01 2.53 2.14 1.80 1.51 1.26 1.07 .87 .68 .53 Jan -Feb. 4.86 3.79 3.06 2.53 2.14 1.80 1.51 1.26 1.07 .87 .68 .53 Mar. 4.66 3.64 2.92 2.43 2.04 1.70 1.46 1.21 1.02 .83 .63 .53 Apr. 4.37 3.40 2.72 2.28 1.94 1.65 1.36 1.17 .97 .78 .63 .49 Note: 1- and 3 -hour duration PMP values were not computed for this large- area basin. 120 1. 2. 9.07. Convergence PMP for Tuolumne Basin (Restricted convergence PMP to be combined with orographic PMP.) Basin average probable maximum convergence precipitation index (fig- ure 4-12): 2.26 inches 6 -hourly incremental percents of convergence PMP index (figures 4-13a, b, and c) 6 -Hour Period Mid- month 1 2 3 4 5 6 7 8 9 10 11 12 Percents of convergence PMP index Oct. 94 30 20 16 14 12 11 10 9 9 8 8 Nov. 85 38 26 20 16 14 13 11 10 10 10 10 Dec. 79 37 26 21 18 16 13 12 11 11 10 10 Jan. -Feb. 74 40 28 23 19 16 14 13 12 11 11 11 Mar. 76 39 28 22 19 16 13 11 10 10 9 9 Apr. 78 36 27 21 18 14 12 10 9 9 8 8 6 -hourly incremental restricted convergence PMP; of convergence PMP index 2.26 times percents 6- •Hour Period Mid- month 1 2 3 4 5 6 7 8 9 10 11 12 6 -hourly incremental restricted convergence PMP in inches Oct. 2.12 .68 .45 .36 .32 .27 .25 .23 .20 .20 .18 .18 Nov. 1.92 .86 .59 .44 .36 .32 .29 .25 .23 .23 .23 .23 Dec. 1.79 .84 .59 .48 .41 .36 .29 .27 .25 .25 .23 .23 Jan. -Feb. 1.67 .91 .63 .52 .43 .36 .32 .29 .27 .25 .25 .25 Mar. 1.71 .88 .63 .50 .43 .36 .29 .25 .23 .23 .20 .20 Apr. 1.77 .81 .61 .48 .41 .32 .27 .23 .20 .20 .18 .18 Note: Because of pronounced orographic index for this basin, unrestricted convergence was not computed. 121 1. 9.08. Total PMP for Tuolumne Basin 6-hour ly orographic PMP increments from 9.06.5 added to 6 -hourly re stricted convergence PMP increments from 9.07.3 (inches) 6 -Hour Period Mid- month 1 2 3 4 5 6 7 8 9 10 11 12 6 -hourly incremental convergence and orographic PMP in inches Oct. 6.8 4.4 3.4 2.8 2.4 2.0 1.7 1.4 1.2 1.0 .9 .7 Nov. 6.7 4.5 3.6 2.9 2.5 2.1 1.8 1.5 1.3 1.1 .9 .8 Dec. 6.6 4.6 3.6 3.0 2.6 2.2 1.8 1.5 1.3 1.1 .9 .8 Jan. -Feb. 6.5 4.7 3.7 3.0 2.6 2.2 1.8 1.6 1.3 1.1 .9 .8 Mar. 6.4 4.5 3.6 2.9 2.5 2.1 1.8 1.5 1.2 1.1 .8 .7 Apr. 6.1 4.2 3.3 2.8 2.4 2.0 1.6 1.4 1.2 1.0 .8 .7 2. Combined orographic PMP and restricted convergence PMP accumulated Duration (hrs) Mid- month 6 12 18 24 30 36 42 48 54 60 66 72 Convergen ze and orographic PMP in inches Oct. 6.8 11.2 14.6 17.4 19.8 21.8 23.5 24.9 26.1 27.1 28.0 28.7 Nov. 6.7 11.2 14.8 17.7 20.2 22.3 24.1 25.6 26.9 28.0 28.9 29.7 Dec. 6.6 11.2 14.8 17.8 20.4 22.6 24.4 25.9 27.2 28.3 29.2 30.0 Jan. - Feb. 6.5 11.2 14.9 17.9 20.5 22.7 24.5 26.1 27.4 28.5 29.4 30.2 Mar. 6.4 10.9 14.5 17.4 19.9 22.0 23.8 25.3 26.5 27.6 28.4 29.1 Apr. 6.1 10.3 13.6 16.4 18.8 20.8 22.4 23.8 25.0 26.0 26.8 27.5 Select month of critical PMP on basis of hydrologic factors. Winds and temperatures for computing snowmelt contribution to probable maximum flood are given in chapter X. Arrangement of selected 6 -hourly PMP in- crements and similar arrangement of accompanying winds and temperatures is covered in chapter VII. 122 II. Small Coastal Basin San Lorenzo Creek above Palomares, California. Basin Area: 20 square miles 9 . 09 . Orographic PMP for San Lorenzo Basin 1. Basin average probable maximum orographic precipitation index (figure 5-35): 2.00 inches 2. Basin representative width (figure 5-30): 12 miles 3. Basin-width adjustment factor (figure 5-39): 1.00 4. Basin-width adjusted probable maximum orographic precipitation index: 2.00 X 1.00 = 2.00 inches 5. All 6 -hourly increments of orographic PMP: 2.00 times Coastal Range percentages from table 5-5 6 -hour Period Mid- month 1 2 3 4 5 6 7 8 9 10 11 12 6 -hourly incremental orographic PMP in inches Oct. 1.84 1.44 1.16 .96 .82 .68 .56 .48 .40 .34 .26 .20 Nov. 1.88 1.46 1.18 .98 .82 .70 .58 .48 .42 .34 .26 .20 Dec. 1.96 1.54 1.24 1.02 .86 .72 .60 .52 .44 .36 .28 .22 Jan. -Feb. 2.00 1.56 1.26 1.04 .88 .74 .62 .52 .44 .36 .28 .22 Mar. 1.88 1.48 1.20 .98 .84 .70 .58 .50 .42 .34 .26 .20 Apr. 1.74 1.36 1.10 .90 .76 .64 .54 .46 .38 .32 .24 .20 6. Multiply the 1st 6-hour orographic PMP by 20 and 54 percent to obtain orographic PMP for 1 and 3 hours, respectively Mid -month Duration Oct. Nov. Dec. Jan. Feb* Mar. Apr. Orographic PMP in inches 1 hr .37 .38 .39 .40 .38 .35 3 hrs .99 1.02 1.06 1.08 1.02 .94 123 9.10. Restricted convergence PMP to be combined with orographic PMP 1. Basin average probable maximum convergence precipitation index (figure 4-12): 4.21 inches 2. 1- and 3 -hour percentages and 6 -hourly incremental percentages of con- vergence PMP index (figures 4-13a, b and c) Duration 6 -Hour Pei riod Mid- (hrs) month 1 3 1 2 3 4 5 6 7 8 9 10 11 12 Percent s of convergence PMP index Oct. 69 118 155 36 23 17 14 12 11 10 9 9 8 8 Nov. 62 105 141 42 27 20 16 14 13 11 10 10 10 10 Dec. 56 96 129 43 29 21 18 16 13 12 11 11 10 10 Jan. - Feb. 52 89 122 45 30 23 19 16 14 13 12 11 11 11 Mar. 53 90 125 47 31 23 19 16 13 11 10 10 9 9 Apr. 55 96 130 44 30 23 18 14 12 10 9 9 8 8 1- and 3-hour duration and 6-hour ly incremental restricted convergence PMP: 4.21 times percents of convergence PMP index Mid- month Duration (hrs) 1 3 1 6 -Hour Period 4 5 6 7 8 10 11 12 Restricted convergence PMP in inches Oct. 2.90 4.97 6.52 1.52 .97 .72 .59 .51 .46 .42 .38 .38 .34 .34 Nov. 2.61 4.42 5.94 1.77 1.14 .84 .67 .59 .55 .46 .42 .42 .42 .42 Dec. 2.36 4.05 5.44 1.81 1.22 .89 .76 .67 .55 .51 .46 .46 .42 .42 Jan. - Feb. 2.19 3.75 5.14 1.89 1.31 .97 .80 .67 59 55 .51 .46 .46 .46 Mar. 2.23 3.79 5.26 1.98 1.31 .97 .80 .67 .55 .46 .42 .42 .38 .38 Apr. 2.32 4.05 5.48 1.85 1.26 .97 .76 .59 .51 .42 .38 .38 .34 34 124 9.11. Unrestricted convergence PMP 1. 1- and 3 -hour duration and 6 -hourly incremental unrestricted convergence PMP. Restricted convergence PMP times 1.33 Duration 6 -Hour Period Mid- (hrs) month 1 3 1 2 3 4 5 6 7 8 9 10 U 12 Unrestricted convergence PMP in inches Oct. 3.9 6.6 8.7 2.0 1.3 1.0 .8 .7 .6 .6 .5 .5 .5 .5 Nov. 3.5 5.9 7.9 2.4 1.5 1.1 .9 .8 .7 .6 .6 .6 .6 .6 Dec. 3.1 5.4 7.2 2.4 1.6 1.2 1.0 .9 .7 .7 .6 .6 .6 .6 Jan. - Feb. 2.9 5.0 6.8 2.5 1.7 1.3 1.1 .9 .8 .7 .7 .6 .6 .6 Mar. 3.0 5.0 7.0 2.6 1.7 1.3 1.1 .9 .7 .6 .6 .6 .5 .5 Apr. 3.1 5.4 7.3 2.5 1.7 1.3 1.0 .8 .7 .6 .5 .5 .5 .5 2. Accumulated unrestricted convergence PMP Mid- I.JLVJ11 \ month 1 3 6 12 18 24 30 36 42 48 54 60 66 72 Unrestricted convergence PMP in inches Oct. 3.9 6.6 8.7 10.7 12.0 13.0 13.8 14.5 15.1 15.7 16.2 16.7 17.2 17.7 Nov. 3.5 5.9 7.9 10.3 11.8 12.9 13.8 14.6 15.3 15.9 16.5 17.1 17.7 18.3 Dec. 3.1 5.4 7.2 9.6 11.2 12.4 13.4 14.3 15.0 15.7 16.3 16.9 17.5 18.1 Jan. - Feb. 2.9 5.0 6.8 9.3 11.0 12.3 13.4 14.3 15.1 15.8 16.5 17.1 17.7 18.3 Mar. 3.0 5.0 7.0 9.6 11.3 12.6 13.7 14.6 15.3 15.9 16.5 17.1 17.6 18.1 Apr. 3.1 5.4 7.3 9.8 11.5 12.8 13.8 14.6 15.3 15.9 16.4 16.9 17.4 17.9 125 9.12. Total PMP 6-hour ly orographic PMP increments from 9.09.5 added to 6-hour ly re- stricted convergence PMP increments from 9.10.3. 1- and 3-hour values similarly added Mid- Duration month (hrs) 1 3 6 -Hour Period 8 10 11 12 and 3 -hour duration and 6 -hourly increments of orographic and convergence PMP in inches Oct. 3.3 6.0 8.4 3.0 2.1 1.7 1.4 1.2 1.0 .9 .8 .7 .6 .5 Nov. 3.0 5.4 7.8 3.2 2.3 1.8 1.5 1.3 1.1 .9 .8 .8 .7 .6 Dec. 2.8 5.1 7.4 3.4 2.5 1.9 1.6 1.4 1.2 1.0 .9 .8 .7 .6 Jan. - Feb. 2.6 4.8 7.1 3.4 2.5 2.0 1.7 1.4 1.2 1.1 1.0 .8 .7 .7 Mar. 2.6 4.8 7.1 3.5 2.5 2.0 1.6 1.4 1.1 1.0 .8 .8 .6 .6 Apr. 2.7 5.0 7.2 3.2 2.4 1.9 1.5 1.2 1.1 .9 .8 .7 .6 .5 2. Combined orographic PMP and restricted convergence PMP accumulated Duration (hrs) Mid- month 1 3 6 12 18 24 30 36 42 48 54 60 66 72 Orographic and convergence PMP in inches Oct. 3.3 6.0 8.4 11.4 13.5 15.2 16.6 17.8 18.8 19.7 20.5 21.2 21.8 22.3 Nov. 3.0 5.4 7.8 11.0 13.5 15.1 16.6 17.9 19.0 19.9 20.7 21.5 22.2 22.8 Dec. 2.8 5.1 7.4 10.8 13.3 15.2 16.8 18.2 19.4 20.4 21.3 22.1 22.8 23.4 Jan. - Feb. 2.6 4.8 7.1 10.5 13.0 15.0 16.7 18.1 19.3 20.4 21.4 22.2 22.9 23.6 Mar. 2.6 4.8 7.1 10.6 13.1 15.1 16.7 18.1 19.2 20.2 21.0 21.8 22.4 23.0 Apr. 2.7 5.0 7.2 10.4 12.8 14.7 16.2 17.4 18.5 19.4 20.2 20.9 21.5 22.0 Comparison of unrestricted convergence PMP (9.11.2) with combined oro- graphic PMP and restricted convergence PMP (9.12.2) shows that the un- restricted convergence PMP is greater for 1 and 3 hours duration for each month; at 6 hours duration, the combined orographic and restricted convergence PMP is greater than the unrestricted convergence PMP in the winter season; for 12 hours and longer durations the combined values are greater in each month. Hydrologic factors will determine which storm type and month is most critical. Snowmelt winds and temperatures, if applicable, are given in chapter X. Arrangements of winds, temperatures, and PMP increments in the same critical storm sequences are given in chapter VII. 126 Chapter X TEMPERATURE AND WIND CRITERIA FOR SNOWMELT 10.01. Temperatures and winds associated with probable maximum precipi- tation are two important snowmelt factors amenable to generalization for snowmelt computations. Other items which need to be considered in determin- ing basin melt such as optimum depth, areal extent and type of snowpack as well as vegetal cover are integral characteristics of each drainage basin and cannot readily be generalized over the State. The derivation of generalized winds and temperatures for a PMP storm and how they may be obtained for a basin are given in this chapter. An example of derived winds and temperatures for a specific location is also presented. Temperature during PMP storm 10.02. Enveloping 1000-mb (sea level) 12-hour persisting dew points for February developed in chapter IV (figure 4-5b) and the average seasonal var- iation of moisture (table 4-1) establish the 12-hour temperature using the assumption of a saturated pseudoadiabatic atmosphere during the PMP storm. Likewise the sea- level temperatures for each 6 -hour increment for the 72-hour storm are determined from the adopted moisture variation with duration given in table 4-3. The variations in both tables are expressed in terms of pre- cipitable water (W p ) . The 6-hour incremental sea-level temperatures (1000 mb) for an area for a particular month may be obtained from figure 4-5b and tables 4-1 and 4-3 through the use of auxiliary figure 10-1, by the following steps: 1) Read the 12-hour February dew point (temperature) at the area of in- terest from figure 4-5b. 2) Obtain the Wp corresponding to this temperature from figure 10-1. Enter this figure with the 12-hour February temperature on the ab- scissa, read the corresponding W on the ordinate. 3) Multiply the W by the appropriate percent of February (table 4-1) for the month of interest. 4) Multiply the resulting W by the percentages of table 4-3 to obtain W for each 6 -hour increment. 5) Obtain 6-hour temperatures from figure 10-1 by reading the tempera- ture corresponding to each 6-hour W of step 4. These temperatures then are adjusted to the elevation of the area of interest by using the variation of temperature with height in a saturated 127 pseudoadiabatic atmosphere. This is given in figure 10-2 and is used by starting on the abscissa with each sea- level temperature, proceeding parallel to the sloping line to the basin elevation, and reading the adjusted tempera- ture that is vertically downward on the abscissa. 10.03. Height of the freezing level during the PMP storm may be de- termined, under the saturated pseudoadiabatic atmosphere assumption, from 6-hour ly sea-level temperatures. Enter figure 10-2 with sea-level tempera- ture on the abscissa, proceed parallel to the sloping line and read the elevation at the 32 °F isotherm. Temperatures prior to the PMP storm 10.04. Temperatures prior to the onset of the PMP storm are a factor in determining the availability and condition of the snowpack. High ante- cedent temperatures could bring snowmelt runoff to the stream concurrently with the probable maximum precipitation. Below- freezing antecedent tempera- tures on the other hand, will avoid depletion of the available snowpack. Whether warm or cold temperatures are critical will depend on the magnitude of the snowpack. Since this varies greatly from place to place, a range of possible antecedent temperatures have been determined which will give the hydrologist the general limits of temperatures for snowmelt computations. These limits were derived from a survey of observed temperatures antecedent to major California storms. 10.05. Figure 10-3 shows the wide range in temperatures observed prior to the maximum 3-day precipitation in recent great California storms. Curves labeled A^ and A2 are the upper and lower envelopes of differences between the mean daily temperatures on the day of onset of a 3-day storm and 1 and 2 days prior to the day of onset at key Central Valley stations. Curve B envelops the largest day-to-day increases in temperatures observed during snow cover periods between 1949 and 1958 at Mt. Wilson, Mt. Hamilton, Blue Canyon, and Mt. Shasta. 10.06. Antecedent temperatures given in figure 10-3 are used in the following manner. After the initial 6-hour temperature (or dew point) at the onset of the PMP storm is determined, (dependent on the selected PMP storm time sequence, reference paragraphs 7.10-12) and assuming highest antecedent temperatures are most critical in this particular instance, add the tempera- ture differences obtained from curve Ai in figure 10-3 for each time before beginning of PMP storm to the temperature at the storm onset. Dew points during and prior to PMP storm 10.07. Dew points, for computing condensation melt, during the 3-day PMP storm are the same at each elevation as the temperature. Prior to the storm, the dew points associated with the lower limit of temperatures (curve A2 or B) should be 2 or 3 degrees colder. If high temperatures are critical 128 (curve Ap the appropriate corresponding dew points are indicated by curve C. This curve is derived from the mean variation of maximum persisting dew points in California for durations up to 5 days. Snowmelt winds during the PMP storm 10.08. Free-air windspeeds derived for computing orographic PMP are used, with adjustment, for defining the windspeeds over a snow cover. These maximum winds are shown on figures 5-26 and 5-27 by solid lines for January at 38 °N for the Coast and Sierra Ranges respectively. Seasonal and latitudi- nal variations, of the maximum winds, shown in figures 5-37 and 5-32 respec- tively, should be applied. Figure 10-4 is provided to conveniently convert from pressures to heights. 10.09. In order to determine a factor for reducing free-air winds to those which would be expected at the surface of a snowpack, a comparison study was made of free- air winds from the Oakland sounding and simultaneous Blue Canyon (station elevation 5280 feet) anemometer- level winds, at the same ele- vation above mean sea level. Periods of strong winds at each location were considered. The mean ratio of the Blue Canyon anemometer wind to the free- air wind was found to be 0.75. This reduction may be used for arriving at winds for other locations which have exposure and topographic features sim- ilar to that of Blue Canyon. The Blue Canyon Weather Bureau Station is well exposed toward the southwest. The anemometer is 50 feet above the ground level and downwind from the landing field during the average southerly storm winds. There is relatively little reduction of wind by nearby forest. 10.10. Areas more sheltered than the Blue Canyon site should have cor- respondingly greater reduction to be estimated by the user. 10.11. A check on the magnitude of the computed winds for the PMP storm is shown in table 10-1. Table 10-1 COMPARISON OF REDUCED PMP WINDS FROM FIGURE 5-27 WITH MAXIMUM OBSERVED WINDS AT BLUE CANYON 72 36 23 Duration (hours) 6 12 24 48 Speed (mph) January computed winds 61 54 46 39 Maximum observed Blue Canyon winds 49 42 35 29 129 In table 10-1 maximum observed Blue Canyon persisting winds, for the du- rations indicated, from a survey of two complete winter seasons and selected major storms are compared with computed winds derived by multiplying speeds from figure 5-27 by 0.75. The two winter seasons surveyed for observed Blue Canyon winds were 1954 and 1955. The major storms surveyed in other seasons were November 1950, January, February 1945, January 1943, January 1940, and December 1937. Snowmelt winds prior to PMP storm 10. 12. Winds prior to the PMP storm could vary even more than the temperatures prior to the onset. As an expedient which gives a reasonably critical wind, the wind for the 72-hour duration may be extended for two days prior to the storm. Example of computed snowmelt winds and temperatures 10.13. An example of computed snowmelt winds, temperatures, and dew points prior to and during a PMP storm is given for a hypothetical basin on the following pages. L 130 Example of computed snowmelt winds and temperatures Hypothetical basin: near Blue Canyon. Average elevation: 7000 feet Month: mid-November. A. Temperatures and dew points during PMP storm 1) Average 12-hour February sea level dew point over basin (figure 4-5b); 59.0°F. 2) Precipitable water (W p ) for 59.0°F (figure 10-1): 1.31 inches. 3) W p for February times seasonal adjustment for November (table 4-1): 1.31 times 111 = 1.45 inches. 6-hour period 123456769 10 11 12 4) Wp corresponding to 6-hour temperature in- crements during PMP storm. 1.45 x %'s of table 4-3 (inches) 1.51 1.45 1.41 1.38 1.35 1.32 1.29 1.27 1.25 1.23 1.22 1.21 5) 6-hour incremental sea- level temperatures and dew points from figure 10-1 (°F) 61.8 61.0 60.5 60.0 59.6 59.2 58.8 58.4 58.1 57.8 57.6 57.5 6) Sea- level tempera- tures and dew points adjusted to 7000 feet elevation. Fig- ure 10-2 (°F) 43.1 42.0 41.4 40.8 40.3 39.8 39.3 38.8 38.3 38.0 37.7 37.6 7) Height of 32°F above mean sea level. Figure 10-2 (1000' s feet) 10.7 10.3 10.1 9.9 9.7 9.5 9.3 9.2 9.1 8.9 8.8 8.8 8) The temperatures and elevations in steps 6 and 7 should be arranged in time se- quence corresponding to the selected PMP storm sequence, (see E) 131 B. Temperatures prior to PMP storm (For this example highest temperatures are considered critical.) Hours prior to storm onset 48 42 36 30 24 18 12 1) Differences between temperature at beginning of storm and at indicated hours prior to storm. From figure 10-3, curve Ax (°F) 10.0 9.5 9.0 8.0 7.0 6.0 4.5 3.5 2) The above differences are added to the initial temperature determined in step 10.13 A8. C. Dev points prior to PMP storm Hours prior to storm onset 48 42 36 30 24 18 12 6 1) Differences between dew point at beginning of storm and at indicated hours prior to storm. Figure 10-3, curve C (°F) 3.0 2.5 2.0 2.0 1.5 1.0 1.0 0.5 2) The above differences are subtracted from the initial temperature (dew point) determined in step 10.13 A8. Snowmelt winds 6-hour period 3 4 5 6 7 8 9 10 11 12 1) Winds from figure 5-27 and interpolations at 7000 ft msl (7000 ft = 775 mb) ref . figure 10-4 (mph) 87 78 72 68 65 62 60 58 56 55 54 54 2) Winds reduced to surface conditions similar to Blue Canyon. Step 1 winds x 0.75 (mph) 65 59 54 51 49 47 45 43 42 41 40 40 3) Surface winds adjusted to November. Step 2 winds x 0.84 (from figure 5-37) (mph) 55 50 45 43 41 39 38 36 35 34 34 34 4) Arrange 6-hour winds (step 3) in time sequence similar to arrangement of pre- cipitation and temperatures in PMP storm (see £). 132 E. Time sequence of temperatures, winds and precipitation during PMP storm 6-hour period 123456789 10 11 12 1) November 6 -hourly PMP increments for hy- pothetical basin near Blue Canyon obtained by procedures of chap- ter IX. (inches) 9.2 5.8 4.6 3.8 3.2 2.6 2.2 1.9 1.6 1.4 1.1 0.9 2) 6-hour PMP incre- ments arranged accord- ing to sequence (c) of figure 7-3. (inches) 12 Time in hours from beginning of storm 18 24 30 36 42 48 54 60 66 72 0.9 1.4 1.6 1.1 3.8 5.8 9.2 4.6 1.9 2.6 3.2 2.2 3) 6-hour tempera- tures from 10.13 A6 arranged in same se- quence (°F) 37.6 38.0 38.3 37.7 40.8 42.0 43.1 41.4 38.8 39.8 40.3 39.3 4) 6-hour winds from 10.13 D3 arranged in same sequence (mph) 34 34 35 34 43 50 55 45 36 39 41 38 5) Height of freez- ing level from 10.13 A7 in same sequence (1000' s ft) 8.8 8.9 9.1 8.8 9.9 10.3 10.7 10.1 9.2 9.5 9.7 9.3 6) Temperatures prior to storm. Differences of 10.13 Bl added to 37.6 (°F). 48 42 Hours prior to storm onset 36 30 24 18 12 47.6 47.1 46.6 45.6 44.6 43.6 42.1 41.1 37.6 7) Dew points prior to storm. Differ- ences of 10.13 CI sub- tracted from 37.6 (°F) 34.6 35.1 35.6 35.6 36.1 36.6 36.6 37.1 37.6 8) Winds prior to storm may be assumed to be 34 mph (ref. paragraph 10.12) for two days prior to storm. 133 ACKNOWLEDGMENTS This report was prepared under the direction of Charles S. Gilman, Chief of Hydrometeorological Section, by the following meteorologists, each of whom was primarily responsible for various parts and chapters: Vance A. Myers, George A. Lott, John T. Riedel, Francis K. Schwarz, and Robert L. Weaver. Meteorologists Calvin W. Cochrane, Lillian K. Rubin, William W. Swayne, and Roger R. Watkins assisted. Corps of Engineers personnel in California and Washington offered many valuable criticisms and suggestions. Particular acknowledgment is due Mr. Dwight E. Nunn of the Office of Chief of Engineers for many detailed consultations. Thanks are due to Meteorological Technician Pool for skillful and time- ly data processing. More than twenty- five technicians assisted at some time during the several years of the project. 134 REFERENCES 1. U. S. Weather Bureau, "Generalized Estimates of Maximum Possible Precipitation over the United States East of the 105th Meridian for Areas of 10, 200, and 500 Square Miles", Hydrometeoro logical Report No, 23 , Washington, 1947. 2. U. S. Weather Bureau, "Seasonal Variation of Probable Maximum Precipitation East of the 105th Meridian for Areas from 10 to 1000 Square Miles and Durations of 6, 12, 24 and 48 Hours", Hydrometeorological Report No. 33 , Washington, 1956. 3. U. S. Weather Bureau, "Generalized Estimates of Probable Maximum Precipitation West of the 105th Meridian", Weather Bureau Technical Paper No. 38 , Washington, 1960. 4. U. S. Weather Bureau, "Meteorological Characteristics of Hydrologi- cally -Critical Storms in California", Hydrometeorological Report No. 37. (In preparation). 5. Corps of Engineers, U. S. Army, "Standard Project Rain-Flood Criteria, Sacramento -San Joaquin Valley, California", Sacramento, 1957. 6. Corps of Engineers, U. S. Army, "Ten -Year Storm Precipitation in California and Oregon Coastal Basins", Technical Bulletin No. 4 , Sacramento, 1957. 7. U. S. Weather Bureau, "Meteorology of Flood -Producing Storms in the Mississippi River Basin", Hydrometeorological Report No. 34 , Wash- ington, 1956. 8. U. S. Weather Bureau, "Maximum Possible Precipitation, Small Basins in the Los Angeles Area During the Winter Season", Preliminary Estimate HMS 5004 , Washington, 1951. 9. Fletcher, R. D. , "Computation of Thunderstorm Rainfall", Transactions of American Geophysical Union , Vol. 29, No. 1, pp. 41-50, February 1948. 10. U. S. Weather Bureau, "Highest Persisting Dewpoints in Western United States", Weather Bureau Technical Paper No. 5 , Washington, 1948. 11. U. S. Weather Bureau, "Revised Report on Maximum Possible Precipi- tation, Los Angeles Area, California", Hydrometeorological Report No. 21B, Washington, 1945. 12. U. S. Weather Bureau, "Maximum 24-Hour Precipitation in the United States", Weather Bureau Technical Paper No. 16 , Washington, 1952. 135 13. U. S. Weather Bureau, "Climatological Data for the United States by Sections", Washington, Series. 14. Corps of Engineers, U. S. Army, "Storm Rainfall in the United States", Washington, 1945 -. 15. U. S. Weather Bureau, "Maximum Possible Precipitation, San Joaquin Basin, California", Hydrometeorological Report No. 24 , Washington, 1947. 16. Myers, Vance A. , "Airflow on the Windward Side of a Large Ridge", U.S. Weather Bureau, Washington, (In preparation). 17. Laws, J. 0. and D. A. Parsons, "The Relation of Raindrop Size to Intensity", Transactions of American Geophysical Union , Part II, pp. 452-459, 1943. 18. Gunn, R. and G. D. Kinzer, "The Terminal Velocity of Fall for Water Droplets in Stagnant Air", Journal of Meteorology , Vol. 6, No. 4, pp. 243-248, August 1949. 19. Laws, J. Otis, "Measurements of the Fall -Velocities of Waterdrops and Raindrops", Transactions of American Geophysical Union , pp. 709-712, 1941. 20. Anderson, L. J. , "Drop -Size Distribution Measurements in Orographic Rain", Bulletin of the American Meteorological Society , Vol. 29, pp. 362-366, 1948. 21. Blanchard, D. C. , "Raindrop Size-Distribution in Hawaiian Rains", Journal of Meteorology , Vol. 10, No. 6, pp. 457-473, December 1953. 22. Langleben, M. P., "Terminal Velocity of Snowf lakes", Quarterly Jour- nal of Royal Meteorological Society , Vol. 80, No. 344, pp. 174-181, 1954. 23. Douglas, R. H. , K.L.S. Gunn and J. S. Marshall, "Pattern in the Verti- cal of Snow Generation", Journal of Meteorology , Vol. 14, No. 2, pp. 95-114, April 1957. 24. Knox, Joseph B. , "Procedures for Estimating Maximum Possible Precipi- tation", Bulletin 88 , California State Department of Water Resources, May 1960. 25. U. S. Weather Bureau, "Maximum Possible Precipitation, Sacramento River Basin", Hydrometeorological Report No. 3 , Washington, 1943. 26. Hershfield, D. M. , "Estimating the Probable Maximum Precipitation", Journal of the Hydraulics Division , Proceedings of the ASCE, Vol. 87, No. HY 5, pp. 99-116, September 1961, Part 1. 136 27. Chow, V. T. , "A General Formula for Hydrologic Frequency Analysis" Transactions of American Geophysical Union , Vol. 32, No. 2, 231-237, April 1951. PP 28. U. S. Weather Bureau, "Rainfall Frequency Atlas of the U. S. for Du- rations from 30 Minutes to 24 Hours and Return Periods from 1 to 100 Years", Weather Bureau Technical Paper No. 40 , Washington, 1961. 29. Corps of Engineers, U. S. Army, "Sacramento Method of Correlating Storm Precipitation with Normal Seasonal Precipitation and Runoff", Sacramento, 1941. 137 FIG. 3-1. LOW-LATITUDE -TYPE MAJOR OROGRAPHIC STORM (NORTHERN AND CENTRAL CALIFORNIA) TW^rm FIG. 3-2. HIGH-LATITUDE TYPE (SOUTHERN CALIFORNIA) 138 FIG. 3-3. MID-LATITUDE -TYPE, SOUTHWESTERLY APPROACH (NORTHERN AND CENTRAL CALIFORNIA) FIG. 3-4. COOL-SEASON CONVERGENCE STORM CENTERED AT SACRAMENTO APRIL 20-21, 1880 139 70 68 66 64 62 60 o H 56 5 % 54 UJ o 52 50 48 46 44 42 •^ V^ Sea Surface Temperature ^ Ck (•) jCjOO-Year Return Period[ -- "* \^t\ - — -*— ^rJ4^~'" 1 Rett 50-Year Return Period ^^10-Year Return Period ^o 2-Year Return Period LOS ANGELES OCT NOV DEC JAN FEB MAR APR 52 50 48 46 44 42 FIG. 4 SAN DIEGO 10- Year Return Period 2- Year Return Period Legend for 4-la to 4-ld Seasonally- and geographically- smoothed maximum observed rTd envelope. Dew point maps (figs. 4-5a & b) from this. Smooth 2-year return-period dew point. Smooth 10-year return-period dew point. Smooth 50-year return-period dew point. Smooth 100-year return-period dew point. Range in 100-year return-period dew point (eye-fitted curves) Monthly mean sea-surface temperature (600 n. mi. SW) Application of mean seasonal variation to each station. Highest observed representative dew point. ( ) rejected. All dew points are 12-hour persisting reduced to 1000 mb . OCT NOV DEC JAN FEB MAR APR la. SEASONAL ENVELOPE OF MAXIMUM OBSERVED DEW POINTS 140 70 68 66 64 62 60 58 5 56 5 a. £ 54 •^<. (•) ®r 52 50 48 46 44 42 °k ■Sea Surface Temperature ® 1950 /00-Year ^Return Period ~— f— 50-Year Return Period V0 -Year Return Period _ — -- " o „- 2 -Year Return Period SACRAMENTO OCT NOV DEC JAN FEB MAR APR 70 68 66 64 62 60 Z 58 z 56 o a. £ 54 52 50 48 46 44 42 .G. 4- ■lb. 10 -Year Return Period ^2 -Year Return Period FRESNO OCT NOV DEC JAN FEB MAR APR SEASONAL ENVELOPE OF MAXIMUM OBSERVED DEW POINTS (CONT'D) 141 70 68 66 64 62 60 58 z 56 O a. £ 54 52 50 48 46 44 42 50-Year Return Period 10-Year Return Period X 2- Year Return Period EUREKA — — — ° OCT NOV DEC JAN FEB MAR APR 70 68 66 64 62 60 £ 58 I 56 O a. £ 54 o 52 50 48 46 44 42 -® rr-^& *-l-rJ - 50- Year Return Period 10 -Year Return Period _ Q — -o •2 -Year Return Period - SAN FRANCISCO FIG. 4-lc, OCT NOV DEC JAN FEB MAR APR SEASONAL ENVELOPE OF MAXIMUM OBSERVED DEW POINTS (CONT'D) 142 68 66 64 62 60 58 £ 56 (- z 54 o Q. U 52 o 50 48 46 44 42 40 74 72 70 68 66 64 iZ 62 z 60 5 Q. £ 58 UJ Q 56 54 52 50 48 46 \ Sea Surface Temperature ® 10- Year Return Period 2-Year Return Period MEDFORD I OCT NOV DEC JAN FEB MAR APR — ® RED BLUFF -Sea Surface Temperature 100 -year Return "• - - mPer i&fL. — 50-Year Return Period '10 -Year Return Period ^ " ° ▼ 2- Year Return Period ? I I I OCT NOV DEC JAN FEB MAR APR FIG. 4-ld. SEASONAL ENVELOPE OF MAXIMUM OBSERVED DEW POINTS (CONT'D) 143 CO ON I o w o On o I 00 o 2 o 00 1 r 1 , y~" J Uj o 2 / r ^ — "q / z . A. \ ( ^^x — — — — 7* — 1 / r / s / ^ J / / / s / c" r" r (O ^0 CO u. ^3/ C 1 -' / ^ 1 J o f 1 Q *% / V / s \— it to o _^ 2 co ^ is. s y-»&y / p ' 52 S J <{ * S 2 O Q to to 5: 5 / t ^■^.s _y ^ — • •^^ >• — . .>• -^ — — — 1.01 1.5 2 5 10 50 100 RETURN PERIOD (YEARS) FIG. 4-3. MAXIMUM ANNUAL OCTOBER 12-HOUR PERSISTING DEW POINT, FRESNO 110 CD I o o o * g 100 1 I- c\j < ■" ce cr w o £ UJ UJ h- V- M 3 6 t CD a. z O (- UJ CO Kg ^ UJ r> Q- 90 80 70 — 60 12 24 1 1 1 ^~ 1 LEGEND i \. - ADOPTED DURATIONAL DECAY FROM \ HIGHEST PERSISTING DEWP0INTS ^s. Rl, G3 • PERSISTING DEWP0INTS WITH N. COMPARABLE DECAY i DURING • Fl, B2 . Fl REC ENT MAJOR STORMS • A2 • Al • Al • Al • E4, Fl •— ^Fl A2, Dl AI,^C3 E4, A3*^. Bl, Dl, A2 Al B2, E4, E4 A3^ • C3 • Bl, Dl . A2 """^A2 LETTER-STATION .[A3 E4 • A3 E4 A SAN FRANCISCO LBI Bl B SACRAMENTO _C LOS ANGELES NO STORM D FRESNO I DECEMBER 1955 E SAN DIEGO 2 NOVEMBER 1950 F RED BLUFF 3 DECEMBER 193 7 G REDDING 1 1 1 J_ r JANUARY 1943 1 36 48 DURATION-HOURS 60 72 84 FIG. 4-4. COMPARISON OF OBSERVED AND ADOPTED MOISTURE DECAYS 145 FIG. 4-5a. ENVELOPING 12-HOUR PERSISTING 1000-MB DEW POINT MAPS (°F) 146 FIG. 4-5b. ENVELOPING 12-HOUR PERSISTING 1000-MB DEW POINT MAPS ( °F) (CONT'D) 147 129 116 107 OCT NOV DEC JAN FEB MAR APR FIG. 4-6. ENVELOPING PRECIPITABLE WATER IN PERCENT OF JANUARY 148 10 Point Duration P/M Station Date Rain rTd W P (in) No. (hrs) Ratio (in) (°F) 1 1 1.6 Fresno 4/8/26 1.4 51 0.878 2 1 1.1 San Franc isco 3/5/12 1.0 51 0.878 3 20 5.4 Or land 2/10-11/25 4.3* 49 0.795 4- 22 6.2 Willows 2/11-12/25 4.9 a 49 0.795 5 24 7.4 Colusa 1/2-3/16 5.6" 48 0.756 6 24 6.0 Gardena 1/25-26/56 6.5 C 55 1.076 7 24 5.8 Marysville 1/2-3/16 4.4a 48 0.756 8 24 4.7 Lodi 12/11/06 4.1^ 51 0.878 9 24 4.7 Corning 3/31/06 4.6* 53 0.972 10 24 4.6 Willows 12/29/33 3.8* 50 0.836 11 24 4.3 Davis 12/18-19/55 4.4 54 1.023 12 24 4.0 Davis 1/20-21/43 4.1 54 1.023 13 48 7.8 Colusa 1/2-3/16 5.9 48 0.756 14 48 7.6 Los Angeles 12/31/33- 1/1/34 8.2 d 55 1.076 a Maximum 24-hr amount estimated for non-recorder station by mass curves. b Some doubtful aspects to time distribution. c Reduced from total of 7.1 inches for possible orographic effect. d Total rain amount may contain orographic effect. Illllllllll llllllllllll lllllll i I llllllllllllllllll DURATION (HOURS) FIG. 4-7. MAXIMUM P/M RATIOS (WITH OROGRAPHIC STORM) 149 30 36 42 DURATION (HOURS) FIG. 4-8. MAXIMUM P/M RATIOS (CONVERGENCE -ONLY STORM) 150 APR DEC JAN FEB MAR RATIO OF 72- TO 24-HOUR PRECIPITATION APR h. CT 150 80 a. o OCT • EASTERN U S. - AVERAGE OF ZONES /, 2, 3, 4, 6, AND 7 - HMRS 33 * CALIFORNIA - AVERAGE OF HIGHEST 6 AND 24 HOUR STORMS FOR 21 CENTRAL VALLEY RECORDER STATIONS. NOV DEC - JAN FEB MAR FIG. 4-9. RATIO OF 6- TO 24 -HOUR PRECIPITATION. APR AVERAGE OF 10 HIGHEST 24- HOUR AND 10 HIGHEST 72-HOUR RAINS . BY MONTHS FOR 50 STATIONS IN THE CENTRAL VALLEY NOV FIG. 4-10, DEC JAN FEB MAR RATIO OF 72- TO 24-HOUR PRECIPITATION APR FIG. 4-11. EFFECTIVE ELEVATION AND BARRIER HEIGHTS Vh — j^c ^ v™^^^^>4JMsJ FIG. 4-12. CONVERGENCE PMP INDEX. 6-HR 200-SQ Ml JANUARY (inches) 151 i n ^ * i ^ ^ °° ~ V 3 -HOUR \ _ 1 1 1 1 1 1 1 II—- — JR PE 9 10 9 9 OBEF 6-HOL 7 8 n 10 OCT f* ^ ^ £ ^ ^ o ^ 5 Q k £ -RCEN HR. PL PERC ^HyS ^ ^ § — -"^ I ^^^^ 1 .. ..... .. 8 *> __- 1 1 1 1 1 l 1 I 1 I 1 i i I I i i i l o o o o (S3~IIIN 3dVnOS) V3UV 5 5 zg o "■ o UJ , 01 2 CO O > rH 152 1 1 1 S SM ^ \ FEBRUARY - 1 1 1 1 1 1 1 1 PERIL II 1 II 1 JARY * S - ^ £ <* CM ^ t{> <*> ^ (V k ^1- i ^ <0 <0 Q "> Q> q- **" fn k Q> k. 5 III * _____ ^ ki s ki i ' ^^^~^ S- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — Q 2 *0 O — 0- 5 u c _ Q- o O 9 uj CJ o 2 O LU 25 0) C3 O UJ M O > fr *>c5 s D ^fe Q ^ 1- Q c_> 1 ss W L ° 0. N M o CO ^1- 25 o M to CO o 2 CM p: h o < o < 00 (S3~IIIAI 3dvnOS) V3UV 1 1 1 IST\6-H0UR PERIOD 1 1 1 1 1 1 1 1 1 iC -. cc § ^ ^ CD 1 0> ^ 2 <0 "*- LlJ (v °° SM o 2 k s y 5; < Q g * 5 k S P= ki S $ ki o > CO 2 o * o U3 y ^ CO ^ o r-t | 10 s ^ 0i :E ct ^ "> o ^ ^ 0> < < Oi Q ^ Co ^ OTHE 6 7 16/3 PERIL RCEN ^>-~^^ — Mill 1 1 1 III.* 1 1 1 1 1 1 1 1 o o W N H CO M I PQ H % o l-M CD w CJ IT) z w o £! a o > CD 2 o o • o .. o ^ o ro i—i 10 uj i o or • X }f O M fo o CD o PA w CO § CM I m M (SIAJ) 3dnSS3dd 156 500 600 CD 2 700 UJ a: Z> 05 UJ £ 800 850 900 950 1000 .10 .10- .20 .30 .40 .50 .60 .70 .80 .90 1.00 1. 10 1.20 VcA 'ac FIG. 5-3. COASTAL V /V PROFILES c gc 500 600 700 UJ UJ £ 800 850 900 950 1000 EY Vc/ Vgc PROFITED .10 .20 .30 40 .50 60 .70 80 .90 1.00 1.10 VcA gc FIG. 5-4. CENTRAL VALLEY V /V PROFILES c gc 157 X o o O PQ 2 o m pq X o o o o 00 o s ss i 158 NODAL SURFACE v.. 7 8 > 6 > §—— 4 , :. ►■ 2 \ \ \ 3 ^^^^ E i 3 L^<< \ \\ FIG* 5-6. SCHEMATIC AIR STREAMLINES IN OROGRAPHIC STORM UJ tr => (/) if) q: CD O I OUTFLOW SOUNDING ALONG UPPER STREAMLINE AREA -A INFLOW SOUNDING ALONG LOWER STREAMLINE TEMPERATURE FIG. 5-7. SCHEMATIC PLOT OF TEMPERATURES AND PRESSURES IN OROGRAPHIC STORM ON THERMODYNAMIC DIAGRAM 159 100 90 70 ^ 60 > h- 50 < UJ 01 40 30 20 25 %.I25 ■ .25 ^A (FULL EVAPORATION) A./25 a 125 ■ 125 x.25 — *T Tji* 7V\ .25.x. 125 — C (ADOPTED CURVE) • /25 / s i> X \ „- ^> ^C___ xr .S l I \ \ 7v> \ ' \ / / / / PR EC IP/ TA TION (IN. /HR. ) AT — —■■>«* / \ * RED BLUFF ? *. y i i o CHICO £ (NO EVAPORATION) / + SACRAMENTO \ •" ^~' ■ MERCED * BAKERSFIELD \ \ /- / • rarr \j— 1 1 i \ i 2 5 o X 4§ UJ 6 E tr 7 < 8 m RED BLUFF CHICO SACRAMENTO MERCED BAKERSFIELD TAFT FIG. 5-8. CENTRAL VALLEY DEGREE -OF -SATURATION FOR PMP CONDITIONS 60 o 52 44 -<■— .22 > 1 < .03 > 1 < ,54 > 1 < .07 > 1 ■< .01 >\< .12 > 1 < .35 > | < T -»- BAKERSFIELD / 6-HR. RAINFALL (INCHES) A (FULL EVAPORATION) / — ^^^^^ y^ 1 / / / f \ C (OBSERVED BAKERSFIELD) X'- x XX - / \D (OBSERVED TAFTF^ SI \ / \^\ i i /*-B (NO EVAPORATION) / ^ / XX , 1 1 1 1 1 38 00302 06302 FEB I, 1945 1230 2 18302 0030 2 0630 2 1230 E FEB 2, 1945 TIME 18302 00302 FEB 3, 1945 FIG. 5-9. SAN JOAQUIN VALLEY DEW-POINT VARIATIONS FIG. 5-10. CENTRAL VALLEY SURFACE-RELATIVE-HUMIDITY FOR PMP CONDITIONS 161 I Moumo A li > \ A /An V- ^ 1 ' — ; '. ii : ; - ; / 1 1/ \|!\ \ \ $7 \i feM \ ^ — % _ i ■ v / 1 \ J Ay Kl f ! i i h *§/ i 1 Ujl ;~ 1 1 \ i i $L k - r t 1 2T ^1 i 51 i I *°1 1 cc J ^ M01JNI i i a i i . J i i \ I ' o o to o o o o LO o o CD O O <0 o o CO o o (J) CO UJ CD LO -r ro OJ < o O CO M H >- 3 I— n i o ^ en 3 X • 1-1 O r-4 Ll_ 1 O LU O LL M CO &u «- _ ^ o o o (qiai) 3dnss3dd 162 FIG. 5-12. STORM CALIBRATION AREAS 163 o o o o O CM o 00 tO / „ $ ^ f i \ \ \ r% \ _____ to $ 3:5 — — ^ to 5> S 3: fie • ^ ; ^ O ^ * i ^ 1 \ — ' <0 1 V |l %\- < w- * cr (Z \ ^ C/) i 1 1 a M s tX« 2 O H-l UJ o 5 cu o h- w ro CO o Q • vO r-l 1 O C\J • o CO CVI (S3H0NI) O cn uj en Cj* Q-z UJ :> — CM Q oor _J UJ 3 > Q _ or a. a. ui to w> w .2 ^r 5 a 1 n o 5 O i- "■owe c a> o o O or 0- co < 00 CO u I 8- S o < O £ 10 rr CM Q oco co.ro CD — co- co j_J I L I I I 1 I I L_l I M (Md|M) Q33dS 167 Q33dS QNIM 0IHdOaiSO3D 33VdUDS/8lM OOS OI1VU 168 o O o o o o o o o O o O o o o o lO o m o rO ^r IT) to r^- CD CO cr> CD o (aw) 3dnss3dd 169 (HdlAI) Q336S o o o o o o o o O o 0> 00 l^- CD LO CO N CD to <3- rO CVJ (SdlAI) Q33dS 171 300 B 600 UJ co CO w 700 r~\ i i i 50- YEAR OAKLAND (FROM FIG. 5-20)^ 50 -YEAR SANTA MARIA (FROM FIG. 5-2/1 GEOS TROPHIC A LLY- DERI VED MAXIMUM WIND (FROM FIG. 5-19) 130 150 170 WIND SPEED (MPH) J L 250 210 230 FIG. 5-22 COMPARISON OF STATISTICAL WITH GEOSTRGPHICALLY -DERIVED MAXIMUM WINDS, COASTAL 300 400 500 — 600 cc 3 CO CO £ 700 Q. 800 850 900 950 1000 1 1 1 1 1 1 1 1 1 1 1 1 [LONG BEACHy^]^ | 1 1 JX ^/n// J S^y/Z / — OAKLAND tT > — / X B — OAKLAND • — — S SEATTLE J / SANTA MARIA / / / OAKLAND / / / — 1 ^•SEATTJ^y^^^ — * K^^^TI 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 40 60 80 100 120 140 160 SPEED (MPH) 180 200 220 240 260 FIG. 5-23. ADOPTED MAXIMUM 1-HOUR WINDS AND SUPPORTING DATA, COASTAL (A) COMPOSITE, (B) GEOS TROPHICALLY -DERIVED, (C) ADOPTED, (D) 50 -YEAR, OAKLAND 172 too WINDY PERIODS 6 12 18 FIG. 5-24. VARIATION OF 900-MB WINDSPEED, OAKLAND 100 95 90 85 80 LJ co 75 cr ° 70 S 65 I- LU 60 55 50 45 40 3 5 \ SOLID CURVES USED IN REPORT — "% — OBSERVED INCREMENTAL DECAY OF - %> WINDS ALOFT AT OAKLAND . I i - \\N\ ^\ - \X - ^v GE05TR0PHIC WIND DECAY \^ (AT 30 MILES) (FROM FIG 5-26) — ^ ^ ""' — T 500 MB ^^ 700 MB **^^ 900 MB \^^ INCREMENTAL DECAY OF SURFACE WIND ^^ ' — SEA LEVEL AT OAKLAND (AVERAGE OF 6 STORMS) ^ "-^ II III 1 "TS 1 6 12 18 24 30 36 42 48 54 60 66 72 78 82 DURATION (HOURS) FIG. 5-25. ADOPTED VARIATION OF WINDSPEED WITH DURATION 173 36 a/ (aiAi) 3dnss3dd 174 o6a/o o o m o CJ ro o o 3dnSS3dd 175 90 — \ 1 1 1 1 1 1 1 1 1 r t 80 ^^ — 70 — i 60 a. 2 — PRESENT ESTIMATE — q 50 UJ LU Q. 40 — HYDROMETEOROLOGICAL REPORT NO. 3 — 30 — (SACRAMENTO RIVER BASIN) — 20 — 10 — III! _J 1 1 1 1 i i 6 12 18 24 30 36 42 48 54 60 DURATION (HOURS) 5-28. MAXIMUM 4000-FOOT WINDSPEED COMPARISON, COASTAL 66 72 176 LOW 1 1 • • 1.60 • - ~ 1.40 l- _ • • • • • • • • • • • • z • y 1.20 . o • • U- • • u. I • uj 1.00 • • O • •• • • o • • uj .80 • • • • - Q • O • 5 .60 •• • • • • • • • - .40 • • - .20 00 "(a I ) I i ' • • • i • i i i I 2 3 4 5 6 7 8 RANK (of Computed Precipitation) iO 2.00 1.80 1.60 :5i.4o ^1.20 o UJ 1.00 o u uj 80 a o 2 60 .40 .20 .00 — I 1 i • I 1 I 1 • • • • • • • • • • • • • • — • t • • • • - — • t • • • • • • • • • • • • — >^^^ — (b) 1 1 1 • 1 1 * 1 1 ' 1 " 4 5 AVERAGE OF RANKS 8 FIG. 5-29 MODEL -COEFFICIENT -VARIATION TESTS (a) X VS. RANK OF COMPUTED PRECIPITATION, (b) X VS. RANK OF AVERAGE OF COMPUTED AND OBSERVED PRECIPITATION I Si- ft. ,^3 176 1.80 2 3 4 5 6 7 8 RANK (of Computed Precipitotion) d.VV 1.80 i • • i i T 1.60 • 3 1.40 i- • • • • • • • • - z » — ""'^ • a i.2o - o • • U_ • • U_ t • uj 1.00 — • • - o o • - • • • u 80 t • • - Q O • • • ^ ~~ • • .60 • • • • • • ^~"""'-- .40 — • • ^^" .20 nn (b) 1 1 1 1 1 * 1 1 • • 1 4 5 AVERAGE OF RANKS 8 FIG. 5-29, MODEL -COEFFICIENT -VARIATION TESTS (a) X VS. RANK OF COMPUTED PRECIPITATION, (b) X VS. RANK OF AVERAGE OF COMPUTED AND OBSERVED PRECIPITATION FIG. 5-30. OROGRAPHIC PMP COMPUTATION AREAS 177 — 23/ /24 — — /Z2/ *H 1 1 1 ' 1 1 1 — 20 30 40 50 60 70 10 20 30 40 50 60 70 80 — S" 6 / — — 15 S — — — - 'T ' 17 — ^rf-i— -t 1 1 l 1 1 " 10 20 30 40 50 60 70 10 20 30 40 50 60 70 80 DISTANCE (MILES) — — — — — / y , 9 '8 1 1 1 " ~6n 1 1 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 FIG. 5-31. ADOPTED GROUND PROFILES (PMP AREAS NUMBERED, SEE FIG. 5-30) 1.00 cc o § .90 UJ Q < 80 70 1 1 1^ ^L. 1 — vS2*> V 1 1 1 1 1 44 42 40 3.8 36 LATITUDE-DEGREES 34 32 FIG. 5-32. LATITUDINAL VARIATION OF MAXIMUM WINDS 178 o o o o o o o o o o o o o CO CO LLI tt LU I CO -LU- GO < LU -J * ,fi XI FIG. 5-35. OROGRAPHIC PMP INDEX. 6-HR JANUARY (inches) FIG. 5-35 REV. OROGRAPHIC PMP INDEX. 6-HR JANUARY (inches 179 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Nth 12th 6-HOUR PERIOD FIG. 5-36. VARIATION OF OROGRAPHIC PMP WITH DURATION 1.00 UJ h- Z> "3 Q < FIG. 5-37. JAN. FEB. MID-MONTH SEASONAL VARIATION OF MAXIMUM WINDS 180 O 8- O < Id 1.00 SIERRA .90 COASTAL ERRA COASTAL CO Q < 80 OCT. NOV. FEB DEC. JAN. MID-MONTH FIG. 5-38. SEASONAL VARIATION OF OROGRAPHIC PHP MAR. APR. 20 40 60 80 100 120 BASIN WIDTH (MILES) 140 160 180 200 FIG. 5-39. BASIN-WIDTH VARIATION 181 20 40 0.60 080 100 120 140 160 180 2 00 2 20 2 40 2.60 2.80 SPILLOVER PRECIPITATION (INCHES PER HOUR) 1 1 1 1 1 1 1 1- 1 2000 1 1 1 FOOT BARRIER 20 " 10 9 — \\\ — 8 — 7 — 6 — 5 - 4 - 3 \j> — 2 1 \° \rr\ 1 Yi \° \° X Vs. \ \r \ 1 1 \ 1 l\l 1 1 1 — 20 040 060 0.80 100 120 140 160 180 200 2.20 2 40 2 60 2 80 SPILLOVER PRECIPITATION (INCHES PER HOUR) 0.20 40 60 80 100 120 140 1.60 180 2.00 2.20 2 40 2 60 2 80 SPILLOVER PRECIPITATION (INCHES PER HOUR) 00 20 040 060 080 100 120 140 1.60 180 2.00 2 20 2 40 2.60 2.1 SPILLOVER PRECIPITATION (INCHES PER HOUR) FIG. 6-1. OROGRAPHIC PLATEAU SPILLOVER 182 WW 1 1 1 1 1 1 1 1 6000 1 -FOOT 1 1 BARRIER 20 35 '0 j 9 Z 8 4! 7 o IT 6 5 g 5 u. o 4 2 < 10 Q 3 — \-*- \o 2 \° V*- — \w \a \° V** w yj> \tn 1 1 1 l\ 1 \ 1 1 1 1 l\ 1 1 020 040 060 080 100 120 140 160 180 2.00 2.20 2 40 2 60 2 80 SPILLOVER PRECIPITATION (INCHES PER HOUR) 0.20 040 0.60 080 1.00 1.20 1.40 1.60 180 2.00 2 20 2 40 2 60 2 80 SPILLOVER PRECIPITATION (INCHES PER HOUR) i i i I I i r 7000- FOOT BARRIER I 1 I I \ I LJU I I I LXJ L 20 040 060 80 100 120 140 160 180 2.00 2.20 240 2 60 2 80 SPILLOVER PRECIPITATION (INCHES PER HOUR) FIG. 6-2. OROGRAPHIC PLATEAU SPILLOVER (CONT'D) 183 .30 .35 .40 .45 .50 .55 .60 .65 EVAPORATION (INCHES PER HOUR) FIG. 6-3. LEEWARD EVAPORATION CO LU I i 3 o < E2 g ' MEAN OF 2 6- HOUR PERIODS ENDING- 1800 AND 2400 PST DECEMBER 21, 1955 \. OBSERVED OROGRAPHIC ^ , .^OBSERVED OROGRAPHIC ^PLUS CONVERGENCE COMPUTED OROGRAPHIC (NO EVAPORATION) X COMPUTED OROGRAPHIC ('/^ASSUMPTION) 10 15 20 25 30 DISTANCE FROM RIDGE (MILES) 35 40 45 FIG. 6-4. SPILLOVER COMPARISON - COASTAL (See figure 5-15) 184 MEAN OF 2 6 -HOUR PERIODS ENDING' 1800 AND 2400 PST DECEMBER 21, 1955 COMPUTED OROGRAPHIC (NO EVAPORATION) 28 30 32 12 14 16 18 20 22 24 DISTANCE FROM RIDGE (MILES) FIG* 6-5. SPILLOVER COMPARISON - SIERRA (See figure 5-15) 34 36 100 • COMPUTED (MODE) x STATISTICAL 24-HOUR PMP ° MAX OBSERVED 24- HOUR POINT PRECIPITATION ♦ OROGRAPHIC INDEX BASED ON 10 -YEAR MAP f OROGRAPHIC INDEX MODIFIED BY COMPUTED SPILLOVER 10 12 14 16 18 20 DISTANCE FROM RIDGE (MILES) 22 24 26 28 30 FIG. 6-6. SPILLOVER COMPARISON — PMP AND MAXIMUM OBSERVED PRECIPITATION 185 (Hdlfl) Q33dS ON/M M01JNI o o to (8W) BUflSSBUd 186 SEQUENCES OF OBSERVED 6-HOUR PRECIPITATION FEATHER RIVER u r ^mr? , % DEC 21-23, 1955 % '/mm 24 6 12 18 24 6 12 18 24 6 12 18 24 21st 22nd 23rd NOV 16-18, 1950 A 24 6 12 18 24 6 12 18 24 6 12 18 24 16th 17th 18th DEC 9-12, 1937 xrrm m WM//MA TMAzZZLkzzm 6 12 18 24 6 12 18 24 6 12 18 24 6 9th 10th llth 12th I DEC. 30, 1913 - JAN 2, 1914 / kMi//L^jM// / . -w mm MAR. 16-19, 1907 '/////"UJ/ mmm 6 12 18 24 6 12 24 6 12 18 24 6 18th 19 TIME (HOUR-PST) SEQUENCES OF OBSERVED 6-HOUR PRECIPITATION SOUTHERN SIERRAS DEC 9-12, 1937 STORM ■MAXIMUM STATION RAINFALL-TOTAL 173" (CENTRAL CAMP) ^■AVERAGE RAINFALL OVER 1670 SO Ml. - TOTAL 13.7" 1 I I I J L 12 18 24 6 12 18 24 6 12 II th TIME (HOUR-PST) JAN. 20-24, 1943 STORM 1 I I i ■*— MAXIMUM STATION RAINFALL -TOTAL 19.3" (CENTRAL CAMP) . — AVERAGE RAINFALL OVER 1670 SO Ml. -TOTAL 14. 0" J I I I I L J I L 24 6 12 19th 20th 24 6 12 21st 18 24 6 12 18 24 6 12 23 rd 24 6 12 24th TIME (HOUR-PST) SEQUENCES OF OBSERVED 6-HOUR PRECIPITATION BLUE CANYON TOTAL 13.2" I MAXIMUM 48-HOUR - I n STORM DEC. 2- 8, 1950 i MAXIMUM 72-HOUR i i i i i i Ln l n e£i 5 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 ~ 2nd 3rd 4th 5th 6th 7th 8th o TIME (HOUR-PST) CALAVERAS TOTAL 10.9" MAX, 36-HOUR, STORM DEC 2-8, 1950 MAXIMUM 72- HOUR j i i i h i i i i i i i i l l U l 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 6 12 18 24 6 12 IB 24 6 12 18 24 2nd 3rd 4th 5fh 6th 7th 8th TIME (HOUR-PST) SEQUENCES OF OBSERVED 24-HOUR PRECIPITATION LOS GATOS TOTAL 43.2" 72 HOURS IMAXIMUM 72 HRS 72 HOURS 1 r " T 1 „ DEC. 16-27, 1955 STORM 10 9 55 8 I z 7 z 2 6 9: 5 o a. a. 4 3 2 1 m rr 1 i i i i i i _L I M 1 15 16 17 18 19 20 21 22 23 24 25 26 27 28 TIME (DAYS) FIGo 7-2. SEQUENCES OF OBSERVED PRECIPITATION 187 o^ § o k r- Og 03 «3 CD CD M- J — CO CO Q O <° 2 . o * r- M- 1 1- K •^ u_ O* u. T> si Nt- 00 ° * co z z ^5 o> § L IT o n- W CO or o u. ro CO c^> co uj ~ 2 CM 00 QJ s 1 § r- »o 1- C\l CN) 03 \> ig 03 Ci ^ N> >T» CO \- co «o n> Q ^ 1 1 *. 1 1 1 1 * 1 1,1. w i ». v _, ^ oo co o ao co ^j- cj o $ ( Nl) NOIlVlldlOSdd ( Nl) N0llVlldl03dd 1 ■>. -N. ^> £ £ Cj o k ^ 0^ CNJ CM N> CNJ > N 03 l<- S 03 03 Qi M- CO SI- CO K3 (0 CO CO M- CD <\J CO 03 ON \* o n> o •o o CD 5 or CO 5 03 CO s \> * 2 "O *• o •o S fc P '- if) H co Ql CO H co § oo o u. 00 o Qi u. CO o * 1 * o <\j ^1- CO <\j * CO ci z <\j z o CNJ 2 ICJ si K CO <0 CO vo CO *< UJ Krj UJ *i UJ *c> CO ^ IQ s o •o CD *> ro 5 o •r> OD CO Oi 0> Oi 10 2 o si a: <\i or N or 0 or 03 03 CNJ I In z Qi z 03 z i^ T> Nt 00 , , 00 UJ 00 UJ ^ 1 — UJ N> - s 1- "O [^ 1— to N> .CM CVJ CM > o. Q § oS OS > N> CO m — CD CO N> M- N> 1 1 °i 1 III 03 1 1 1 1 °3 1 1 1 >, 1 1 1 1 *, 1 t 1 1 >. 1 00 D «fr c\J o O 00 CD ^t CNJ O O 00 CD ^ CNJ O (Nl) NO \1\ ti id 103 dd (Nl) N 011V lie dl' D3Ud (Nl) N 311V lie ia 3 dc CO O 2 w I LO I H Ex- FIG. 8-1. TEST AREAS FOR COMPARISON OF STORM VALUES WITH PMP FIG. 8-2. COMPARISON OF PMP FROM HYDROMETEOROLOGICAL REPORT NO. 33 WITH STATISTICAL PMP FOR 24 HOURS AND 10 SQUARE MILES 189 FIG. 8-3. STATISTICAL PMP FOR 24 HOURS AT A POINT, CALIFORNIA 190 1 • ' • \ ' 1 . ' 1 ' • • \ • • • • • • • \ \ • • • • • X. * — • • • • • • \.l • CO * ** * * k • • • • 1 • • • • • • • • k og Cvj cy, \ — S • • • * \ 5 -J • • • • ? • if • • * ***** \* • • • • > • ^ ^ • • T" ^ X«M 1 k • • • x* £ • • • • • • ^ -J "J *Vi *vi ^ • • V • • • X C\| Cvj "i X 5- 5 s. ct 5 \ \ £ ^ X k 3 1 1 1 1 1 1 1 \ o lO O m O CM 7 — R / y" 9 ..,/ f^m™ ^i "«>0 ^.O N»fr- <> k ,K O, N JN. £ k.^ o.co ^£ s s 2 ° • O ^.(^ 00.00 >n 15 " — 'j cr • co S*^ S»o! °«£ 2«" °°«2 s»2 :=•<> 2't2 ?->2 2>- -V- • ^ S-S o-»-o 5:2:.^ o # - C0 # O 2»°ti^i" OO, CN co,o~ ,00 o^.co jo.cm |-. „ Ki = | 2( .2'"*0. 2 ».« wijn V o § o_ a 2 ■ a. 8.1 « E S - o ^ a. a. a> o -o S" O i \ ,cn <2.™ 2:«5 £.° ^;*^C*i'^ — fs-'g.&dS.s s-s/*ifc | • 1 1 1 O0 X z z X Q CO co CO CM Pd o I CO M US H 1 I O M H CO M CO O § CO I 00 e> M 191 1 1 / y ( x S x V J g. g. ^ s./ c ■Si §$ £e »•/ ' Is ^ "* • J >X S / 2 / "* 1 i ] / / ygf * §- • oo» n» X X oo» co» ■O -O /• --> X x I * °-> ui» -» !^# ^i ^, -h (>._ k. pxl o*} -** CO* Uj oof ' y * *>* <•" -. l/ "^ «. *• *• £• £x X X o 5 2x Xqx, X X ^x ^^ K» -">• u">» > >0»- -S iO» "» "» ■<», ^ ■<» O Tj^ x M r^ /V£/ y^ ■* >o i y z *«•* — ** of Jo?' ^ ™ 7 | °jf S, 5. sy ^ _ j — . - I ~ o a —i E 2 s — O * £ O "" < X n S" -• > s-\^-& ">' ' £?■ — —pit- ™» «-> 1 1 • 1 i CO < CO CO ad O o rs, 'cd ,oo - c oo O oo o oo.' rs^oo ^ rv? o'.oo CO PL. CO Pn o O CO 1 i 00 C3 M 192 t ' ( lyo ^2*io n # vo^ R o ^3 / •o g«5 S^^S o : o o •o ^ rs»S o # o oo»£ ♦S S ^sS £•£ o a -v o ' m 2 §-o 5#S a S. _ _ O' 00 00 <0 ~ f> S"5-««k— S»2— ft«5-S^S— &8 S»2 ?.°S> ^ LiJ 5 8 C — iv cs o *<'& - S3 S.g 5-S 5.^45 5 ( k «•« s*s <>5 » 1— J . fc oo £!«o to oo o' o is ?«"> (NO O'o O* 00 (N v oo ^ O v^ ro'ls "» »/ (N * |0O o Or (O DEPTH IN TENTHS OF INCH Grid Model m PMP X SPS FROM LOCAL ST0 i s o* CO o o CM S2 O S3 I 00 ! ~ T" •° ^ co t: cv| .' — .^_ co # <*> £ -0 CO co»co J>^r J ' • oo. -I 00.00 I in. ^ /- — £. ^ X / te LiO -O ° co." p •rN -o*2 -o J2 # 1 IN. / lO ---"I-" — / •O O -O.fN n N *•" S>= O ' OiS -*■" o- O to n o» c^V. ft n«co) Sg / CN,00 CQ % ^ vS oV T* / i "T~ / / fCN»CO O*^ / J — 5 o»S £•£ j.S "•* 5»Js / — ^ S C _ CN ^ CN ~ ^ \- -^i / S.S fe.5 g.5 |»*s -.£ co.S i ^4 fc CO S 3 2*5 5-2 ^^n S-2 s.o ^.S SiglK^T s to -J * ^ oo « • c^> (\ -T / :S 2-S^-^S^.S.S St 2 S-3 5 .5 2.S ^C-.-- co _ co Tf o N. ^ _--\r»*fr y' IT w co co.cn cn-k =.^.^5-^.3 £*.<$ 0.0/Sosfc; | g 2«S 5.S rj.^ fejfe s.& §.£// V r v q 2 ! 1 — i 1 1 | u 5 ^lo. g X "= 8 J 5 L94 \ 2»0^ ^_ (N*^ • £•2; rvitv_ p- Jo f~ 00 ■« ^S-" r- 1 •■*3-«** B -v / IS (* ££> a-3 s-s 1 { bj i / i " " A/ ceo / ^J — CN — n / ^ _, ^„ •^ CO CN*-0 0- eV 2>S ^ft co'cS -«* — ~h ' -v ^S? fr ^ S"S 5>2 §«n S^ 3^o S>°: S»« o>2 ^»Z £»£ Sf ^,3*2 S>= 2«§ c >f~ / £ 0= / L — / — «o ^> l/o "0 2*i2 £■ 5*2^ 2*°-/^^o <-> «•> K co / E 5^ 1 ^•0 5»g 0^^ | S f f M CO «1 » "-'"(n'Ou^'S "1 -.§"') s- )• 8> §"5- S« °* 2 2^ 8«/ ~ (? • ^ 1 3 / .CO- 00. ^. ' \ Q . "^ /s. > l ^~. 3« s> £• \. • a / X. 5- 8- »3- 8- 8- ■> oj — 32=^« S— ^yS^^^ °- I 1 ■q ^ *: a r> I a* a CM 3 S3 CO I o g O M H 197 3 oS § i CO % as § i I o I 00 198 (S3H0NI) H±d3Q 55 ^ <* q [ 1 ^ \ 1 I \ 1 1 \ 1 *NV 1 1 1 1 1 1 -r^ CNJ T* * z to 2 ro (- ^ Q CM (S3H0NI) H±d3Q 1 1 1 1 ^ \ ^ \ \ k! kj ct \ \ ^ CO \ \ 18 ^ ki \\\ : 1 1 i i i T^P^* (S3H0NI) H±d3Q (S3H0NI) Hld3Q ^ \ { I : fc: \ \ CO Q ki \ \ : M \ \ <*> ki ^ 0: \ \ - S^ \\ - 1? \\\ - ^= i i i i i i S>^ _ CO o CD CD O ro ji n 3 CVJ CD H o Pn 00 § oi W 5! Pl. CO M PQ CJ W W H H O • 3 PQ W CO CO (S3H0NI) Hld3Q (S3H0NI) H±d3Q o M si I CM l 00 O M f»4 O H CO H W >-> S 04 199 H 8 i w M X H PC! H oo o z w 5! Cm 3 en la • CO - -o CO CM — _ 'inO;,-, — • ! 2 |S m» o CO »o ■o I XT O c-> -^ "O V""> < CN o -o 1 cn rv v n s-4— o- ""* s.'* J0VN, A /» 5 • CN CN o CN V _ -*CN CN y oo»-o ^.rv« # ^o^__/ ^ t -/' ^\ COf -Sj-O* "— 'CKjf t^ ^ \ / ' ' <=. - „,__, Co y ~J 1 fc ,. ; .. ^ i / /; _ «.„ -. § «• «?• > /•■?# cN.' r ,-^.3 i>, v« * / « » cm • o. ^v* <"^ • co# co« , ^ r^. -<» « "~ " V s ^, ■Oi. t?« >o. -•— i><^ ► ^?o. ~. §.; cm. §co«- *>• u-,. -j^- O f u- X a. U lO + „ * » ^ # "?• <£?• CM*^lC_i*rM 2 ? °- "*"' .52 o. 2 lO 00 - c — O z> co a £ Z O 2 t x co = 7 O) m CO 2 S- -5 d lOu •"»• co» io. \ ~< r- 7 - £W >yM i g< || | | 5 *< «?• «• <«• 5? «o -^ -— — / % o> /»*o g:.S «-o $*s o»k S«S 2»!o ^'S^ 5'« \- «^l / 5+K 2«2 2-5 |2. » *< S^ 2»|^Vf: 1 "dQ iS ^ _i O-' CO # -0 Q,*^ o.*^ -J(M»- -«»(V o-*00 oo ■£ £ 3: i Bf3 S^3 g.3 S.S Sis ^ 5.g/ ^ z i '"" CM „. ^~~~^ ^^ 55 z -0 1 Mi- -cm. - cm. 00 ^.tv «1k/ £ S si cr 2 Pi CO O CO S3 S SS vO I CO o Pbi 201 2.6 I | 1 | 1 | 1 | 1 | 1 | 1 I 1 / 24 / — 2.2 - Saturated Psuedo-Adiabatic Atmosphere / Sao o c — 1.8 / — 0) I -.6 / 0) |l.4 Q. O a> 1.2 0. - yS — 1.0 - 0.8 — 0.6 n a. 1 1 > I i 1 i 1 i 1 i 1 i 1 1 1 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 1000 mb Dewpoint Temperature (°F) FIG. 10-1. VARIATION OF PRECIPITABLE WATER WITH 1000-MB DEW POINT TEMPERATURE i 1 1 r—. — r Pseudoadiabatic Atmosphere FIG. 10-2. DECREASE OF TEMPERATURE WITH ELEVATION 202 CM CD GO (^ CD ID ^J" (jasj jo spuosnom) m6jaH ro c\J 1 ! ' 1 1 AO \ \ 1 in a> o c E o W CO -Q Sis 0) > — 0) a> O) _ rved i r peri ssocia I CO o o O) fc E X c f obse w cove urve a — E o n o o o c CD co ■£ i ■ — u. o a. £ —> 1 o\ n \ CL o ao o ic a o > _ ? c ,■ «_ c i3 a> 1 LU ex Q. LU "O Q < QQ 6* I I 1 1 1 1 1 I ! 1 1 1 \ | loOlOOlO toOiOO OJCVJ-— o __0J + 4- + + + I I I I (j ) uncus o\ jou<_ sAoa ^ oj dn puo ujjojs jo &uiuui6ag jo ajnjDjiadLuai uaaMjeg aouajajjiQ CD CO 00 E _. o (?> a. _c 'c c en a> QQ a> _> o *♦— oo o •H U a* m CO o M CM o CD CM i v^uocoocomcocNO CMCMCMC>J»-^coOr^cMCMCNf-«r-ir-4 cx\r^3""^coco OOOvOsfOvOHOO^O cooooooooocor^rsrv. ooooooooo ooooooooo o •H 0) CM o •l-i M cu CM cMcn»-stcN vOcr\moovoeMONCN»-< NOQOmNcMnrOH cMvomr-icM^r-ir^oo mOOvO-»sO uo-Nf Oo>oor>»v£>rs OOOOOOOOO ooooooooo