C 5S.2B15Z NOAA HYDROMETEOROLOGICAL REPORT NO. 52 Application of Probable Maximum Precipitation Estimates - United States East of the 105th Meridian U.S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION U.S. DEPARTMENT OF THE ARMY CORPS OF ENGINEERS WASHINGTON, D.C. August 1982 *No. 1. *No. 2. *No. 3. *No. 4. *No. 5. *No. 6. *No. 7. *No. 8. HYDROMETEOROLOGICAL REPORTS 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. (Unpublished.) Supplement, 1938. A hydrometeorological analysis of possible maximum precipitation over St. Francis River Basin above Wappapello, Mo. 1938. *No. 9. A report on the possible occurrence of maximum precipitation over White River Basin above Mud Moun- tain Dam site, Wash. 1939. Maximum possible rainfall over the Arkansas River Basin above Caddoa, Colo. 1939. Supplement, 1939. A preliminary report on the maximum possible precipitation over the Dorena, Cottage Grove, and Fern Ridge Basins in the Willamette Basin, Oreg. 1939. Maximum possible precipitation over the Red River Basin above Denison, Tex. 1939. A report on the maximum possible precipitation over Cherry Creek Basin in Colorado. 1940. The frequency of flood-producing rainfall over the Pajaro River Basin in California. 1940. A report on depth-frequency relations of thunderstorm rainfall on the Sevier Basin, Utah. 1941. A preliminary report on the maximum possible precipitation over the Potomac and Rappahannock River Basins. 1943. Maximum possible precipitation over the Pecos Basin of New Mexico. 1944. (Unpublished.) Tentative estimates of maximum possible flood-producing meteorological conditions in the Columbia River Basin. 1945. Preliminary report on depth-duration-frequency characteristics of precipitation over the Muskingum Basin for 1- to 9-week periods. 1945. An estimate of maximum possible flood-producing meteorological conditions in the Missouri River Basin above Garrison Dam site. 1945. A hydrometeorological study of the Los Angeles area. 1939. Preliminary report on maximum possible precipatlon, Los Angeles area, California. 1944. Revised report on maximum possible precipitation, Los Angeles area, California. 1945. 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. Maximum possible precipitation over the San Joaquin Basin, California. 1947. Representative 12-hour dewpoints in major United States storms east of the Continental Divide. 1947. Representative 12-hour dewpoints in major United States storms east of the Continental Divide. 2d edition. 1949. Analysis of winds over Lake Okeechobee during tropical storm of August 26-27, 1949. 1951. Estimate of maximum possible precipitation, Rio Grande Basin, Fort Quitman to Zapata. 1951. Generalized estimate of maximum possible precipitation over New England and New York. 1952. Seasonal variation of the standard project storm for areas of 200 and 1,000 square miles east of 105th meridian. 1953. Meteorology of floods at St. Louis. 1953. (Unpublished.) Analysis and synthesis of hurricane wind patterns over Lake Okeechobee, Florida. 1954. 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. Meteorology of flood-producing storms in the Mississippi River Basin. 1956. Meteorology of hypothetical flood sequences in the Mississippi River Basin. 1959. Interim report — probable maximum precipitation in California. 1961. Also available is a supplement, dated October 1969. Meteorology of hydrologically critical storms in California. 1962. Meteorology of flood-producing storms in the Ohio River Basin. 1961. Probable maximum precipitation in the Hawaiian Islands. 1963. Probable maximum precipitation, Susquehanna River drainage above Harrisburg, Pa. 1965. Probable maximum and TVA precipitation over the Tennessee River Basin above Chattanooga. 1965. Meteorological conditions for the probable maximum flood on the Yukon River above Rampart, Alaska. 1966. Probable maximum precipitation, Northwest States. 1966. Probable maximum precipitation over South Platte River, Colorado, and Minnesota River, Minnesota. 1969. *No. 10. *No. 11. *No. 12. *No. 13. *No. 14. *No. 15. *No. 16. *No. 17. *No. 18. *No. 19. *No. 20. *No. 21. *No. 21A *No. 21B *No. 22. *No. 24. *No. 25. *No. 25A *No. 26. *No. 27. *No. 28. *No. 29. *No. 30. *No. 31. *No. 32. No. 34 No. 35 *No. 36 No. 37 No. 38 No. 39 No. 40 No. 41 No. 42 No. 43 No. 44 *Out of print. (Continued on inside back cover) U.S. DEPARTMENT OF COMMERCE U.S. DEPARTMENT OF THE ARMY NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION CORPS OF ENGINEERS NOAA HYDROMETEOROLOGICAL REPORT NO. 52 Application of Probable Maximum Precipitation Estimates United States East of the 105th Meridian Prepared by E.M. Hansen, L.C. Schreiner & J.F. Miller Hydrometeorological Branch Office of Hydrology National Weather Service WASHINGTON, D.C. August 1982 0i o o £• o TABLE OF CONTENTS Page ABSTRACT 1 1. Introduction 1 1.1 Ba ckground 1 1.2 Objective 1 1.3 Definitions 2 1.4 Summary of procedures and methods of this report 3 1.5 Application to PMP 5 1.6 Some other aspects of temporal and spatial distri- buti on s 5 1.6.1 Moving rainfall centers 5 1.6.2 Distributions from an actual storm 6 1.7 Other meteorological considerations 7 1.7.1 PMP for smaller areas within the total drainage 7 1.7.2 Bains for extended periods 7 1 * 8 Report prepa ra ti on * 7 2. Temporal distribution 7 2.1 Introduction 7 2.2 Observed sequences of 6-hr increments in major storms.... 10 2.3 Recommended sequences for PMP increments 15 3. Isohyetal pattern 15 3 . 1 Introducti on 15 3.2 Isohyetal shape 16 3.3 Summary of analysis 20 3.4 Recommended isohyetal pattern for PMP 20 3.5 Application of isohyetal pattern 23 3.5.1 Drainage-centered patterns 23 3.5.2 Adjustment to PMP for drainage shape 23 3.5.3 Pattern applicable to PMP 24 4. Isohyetal orientation 25 4.1 Introduction 25 4.2 Data 25 4.2.1 Average orientations 25 4.2.2 Orientation notation 27 4.3 Method of analysis 27 4.4 Analysis 27 4.4.1 Regional variation 27 4.4.2 Generalized isohyetal orientations 29 4.4.3 Variation of PMP with pattern orientation applied to drainage 30 4.4.3.1 Range of full PMP 30 4.4.3.2 Reduction to PMP for orientation outside of range.... 32 4.4.3.3 Variation due to area size 33 4.4.4 Noncoincidental rainfall pattern 36 4.4.5 Comparison to other studies 36 iii Page 4.5 Meteorological evaluation of isohyetal orientations 37 4.6 Application to HMR No. 51 42 5 . Isohyet va lues 42 5.1 Introduction 42 5.2 Within/without-storm D.A.D. relations 43 5.2.1 MP increments for which isohyet values are required 43 5.2.2 Isohyet values for the greatest 6-hr PMP increment 44 5.2.2.1 Depth-area relations 44 5.2.2.2 Isohyetal profile 45 5.2.2.3 Nomogram for isohyet values 49 5.2.3 Isohyet values for the second greatest 6-hr PMP increment 50 5.2.4 Isohyet values for the third greatest 6-hr PMP increment 50 5.2.5 Residual-area precipitation 56 5.2.6 Tables of nomogram values 56 5.3 Area of pattern applied to drainage 71 5.4 Multiple rainfall centers 71 5.4.1 Development of a multicentered isohyetal pattern 71 5.4.2 Arrangement of centers 73 6. Short duration precipitation 73 6 .1 Introduction 73 6.2 Data 73 6.3 1-hr PMP 76 6.3.1 Depth-duration ratios 76 6.3.2 1-hr 1-mi 2 PMP 77 6.3.3 Depth-area ratios 79 6.3.4 1-hr PMP for areas to 20,000 mi 2 85 6.4 PMP for durations less than 1 hr 85 6.5 Isohyet values for durations less than 1 hr 97 6.5.1 Description of procedure 97 6.5.2 Application of nomogram for short duration isohyet s.... 98 6.5.3 Isohyet values for short duration residual isohyets.... 100 7. Procedure and example application 100 7.1 Stepwise procedure 100 7.2 Example No. la 108 7.3 Example No. lb 126 7.4 Example No. 2a 133 7.5 Example No. 2b 152 Acknowledgements 153 References 157 Appendix 159 iv LIST OF FIGURES Number Page 1 Schematic diagram showing the relation between depth-area curve for PMP and the within/without-storm relations for PMP at 1,000 mi 2 4 2 Examples of temporal sequences of 6-hr precipitation in ma jor storms 12 3 Schematic example of one temporal sequence allowed for 6-hr increments of PMP 16 4 Homogeneous topographic/climatologic subregions used in study of regional variation of isohyetal patterns 18 5 Standard isohyetal pattern recommended for spatial distribu- tion of PMP east of the 105th meridian (scale 1:1,000,000) 21 6 Schematic example of problem in averaging isohyetal orienta- tions 26 7 Location and orientation of precipitation pattern for 53 major storms listed in HMR No. 51 28 8 Analysis of isohyetal orientations for selected major storms adopted as recommended orientation for PMP within ± 40° 31 9 Distribution of isohyetal orientations for 50 major storms (from sample listed in the appendix) that occurred in the gulf coast subregion 34 10 Model for determining the adjustment factor to apply to isohyet values as a result of placing the pattern in figure 5 at an orientation differing from that given in figure 8 by more than 40°, for a specific location 35 11 Track of hurricane Agnes (6/19-22/72) showing frontal posi- tions and orientation of the greatest 20,000-mi precipi- tation area centered at Zerbe, PA 40 2 12 Frontal positions and orientation of the greatest 20,000-mi precipitation area centered at Golconda , IL (10/3-6/10) 41 13 6-hr within/without-storm average curves for standard area sizes 46 14 Within/without-storm curves for PMP at 37°N, 89°W for standard area sizes 47 15 Isohyetal profiles for standard area sizes at 37°N, 89°W 48 Rage 16 Nomogram for the 1st 6-hr PMP increment and for standard isohyet area sizes between 10 and 40,000 mi 51 17 12-hr within/without-storm curves for standard area sizes 53 18 Nomogram for the 2nd 6-hr IMP increment and for standard isohyet area sizes between 10 and 40,000 mi 54 28 Nomogram for the 3rd 6-hr PMP increment and for si isohyet area sizes between 10 and 40,000 mi . ... 19 Nomogram for the 3rd 6-hr PMP increment and for standard 55 20 Nomogram for the 4th through 12th 6-hr PMP increments and for standard isohyet area sizes between 10 and 40,000 mi 57 21 Schematic showing difference in isohyetal patterns for 3 greatest 6-hr PMP increments and that for fourth through 12th 6-hr increments for a 1,000-mi storm 58 22 Schematic showing an example of multiple centered isohyetal pattern 72 23 1- to 6-hr ratio of precipitation based on major storms used in HMR No. 51 and rainfall frequency studies 78 24 1-hr 1-mi 2 PMP analysis based on figure 23 and 6-hr 10-mi 2 precipitation from HMR No. 51 79 25 Maximized observed 1-hr point amounts and moisture maximized values from major storms listed in table 21 82 26 Example of transposition limits as applied to the Smethport, PA. storm (7/17-18/42) 83 2 27 Depth-area data plotted as percent of maximum 1-hr 1-mi amount for storms where the maximum 1-hr 1-mi amount was determined from a dense network of observations or bucket survey amounts 84 Depth-area relation for 1-hr PMP in percent of maximum point (1-mi ) amount 86 29 1-hr 10-mi 2 PMP analysis for the eastern United States 87 30 1-hr 100-mi 2 PMP analysis for the eastern United States 88 31 1-hr 200-mi 2 PMP analysis for the eastern United States 89 32 1-hr 1,000-mi 2 PMP analysis for the eastern United States 90 33 1-hr 5,000-mi 2 PMP analysis for the eastern United States 91 34 1-hr 10,000-mi 2 PMP analysis for the eastern United States 92 vi Rage 35 1-hr 20,000-mi 2 PMP analysis for the eastern United States 93 36 Ratio analysis of 5- to 60-nri.n precipitation used to obtain 5-min PMP 94 37 Ratio analysis of 15- to 60-nri.n precipitation used to obtain 15-min PMP 95 38 Ratio analysis of 30- to 60-min precipitation used to obtain 30-min PMP 96 39 Index map for 1- to 6-hr ratios for 20,000-mi 2 "A" isohyet 98 40 Regionally^ vera ged nomogram for 1-hr isohyet values in percent of 1st 6-hr isohyet values 99 41 Example of computation sheet showing typical format 104 2 42 Leon River, TX (3,660 mi ) above Belton Reservoir showing drainage 109 43 Depth-area -duration curves for 31°45'N, 98°15'W applicable to the Leon River, TX drainage Ill 44 Depth-duration curves for selected area sizes at 31 45 f N, 98 15 f W 112 45 Smoothing curves for 6-hr incremental values at selected area sizes for Leon River, TX drainage 113 46 Isohyetal pattern placed on the Leon River, TX drainage to give maximum precipitation volume 115 47 Volume vs. area curve for 1st three 6-hr increments for Leon River, TX drainage 121 48 Smoothed durational curves used to interpolate short-duration isohyet values for the Leon River, TX drainage 127 49 Alternate placement of isohyetal pattern on Leon River, TX drainage such that no adjustment is applicable for orientation 128 2 50 Ouachita River, AR (1,600 ml ) above Rennel Dam showing drainage 134 51 Depth-area -duration curves for 34°36'N, 93°27'W applicable to the Ouachita River, AR drainage 135 52 Depth-duration curves for selected area sizes at 34°36'N, 93°27'W 136 vii Page 53 Smoothing curves for 6-hr incremental values at selected area sizes for Ouachita River, AR drainage 138 54 Isohyetal pattern placed on the Ouachita River, AR drainage to give maximum precipitation volume 139 55 Volume vs. area curve for 1st three 6-hr increments for Ouachita River, AR drainage 145 56 Isohyetal pattern placed on the Ouachita River, AR drainage rela tive to subdrainages 150 57 Alternate placement of isohyetal pattern on Ouachita River, AR drainage typical of determination of peak discharge 153 A.l Regional distribution of 253 major storms listed in table A.l showing orientation of total-storm precipitation patterns 168 LIST OF TABLES 1 Major storms from HMR No. 51 used in this study 8 2 Major storms from table 1 used in study of temporal distributions 11 3 Summary of rain burst characteristics of 28 major rainfalls listed in table 2 14 4 Shape ratios of isohyetal patterns for 53 major rain events 17 5 Shape ratios for six subregions 17 2 6 Shape ratios of 20,000-mi isohyetal patterns for six subregions 19 7 Shape ratios of major isohyetal patterns relative to area size of total storm 19 8 Axial distances (mi) for construction of an elliptical isohyetal pattern for standard isohyet areas with a 2.5 shape ratio 22 9 Averages of isohyetal orientations for major storms within selected subregions of the eastern United States 28 10 Average of isohyetal orientation for the large sample of storms within selected subregions in the eastern United States 29 11 Major storm orientations relative to generalized analysis including summary information 32 viii Page 12 Frequency of various difference categories between observed and preferred orientations 33 13 Meteorological factors pertinent to isohyetal orientation for major storms used to develop regional analysis (fig. 8) 38 14 Major storms from table 1 used in depth-area study 44 15 1st 6-hr nomogram values at selected area sizes 59 16 2nd 6-hr nomogram values at selected area sizes 62 17 3rd 6-hr nomogram values at selected area sizes 65 18 4th to 12th 6-hr nomogram values at selected area sizes 68 19 Storms used in analysis of 1-hr storm-area averaged FMP values 74 o 20 Storms used to define 1- to 10-mi area ratios for 6 and 12 hours 75 o 21 Extreme 1-hr amounts used as support for 1-hr l-mL PMP map 80 22 Completed computation sheets for the 1st, 2nd and 3rd 6-hr increments for Leon River, TX drainage 117 23 Completed computation sheet for the 1st to 3rd 6-hr increments for supplemental isohyets on the Leon River, TX drainage 120 24 Isohyet values (in.), Leon River, TX, for example la 122 25 Completed computation sheets showing typical format to get incremental drainages vera ge depths, Leon River, TX 123 26 Completed computation sheets for 1st three 6-hr increments for alternate placement of pattern on Leon River, TX drainage 129 27 Completed computation sheets for 1st three 6-hr increments for Ouachita River, AR drainage 140 28 Isohyet values (in.), Ouachita River, AR, for example 2a 147 29 Completed computation sheets showing typical format to get incremental drainage-average depths, Ouachita River, AR 148 ix Page 30 Completed computation sheet for determining average depths for 1st three 6-hr increments over subdrainage between Blakely Mt. Dam and Washita, AR 151 31 Completed computation sheets for 1st three 6-hr increments for alternate placement of pattern on Ouachita River, AR drainage 154 A.l 253 major storms 160 A. 2 Distribution of 253 major storms by duration and area size classes 167 A. 3 Shape ratios of 253 major storm isohyetal patterns relative to area size classes 167 APPLICATION OF PROBABLE MAXIMUM PRECIPITATION ESTIMATES - UNITED STATES EAST OF THE 105TH MERIDIAN E. M. Hansen, L. C. Schreiner* and J. F. Miller Water Management Information Division National Weather Service, NOAA, Silver Spring, Md. ABSTRACT — This study provides a stepwise approach to the temporal and spatial distribution of probable maximum precipitation (PMP) estimates derived from Hydrometeorological Report No. 51, "Probable Maximum Precipitation Estimates - United States East of the 105th Meridian." Included are discussions of the shape and orientation of isohyetal patterns for major rainfalls of record. An elliptical isohyetal pattern with a ratio of major to minor axes of 2.5 to 1 is recommended, and a procedure is outlined for obtaining appropriate isohyet values. A procedure is given to determine PMP values for durations less than 6 hours. Example applications have been worked through to serve as guidance in the use of this procedure. 1. INTRODUCTION 1.1 Background Generalized estimates of all-season probable maximum precipitation (PMP) applicable to drainages of the United States east of the 105th meridian are provided in Hydrometeorological Report No. 51 (Schreiner and Rledel 1978). Hereinafter, that report will be referred to as HMR No. 51, and references to other reports In this series will be similarly abbreviated. The terminology in HMR No. 51 has not always been precise, particularly where PMP estimates are referred to as being for drainages from 10 to 20,000 mi . It is important to realize that the term drainages as used in that report is a rather loose interpretation when the more precise term is areas. The term drainage or drainage area in the present report will apply to a specific drainage only. HMR No. 51 provides storm-area PMP estimates for a specific range of area sizes (10 to 20,000 ml 2 ) and durations (6 to 72 hr) . 1.2 Objective The objective of this report is to aid the user in adapting or applying PMP estimates from HMR No. 51 to a specific drainage. This report recommends a procedure for the application of PMP estimates to a drainage for which both the temporal and spatial distributions are needed. This information is necessary for the determination of peak discharge and can be useful in estimating the maximum volume in evaluations of the probable maximum flood (PMF) . ♦Current affiliation Bureau of Reclamation, Denver, Colorado. 1.3 Definitions Probable Maximum Precipitation (PMP) . Theoretically the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of the year. (This definition is a 1982 revision to that used previously (American Meteorological Society 1959) and results from mutual agreement among the National Weather Service, the U.S. Army Corps of Engineers, and the Bureau of Reclamation.) PMP Storm Pattern. The isohyetal pattern that encloses the PMP area plus the isohyets of residual precipitation outside the PMP portion of the pattern. Storm-centered area-averaged PMP . The values obtained from HMR No. 51 corresponding to the area of the PMP portion of the PMP storm pattern. In this report all references to PMP estimates or to incremental PMP infer storm-area averaged PMP. Drainage-averaged PMP. After the PMP storm pattern has been distributed across a specific drainage and the computational procedure of this report applied, we obtain drainage-averaged PMP estimates. These values include that portion of the PMP storm pattern that occur over the drainage, both PMP and residual. Temporal Distrlbntlon . The order in which 6-hr incremental amounts are arranged Tn a 3 -day sequence (72 hr) . This report includes information regarding determination of hourly and smaller units within the maximum 6-hr increment, but does not discuss the distribution of units less than 6-hr. Spatial Distribution . The value of fixed isohyets in the idealized pattern storm for each 6-hr increment and shorter durations within the maximum 6-hr increment of PMP when area-averaged PMP is to be distributed. Total Storm Area and Total Storm Distribution . The largest area size and longest duration for which depth-area-duration data are available in the records of major storm rainfall. Standard Areas . The specific area sizes for which PMP estimates are available from the generalized maps in HMR No. 51, i.e., 10-, 200-, 1,000-, 5,000-, 10,000-, and 20,000-mi 2 areas. Standard Isohyet Area Sizes. In this report, the standard isohyet area sizes are are those enclosed by the isohyets of the recommended pattern, i.e., 10, 25, 50, 100, 175, 300, 450, 700, 1,000, 1,500, 2,150, 3,000, 4,500, 6,500, 10,000, 15,000, 25,000, 40,000, and 60,000 mi 2 . Residual Precipitation. The precipitation that occurs outside the area of the PMP pattern placed on the drainage, regardless of the area size of the drainage. Because of the irregular shape of the drainage, or because of the choice of a PMP pattern smaller in area than the area of the drainage, the residual precipitation can fall within the drainage. A particular advantage in the consideration of residual precipitation, is that of allowing for the determination of concurrent precipitation, i.e., the precipitation falling on an adjacent drainage as compared to that for which the PMP pattern has been applied. Isotayetal Orientation . The orientation (direction from north) of the major axis through the elliptical pattern of PMP. The term is used in this study also to define the orientation of precipitation patterns of major storms when approximated by elliptical patterns of best fit. Within/Without-Storm Depth-Area Relations . This relation evolves from the concept that the depth-area relation for area -averaged PMP represents an envelopment of maximized rainfall from various storms each effective for a different area size(s). The within-storm depth-area relation represents the areal variation of precipitation within a storm that gives PMP for a particular area size. This can also be stated as the storm that results in PMP for one area size may not give PMP for any other area size. Except for the area size that gives PMP, the within-storm depth-area relation will give depths less than PMP for smaller area sizes. This concept is illustrated in the schematic diagram shown in figure 1. In this figure, precipitation for areas in the PMP storm outside the area size of the PMP pattern describes a without-storm depth-area relation. The precipitation described by the without-storm relations is the residual precipitation defined elsewhere in this report. 1.4 Summary of Procedures and Methods of this Report All procedures described in this study are based on information derived from major storms of record, and are applicable to nonorographic regions of the eastern United States. The temporal distributions provided allow some flexibility in determining the hydrologically most critical sequence of incremental PMP. The procedure used to determine" the temporal distributions has been used in some other Hydrometeorological Branch reports (RLedel 1973, and Schwa rz 1973 for example), and is described in chapter 2. We have surveyed major storm isohyetal patterns for statistics on pattern shape, and have adopted an elliptical shape having a 2.5 to 1 ratio of major to minor axes as representative of a precipitation pattern. This elliptical shape has been adopted for PMP and is applied to all 6-hr incremental patterns. The discussion of the shape of the isohyetal patterns is found in chapter 3. Another aspect of this study is a generalized approach to adjustments for pattern orientation to fit the drainage when inconsistent with the orientation determined for the PMP isohyetal pattern. Outlined in chapter 4 is an empirical method that allows up to 15 percent reduction to storm-centered area-averaged PMP for drainage areas larger than 3,000 mi which differ by more than 40 degrees from the orientation consistent with PMP-producing storms. In determining spatial distribution a basic assumption is that rainfall depths for areas smaller and larger than the total area for which PMP is needed over a particular drainage, are less than PMP. (See within/without-storm depth-area definitions.) This assumption, for areas smaller than the PMP, has been commonly made in some other studies by this branch (Riedel 1973, Riedel, et al. 1969, and others), and results in what has been referred to in those reports as within- storm or wi thin-drainage depth-area -duration (D.A.D) relations. Application of a similar assumption to areas larger than that for the PMP is a consideration unique to the present study and introduces the concept of residual precipitation. \ PMP DEPTH-AREA RELATION WITHOUT-STORM RELATION FOR AREAS OUTSIDE THE PATTERN STORM 1000 i < AREA SIZE FOR WHICH PMP PATTERN STORM IS CONSIDERED WITHIN- STORM RELATION FOR AREAS WITHIN THE PATTERN STORM DEPTH (inJ Figure 1. — Schematic diagram shoving the relation between depth-area curve for IMP and the withln/vithout-storm relations for PMP at 1,000 mi*. (See sec. 1.3 definitions.) Discussion of the procedure to obtain the spatial distribution of RIP and the residual precipitation is given in chapter 5. For many drainages, it is frequently necessary to have values for durations less than 6 hours. Procedures for obtaining the percentage of the greatest 6-hr increment that occurs in the maximum 5, 15, 30 and 60 min are provided in chapter 6. We do not in this report attempt to define the temporal distribution within the greatest 6-hr increment except to suggest that the 5-, 15- and 30-min values should be included within the maximum 60 min. It is anticipated that the time of occurrence of the maximum 60 min within the 6-hr increment will be the subject of a future study. 1.5 Application to RIP For those interested in the application of PMP from HMR No. 51 (nonorographic region only) to a specific drainage, chapter 7 is most important. This chapter provides a step-by-step approach to guide the user through the application of procedures developed in this report. Examples have been worked out in sufficient detail to clarify important aspects of these procedures. The examples in chapter 7 give the user a procedure to obtain the maximum volume of rainfall for a drainage. Finding the maximum volume of rainfall is only part of the hydrologic problem. Another important question is the probable maximum peak flow that could occur at the proposed hydrologic structure. The solution is somewhat more difficult to directly ascertain than finding the maximum volume. The calculation of peak flow is highly dependent on a mixture of basin parameters such as lag time, time of concentration, travel time, and loss rate functions in combination with the amount, distribution and placement of the PMP storm within the drainage. Because of the interaction of these parameters, we cannot provide a simple stepwise procedure to determine peak flow. The user must weigh carefully the effect of the various parameters, drawing on his experience and knowledge of the drainage under study, and determine, through a series of trials, what combination of hydrologic parameters will produce the maximum peak flow. 1.6 Some Other Aspects of Temporal and Spatial Distributions Although we present a procedure that leads to temporal and spatial distribution of PMP, we recognize that some considerations have not been discussed in this study. When storm data become sufficiently plentiful, and when our knowledge of storm dynamics permits, these considerations may lead to improvements in the current procedures. Meanwhile only brief comments follow regarding two such considerations for future study. 1.6.1 Moving rainfall centers Our procedure assumes that isohyetal patterns for all 6-hr PMP increments remain fixed with time, i.e., all are centered at the same location. For large drainages (greater than 10,000 mi , for example), it is meteorologically reasonable for the rainfall center to travel across the drainage with time during the storm. It is conceivable that such movement could result in a higher flood peak if the direction and speed of movement coincides with downstream progression of the flood crest. It was decided jointly by the Corps of Engineers and the Hydrometeorological Branch that the present report would not cover application of moving centers. Generalization of moving centers would require analysis of observational data such as incremental storm isohyetal patterns that are presently not available. It is anticipated that a future study will cover moving centers. 1.6.2 Distributions from an actual storm Use of elliptical patterns for spatial distribution permits simplicity in generalized depth-area relations and in determining isohyet values. It also helps maintain consistency in results among drainages, area sizes, and durations. Such consistency is also maintained by the recommended temporal distributions. An alternate but unrecommended procedure is to adopt the distributions of a record storm precipitation that occurred on the drainage or within a homogeneous region including the drainage. The isohyetal pattern from an actual storm might "fit" a drainage better than an elliptical pattern, and multiplying the isohyets by percent of PMP (say for 6 hours for the drainage, divided by the drainage depth from the storm pattern after it is located on the drainage) will give isohyet values for PMP. Such isohyets, however, quite possibly could give greater than PMP depths for smaller areas within the drainage. The temporal distribution of such a storm could also be used for PMP. Again, however, there could very likely be problems. The most intense three 6-hr rain increments in a 72-hr storm may be widely separated in a time sequence of incremental rainfall (mass curve). Thus, 12- or 18-hr PMP could not be obtained unless rain bursts somehow were brought together. However, such arrangement is often done as a maximization step and PMP depths from HMR No. 51 used. These modifications would be towards the generalized criteria of the present study in which there are no results that are inconsistent or irreconcilable. Paulhus and Gilman (1953) published a technique for using an actual pattern for distributing PMP. The referenced paper describes a "sliding" technique for obtaining the spatial distribution of PMP that has its greatest merit in applications in the more orographic regions (stippled zones in HMR No. 51) covered by this study, such as the Appalachians and along the western border to the region, where site-specific studies are recommended. However, we advise caution in application of this technique directly as Paulhus and Gilman have proposed, in that it is possible to obtain PMP for a much smaller area size than that for the drainage to which it is applied. Since this disagrees with our within-storm concept, we therefore suggest adherence to the following modifications to the technique presented by Paulhus and Gilman, if it is used: a. Use a set of depth-area relations (from HMR No. 51) which, when "slid over" the depth-area relations for the storm, will give PMP for an area size within 10 percent of the area of the drainage of concern. b. It is desirable that PMP (from HMR No. 51) be obtained for at least the hydrologically critical duration. c. For other durations between 6 and 72 hours, stay within 15 percent of PMP as specified in HMR No. 51. For additional information regarding application of this technique, the reader is referred to the Paulhus and Gilman paper. 1.7 Other Meteorological Considerations Other aspects of extreme rainfall criteria can be important to determinations of peak flow. Some of these aspects are described here. 1.7.1 PMP for smaller areas within the total drainage. Our previous studies have concentrated on defining PMP for the total drainage area. In fact, in the present study we recommend spatial distributions resulting in somewhat less than PMP for smaller as well as larger areas than the PMP pattern. The question can naturally be asked, does PMP for a smaller area size than the storm area size that is applicable to the entire drainage, which when centered over a portion of the drainage (experiencing more intense rainfall than that for the entire drainage), result in a more critical peak flow? There is a possibility that PMP covering only a subportion of the drainage could provide a hydrologically more critical peak discharge, and the hydrologist should consider such a possibility. The depth of rainfall to use over the remaining portion of the drainage would need to be specified. (See discussion on residual precipitation in sections 3.5.3 and 5.2.5.) 1.7.2 Rains for extended periods Especially for large drainages, rainfalls for durations longer than 3 days could be important in defining critical volumes for hydrologic design. As examples, the Hydrometeorological Branch, working with Corps of Engineers hydrologists, has evaluated the meteorology of hypothetical sequences of record storms transposed in space and recommended how close together such storms can follow each other (Myers 1959, and Schwarz 1961). Similar studies may be needed for other • large drainage projects. Sufficiently severe assumptions, however, relative to how full reservoirs are prior to the PMF and the antecedent soil conditions, could obviate the need for such studies. 1.8 Report Preparation Preparation of this report began in 1977 as follow on studies to HMR No. 51. Initial discussions with the Corps of Engineers outlined the scope of the project. As Indicated in a previous section, certain problems were left to be considered in later studies. The basic studies were undertaken when all the authors were affiliated with the National Weather Service (NWS). These studies were completed after one of the authors, L. Schreiner, transferred to the Bureau of Reclamation (USBR). Several of the concepts and procedures included in this report evolved after Mr. Schreiner f s transfer, as a collaborative effort of the three authors and other meteorologists affiliated with both the NWS and the USBR. 2. TEMPORAL DISTRIBUTION 2.1 Introduction When applying PMP to determine the flood hydrograph, it is necessary to specify how the rain falls with time, that Is, in what order various rain increments are arranged with time from the beginning of the storm. Such a rainfall sequence in an actual storm is given by what is called a mass curve of rainfall, or the accumulated rainfall plotted against time from the storm beginning. 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We leave the determination of criticality to the hydrologist , but recognize that the mass curve or temporal distribution selected for IMP is important. PMP estimates can be obtained in HMR No. 51 for 6-, 12-, 24-, 48- and 72-hr durations. A plot of these depths against duration joined by a smooth curve defines PMP for all durations between 6 and 72 hours. In many applications, definition of PMP by 6-hr time increments is sufficient. Thus, PMP values for 6, 12, 18, 24, ..., 72 hr can be read from such a smooth curve. Successive subtraction of the PMP for each of these durations from that of the duration 6-hr longer gives 6-hr increments of PMP. We have shown in HMR No. 51 that, in general, allowing PMP for all durations (6 to 72 hr) to occur in a single storm is not an undue maximization. 2.2 Observed Sequences of 6-hr Increments in Major Storms We considered the sequences of 6-hr rain increments of the more important storms east of the 105th meridian as guidance for recommending sequences for PMP. These storms, 53 of which are given in the appendix of HMR No. 51, are listed in table 1 and represent a primary data base for this study. Table 1 includes information on storm location, duration, areal extent, and the orientation of the isohyetal pattern (refer to chapter 4). To obtain information on the chronological sequence of 6-hr increments of precipitation, we referred to storm data summarized for most major storms listed in table 1 (not available for the 2 storms of 9/16-17/1932, and those of 6/19- 20/1939, 6/23-24/1948, 10/14-15/1954, and 8/3-4/1957). For the 47 remaining storms, these data are contained in what we refer to as Part 2 storm study files in which point data are grouped to obtain chronological sequences of areally averaged depths. A search was made through these storms for cases in which depths were given for both 100- and 10,000-mL approximate areas for the storm center with maximum precipitation. The storms were further limited to those for which 6-hr incremental depths occurred over a period of more than 48 hr, to assure us that we were considering representative 3-day storms. Table 2 lists the 28 storms that met these conditions, and separates them by storm type — tropical and nontropical. The remaining 19 storms had rainfall durations or areas that failed to meet our threshold. It should be pointed out that the limitations for 48-hr sequences from the Part 2 data do not necessarily agree with the listing of total-storm duration given in table 1. For example, the Greeley, Nebraska (6/4-7/1896) storm in table 1 is considered to have a total storm duration of 78 hr (U.S. Army Corps of Engineers 1945- ). This same storm for the 100- and lOjOOO-mi^ approximate areas in the maximum storm rainfall center provides sequences of depths only up to about 24 hr (~100 mi ) and 36-hr (~10,000 mi 2 ). A rainfall was considered tropical if it occurred within 200 miles of a storm track, contained in Neumann, et al. (1978), and if the rain occurred within 2 days prior to passage of the storm. Other storm rainfalls were also designated tropical if they occurred within 500 miles beyond and within 2 days after the last reported position of a tropical cyclone track in Neumann. In such cases, the assumption made was that moisture from the tropical cyclone continued to move 10 Table 2. — Major storms from table 1 used In study of temporal distributions Storm assignment Location Date number TROPICAL 9/10-13/1878 OR 9-19 Jefferson, OH Hearne, TX 6/27-7/1/1899 GM 3-4 Paterson, NJ 10/7-11/1903 GL 4-9 Altapass, NC 7/15-17/1916 SA 2-9 Big Meadows, VA 10/11-17/1942 SA 1-2 8A Yankee town, FL 9/3-7/1950 SA 5-8 Vic Pierce, TX 6/23-28/1954 SW 3-22 Westfield, MA 8/17-20/1955 NA 2-2 2A Sombreretillo, Mex. 9/19-24/1967 SW 3-24 Zerbe, PA 6/19-23/1972 NA 2-2 4A NONTROPICAL 7/18-22/1897 UMV 1-2 Lambert, MN Jewell, MD 7/26-29/1897 NA 1-7B Eutaw, AL 4/15-18/1900 LMV 2-5 Medford, WI 6/3-8/1905 GL 2-12 Warrick, MT 6/6-8/1906 MR 5-13 Meeker, OK 10/19-24/1908 SW 1-11 Merryville, LA 3/24-28/1914 LMV 3-19 Springbrook, MT 6/17-21/1921 MR 4-21 Tbrall, TX 9/8-10/1921 GM 4-12 Savageton, WY 9/27-10/1/1923 MR 4-23 Elba, AL 3/11-16/1929 LMV 2-20 Simmesport, LA 5/16-20/1935 LMV 4-21 Hector, NY 7/6-10/1935 NA 1-27 Hayward, WI 8/28-31/1941 UMV 1-22 Warner, OK 5/6-12/1943 SW 2-20 Stanton, NE 6/10-13/1944 MR 6-15 Collinsville, IL 8/12-16/1946 MR 7-2B Council Grove, KS 7/9-13/1951 MR 10-2 beyond tbe dissipated circulation system and possibly combined with frontal or orographic mechanisms to produce the observed extreme rain. Such probably was the case with the Big Meadows, Virginia (10/11-17/1942) rain listed in table 2. A further check was made of daily weather maps to determine if any of these rains may have been associated with tropical disturbances of less intensity than covered in Neumann, et al. The Hearne, Texas (6/27-7/1/1899) rain, as an important example, is believed to have resulted from extreme moisture associated with one of these weaker systems located off the Texas Gulf Coast, and which moved rapidly inland. More discussion on meteorological factors in extreme rainfalls is given in chapter 4. While the sample of storms in table 2 is too small to set quantitative differences, we wish to see if qualitative differences appear. Figure 2, as an example, shows sequences of 6-hr increments for 5 of the storms in table 2. (Two of the five are tropical.) In this figure, the 100-mi results are shown as solid lines and the 10,000-mi results as dashed lines. Incremental amounts are expressed as a percentage of the 72-hr rainfall. 11 5 Or ru -F MR 5-13 6/6-8/06 * 50 r CO »- Z o < 1 2 3 4 5 6 7 8 9 10 11 12 UMV 1-22 8/28-31/41 o' f=i 1 — f= i — — h — T 5 50 r < =1 1 1 23 4 5 6 7 8 9 10 11 12 MR 10-2 7/9-13/51 3= ^_ CN l*v Z UJ U UJ 50 1 2 3 4 5 6 7 8 9 10 11 12 SW 3-24 9/19-24/67 (TROPICAL) .TTZbzzz T" I I 4 £ =1 h 50 12 3 4 5 6 7 8 9 10 11 12 NA 2-24 A 6/18-25/72 (TROPICAL) f=f=T 1 2 I I I J==T. H h 1— - r , 4 5 6 7 8 9 101112 6-hr INTERVALS 100- Ml 2 RAINFALL AMOUNTS (SEE TEXT) 10,000-MI^ RAINFALL AMOUNTS Figure 2. — Examples of temporal sequences of 6-hr precipitation In major storms. 12 We defined a rain burst as one or more consecutive 6-hr rain Increment(s) for which each individual increment has 10 percent or more of the 72-hr rainfall. A second set of results was obtained by redefining a rain burst as 20 percent or more of the 72-hr rainfall. Examination of the incremental rainfall sequences for each of the 28 storms in table 2 allowed us to compile some constructive information. We tallied the number of bursts in each sequence, the duration of each burst, and the time interval between bursts. Table 3 summarizes this information by area size and storm type for the 28 storms in table 2. (Values in parentheses represent data based on a burst defined as >_ 20 percent of the 72-hr rainfall.) Part (a) summarizes the number of rain bursts in the 72-hr period of maximum rainfall; part (b) the duration (in hours) of the rain bursts; and part (c) the number of hours between bursts. The first example in figure 2 for the storm of June 6-8, 1906, is used to illustrate these three temporal characteristics. There are two bursts observed for the 100-mi area and 3 bursts for the 10,000-mi area. These counts went into part (a) of table 3. For 100 mi 2 , the first rain burst is 12 hr long and the second is 6 hr long. These are separated by 6 hr. The first burst for 10,000 mi is 6 hr long separated by 12 hr from the second burst of 12 hr, which is separated by 6 hr from the last burst of 6 hr. These values are included in parts (b) and (c) of table 3. Some conclusions drawn from the summaries in table 3 are the following: 1. In part (a), fewer rain bursts are observed when the 20 percent threshold is applied than with the 10 percent threshold. 2. For the 10 percent threshold, a larger fraction of tropical storms (8/10 at 100 mi 2 and 6/10 at 10,000 mi 2 ) tends to have single bursts in a 72-hr period than do nontropical storms (6/18 at 100 mi 2 and 6/18 at 10,000 mi ). This is indicative of the greater occurrence of short-duration thunderstorms which cause multiple bursts in nontropical storms. However, when a rain burst is defined as 20 percent or greater of the 72-hr total rainfall, the tendency is to lessen the difference between storm types (6/10 vs. 14/18 at 100 mi 2 and 6/10 vs. 13/18 at 10,000 mi 2 ). 3. Rain burst lengths between 6 and 24 hr dominate for both area sizes and storm types (part (b)). There appears to be a significant difference between storm type and the length of rain bursts, based on this limited sample. Nontropical storms show notably shorter-duration bursts (89 percent are 12 hr or less) than do tropical storms (77 percent are 12 hr or less). 4. The number of hours between rain bursts in tropical storms typically is about 6 to 12 hr, while nontropical storms showed intervals between 6 and 30 hr (part (c)). 13 Table 3. — Summary of rain burst cbaracteristics of 28 major rainfalls listed in table 2 Part ( a); Number of bursts ( ) Number of rain bursts in a 1 2 72-hr period 3 Total Area (mi 2 ) T NT T NT T NT T NT T NT 100 10,000 0(2) 0(4) 0(0) 0(1) Number of Storms 8(6) 6(14) 0(2) 7(4) 6(6) 6(13) 3(0) 7(4) 2(0) 1(0) 5(0) 5(0) 10 18 10 18 Part (b); Duration of bursts 12 Duration of rain bursts (hr) 18 24 30 36 Total Area (mi 2 ) NT NT NT NT NT NT NT 100 10,000 Number of bursts 3(7) 19(14) 3(3) 12(8) 3(0) 4(0) 3(0) 0(0) 2(0) 0(0) 0(0) 0(0) 3(2) 14(14) 5(3) 13(7) 0(0) 7(0) 4(1) 0(0) 2(0) 0(0) 1(0) 1(0) 14(10) 35(22) 15(6) 35(21) Part (c); Duration of intervals Number of hours between rain bursts (length of intervals) 6 12 18 24 30 36 Total Area (mi 2 ) NT NT NT T NT NT T NT NT 100 10,000 Number of intervals 2(2) 6(0) 2(0) 5(0) 0(0) 3(3) 0(0) 1(0) 0(0) 2(1) 0(0) 0(0) 4(0) 5(1) 1(0) 7(0) 0(0) 4(2) 0(0) 0(0) 0(0) 1(1) 0(0) 0(0) 4(2) 17(4) 5(0) 17(4) T - tropical, NT - nontropical ( ) - Values in parentheses are for results when definition for rain burst is increased from > 10% to > 20% of the 72-hr total rain (see text) . 14 2.3 Recommended Sequences for PMP Increments While the 28-storm sample shows some evidence for rain burst sequences to differ depending on the storm type, table 3 suggests the difference may be in part due to the choice of threshold value. Furthermore, differentiation by storm type would necessitate delineating regions of control on PMP. This is not recommended since anomalies in major rains related to storm type occur. An example of this is one of the most extreme rain events for large areas along the gulf coast, the Elba, Alabama storm of 3/11-16/1929. This was a nontropical storm. Another reason for not distinguishing time sequences for PMP by storm type is that the PMP in coastal regions may be produced by a complex weather situation that is a mixture of both tropical and nontropical influences. Therefore, one standard set of temporal sequences, independent of storm type, is recommended for the PMP increments determined as described in section 2.1. The limited sample of storms in table 2 was further examined for guidance on how to arrange the increments of PMP. Almost any arrangement could be found in these data. The Warner, Oklahoma, (9/6-12/1943) storm showed the six greatest 6- hr increments to be consecutive in the middle of the 72-hr rain sequence, while the Council Grove, Kansas (7/9-13/1951) storm showed daily bursts of 12 hr with lesser rains between. To get PMP for all durations within a 72-hr storm requires that the 6-hr increments be arranged with a single peak (fig. 3). We chose a 24-hr period as including most rain bursts in major storms, and set this as the length of rain bursts for the PMP, giving three 24-hr periods in a 72-hr period. Based on results from examination of the 28-storra sample, guidance follows for arranging 6-hr increments of PMP within a 72-hr period. To obtain PMP for all durations: A. Arrange the individual 6-hr increments such that they decrease progressively to either side of the greatest 6-hr increment. This implies that the lowest 6-hr increment will be at either the beginning or the end of the sequence. B. Place the four greatest 6-hr increments at any position in the sequence except within the first 24-hr period of the storm sequence. Our study of major storms (exeeding 48-hr durations) shows maximum rainfall rarely occurs at the beginning of the sequence. 3. ISOHYETAL PATTERN 3.1 Introduction There are two important considerations relative to the isohyetal pattern used for PMP rainfalls. The first is the shape of the pattern and how it is to be represented. The second is the number and magnitude of isohyets within the pattern. This chapter deals with the selection of the pattern shape and the number of isohyets considered to represent the shape. The magnitude of the individual isohyets will be determined from the procedure described in chapter 5, Isohyet Values. In addition to establishing the shape of the isohyetal pattern for 15 i 1 r 9 7 | 6 5 3 2 4 1 1 1 1 1 1 8 1 12 f \ 1 ! 1 1 1 < — 1 st 24-hr — > PERIOD 72 hr > Figure 3. — Schematic example of one temporal sequence allowed for 6-hr increments of RIP. See text for restrictions placed on allowed sequences. distributing area -averaged IMP over a drainage for the three greatest increments, it should be emphasized that this shape applies as well to the remaining 6-hr increments of PMP for distribution of residual precipitation and other adjustments. 3.2 Isohyetal Shape To understand more about the shape of isohyetal patterns, we considered those for the 53 major rainfalls listed in table 1. It was apparent from this sample of storms as well as from our experience with other samples that the most representative shape for all such storms is that of an ellipse. Actual storm patterns in general are extended in one or more directions, primarily as a result of storm movement, and one finds that an ellipse having a particular ratio of major to minor axis can be fit to the portion of heaviest precipitation in most storms. Therefore, one question we posed was, what was the most representative ratio of axes for the major storms in our sample. Also of interest was to learn the variation of pattern shape with area size and with region. To determine the shape ratio (i.e., the ratio of the major to minor axis) for the storms in our sample, we developed a number of elliptical templates that were scaled to contain 20,000 mi , relative to the small isohyetal maps portrayed in "Storm Rainfall in the United States" (U.S. Army Corps of Engineers 1945- ), 16 hereafter referred to as "Storm Rainfall." These templates had shape ratios that varied between 1 and 8. For each storm, we chose the template which best fit the shape of the isohyets that enclosed approximately 20,000-mi 2 areas of greatest rainfall. Judgment of fit was necessary, particularly for storms with large areas, or those near coastal zones where only partial isohyetal patterns were available. For those smaller area storms, a shape ratio was determined based on the ratio of major to minor axis measured on the storm isohyetal pattern. The variation of shape ratios for the 53-storm sample is summarized in table 4. Shape ratios of 2 are most common, followed by those of 3 and 4. Of the storms in table 4, 62 percent had shape ratios of 2 or 3, and 83 percent had shape ratios of 2 to 4. Table 4. — Shape ratios of isohyetal patterns for 53 major rain events (see table 1) 1 2 Shape Ratio 3 4 5 6 7 8 Total No. of patterns % of total Ac cum. % 2 22 3.8 41.5 4 45 11 11 4 20.8 20.8 7.5 66 87 94 2 3. 98 1 8 1.9 100 100 53 100 Before we draw any conclusions from table 4, we wanted to know if there was a variation in shape ratio with region or area size. To check the regional variation of shape ratios, we chose to separate the region into meteorologically homogeneous subregions as shown in figure 4. These subregions were not meant to represent the entire region of homogeneity but to be sufficiently independent portions of such broadscale subregions among which one might expect to find differences in shape ratios. These regions, shown in figure 4, contained 33 (62%) of the 53 storms. Table 5 shows the distribution of shape ratios within each of the six subregions, and although the number of storms in each is small, the percent of total shown at the bottom of the table is somewhat similar to that for the entire sample given in table 4. The number of storms in table 5 is too small to be significant, but distinguishable regional differences are not apparent, all tending to support shape ratios of 2 or 3. Table 5. — Shape ratios for six subregions Shape Ratio Total no. Subregions 1 2 3 4 5 6 7 8 of storms % of storms in regi on Atlantic Coast 20 40 20 20 5 Appalachians 20 40 20 20 5 Gulf Coast 56 22 11 11 9 Central Plains 67 17 17 6 North Plains 50 25 25 4 Rocky Mt. 50 25 25 4 Slopes ^^33 % of total 6 45 18 12 12 3 3 99~^\_ 17 107 103 100 100 200 300 400 KILOMETERS 103 Figure 4. — Homogeneous topographic/climatologic subregions used in study of regional variation of isohyetal patterns. The appendix contains a discussion of a larger sample of storms, 183 of which occurred in these same six subregions. Results from these storms are shown in table 6. Information from table 6 Indicates that the Atlantic Coast and North Plains regions have the greatest percentage (16) of storms with shape ratios greater than 5. The North Plains also has the greatest percentage (16) of approximately circular patterns. The Appalachians show the greatest percentage of storms with shape ratios of 4 and 5. This may be a reflection of an orographic effect of the mountains combined with the northeastward movement of storms along the east coast. These results are not typical of all orographic regions, for shape ratios of 2 predominate on the Rocky Mountain Slopes. This is meteorologically reasonable since many large storms in this region result from nearly stationary weather systems over or near the east face of the mountains. 18 Table 6. — Shape ratios of 20,000-mt isohyetal patterns for six subregions Shape Ratio Total no. Subregions 1 2 3 4 5 6 7 8 of storms % of storms in region Atlantic Coast 4 31 19 15 15 12 4 26 Appalachians 4 17 13 30 30 4 23 Gulf Coast 6 42 28 10 6 2 2 4 50 Central Plains 2 26 35 16 9 9 2 43 North Plains 16 28 28 8 4 8 4 4 25 Rocky Mt. Slopes 6 56 19 13 6 16 % of total ^-^^183 subsample 6 33 25 14 12 5 2 3 100^-^^_ Although some of the differences are meteorologically reasonable and may in fact represent variations over a regional extent, it must be recognized that the regional samples in table 6 are somewhat small in all but the Gulf Coast and Central Plains. It is difficult to compare the results in tables 5 and 6. Seven storms in table 5 that had particularly small total areas were not included in the sample for table 6. Nevertheless, it was concluded from these tables that there is little apparent regional variation amongst shape ratios. The variation of shape ratios with area size for the 53 storm sample, regardless of duration, is shown in table 7. Here too the results show no strong variation with area size. Table 7. — Shape ratios of major isohyetal patterns relative to area size of total storm Area size Shape Ratio Total no. (10 mi 2 ) 1 2 3 4 5 6 7 8 of storms % of storm in category <0.3 0.31 - 5.0 (w) 20 20 20 5 5.1 - 10.0 o7 33 3 10.1 - 20.0 57 28 14 7 20.1 - 30.0 12 50 12 25 8 30.1 - 40.0 40.1 - 50.0 50 50 33 17 50 6 2 50.1 - 70.0 22 33 11 22 11 9 70.1 - 90.0 28 43 28 7 >^ 90.0 33 50 17 6 % of total 6 40 21 8 4 2 53 In table 7, the larger values in each row have been circled. In this sample, there appears to be a tendency for larger percentages of storms to be circular at the smaller area size. In the same manner, there is a tendency for shape ratios to increase from 2 for areas between 5,000 mi^ and 50,000 mi 2 to 3 for larger areas. Although these results are perhaps handicapped by the small size of the sample, somewhat similar results were obtained from the larger sample of storms discussed in the appendix. 19 3.3 Summary of Analysis The following conclusions were drawn from analysis of shape ratios of major storm isohyetal patterns. 1. Approximately 60 percent of our sample of major storms had shape ratios between 2 and 3. 2. No strong regional variation of shape ratios was apparent, although some meteorologically reasonable trends could be obtained from the data. 3. No strong relation was found between shape ratio and total- storm area size, but there was some evidence that lower shape ratios occur with the smaller area sizes. 3.4 Recommended Isohyetal Pattern for RIP Since a majority of the storms considered in this study had shape ratios of 2 and 3, we recommend an idealized (elliptical) isohyetal pattern with a ratio of major to minor axis of 2.5 to 1 for distribution of all 6-hr increments of precipitation over drainages in the nonstippled zones east of the 105th meridian (see figs. 18-47 of HMR No. 51). The choice of a single shape ratio for the entire region east of the 105th meridian simplifies the procedure for determining the hydrologically most critical pattern placement on a drainage, does not violate the data, and tends to be in the direction of the small-area patterns observed in major storms of record. A recommended pattern is given in figure 5, drawn to a scale of 1 to 1,000,000. This pattern contains 14 isohyets (A through N) , that we think would provide reasonable coverage of drainage areas up to about 3,000 mi . Since it would be cumbersome to include a pattern drawn to 1:1,000,000 scale with isohyets enclosing the largest suggested area, we have limited figure 5 to only 6,500 mi . All discussion of figure 5 implies a pattern of 19 isohyets extending from A to S and covers an area of 60,000-mi . It is necessary to provide patterns larger than 20,000 mi 2 (the limit of PMP given in HMR No. 51) in order to cover a narrow drainage with isohyets, particularly if the pattern and the drainage have different axial orientations, or if you want to consider non-basin centered placements. The 10-mi isohyet is taken to be the same as point rainfall. If it is desired to apply figure 5 to some other scale or to add larger isohyets to the pattern, and suitable templates are not available, table 8 aids the reproduction of figure 5 and gives the length in miles of the semi-minor and semi-major axes of an ellipse along with selected radials that enclose the suggested areas for a shape ratio of 2.5. For example, to obtain a 2,150-mi ellipse, the minor axis is twice the value of 16.545 given in table 8, or 33.09 mi. The major axis is then 82.725 mi. The information in table 8 is sufficient to obtain isohyets that enclose areas for which HMR No. 51 is applicable. The procedure in chapter 7 for determining isohyet values suggests that at times it may be necessary to consider isohyets supplementary to those specified in figure 5. To aid in construction of any additional isohyets, we provide the 20 < ' UJ a. z < S o I o o o oo o o o oo o o o o o o m in o o — — cm •» I I I I I O Q- O CfclO in < < O"000>00000 ooooo --(niooi^o'ooo © m o o o „-nt so 10— o>oio — — r» « •» ■<> I I I I I I I I I I I I I I o_ o o o 4J 4J cd Cl H (5 4J 0) ►» JC « • •H /"N "0 P « * t a ed 4J * w H 1 • • 1 H t in 01 H 01 re u p CO 21 Table 8. — Axial distances (mi) for construction of an elliptical isohyetal pattern for standard isohyet areas with a 2.5 shape ratio (Complete four quadrants to obtain pattern) Standard isohyets Isohyet enclosed Incremental Radial axi s (deg.)* label area (mi ) area( mi/) 15 30 45 60 90 A 10 10 2.820 2.426 1.854 1.481 1.269 1.128 B 25 15 4.460 3.836 2.933 2.342 2.007 1.784 C 50 25 6.308 5.426 4.148 3.313 2.839 2.523 D 100 50 8.920 7.672 5.866 4.685 4.014 3.568 E 175 75 11.801 10.150 7.758 6.198 5.310 4.720 F 300 125 15.451 13.289 10.160 8.115 6.953 6.180 G 450 150 18.924 16.276 12.444 9.939 8.516 7.569 H 700 250 23.602 20.301 15.521 12.397 10.622 9.441 I 1,000 300 28.209 24.263 18.550 14.816 12.965 11.284 J 1,500 500 34.549 29.717 22.720 18.146 15.549 13.820 K 2,150 650 41.363 35.577 27.200 27.725 18.614 16.545 L 3,000 850 48.860 42.026 32.130 25.662 21.989 19.544 M 4,500 1,500 59.841 51.470 39.351 31.430 26.930 23.936 N 6,500 2,000 71.920 61.860 47.294 37.774 32.366 28.768 10,000 3,500 89.206 76.728 58.661 46.853 40.145 35.682 P 15,000 5,000 109.225 93.973 71.846 57.383 49.168 43.702 Q 25,000 10,000 141.047 121.318 92.752 74.082 63.476 56.419 R 40,000 15,000 178.412 153.456 117.323 93.707 80.292 71.365 S 60,000 20,000 218.510 187.945 143.691 114.767 98.337 87.404 * 0° radial axis = semi -major axis. 90° radial axis = semi -minor axis. following relations, where a is the semi-major axis, b is the semi-minor axis, and A is area of the ellipse. For this study For a specific area, A, Radial equation of ellipse, r^ = a = 2 ,5b b J A \ l/2 I : >.5 rr 1 r 2 a b a 2 sin 2 e + b 2 cos 2 e where r = distance along a radial at an angle 9 to the major axis. 22 Although there is a slight tendency for circular patterns to occur for small area storms, we recommend the elliptical pattern in figure 5 for all drainage areas covered by HMR No. 51. 3.5 Application of Isohyetal Patterns 3.5.1 Drainage-centered patterns This study recommends centering the isohyetal pattern (fig. 5) over a drainage to obtain the hydrologically most critical runoff volume. For many drainages that are not divided into sub-basins for analysis, the greatest peak flow will result from a placement of the isohyetal pattern that gives the greatest volume of rainfall within the drainage. The hydrologic trials to determine the greatest volume in the drainage discussed in section 5.3 may result in a placement that does not coincide with the geographic center of the drainage, particularly in irregularly shaped drainages. Centering of the isohyetal pattern as described here applies to the incremental volumes determined for each of the 6-hr PMP increments, each of which will be centered at the same point. For some drainages, it may be hydrologically more critical to center the isohyetal pattern at some other location than that which yields the greatest volume. That is, recognizing that any location other than drainage-centered may result in less volume of rainfall in the drainage, it may nevertheless be possible to obtain a greater peak flow by placing the center of the isohyetal patterns nearer the drainage outlet. Characteristics of the particular drainage would be an important factor in considering these trial placements of isohyetal patterns. Should this secondary consideration for a nondrainage-centered pattern be used, the data in table 8 are believed sufficiently large in area covered to allow considerable flexibility in alternative placement of patterns, while still giving spatial distribution throughout the drainage. When it is determined that the zero isohyet occurs within the drainage, the area to use in hydrologic computations is that contained within the zero isohyet, and not the area of the entire drainage. An additional benefit may be derived from the extent of coverage provided in table 8. This appears in the form of concurrent precipitation; i.e., if PMP is applied to one drainage, the extended pattern in many instances is sufficient to permit estimation of the precipitation that could occur on a neighboring drainage. This information is useful in evaluating effects from multiple drainages contributing to a hydrologic structure. 3.5.2 Adjustment to PMP for drainage shape Whenever isohyetal patterns are applied to a drainage, there will be disagreement between the shape of the outermost isohyets and the shape of the drainage. Adjustment to drainage averaged PMP for this lack of congruency has been referred to in some past studies as a "fit factor" or a "basin shape" adjustment. In those studies, a comparison was made between the drainage- averaged PMP determined from planimetering isohyetal areas within the drainage and the total PMP (generally for 72 hr) derived from depth-area-duration data. It has generally been the case that the ratio of these depths, termed the fit factor, was then applied to each durational increment of the PMP. 23 Since we have established that there is a pattern shape assigned to each 6-hr increment, we can reasonably expect that there will be some reduction to the volume precipitation determined from the isohyetal pattern when the pattern is "fit" to an irregularly shaped drainage. Comparison of the drainage-averaged volume of precipitation and that from the depth-area curve derived from HMR 51 for a 6-hr period is indicative of the percentage reduction due to the drainage shape. The largest reduction occurs in the first 6-hr period and decreases with each succeeding 6-hr period. 3.5.3 Pattern applicable to PMP When the isohyetal pattern in figure 5 is applied to a drainage, both drawn to the same scale, one might ask whether it is necessary to use all the isohyets given, since the outermost isohyet encloses 60,000 mi , well above the area size for which PMP is given. The answer to this question depends upon the shape of the drainage. It is only necessary to use as many of the isohyets of figure 5 as needed to cover the contributing portion of the drainage. If one has a perfectly elliptical drainage of 2,150 mi ? with a shape ratio of 2.5, then it is only necessary to evaluate isohyets A through K in the pattern in figure 5. Since almost all drainages are highly Irregular in shape, the K isohyet is unlikely to provide total coverage for a drainage of this size, and for an extremely long 2,150-mi drainage, even though one is applying the 2,150-mi 2 PMP, it may be necessary to evaluate the M, N or larger isohyets. At this poJLnt in our discussion, we note that figure 5 is applied only to the three greatest 6-hr increments of PMP (18-hr PMP). For the nine remaining 6-hr increments of PMP in the 3-day storm, we recommend a uniform distribution of PMP throughout the area of PMP. This means that for each of the three greatest increments, the magnitude of PMP is such that it is reasonable to expect it to be spatially distributed according to the Isohyets in figure 5. However, the magnitudes of the increments of PMP decrease rapidly after the greatest 6-hr amount, and by the fourth 6-hr period are reduced to a level at which we assume they can be approximated by constant values over the PMP portion of the pattern for the fourth through 12th 6-hr periods. Since most drainages have irregular shapes and as we have already discussed earlier in this section, the pattern shape in figure 5 will not fit when placed over the drainage. Therefore, there will be portions of the drainage that may for some unusually shaped drainages be uncovered by the pattern for a particular area size of PMP. (Chapter 5 discusses how to determine what area pattern to place on a drainage.) We are faced with the problem of what precipitation to expect outside the area of the PMP pattern. The solution lies in the concept of residual precipitation. Residual precipitation is the precipitation that occurs outside the PMP area size pattern. For example, if we find the pattern area size that gives the maximum volume of PMP in the drainage is 2,150 mi , then for the 3 greatest 6-hr increments, apply figure 5, where the K isohyet encloses the PMP area. The isohyets inside and outside of K represent values that will give areal average depths somewhat less than PMP. In this example, the isohyets outside of K determine the residual precipitation. It should also be emphasized that residual precipitation Is that outside the area of the PMP pattern, and not necessarily outside the drainage. 24 Now, for the fourth through 12th 6-hr periods we have assumed a constant value approximates the respective 6-hr increment of PMP through the area size of PMP. Therefore, for these increments, there would be no A through J isohyets in the patterns applied. But, there would remain isohyets outside the isohyet for the area size of the PMP (outside K in the above example), and thus there is a residual precipitation pattern assigned to each of the fourth through 12th 6-hr increments of PMP, in addition to the patterns for the three greatest 6-hr increments. (See discussion in section 5.2.5 and fig. 21.) Although the concept of residual precipitation and its application and representation in isohyetal patterns is new, and perhaps confusing at this point, further discussion in chapter 5 and the examples in chapter 7 should be helpful. 4. ISOHffiTAL ORIENTATION 4.1. Introduction The subject of isohyetal orientation arises quite naturally from discussion of placing isohyetal patterns over a drainage, since the orientation of a PMP pattern and that of the drainage over which it is placed may be entirely different. Guidance is needed on how well these orientations match for the PMP storm. It is assumed, though perhaps not always true, that the greatest volume of rainfall within a drainage results when the isohyetal pattern and the drainage are similarly oriented. An objective of this section, therefore, is to determine whether there are meteorological restrictions or preferences for certain orientations. We are also interested in determining if there are any regional variations or constraints on orientations due to terrain or other factors. As in the previous chapter, we rely on major observed storm rainfalls and apply the results to adjust the isohyetal orientation of the 6-hr PMP increments. (See section 5.2.1.) Since 6-hr incremental isohyetal patterns are available only for a very few storms, we assume that the orientation of isohyets for the 6-hr incremental patterns of rainfall is the same as that for the total storm. Limited support for this assumption is found in the few incremental isohyetal patterns given in a study of Mississippi River basin storms by Lott and Myers (1956). For 10 of the 18 storms studied by Lott and Myers, 6-hr isohyetal patterns were determined. The orientations of the 6-hr isohyetal increments for these 10 storms vary from the total-storm orientations by no more than 40°. 4.2 Data The sample of Isohyetal patterns from the 53 major storms in table 1 were considered for the study of isohyetal orientations. 4.2.1 Average orientations In this chapter, reference is sometimes made to the average of several orientations. It is believed important to remark here on how these averages were obtained, because averages of angular measure do not follow that of simple arithmetic averages. First, recognizing that every orientation line (or axis) is 25 Problem: Obtain an average of three orientation lines given below* If the lines are designated as #1 = 020° or 200°, #2 = 150° or 330° , and #3 = 165° or 345° } then if we average 020° , 150° and 165° > we get 112° t which is seen to represent a false average. Solution: Choose values to average from ends of the lines (quadrants) that give the minimum range. Here the range of 200° minus 150° 3 or 380° minus 330° t is the minimum (50° range). Thus, the representative average is 172° t or 352° respectively. w- ^^ FALSE AVERAGE =112 TRUE AVERAGE = 172 Figure 6. — Schematic example of problem in averaging isohyetal orientations. 2-valued, we obtain different averages relative to which value is chosen to represent a particular orientation. Therefore, a rule must be developed, when averaging such values, on which of the 2 values to use so that everyone obtains a comparable and representative result. The rule we applied was to use those values that would give a minimum range for all the values to be averaged. This procedure will be illustrated by the following example. Average the three orientation lines in figure 6 (#1 is 020° - 200°, #2 is 150° - 330°, and #3 is 165° - 345°). (Three orientations are considered here only to keep the problem simple; the procedure is the same regardless of the number of orientations to be averaged). If one chose to average the three smallest values (reading from north) of 20°, 150° and 165°, the result would be 112° given by the dashed line 26 in figure 6. This is an unrepresentative average when compared to the three solid lines in this figure. We say the range of those 3 values is 145° (165° minus 020°). However, following the rule to obtain a minimum range, consider the three values of 150°, 165° and 200° (representing the same three orientations, but reading the other end of the 020° - 200° line). We get a range of 50° (i.e., 200° minus 150°), and similarly a 50° range is obtained for the set of other ends to these same 3 lines (380° minus 330°). Since 50° is the least difference we can obtain from any set of directions, for these 3 particular lines, the correct values to average are either 150°, 165° and 200° or, 020° + 360°, 330° and 345°, for which the average orientation is 172° or 352°, respectively shown by the dotted line in figure 6. 4.2.2 Orientation notation Although each orientation line is 2-valued, we have chosen to represent each orientation by only one value in the remainder of this chapter. This convention greatly simplifies the notation assigned to graphs and tables. In selecting the one value to identify each orientation, we could have arbitrarily chosen values between 0° and 180° (from north). However, this choice is but one of many possible choices, each covering a range of 180°, and we adopted the 180° sector between 135° and 315° for this study. This particular choice resulted from considerations of meteorological bases for the observed pattern orientations, which are related to the moisture bearing inflow winds. Wind is commonly reported as the direction the wind is blowing from. Atmospheric winds during periods of maximum moisture In the United States east of the 105th meridian are predominantly in the quadrant from the south to west. In addition, analysis for our storm sample indicated that most rainfall patterns had orientations that varied about a southwest-northeast axis. 4.3 Method of Analysis An isohyetal orientation was determined for each of the major total-storm rainfall patterns in table 1. We prescribed that the orientation line for each pattern pass through the location of maximum reported point rainfall. Some complex isohyetal patterns necessitated subjective judgments on the orientation, because of multiple possible orientations or incomplete total-storm patterns. The latter was particularly the case along coastal zones. Direction of the orientation in each rainfall pattern was read to the nearest 5 degrees. Orientations determined for the 53 storms, listed in table 1, have been plotted at their respective locations in figure 7. 4.4 Analysis The amount of variation in orientations given in table 1 and figure 7 gave rise to the question, whether it was possible to generalize these orientations into a consistent pattern over the entire study region. 4.4.1 Regional variation The same six subregions used to study shape ratios were used to determine regionally averaged orientations. Averages of the orientation for the major storms in each subregion are given in table 9. The range of orientations for storms considered in each subregion is also indicated. 27 107 103 99 100 100 260 300 460 KILOMETERS Figure 7. — Location and orientation of precipitation pattern for 53 major storms listed in HMR No. 51. Identification numbers refer to table 1. Table 9. — Averages of isobyetal orientations for major storms within selected subregions of the eastern United States (storms contained in appendix of H4R No. 51) No. of Average Range in Subregion Storms orientation (deg) orientations (deg) Atlantic Coast 5 202 170 to 230 Appalachians 5 194 145 to 270 Gulf Coast 9 214 170 to 290 Central Plains 6 235 160 to 285 North Plains 4 270 230 to 295 Rocky Mt . Slopes 4 224 200 to 240 28 Although the results in table 9 represent a small sample, we feel that a tendency Is shown for some regional variation among these subregions. Support for this conclusion was based in part on results from a similar analysis of the larger sample of storms discussed in the appendix and summarized in table 10. We subdivided the Appalachians into storms that occurred east and west of the ridgeline. By so doing, the results for the Appalachians suggest that orientations in this region closely agree with the subregions to the east (Atlantic Coast) and to the west (Central Plains). This distinction does not appear in the results for table 9, because none of the storms considered occurred to the west of the ridgeline. A general picture of the regional variation of isohyetal orientation is obtained from these two samples: orientations are southwesterly east of the Appalachians, along the Gulf Coast, and along the east slopes of the Rocky Mountains, but become more westerly in the Plains States. Meteorological bases for those observed orientations will be discussed in section 4.5. liable 10. — Average of isohyetal orientation for the large sample of storms within selected subregions in the eastern United States No. of Average Range in Subregion storms orientation (deg.) orientations (deg.) Atlantic coast 26 204 140 to 305 Appalachians (East) 17 204 155 to 240 Appalachians (West) 6 278 240 to 305 Gulf Coast 50 235 140 to 300 Central Plains 43 256 195 to 300 North Plains 25 257 185 to 310 Rocky Mt. Slopes 16 214 170 to 290 4.4.2 Generalized isohyetal orientations Assuming from tables 9 and 10 that there is a regional variation in isohyetal orientations of major storms, we want to determine the regional variation that represents PMP. It would be desirable to generalize orientations by a continuous analysis across the entire study region. As a first approach we plotted the subregion averages from table 9 at their respective locations, centered to represent the centroids of the storms averaged. From this basis, a rough pattern was drawn to show regional variation (not shown here). It was felt that although a general pattern could be obtained in this manner, drawing to five data points for so large a region was less than desirable. A decision was made to consider a number of major storms distributed throughout the region and develop the generalized pattern from their orientations. Storms were selected from table 1 according to the following conditions: 1. No other major storm in table 1 occurred within a radius of 100 miles of the storm chosen. When two or more storms were within 100 miles of one another, only the storm with the larger 24-hr 1,000-mi depth was considered. 2. No storm was selected whose total storm duration was less than 24 hr, as they were believed to represent local storms for which almost any orientation is believed possible. 29 With this guidance, 25 storms (roughly one-half the storms in table 1) were selected. In addition, to the 25 major storms from table 1, six storms were selected from "Storm Rainfall" (U.S. Army Corps of Engineers 1945- ) to fill in portions of the region not represented by storms in table 1. These storms also met the selection criteria noted above. The 31 storms were plotted at their respective locations as shown in figure 8. Through considerable trials, a generalized pattern was drawn which attempted to match as many of the storm orientations as possible and yet maintain some internal consistency regarding gradients and smoothness. Also shown in figure 8 is the result of this analysis. In making the analysis shown in this figure, we attempted to control the variation from observed orientation whenever possible. Table 11 lists the 31 differences. It is apparent that some large variations occur, e.g., 72° at Smethport, Pennsylvania. For the most part, variations are considerably less, as summarized by 10° categories in table 12. Two-thirds of the analysed orientations are within 30° of the observed orientations, while nearly 94% are within 50°. Although there are some portions of the region (e.g., eastern Great Lakes) that show rather large variation from the analysis, a decision was made not to complicate the analysis further by creating regional anomalies. Therefore, the analysis shown in figure 8 was adopted to represent the pattern of orientations for our data, and we further assumed that this pattern applied to the most favorable conditions for PMP. For drainages that lie outside the region covered by the analysis (for example in northern Michigan), use the orientation of the nearest isopleth. 4.4.3 Variation of IMP with pattern orientation applied to drainage In application of PMP to specific drainage, figure 8 is used to determine the orientation of the isohyetal pattern most likely to be conducive to a PMP type event. It is unrealistic to expect that figure 8 is without error and that PMP at any location is restricted to only one orientation. For these reasons we recognize that it is more reasonable that PMP occur through a range of orientations centered on the value read from figure 8. Following this line of reasoning, we also expect that for precipitation orientations that do not fall within the optimum range, the magnitude of PMP would be somewhat less. 4.4.3.1 Range of full MP. The range of full PMP (100% PMP) is that range of orientations, centered on the value read from figure 8, for which there is no reduction to the amounts read from HMR No. 51 for orientation. Our concept of PMP is that the conditions resulting in a PMP-type event are somewhat restricted, and we believe that the range of full PMP should also be limited. However, to gain support for this limitation, we again referred to our sample of major storms and, from the summary of orientations in table 12, we chose a range of ±40° (representing about 85 percent of the variation in our sample) to assign to PMP. Therefore, whenever the pattern best fitted to the drainage for which PMP is being determined has an orientation that falls within 40° of the orientation obtained for that location (from fig. 8), full PMP is used. 30 u_ < z -i 3 _J UJ or < or _) < UJ CD -1 Q CO J in r-." 11 1 fl 1 "5! O 01 O B.S w r-» co u u u 3 •n oo T3 d 01 x-i 4J O 4J 0) •d 01 CO CO u C 14-1 4J n CO §S 1-1 *-» s * s* • d P to u H § I sn 01 £* J3 4J ^ s CO •H ■H • "0 u-i e a O Ctj •tf CO » •H +1 CO § t* d •H — Anal wlthl 4J 8 H • Ph d • a •H o> W l-i u 9 O 3 to 4-hr 1000- mi depth Observed Orientation no. from orienta- from analysis Differ- table 1 Ifeme (in.) tion (deg.) (deg.) ences 1 Jefferson, OH 11.0 190 230 +40 7 Eutaw, AL 11.3 230 231 + 1 8 Paterson, NJ 10.9 170 199 +29 14 Beaulieu, MN 10.0 285 251 -34 17 Altapass, NC 15.0 155 218 +63 18 Meek, JM 5.0 200 182 -18 19 Springbrook, MT 11.3 240 241 + 1 20 Thrall, TX 24.3 210 205 - 5 21 Savageton, WY 6.6 230 230 22 Bo yd en , I A 10.6 240 246 + 6 23 Kinsman Notch, NH 7.8 220 200 -20 24 Elba, AL 16.1 250 224 -26 25 St. Fish Htchy, TX 19.0 205 194 -11 27 Ripogenus Dam, ME 7.7 200 198 - 2 30 Hale, CO 7.2 225 213 -12 37 Hayward, WI 9.1 270 253 -17 38 Smethport, PA 13.3 145 217 +72 39 Big Meadows, VA 10.3 200 209 + 9 42 Collinsville, IL 9.0 260 247 -13 44 Yankeetown, FL 30.2 205 200 - 5 45 Council Grove, KS 6.6 280 240 -40 48 Bolton, Ont., Can. 6.4 190 230 +40 49 Westfield, MA 12.4 230 198 -32 51 Sombreretillo, Mex . 11.9 220 170 -50 53 Zerbe, PA 12.3 200 207 + 7 Supplementary storms 54 Broome, TX 13.8 230 195 -35 55 Logansport, LA 14.8 215 225 +10 56 Golconda, IL 7.4 235 244 + 9 57 Glenville, GA 13.1 180 205 +25 58 Darlington, SC 10.8 205 199 - 6 59 Beaufort, NC 11.5 235 196 -39 4.4.3.2 Reduction to HIP for orientation outside of range. We have stated that for orientations that differ from the central value from figure 8 by more than 40°, less than PMP-type conditions are likely, and therefore we feel a reduction can be made to the PMP determined from HMR No. 51. It is also reasonable to expect that as the difference between PMP orientation and orientation of the pattern on the drainage increases, the reduction applied to PMP should increase. 32 Tkble 12. — Frequency of various difference categories between observed and preferred orientations Categ. -50 to -40 to -30 to -20 to -10 to to 10 to (deg.) -41 -31 -21 -11 -1 9 19 Freq. 1 5 1 6 4 7 1 % 3 16 3 19 13 23 3 Categ. 20 to 30 to 40 to 50 to 60 to 70 to Total (deg.) 29 39 49 59 69 79 Freq. 2 - 2 - 1 1 31 % 6 - 6 - 3 3 98 Range Frequency Cum. % ±10° 11 35.5 ±20° ±30° ±40° ±50° ±60° ±70° ±80° 18 21 26 29 29 30 31 58.1 67.7 83.9 93.5 93.5 96.8 100.0 Because we anticipated there could be a regional variation, we considered the subregions in figure 4. Our sample in table 1 of major storms within these subregions is too small to be useful, and we relied on the increased sample described in the appendix. Within each subregion, storms were ranked according to magnitude of 72-hr 20,000-mi depth, and then converted to percent of the maximum depth occurring in each region. We plotted the percent of maximum rainfall vs. orientation for each storm by geographic region. An enveloping curve drawn on these graphs provided guidance on the range of orientations that should be permitted without reduction and on the appropriate reduction for greater variations. The data for the Gulf Coast region are shown in figure 9, as an example of these plots. In figure 9, the Hearne, Texas (6/27-7/1/1899) storm gave the maximum depth, and the Elba, Alabama (3/11-16/1929) storm was the second greatest at about 80 percent of the Hearne depth. We remind the reader that since orientation is a form of circular measure, the left-hand end of the scale in figure 9 is identical with the right-hand end of the scale. Considering each of the subregional distributions, of which figure 9 is an example, we developed a model based essentially on envelopment of subordinate depth storms. The model shows that 100 percent of RIP applies within ± 40° of the central value as indicated in section 4.4.3.1. Maximum reduction to PMP is limited to 15 percent applicable to orientation differences of ± 65° or more. This model is given in figure 10, in which the adjustment factor (100% minus the percentage reduction) to PMP is read from the right-hand axis for differences of orientation from the central value obtained from figure 8 (represented by the value on the left of the model). 4.4.3.3 Variation due to area size. It appears reasonable that no reduction should be applied to storms on the scale of a single thunderstorm cell (or 33 u a. UJ CL I I I I I HEARNE,TEX. I I I I I I I ELBA, ALA. 0- ■III x = REFLECTlON POINT II I I I I I I I 140 160 180 200 220 240 260 280 300 320 ORIENTATION (deg) Figure 9. — Distribution of isohyetal orienta- tions for 50 major storms (from sample listed in the appendix) that occurred in the gulf coast subregion. possibly a complex cell). Such a system is expected to have equal intensity at any orientation. An area size of 300 mi vas chosen as the smallest storm area for which a reduction should be applied. A rational argument can also be developed to say that if we limit reduction of R4P for orientation to storm area sizes of 300 mi and larger, it is unreasonable to expect that a discontinuity occurs at 300 mi . On this basis, there should also be some limit at which the maximum reduction of 15% applies. Between these limits, a reduction between and 15% applies. Although we have no data to support our decision, we chose to set a limit of 3,000 mi (ten times the lower limit of 300 mi ) as the area above which 15% reduction is possible. 2 To use figure 10 for pattern areas greater than 300 mi consider the diagonal lines provided for guidance. These lines have been drawn for every 500 mi up to 3,000 mi , and intermediate 100-mi areas are indicated by the dots along the right margin. By connecting the vertex in the upper left with the appropriate dot on the right, the user can determine the adjustment factor corresponding to the orientation difference noted along the abscissa. As an example, for a 1,000- mi isohyetal pattern whose orientation differs by 57° from that determined from figure 8, the adjustment factor read from figure 10 is 97.3%. Note for orientation differences of 65° or larger, the adjustment factor is that given by the scale along the right margin for the respective areas. 34 t — r 111 I PATTERN AREA (mi 2 ) I r I 00 to ±40 Figure as a that ±45 ±50 ±55 ±60 ORIENTATION DIFFERENCE Cdeg.) ±65 to ±90 10.— Model for determining the adjustment factor to apply to isohyet values result of placing the pattern in figure 5 at an orientation differing from given in figure 8 by more than 40°, for a specific location. 35 4.4.4 Noncoinci dental rainfall pattern One nay find through a trial and error approach that, in some hydrologic situations, an isohyetal pattern orientation different from that of the drainage may give a more critical result than that obtained when the orientations coincide. This appears to be possible, for some drainages, because there is a tradeoff between the volume one gets from a rainfall pattern coincident with the drainage, but requiring maximum reduction for orientation relative to PMP, and that from a noncoincident placement of the isohyetal pattern with less or no orientation reduction. To illustrate, assume a precipitation pattern placed on a hypothetical drainage has an orientation differing more than 65 degrees from that given in figure 8 for the location. The recommended procedure in this study is to apply the maximum reduction allowed in figure 10 to all the isohyet values, for orientation differences of this magnitude. However, it might be possible to obtain a more hydrologically critical result if the rainfall pattern placed over the drainage and the drainage orientations were kept dissimilar and the isohyet values were not reduced at all. Because it appears it may be necessary to check a wide range of possible orientation arrangements to determine the hydrologically most critical relationship between PMP and rainfall pattern on drainage orientations, we offer only limited guidance. The most likely situations where non-fit and no reduction would be important are those that involve maximum reductions to PMP for low drainage shape ratios (CO, i.e., "fat" drainage shapes. Another consideration that needs to be noted is that the discussion of pattern placement in this report is primarily directed at drainages that are not affected by orographic influences (the nonorographic region in HMR No. 51). Should it be of interest to estimate PMP from HMR No. 51/52 techniques applied to a drainage in the orographic region, it is necessary to judge whether placement of the pattern to center in the drainage or to align with the drainage is meteorologically possible. An example is the following: if a tropical storm is taken as the PMP storm type for a drainage on the western slopes of the southern Appalachian Mountains, it is unlikely that the isohyetal pattern can be realistically centered more than a few miles west of the ridgeline. Thus, in the orographic regions, one needs to recognize the storm type most likely to give PMP and then determine where and how the idealized pattern can be placed. 4.4.5 Comparison to other studies There are only a few references to orientation of isohyetal patterns in the meteorological literature. HMR No. 47 (Schwarz 1973) discusses the subject of orientation preferences and reduction to PMP for pattern orientation in the Tennessee Valley. Schwarz concludes that 100% of PMP would apply to orientations between 195 and 205 degrees. Riedel (1973) suggests that 100% of PMP applies to orientations between 200 and 280 degrees for the Red River of the North and the Souris River in North Dakota . For these locations, figure 8 gives central orientations between 210 and 245 degrees, and between 240 and 255 degrees, respectively. Our ± 40° range for full PMP, when added to these central orientations, permits general agreement between these two studies and the present study, although in general we allow for more westerly components than were reported in the earlier studies. 36 Huff (1967) reported that in a detailed study of 10 large scale storms (Illinois) in the period 1951-1960 in which 12-hour rainfall exceeded 8 in. at the storm center, the median orientation was 270 degrees. This compares with a range of 245 to 255 degrees for central orientations across Illinois in figure 8. A later study (Huff and Vogel 1976) reported that for heavy rainstorms in northeastern Illinois, 84 percent had orientations between 236 and 315 degrees. 4.5 Meteorological Evaluation of Isohyetal Orientations We believe the basis for the orientations in figure 8 is related to the occurrence of certain meteorological factors conducive to optimum rainfall production. We know that certain combinations of storm movement, frontal surfaces, and moisture inflow can influence the orientation of observed rainfall. We also know that the movements of storm systems are often guided by the mean tropospheric winds (generally represented by winds at the 700- to 500-mb level). An attempt is made In this section to understand some of these large- scale factors relative to the occurrence of the major rainfall events listed in table 11. These factors are listed in table 13. Note that the isohyetal orientations for the total storm given in column 6 of this table are those observed for these individual rainfall cases (from table 11) and are not to be confused with the orientations appearing in figure 8 for the generalized analysis. The following comments explain the information given in table 13: Col. 1 location of maximum rainfall Col. 2 date within the period of extreme rainfall on which the greatest daily rainfall occurred, as derived from selected mass curves shown in "Storm Rainfall" (U. S. Army Corps of Engineers 1945- ) Col. 3 rainfall type categories: tropical (T) for all extreme rains that occur as the result of passage of a tropical cyclone within 200 miles of the site of heavy rain; modified tropical (MT) for those extreme rains that appear to be derived from moisture associated with a tropical cyclone at some distance, or whose moisture has fed into a frontal system that has moved to the vicinity of the rain site. The presence of tropical cyclones has been determined from Neumann et al. (1977). Tropical cyclone rains that become extratropical are also labeled MT; general (G) includes all rains for which no tropical storm was likely involved; local (L) for relatively short-duration small-area storms. Col. 4 the orientation (direction storm is moving from) of the track of low-pressure center passing within 200 miles of the heavy rain, for the date of closest passage of the rain center. When no low-pressure center passes near the rain site, "none" is listed in table 13. 37 Table 13. — Meteorological factors pertinent to isohyetal orientation for major storms used to develop regional analysis (fig. 8) Column 1 2 3 4 5 6 Date of Type of Orient. Orient. Observed max. daily rain- of storm of front. orient, of Storm center rain storm track surface iso. pat. 1. Jefferson, OH 9/13/1878 MT 190 135 190 2. Eutaw, AL 4/16/00 G none 210 230 3. Pater son, NJ 10/09/03 MT 100 180 170 14. Beaulieu, MN 7/19/09 G none none 285 17. Altapass, NC 7/16/16 MT*1 none none 155 18. Meek, N4 9/16/19 MT*2 none none 200 19. Springbrook, Mt. 6/19/21 G 260 200 240 20. Thrall, TX 9/09/21 MT*3 none none 210 21. Savageton, WY 9/28/23 G none none 230 22. Boyd en, IA 9/17/26 G none 210 240 23. Kinsman Notch, NH 11/04/27 MT*4 none 180 220 24. Elba, AL 3/14/29 G none 210 250 25. St. Fish Htchy.,TX 7/01/32 G none 240 205 27. Ripogenus Dam, ME 9/17/32 MT 185 160 200 30. Hale, CO 5/31/35 L none 090 225 37. Hayward, WI 8/30/41 G none 250 270 38. Smethport, PA 7/18/42 L none 190 145 39. Big Meadowns, VA 10/15/42 MT*5 none none 200 42. Collinsville, IL 8/16/46 G none 260 260 44. Yankeetown, FL 9/05/50 T 180*8 none 205 45. Council Grove, KS 7/11/51 G none 250 280 48. Bolton, Ont. Can. 10/16/54 MT 200 200 190 49. Westfield, MA 8/18/55 MT 175 none 230 51. Sombreretillo, Mex. 9/21/67 T 020 none 220 53. Zerbe, PA 6/22/72 MT 150 220 200 54. Broome, TX 9/17/36 MT*6 none none 230 55. Logansport, LA 7/23/33 T 240 245 215 56. Golconda, IL 10/05/10 G none 235 235 57. Glenville, GA 9/27/29 MT*7 230*7 none 180 58. Darlington, SC 9/18/28 T 230 220 205 59. Beaufort, NC 9/15/24 MT 240 210 235 LEGEND T - Tropical G - General MT - Modified Tropical L - Local *1 - Trop. cycl . dissipated in central Georgia on 14th 2 - Hurricane dissipated in southwestern Texas on 15th 3 - Hurricane dissipated on Texas-Mexico border on 8th 4 - Tropical cyclone headed north @ 36°N, 80°W. mid-day 3rd 5 - Tropical cyclone dissipated in eastern North Carolina on 12th 6 - Tropical cyclone dissipated near Del Rio, TX on 14th 7 - Hurricane at Key West on 27th, track given for 30th 8 - Storm looping on 4-5th 38 Col. 5 the orientation (only one end of the 2-ended line given) of the frontal surface if the front is within 100 miles of the rain center (from United States Daily Weather Maps) for the date of greatest daily rainfall. When no frontal surface appears near rain site, "none" is listed in table 13. Col. 6 the orientation of observed rainfall pattern for the total storm from table 11 Eighteen of the 31 rains in table 13 come from tropical or modified tropical storms. A logical question is whether the orientation of the rainfall pattern is the same as the orientation of the storm track. Eleven of the thirteen rainfalls that have storm track information show agreement within 50 degrees between the storm track and rainfall orientations. Some of the modified tropical cyclone rains showed that maximum rainfall occurred where tropical moisture interacted with a frontal surface generally approaching from the west or northwest. This kind of interaction and the complexity involved in ascertaining the cause for the particular isohyetal orientation is illustrated in the case of the Zerbe, Pa. storm (6/19-23/72). Figure 11 shows a cold front through the Great Lakes at 1200 GMT on the 21st that moved eastward and became stationary through western New England by 1200 GMT on the 22nd. The track of the tropical cyclone center is shown by 6-hr positions. After 1200 GMT on the 22nd, the storm center appears to be attracted toward the approaching frontal trough position and recurves inland through Pennsylvania. The orientation (approx. 200°) of the total-storm isohyetal pattern is plotted in figure 11 for comparison. Although the front appears to be dissipating with the approach of the tropical cyclone, the orientation of the total-storm rainfall would suggest that the effect of the frontal surface as a mechanism for heavy rainfall release was important. Thunderstorms along the frontal surface may have moved in a northeasterly direction (200°), steered by the upper-level winds. Since all of these features are in motion, it is likely that the orientation of the isohyetal pattern is the composite result of several interactions. One additional factor that has not been discussed is the effect of the Appalachian Mountains. The ridges comprising these mountains also have a northeast- southwest orientation. We are unable to say at this time how the interaction between moisture flows and these terrain features contribute to the overall orientation of the precipitation pattern. The Springbrook (6/17-21/21) and Savageton (9/27-10/1/23) storms were associated with nontropical low-pressure centers to the south of the respective rainfall maxima, around which moist air drawn from gulf latitudes encountered strong convergence to release convective energy. Reviewing the results given in table 13, one may ask, what meteorological feature provides the source of precipitation for those storms that show "none" in columns 4 and 5. To answer this question requires studies beyond the scope of this discussion, but in many instances we believe the precipitation was caused by horizontal convergence of very moist air. This convergence in most instances was due to meteorological conditions, while in others it may have been enhanced by terrain features. 39 107 103 100 100 2o"o 300 '!00 KILOMETERS Figure 11. — Track of hurricane Agnes (6/19-22/72) showing frontal positions and orientation of the greatest 20,000-mi 2 precipitation area centered at Zerbe, PA. The Golconda, Illinois, storm (10/3-6/10) is representative of most of the other major storms in table 13 in which the isohyetal orientation can be more closely related to the orientation of the frontal surface. For this storm figure 12 shows a weak and dissipating cold front (A) approaching Golconda from the west on the 3rd and 4th. Farther west on the 4th a second cold front (B) is passing through the Dakotas and moves rapidly eastward to a position southwest-northeast through the Great Lakes on the 5th. Twenty-four hours later this second front has passed eastward of Golconda. Prior to its passage, strong southerly surface winds bring moist tropical air northward through the Mississippi Valley. It is presumed that this moist air upon meeting the frontal surface, is lifted to a level at which convective lifting takes over. Thunderstorms, or local storms, triggered along the frontal surface produce the observed rainfall orientation. 40 87* 83° 79° 75° 67 Figure 12. — Frontal positions and orientation of the greatest 20,000-ml' t precipitation area centered at Golconda, IL (10/3-6/10). Almost all of the 31 major storms listed In table 13 included thunderstorm-type bursts of heavy rain. Tendencies for these short-duration bursts are evident in major portions of the mass curves (not shown here) for each storm. Thunderstorms imbedded within widespread rain patterns are common to major rainfalls in the study region. Since thunderstorms are involved, we speculate that the isohyetal pattern orientations probably are controlled to some degree by the upper-level flows (see Newton and Katz 1958, for example). Maddox et al. (1973) studied the synoptic scale aspects of 151 flash floods, 113 of which occurred east of the 105th meridian. (One-third of these had maximum precipitation amounts equal to or exeeding 10 in.) Their results showed that the winds aloft tend to parallel the frontal zone during these events. They also showed that 500-mb winds were representative of the winds aloft between 700 41 and 200 mb, and that mean 500-mb winds for these events varied between 220 and 250 degrees (standard deviation of about 30°). Although they do not discuss regional variation, this range of 500-mb winds agrees well with the orientations adopted for PMP-type rain patterns (fig. 8). Upper-level winds are routinely available only after December 1944 (Northern Hemisphere Daily Maps). Seven storms in table 12 occurred after this date, for which the 500-mb winds were 280° at Collinsville, Illinois, 260° at Council Grove, Kansas, 210° at Bolton, Ontario, 215° at Westfield, Massachusetts, 020° at Sombreretillo, Mexico, and 220° at Zerbe, Pa . , the 500-mb winds were indeterminate for the Yankeetown, Florida rain site because of the occurrence of a small closed low system aloft associated with the surface hurricane. There is agreement within ± 20° between 500-mb winds and the orientation of heaviest rainfall for these storms. Had 500-mb information been available for more of the storms, it is expected that this association would be further supported. 4.6 Application to HMR No. 51 This study of isohyetal orientation of major rainfalls has produced guidelines we recommend for use in adjusting the volume of rainfall obtained from the isohyetal patterns of the 6-hr PMP increments. Figures 8 and 10 are used to reduce the PMP for certain area sizes if the orientation of the pattern placed on the drainage does not fall within ± 40° of the prescribed PMP orientation for that site. To apply these results use the following steps: 1. For a specific drainage, locate its center on figure 8 and linearly interpolate the central orientation for PMP at that location. 2. Obtain the orientation of the isohyetal pattern that best fits the drainage. In the orographic region of HMR No. 51, the orientation of the pattern may not fit the drainage but will be controlled by terrain and meteorological factors. 3. If (1) differs from (2) by more than ± 40° the isohyet values for each of the 6-hr increments of PMP are to be reduced in accordance with figure 10. Differences in orientations of more than ± 65° require the maximum reduction. The reduction that is applicable, however, is a function of the storm pattern area size with no reduction if 300 mi 2 or less, and a maximum of 15% if 3,000 mi 2 or more. 5. ISOBYET VALUES 5.1 Introduction When considering the spatial distribution of rainfall over a drainage, a question that needs to be answered is how concentrated the rain should be. Keep in mind that the concentration or distribution of the drainage-average PMP does not change the total rain volume for idealized elliptically shaped drainages. For this report, the spatial distribution is set by the values of isohyets in the isohyetal pattern. Part of this question has been answered in chapter 3, where we developed an idealized pattern shown in figure 5. This chapter, therefore, 42 deals with determination of the values to assign the lsohyets in that figure for each 6-hr increment. Chapter 6 treats isohyet values for shorter durations. One manner of distributing the drainage-average PMP is to apply the depth-area relation of PMP itself, that is, giving PMP for all area sizes within any particular drainage. Studies made for HMR No. 51, however, showed that the storms, controlling or setting PMP for small area sizes, often did not control for large areas and vice versa. Therefore, we assume that rainfall for areas less than the area of the PMP pattern will be less than the corresponding PMP, and that the depth-area relation of PMP should not be used to determine the isohyet values. The term adopted for the depth-area relations in a storm is thus a "within-storm" relation, since it serves to represent a relation for which one storm controls over all area sizes less than PMP. We have made a similar assumption, in this study, that such a curve also applies to areas larger than the area for which average PMP is being distributed (referred to as without-storm curves, see fig. 1). If one applies the pattern in figure 5 to a drainage in the orographic region in HMR No. 51 there will be an additional modification to the distribution of PMP brought about by terrain effects. It is not the intent of this report to discuss how these local modifications are derived, but their effect will be to modify or warp the pattern in the direction of major storm patterns that have been observed on the drainage. Because these modifications are a function of the specific drainage, it is recommended that each application of HMR No. 51/52 in the orographic region be the subject of an individual study. 5.2 Withln/Wlthout-Storm D.A.D Relations From consideration of the possible depth-area -duration (D.A.D) relations, we recommend a within /without-storm distribution of PMP for a drainage that falls somewhere between a flat average value (uniform distribution) and the depth-area relation of PMP. Such a relation can be patterned after depth-area relations of major storms. The within-storm technique has been used in several HMR reports (Riedel 1973, Goodyear and RLedel 1965). In this chapter, we use the generalization of such within-storm depth-area relations combined with without- storm relations to set the values of isohyets for the adopted pattern. The following sections describe the method used to obtain isohyet values at one location and explain how we generalized the procedure throughout the region. Since the method is somewhat complex, it is necessary to present a more detailed description of its development. To begin this discussion several questions are posed: a.) For which 6-hr PMP increments do we need isohyetal values?, b.) How are within/without-storm depth- area relations for 6-hr PMP increments in (a) determined?, c.) How are isohyetal profiles for a 6-hr incremental PMP used to obtain isohyet values?, and d.) How can we generalize (c) to provide isohyet values for areas between 10 and 20,000 mi anywhere within the study region? 5.2.1 MP increments for which isohyet values are required Record storm rainfalls show a wide variation in D.A.D relations. They all indicate a sharp decrease with area size for the maximum 6-hr rainfall. The remaining 6 hr rainfall increments may vary from showing a decrease, an increase, or no change with increasing area size. This mixture may be due in part to a 43 storm with a complex combination of both high and low rainfall centers with maximum depths controlled by several centers. However, for internal consistency no increase in incremental PMP values with increasing area size was allowed in HMR No. 51. If it were, it would designate a low rather than a high rainfall center, or a doughnut type configuration. We have let the D.A.D relations of PMP in HMR No. 51 set the number of increments for which areal variation is required. These show that most spatial variation occurs in the largest 6-hr increment, and practically none, if any, occurs after the third greatest 6-hr increment. This is to say, as an example, that the fourth greatest 6-hr incremental PMP determined by subtracting 18-hr PMP from 24-hr PMP varies only slightly, if at all, with area size. Therefore, we recommend distributing incremental PMP for only the three greatest 6-hr PMP increments. The remaining nine 6-hr PMP increments are used as storm pattern averages, that is, as uniform depths over the pattern area used for distributing PMP. 5.2.2 Isohyet values for the greatest 6-hr PHP increment Since we need to obtain all isohyet values for only the three greatest 6-hr PMP increments, we have chosen to discuss each increment separately. The procedure we followed began with consideration of the depth-area -duration relations taken from major storms in table 1; we used these data to develop wi thin /without - storm curves which we then converted to isohyetal profiles. Finally, we generalized these profiles in developing a set of nomograms that give isohyet values for any area size. 5.2.2.1 Depth-area relations. We chose to consider depth-area data only for those storms in table 1 that provided moisture maximized transposed depths within 10 percent of PMP for 6 hr. This condition reduced our sample to the 29 storms in table 14. Next, depth-area data for these storms, taken from the appendix of HMR No. 51, were used to form all available ratios of depths. For example, for 10 mi , divide the 10-, 200-, 1,000-, 5,000-, 10,000-. and 20,000-mi 2 depths by the 10-mi depth. Then form all the ratios for 200 mi and so on to the 20,000- mi ratios. Those within/without-storm average ratios, since they are individually done for each storm, are thus given as a percent of the respective standard area size value. Table 14. — Major storms from table 1 used in depth-area study (index numbers refer to listing in table 1) 1. Jefferson, OH 15. Merryville, LA 36. Hallett, OK 2. Wellsboro, PA 16. Bo yd en, I A 38. Smethport , PA 3. Greeley, NE 23. Kinsman Notch, NH 40. Warner, OK 6. Hearne. TX 24. Elba, AL 44. Yankeetown, FL 7. Eutaw, AL 27. Ripogenus Dam, ME 45. Council Grove, KS 8. Pater son, NJ 28. Cheyenne, OK 46. Ritter, IA 10. Bonaparte, IA 29. Simmesport, LA 47. Vic Pierce, TX 12. Knickerbocker, TX 30. Hale, CO 51. Sombreretillo, Mex. 13. Meeker, OK 34. Grant Township, NE 53. Zerbe, PA 14. Beaulieu, MN 35. Ewa n , NJ Because of the relatively small sample of storms, we chose not to consider any regional variation that may exist in these storm ratios. This conclusion is 44 believed justified at this time, however, future study should investigate regional variation in depth-area relations. The ratios obtained for the 29 storms were then averaged and the average was plotted against area size. Since some storms are relatively small in area size while others are much larger than 20,000 mi , not all 29 storms have all the depth data needed to complete all ratios, and the larger area averages are made from fewer and fewer storms. The plotted data are smoothed into a consistent set of curves as shown in figure 13. The solid lines represent within-storm averages for areas less than that of the RIP, and the dashed lines represent without-storm averages for areas greater than the area for PMP, the residual precipitation. Because of our assumption of no regional variation, figure 13 applies to the entire region. Now, by applying the curves in figure 13 to the storm area averaged PMP in HMR No. 51 at a specific location, we obtain a set of curves of the form shown in figure 14. The solid curve connects the 6-hr PMP for various area sizes (in parentheses). The short-dashed lines are the within-storm curves for areas less than the PMP area, and the long-dashed lines are the without-storm curves for areas larger than the PMP area. It is the long-dashed curves covering the residual or without-storm precipitation that are unique to this study. To use figure 14, if one considers PMP for a particular area size, say 1,000 mi , enter the figure on the ordinate at 1,000 mi , and move horizontally to the solid line to obtain the value of PMP at this location, 15.5 in. To determine the corresponding precipitation during this PMP storm for any smaller (larger) area size in that 1,000-mi^ PMP pattern, follow the short-dashed (long-dashed) curves from the point of PMP. In this figure, we have treated the juncture of within- and without-storm curves as a discontinuity, although a tangential approach to the point of PMP may be more realistic. We assume that this decision has little affect on our procedure and on the results obtained. If the PMP is for some area size other than the standard areas shown, then interpolation is necessary, using the indicated curves as guidance. 5.2.2.2 Isohyetal profile. Figure 14 gives a plot of the wi thin/without-storm precipitation relative to area size. In the application of our idealized elliptical pattern, we need to know the value of the isohyet that encloses the specified areas. That is, if we drew a radial from the center of the pattern to the outermost isohyet, it would intersect all the intermediate enclosed isohyets. If we then plotted the value of the isohyet against the enclosed area of that isohyet, we could draw a curve through all the points of intersection and obtain a profile of isohyet values for a particular pattern area of PMP. A different distribution pattern of PMP would give a different isohyetal profile. For 37°N, 89°W, we have converted the within/without-storm curves in figure 14 to the corresponding isohyetal profiles shown in figure 15. The curves in figure 15 were computed by reversing the process generally followed for deriving D.A.D curves from an isohyetal profile. This process has been briefly outlined in the "Manual for Estimation of Probable Maximum Precipitation" (World Meteorological Organization 1973). A necessary assumption for this conversion procedure is that of equivalent radius. That is, since the radius of an ellipse varies with the angle between a particular radius and the axis, different profiles would be obtained, depending upon which radial is chosen. To avoid this problem, we approximate the elliptical pattern by a circular pattern of equivalent areas and 45 -n-r (j!W) 3ZIS V3UV waois 46 00000 50000 40000 30000 20000 LI I I I I i i i i TTT I I I I I I 25 30 I 5 20 (DEPTH (in.) Figure 14.— Within/vithout-storm curves for PMP at 37°N, 89*W for standard sizes* 35 area 47 E < LxJ < 3 O UJ 00 CO st (NJ o C\J ercent are obtained for isohyets A, B, C,...,I contained within the 1,000-mi 2 ellipse, and 60, 44, 32, 21, 12, and 5 percent are obtained for the isohyets of residual precipitation (J to 0) outside the 1,000-mi 2 ellipse. 5.2.3 Isohyet values for the second greatest 6-hr PMP increment Section 5.2.2 describes the development of the procedure to obtain isohyet values for the greatest 6-hr PMP increment. We wish to follow a similar procedure to obtain isohyet values for the second greatest 6-hr PMP increment. To do this, however, we need to return to our data base of storms in table 1 and find the set of storms whose 12-hr moisture maximized and transposed rainfall came within 10 percent of the 12-hr PMP. The 12-hr depth-area data for these storms were used to compute ratios at all the available area sizes. Again, the ratios were averaged and these average ratios plotted against area size to get the 12-hr within/without-storm curves shown in figure 17. Then we converted the curves in figure 17 to depths relative to the 12-hr PMP at 37°N, 89°W (not shown). The computational procedure (World Meteorological Organization 1973) was used again to obtain 12-hr isohyetal profile curves (not shown). At this point, we subtracted the 6-hr isohyetal profile data from the 12-hr profile data to get profiles for the 2nd 6-hr increment (not shown) . Then, reading depths for the standard isohyets chosen in figure 5 and converting these into a percentage of the 2nd 6-hr increment of PMP, we developed the 2nd 6-hr nomogram shown in figure 18. Once again, a check was made for accuracy as represented by the average PMP data from HMR No. 51, and appropriate adjustments and smoothing made where needed. The set of solid curves in figure 18, representing isohyets within the PMP area, tends to have shifted closer to the 100 percent value. This is expected, because as we mentioned earlier, by the fourth increment little to no areal distribution was evident in our study computations; i.e., a value of 100 percent of the incremental PMP applies throughout the PMP portion of the pattern storm (this does not include residual precipitation). 5.2.4 Isohyet values for the third greatest 6-hr PMP increment We used the observation of converging values discussed in section 5.2.3 to obtain isohyet values for the third greatest 6-hr PMP increment, rather than repeat the complex procedure followed for the greatest and second greatest 50 100 120 140 160 ISO PERCENT OF 1st 6-hr PMP INCREMENT Figure 16. — Nomograa for the 1st 6-hr MP increment and for standard isohyet area sizes between 10 and 40,000 wl. . 51 regional locations were less than 2%. In figure 16, t although there is actual precipitat patterns may not regions where th< represent such ch The discontinuity isohyet value vari To use the nomoj the figure at 1,( points of inters approximately 149 C, . . . ,1 contained percent are obtair the 1,000-mi 2 elli 5.2.3 Isohyet val Section 5.2.2 d values for the £ procedure to obta To do this, howeve find the set of i came within 10 pe storms were used t ratios were averaj the 12-hr within/* curves in figure shown) . The corapu used again to obt< we subtracted the profiles for the standard isohyets the 2nd 6-hr incre 18. Once again, a c data from HMR No needed. The set < PMP area, tends expected, because areal distribution percent of the inc storm (this does n 5.2.4 Isohyet val' We used the obs obtain isohyet va repeat the comple: I 00000, p-r i — r 50 I 00 PERCENT OF I 2-hr PMP 250 Figure 17. — 12-hr wlthln/without-storm curves for standard area sizes. increments. Therefore, we plotted the values of the first and second greatest 6- hr PMP increments for each isohyet from the respective nomograms (figs. 16 and 18) and connected them with a smooth curve to a value of 100 percent used to represent the fourth increment. From these simple curves, we then interpolated the percents for the third 6-hr PMP increment. One advantage of this procedure was that it guaranteed consistency between results. The results of this interpolative scheme are shown in figure 19 in percent of the third greatest 6-hr PMP increment. In this figure, we see that the respective curves for PMP (solid lines) are very near to 100 percent. Note the difference in scale of the abscissa between PMP curves and residual precipitation curves, made to facilitate their use. These curves were also checked for 53 40 60 100 PERCENT OF 2nd 6-hr PMP INCREMENT Figure 18. — Nomogram for the 2nd 6-hr PMP increment and for standard isohyet area sizes between 10 and 40,000 mi . 54 20 40 60 80 PERCENT OF 3rd 6-hr PMP INCREMENT 100 100 105 PERCENT OF 3rd 6-hr PMP INCREMENT Figure 19. — Nomogram for the 3rd 6-hr PMP increment and for standard isohyet area sizes between 10 and 40,000 ml 2 . 55 agreement with HMR No. 51 as described for the previous two 6-hr increment nomograms . 5.2.5 Residual-area precipitation The nomograms in figures 16, 18 and 19 were believed sufficient to provide areal distribution of PMP within any pattern area and location. It was mentioned in section 3.5.3, that it was necessary to introduce the concept of residual precipitation, i.e., that which fell outside the area for which PMP was being distributed. Residual precipitation is needed to cover the remainder of the drainage not covered by the elliptical pattern for the area of the PMP. In each of the nomograms the dashed curves give isohyet values for application to the uncovered drainage. For the fourth through 12th increments, we have said that a constant value applies to the area of PMP being considered. Outside this area, there would be a decrease in the precipitation from that of the PMP pattern. The distribution of this residual precipitation for the fourth to 12th increments was determined from the tendencies shown for the residual precipitation isohyet values in figures 16, 18 and 19. The results of extrapolation from these relations are presented as a nomogram for the fourth through 12th 6-hr increments, in figure 20. Note these curves all start from 100%, as compared to the residual precipitation curves in figure 19. To emphasize the difference between precipitation patterns for the 1st three nomograms and that for figure 20, we show two schematic diagrams in figure 21 for a PMP pattern of 1,000 mi , as an example. The figure at the top represents a pattern of isohyets for which values are obtained for the three greatest 6-hr PMP increments. The figure at the bottom shows the pattern of isohyets for which values are obtained for the fourth through 12th 6-hr PMP increments of 1,000-mi PMP pattern. Residual precipitation in both diagrams is indicated by the dashed lines. We have added an irregularly shaped drainage to the patterns in figure 21 to clarify the point that there will be a reduction in the volume of precipitation that occurs even for the fourth through 12th 6-hr periods. That is, even though a constant value applies across the drainage as shown by the I isohyet, only a portion of the area enclosed by this isohyet lies within the drainage. 5.2.6 Tables of nomogram values We have found that different users read slightly different values from the set of nomogram figures provided in this study. To minimize such differences and since the reading of values from these figures is a recurrent process in the application procedure outlined in chapter 7, it was decided that values read from the nomograms would be provided in tabular form. Reference to the tables when making the computations in chapter 7 will assure all users have the same values. Tables 15 to 18 provide nomogram values for each of the standard isohyet area sizes and for an Intermediate area size between each of the standard isohyet area sizes. Note that, although these tables are useful for all computations, it may still be necessary to refer to the nomograms on occasion. One such ocassion would be when one wishes to distribute PMP over an area size other than one of the 56 20 40 . 60 80 00 PERCENT OF 4 THROUGH 12 6-hr PMP Figure 20. — Nome grams for the 4th through 12th 6-hr PMP increments and for standard isohyet area sizes between 10 and 40,000 mi~. 57 ISOHYET PATTERN FOR Mh TO 12 th 6- hr INCREMENT. 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This construction is discussed in chapter 7. 5.3 Area of Pattern Applied to Drainage Up to this point in our discussion we have not indicated specifically how we select the area size of the HIP to distribute across a particular drainage. In previous PMP studies, we have assumed that the maximum peak discharge and the maximum volume of precipitation in the drainage were represented by a basin- centered pattern for PMP equivalent to the area of the drainage. This assumption was necessary because we do not have sufficient information to determine what the hydrologically most critical condition is for peak, discharge. Obviously, as precipitation patterns are moved to centering positions closer to the drainage outlet, greater peaks may occur but volume probably will be reduced. In the present study, we have chosen to base our selection of PMP pattern on maximizing the volume of precipitation within the drainage. This eliminates the assumption used in other Hydrometeorological Reports that PMP be based on an area equal to the drainage area. Maximum volume is a function of pattern centering, of basin irregularity of shape, and of the area size of PMP distributed over the drainage. Of these, we have control over the pattern centering when we recommend that all patterns be centered to place as many complete isohyets within the drainage as possible. The irregularity of the drainage is fixed, and we are left with the area of the PMP pattern as a variable. However, the process of maximizing volume for various area sizes results in a procedure involving a series of trials. To obtain the area that maximizes precipitation within the drainage, we propose that the user start by selecting an area size in the vicinity of that for the drainage. It is convenient to choose areas that match those for the isohyets in our idealized pattern (700, 1,500, 6,500 mi 2 , etc.). Compute the volume of precipitation for each of the 3 greatest 6-hr increments of PMP at the area size chosen and obtain the total volume. Then, choose additional areas on either side of the initial choice, and evaluate the volume corresponding to each of these. By this trial process, and by plotting the results as area size (selected) vs. volume (computed), we can approximate the area size at which the volume reaches a maximum. (This may require drawing supplemental isohyets.) This procedure will be better demonstrated by the examples presented in chapter 7. It will be found that, as experience is gained in the application of patterns to TOriously shaped drainages, one can do a better job at the initial selection of area sizes. 5.4 Multiple Rainfall Centers In general, we recommend a single-centered isohyetal pattern for distributing PMP. From major storms of record we note that as the size of the rainfall pattern increases, the number of rainfall centers increases. This observation has led to the following considerations. 5.4.1 Development of a anl ti centered isohyetal pattern A consideration when discussing the numbers of centers in an isohyetal pattern is how the end product (the flood peak) varies with the number of rainfall 71 PATTERN X PATTERN Y Figure 22. — Schenatlc showing an example of multiple centered Isohyetal pattern (MP portion only). centers. In general, all else being equal, the more centers used, the lower the peak discharge. If multiple centers are to be considered, we therefore recommend a limit of two. The process for deriving these centers within an elliptical pattern is based on the standard isohyets and their values for a single-centered pattern as 72 determined from the nomograms described in sections 5.2.2 to 5.2.5. The multiple centers need not have equal areas nor equal numbers of isohyets. An example of multiple cell construction is shown in figure 22. In this figure, pattern X represents a single center, and pattern Y a double-centered pattern derived from pattern X. In pattern Y the enclosed area of the A isohyet equals that of A in pattern X. The sum of the areas of the two B centers in pattern Y equals that of B in pattern X, and similarly for the C isohyets. This approach satisfies the requirement to keep the volume of PMP constant, regardless of pattern selected. The magnitudes of the A, B and C isohyets in X and Y are the same. Supplemental isohyets may be necessary to provide sufficient isohyets for coverage of small multiple centered patterns. Intermediate isohyets can be determined by the technique in section 3.4. 5.4.2 Arrangement of centers Actual storms' show a multitude of possible placements of the two centers. As the size of the drainage increases, the number of arrangements that are possible also increases. It is left to the user to determine the most critical hydrologic arrangement for a specific drainage situation. This arrangement should not violate the basic elliptical shape of the total isohyetal pattern. 6. SHORT-DURATION PRECIPITATION 6.1 Introduction In applying PMP estimates to determine flood hydrographs, it Is often necessary to determine the amounts that fell within time increments of less than 6 hr. Severe storms have occurred in which all, or nearly all, of the rain fell in periods of less than an hour. In other situations, the rainfall has been much more uniform, with large amounts falling every hour for several days. It is the purpose of this chapter to develop criteria for the maximum 5-, 15-, 30- and 60- min amounts that occur within the largest 6-hr increment of PMP determined from HMR No. 51. Another important feature Is the temporal distribution of these short-duration values within the greatest 6-hr increment. This has not been studied for the present report. It is left to the discretion of the analyst to place these values chronologically in the most critical sequence. 6.2 Data The amount of storm-centered data available for durations between 1 and 6 hr is limited. Of the total storm sample available in the United States east of the 105th meridian only 29, or about 6 percent, had data for the 1-hr duration. These storms are listed in table 19 and provide a basis for much of the analysis in this chapter. For many storms, data are insufficient to define an accurate isohyetal pattern near the storm center. In these cases the value for the largest observation, or the innermost isohyet drawn, is assumed to represent the average depth over a 10-mi area. Of our storm sample, 12 had sufficient data to define the areal distribution to the nearest square mile. These storms are identified by an asterisk in table 19. Many of the storms in table 19 did not last more than a few hours. Since the information in HMR No. 51 is restricted to areas of 10 mi , or larger, it was necessary to define a relationship between point and 10-mi values for 6 and 12 73 Table 19. — Storms used in analysis of 1-hr storm-area averaged HIP values Location of storm center Lat. Long. Storm assignment Nearest station (°) C) C) (*) Date number+ Baltimore, MD 39 17 79 39 7/12/1903 SA 1-6 Bonaparte (nr) , IA 40 42 91 48 6/9-10/1905 IMV 2-5 Cambridge, OH 40 02 81 36 7/16/1914 OR 2-16 Gordon , PA 40 45 76 20 8/21-22/1915 SA 1-7 Oakdale, NE 42 04 97 58 7/16-17/1920 MR 4-18 Lancaster, PA 40 03 76 17 8/18/1920 SA 1-8 Baltimore, MD 39 17 76 37 10/9-10/1922 SA 1-9 Harrisburg, PA 40 13 76 51 8/8/1925 SA 1-10 Toledo, IA 42 00 92 34 8/1-2/1929 IMV 2-17 Lakeville, PA 42 27 75 16 7/24/1933 SA 1-11 Woodward Ranch, TX 29 20 99 28 5/31/1935 GM 5-20 Elm Grove, WV* 40 03 80 40 7/10/1937 OR 9-15 Pickwick, TN 35 05 88 14 8/21-25/1937 OR 3-25 Winchester Spr., TN* 35 12 86 12 7/8/1938 — Lucas Garrison, MO* 38 45 90 23 8/25/1939 UMV 3-19 Washington, D.C. 38 54 77 03 7/23/1940 — Ewan, NJ* 39 42 75 12 9/1/1940 NA 2-4 Plainville, IL* 39 48 91 11 5/22/1941 IMV 2-19 Iowa City, IA* 41 38 91 33 9/8/1942 IMV 2-21 Gering (nr) , NE* 41 49 103 41 6/17-18/1947 MR 7-16 Holt, MO 39 27 94 20 6/22-23/1947 MR 8-20C St. Louis, MO* 38 36 90 18 7/5/1948 IMV 3-27 Marsland (nr), NE* 42 36 103 06 7/27-28/1951 MR 7-10 Kelso, MO 37 12 89 33 8/11-12/1952 IMV 3-30 Ritter, IA 43 15 95 48 6/7/1953 MR 10-8 Tulsa, OK* 36 11 95 54 7/15/1963 — — * 35 22 98 18 9/20-21/1965 — Glen Ullin, ND* 47 21 101 19 6/24/1966 — Greeley (nr), NE 41 33 98 32 8/12-13/1966 ""■ +These numbers are assigned by the Corps of Engineers (Indexed to major drainages) and are given In "Storm Rainfall" (U. S. Army Corps of Engineers 1945- ). Storms without index numbers are from less complete storm studies maintained in the Hydrometeorological Branch. *Storms for which an isohyetal pattern was developed that permitted determination of areal values for 1 mi and larger. hr. For this purpose another storm sample was selected that consisted of all storms in "Storm Rainfall" (U. S. Army Corps of Engineers 1945- ) for which adequate data were available to define depth-area relations between 1 and 10 mi 2 These 54 storms are listed in table 20. 74 2 Table 20. — Storms used to define 1- to 10-nd area ratios for 6 and 12 hr Location of storm center Lat. Long . Storm assignment Nearest station (°) (') (°) (') Date number+ Constableville, NY 43 44 74 46 7/1-5/1890 GL 1-2 S. Camisteo, NY 42 15 77 33 7/8-13/1890 GL 1-4 Blanchard, IA 40 31 95 13 7/6-7/1898 MR 1-3A Girardville, PA 40 48 76 17 8/3-5/1898 SA 1-4 Friesburg, NJ 39 35 75 25 9/12-14/1904 NA 1-9 Bonaparte (nr), IA 40 42 91 48 6/9-10/1905 IMV 2-5 Arkadelphia, AR 34 07 93 03 6/28-7/2/1905 MR 1-16B Elk, m 32 56 105 17 7/21-25/1905 GM 3-13 LaFayette, LA 30 14 91 59 5/7-10/1907 LMV 3-12 Sugarland, TX 29 36 95 38 5/28-31/1907 LMV 3-13 Ardmore, OK 34 12 97 08 7/12-15/1927 SW 2-5 Cheltenham, MD 38 44 76 51 8/10-13/1928 NA 1-18 Algiers, LA 92 56 90 03 9/5-9/1929 LMV 4-13 yleeker, OK 35 30 96 30 6/2-6/1932 SW 2-7 Tribune, KS 38 28 101 46 6/2-6/1932 SW 2-7A St. Fish Htchry., TX* 30 10 99 21 6/30-7/2/1932 GM 5-1 Elka Park, NY 42 10 74 14 10/4-6/1932 NA 1-21 Peeka moose, NY 41 56 74 23 8/20-24/1933 NA 1-2 4A York, PA 39 55 76 45 8/20-24/1933 NA 1-24B Cheyenne (nr), OK* 35 37 99 40 4/3-4/1934 SW 2-11 Cherry Ck., C0*# 39 13 104 32 5/30-31/1935 MR 3-28A Keene, OH 40 16 81 52 8/6-7/1935 OR 9-11 Bentonville, AR 36 22 94 13 9/6-10/1937 SA 2-1 5A Cherokee, OK 36 45 98 22 9/6-10/1937 SW 2-1 5B New Orleans, LA 28 57 90 04 9/30-10/4/1937 LMV 4-2 2A Woodworth, LA 31 08 92 29 9/30-10/4/1937 LMV 4-2 2B Loveland (nr), CO 40 23 105 04 8/30-9/4/1938 MV 5-8 Miller Island, LA* 29 45 92 10 8/6-9/1940 LMV 4-24 Ewan, NJ 39 42 75 12 9/1/40 NA 2-4 Hallett, OK* 36 15 96 36 9/2-6/1940 SW 2-18 Larchmont, NY 40 55 73 46 7/26-29/1942 NA 2-7 Charlottesville, VA 38 02 78 30 8/7-10/1942 NA 2-8 Warner, OK 35 29 95 18 5/6-12/1943 SW 2-20 Mounds (nr), OK* 35 52 96 04 5/12-20/1943 SW 2-21 Pierce (nr), NE 42 12 97 32 5/10-12/1944 MR 6-13 Stanton (nr), NE* 41 52 97 03 6/10-13/1944 MR 6-15 Turkey Ridge St., SD 43 16 97 08 6/10-13/1944 MR 6-15A New Brunswick, NJ 40 29 74 27 9/12-15/1944 NA 2-16 Cedar Grove, NJ 40 52 74 13 7/22-23/1945 NA 2-17 Jerome, IA 40 43 93 02 7/15-17/1946 MR 7-9 75 feble 20. — Storms used to define 1- to 10-od area ratios for 6 and 12 hr - Continued Location of storm center lat. Long. Storm assignment Nearest station (°) (') (°) (') Date number+ Collinsville, IL 39 43 89 59 8/12-16/1946 MR 7-2B Holt (nr), MO 39 27 94 20 6/18-23/1947 MR 8-20 Wickes, AR* 34 14 94 20 8/27-28/1947 SW 3-7A Dallas, TX 32 51 96 51 8/24-27/1947 SW 3-7B Mifflin, WI 42 52 90 21 7/15-16/1950 UMV 3-28 Dumont (nr) , IA 42 44 92 59 6/24-26/1951 IMV 3-29 Council Gr. (nr), KS 38 40 96 30 7/19-23/1951 MR 10-2 Vic Pierce, TX* 30 22 101 23 6/23-28/1954 SW 3-22 New Bern, NC 35 07 77 03 8/10-15/1955 NA 2-2 IB Slide Mtn., NY 42 01 74 25 8/14-15/1955 NA 2-2 IA Big Meadows, VA 38 31 78 26 8/15-19/1955 NA 2-2 2B Westfield, MA 42 07 72 45 8/19-20/1955 NA 2-2 2A Big Elk Mdw. Res. , CO 40 16 105 25 5/4-8/1969 — Broomfield (nr), CO 39 55 105 06 5/5-6/1973 ~ — + - See note for table 19. # - Westernmost center of two large nearly equal amounts, generally known as Cherry Ck. The easternmost center is at Hale CO, 39° 36'N, 102° 08 T W (see table 1) . * - Storms with larger 6- and 12-hr values used in depth-area development. Data for durations less than 1 hr are not available from the storm studies prepared for "Storm Rainfall" (U. S. Army Corps of Engineers 1945- ). For these durations maximum annual values were used. These values were determined from excessive precipitation tables of "Climatological Data" (National Weather Service 1914- ). 6.3 1-hr MP Since maximum 1-hr data are relatively scarce, it has been necessary to resort to indirect methods to develop the 1-hr PMP. The primary tool was the development of depth-duration ratios for point or 1-mi precipitation. These were used to develop 1-mi 1-hr PMP maps. Depth-area ratios developed from storm values were used to develop maps for other area sizes. 6.3.1 Depth-duration ratios The first step in this procedure is to develop depth-duration ratios for dura- tions from 5 min to 12 hr along meridians at 2° intervals starting at 69°W. Depth-duration curves were prepared for each 2° of latitude from 29°N. For 6- and 12-hr durations, the 10-mi values from HMR No. 51 were used. Values for the 2- and 3-hr durations were obtained for the 100-yr recurrence interval from Weather Bureau Technical Paper No. 40 (Hershfield 1961). For the shorter durations, 5, 10, 15, 30 and 60 min, the 100-yr amounts were determined from NOAA Technical Memorandum NWS 35 (Frederick et al. 1977). Along the 105th meridian, 76 however, all rainfall-frequency values were determined from NOAA Atlas 2 (Killer et al. 1973). All values were expressed as a percent of the 6-hr amount, and a smooth set of curves was developed for each meridian. These curves (not shown) indicate that the ratio between amounts for durations less than 6 hr and the 6-hr amount decreased from north to south. This variation was consistent along all meridians. The same trend can be seen by examining 6- to 24-hr ratios in RIP values of HMR No. 51. Although considerable scatter is present when 1- to 6-, 2- tp 6-, or 3- to 6-hr ratios in major storms are examined, a trend toward increasing ratios with latitude can also be detected. After constructing a smooth family of curves along the meridian, the 1- to 6-hr ratios were plotted and regionally smoothed (fig. 23). This smoothing step required changes of less than 2 percent from the values determined from the sets of curves. 6.3.2 1-hr 1-nd 2 IMP 9 The ratio map of figure 23 was used to compute 1-hr 1-mi PMP values over a 2° grid from the 6-hr 10-mi PMP amounts shown in HMR No. 51. These values were plotted and isohyets drawn as shown in figure 24. The 1-hr data used to develop the 1- to 6-hr ratios were based upon single station observations, and the resulting maps can be considered "point" values. We have developed a convention for this report that they should be considered applicable to 1 mi • We do not recommend any increase in these values for smaller areas. 2 Though the paucity of data prevents development of the 1-hr 1-mi PMP by traditional methods, an important step in evaluating the reasonableness of the PMP values developed is to compare the limited data available with the derived map. Table 21 shows the important 1-hr values used in this comparison. In most cases, 1-hr values are not obtainable directly from the observations of the most extreme rainfall in the storm and must be estimated by indirect methods. The technique used for each storm is indicated in the remarks column. These maximum observed amounts together with the moisture maximized values are shown in figure 25. There are only a few storms that provide controlling or near controlling values: a) Smethport, Pennsylvania; b) Glen Ullin, North Dakota; c) Buffalo Gap, Saskatchewan; and d) Simpson P. 0., Kentucky. The moisture maximized amount for Buffalo Gap of 16.3 in. exceeds the value interpolated from figure 24 of 14.4 in. for the northern Great Plains, the region within which it could be transposed. However, the moisture maximization factor for this storm is 155 percent. Since this moisture maximized value is not supported by the values for other storms in the region, we have adopted the convention of limiting the adjustment factor to 150 percent. The Buffalo Gap observation is based upon a D.A.D analysis of the results of a bucket survey. Figure 24 "undercuts" the moisture maximized transposed value by about 1 in. and is about 4 in. larger than the observed precipitation value. Considering all the uncertainties involved, we feel this is a reasonable estimate of the 1-mi 1-hr PMP for this region, and that it is comparable to practices followed in HMR No. 51. (See section 4.1 of that report.) In figure 25, the moisture adjustment factor used for the Cherry Ck. storm is 122 percent. (This percent was also used for the Hale center of the same storm listed in HMR No. 51.) Recently, the dew point for this storm was reevaluated 77 107 103 100 100 260 300 400 KILOMETERS Figure 23. — 1- to 6-hr ratio of precipitation based on major storms used in HMR No. 51 and rainfall frequency studies. and resulted in a revised moisture adjustment factor of 141 percent. Applying this new adjustment factor to the 1-hr value for the storm gives a maximized value of 15.5 in., which more closely supports the 16.7 in. value interpolated from figure 24. The moisture adjusted values show little support for the values shown In the southern portion of the 1-hr 1-mi PMP map. The next step in the traditional method for developing PMP values would be transposition of the maximized amounts within regions of meteorological homogeneity for each extreme storm of record. Figure 26 shows the transposition limits for the Smethport, Pennsylvania storm of July 17-18, 1942, the moisture maximized value at the storm location, and the moisture maximized transposed value for the southwestern extreme of the 78 107* 103' 99* 95* 91* 87* 83* 79* 75* 71* 100 100 260 300 400 KILOMETERS 24" Figure 24. — 1-hr 1-tri. 2 MP analysis based on figure 23 and 6-hr 10-«i 2 precipitation from HMR No. 51. transposition limits. Comparison of this 18.3-in. value wLth the 1-hr 1-nrL 2 IMP from figure 24 shows a difference of 0.6 in. We consider this a reasonable envelopment of a moisture maximized transposed amount. 6.3.3 Depth-area ratios Preparation of 1-hr PMP values over the range of area sizes of interest required development of depth-area reduction ratios. A primary basis for such reduction ratios is the list in table 19 of 12 extreme storms (those noted by asterisks) for which point or 1-mi data are available at 1 hr. A problem with the data from these 12 storms is the limited area of most storms. Nearly 60 percent have an areal extent of less than 240 mi , while one fourth of them 79 _^^ cu I N 1 i-l I a u i I CO « 3 00 4J g I cm 4) • «* ■3 4-> 1 CO ^N • T3 cu l-l 3 a • 4J 0) 4-1 CO CU u 4-1 1 •H p 0) 3 4-1 3 3 1 1 «4-l 1 CO u o 0) 42 £ o 1 > •- 1 2 3 CJ o l-l K ■H •3 H "3 •H 3 CO o 0) 14-1 01 3 c_> •3 l-i O O 3 ^ gB^ g l-l CU CU 0) I-i •H • g 14-1 • x a m 0) 3 "t P CO 1 & P CE 4-> a CO cS? *3 CO CO e I 1 ■>* 4J O cC 4-1 toO-3 >-. 4J i-l I-i a o CU 3 *o 01 3 >N u ON CJ % s CD CO cu 'S 4-1 3 3 "3 o t-l CO O cu a o 3 *T3 o 3 »-i 3 3 g 3 l-l •H H M 3 CO t4 O 3 "3 a 3 CO CO o u i •H 3 4-1 P O u O 01 t-l >» cfl O cu tf CJ i-l o CO 3 & •H A! t-l a • 4-1 •8 4-1 CO CO 4J i-l 3 4= o CJ T3 3 4-1 3 o cO o l-l M 14-1 >n Vj 2 CO £ • U CO 4-1 CJ 4-1 4-1 p > rt •°JS 3 O N CU 4J a g CU *o 0) CO cu 3 ca CO 3 CO 0) o u 3 •H 4-» • I-i & 3 T3 l-l 3 4-1 CO 4-> e a • 0) O V4 > CJ • 3 3 *3 cfl 0) TJ O 4-J co 3 § 3 0) 5] c O 3 CO *T3 l-l 0) >n CO .H cO s-a 3 O « 4-1 CO T3 i-H cu o v^ •H a> t3 g § Ol 3 V-i ? w-o x. cO 4-1 X • co H CJ g CO fi a 4-1 T3 00 v- l > CJ CO f^ CO X CJ /-s 3 * 0) e 01 i-i CO o> ; 3 .3 •H l-l 60 cO tj 3 cu 4-1 X! i-H w 6 ti -u o> CO 3 * CO l-l > cu g >>-* vO O CO 4-1 P o iH > t-l t-l CO i-H o a* 2 3 CO CO •H CJ XI l-l 4-1 9 t-l CU On • 0) cu CO 3 4-1 5 a> CU o •H CO «43-l t-i a) X 1 CO •H 3 O 0^4J 3 3 s s^ CU r-l i-i 4J x. W CJ CO CO Ph 14-1 i-H iw o fe T3 Ph CO o 3 Cm CO •H CO T-l 3 1 co m s & s d C* Pi CO S o O X (0 On CM . vO vO •^ CnI 00 CM m o 1-1 • — co CnI CM CM CM o 00 3 o ^^ /-^ o- o> CO 00 > H 4-> O /"N X W s iH • o A < 55 4J ^ s • Cu o 2 co 4-1 CO o o 4-1 cj >N 0) <2 5 o • a. 3 o 4J O CU O M CU Ol l-l CJ 0) u X CO x A 1-1 0) CJ •o & 4-1 4-1 CU 9 -0 Vw' o 0) i-l > H o •H o o 1 2 H s CO CO 33 CJ 80 a f o MM u I 09 « CO 4J i 4J M 4) H 03 i-4 5 n 4-> I <-< <0 ? c + 01 60 c co co CO ct) I xj 3 co l-< O 4J Cb CO CO c «H cu T3 3 fl c 6 O U -H C Fn 4-> «H in s so 60 s - d o *- .J o 00 d <3 * d O cu o o i-l -u cfl rt 4-1 CO FQ CO* d o • 8 4J o -n cu U >H $* 2 M O W CU CO 4-1 3^4, jj en > CO d D CU u 3 I-l o g eg co CO 'O d >■» CJ CM 9 co (3 •h ^ X § ° 4-1 CO X) ■rt J-i *o CO 0) 4J 01 0) a. n g a. o g •O cO • CU *J 8, r-4 rH rH CO cu 43 2 XI CO o cu o > 4-1 I-i Pn a) % O O 2 os 00 r^. r-» vD v£> I-l C* cs sO d t^ O .H ■H V 4-1 4-> 5 g 73 O d a, w a CO • CO X g « 01 91 "^ > i-i a) co xi o sO SO en i o a-* — 1 o O 4J U-l OJ d (11 H cu cu Xi 4J si 1 2 a o 60 d •H 1 OJ CO cu o 24 hr) requires a sustained moisture inflow that is most likely to occur nearest the coast and decreases inland. This contrasts with the moisture requirements for a short-duration local storm which is likely to occur almost anywhere. The adopted 1-hr depth-area curve, in percent of the 1-mi PMP, is shown in figure 28. This curve covers area sizes as large as 20,000 mi and was determined primarily to provide areal 1-hr values that enveloped available data. Since most of the available data are from small area storms 9 (<500 mi ), there is less reliability with increasing area size. Nevertheless, 1-hr 20,000-mi . data are available for the Bonaparte, Iowa storm (6/9-10/1905), which provided a large-area check of the adopted depth-area relation. 6.3.4 1-hr MP for areas to 20,000 ni 2 The depth-area curve developed in the preceding section (fig. 28) was used to compute PMP for 10, 100, 200, 1,000, 5,000, 10,000 and 20,000 mi (figs. 29 to 35, respectively). The four storms (see section 6.3.4) which provide significant support for the 1-mi 1-hr PMP also provide evidence of the reasonableness of the PMP values for these larger areas. In addition, the moisture maximized value for Cherry Ck., Colorado is within 15 percent of the PMP at the storm location. The moisture maximized- value for the Simpson, P.O., Kentucky storm exceeds the estimated PMP at the storm location by 0.4 in. for 10 and 100 mi . At 200 mi , the PMP and the moisture adjusted value for Simpson are about equal. Since the 1-hr amount was determined from a reconstructed depth-duration curve, it was decided not to revise the PMP estimate based on this difference. 6.4 HIP for Durations Less Than 1-hr As mentioned in section 6.2, there are no storm studies that have data for durations less than 1 hr. The very-short duration data most nearly representative of extreme storm situations can be found in the excessive precipitation tablulations published in "Climatological Data" (National Weather Service, 1914- ). A series of the maximum annual values was determined for each duration of interest for every station in the east where such data are available. These data were examined to see if there was any trend for higher or lower ratios with the magnitude or recurrence Intervals. The data indicate that the ratios have a slight tendency to decrease with increasing magnitude. There is also a slight geographic variation with the ratios with decreasing latitude. These trends have been incorporated into the appropriate ratio maps. Only one set of ratio maps (relative to 1 hr) have been provided, figures 36, 37, and 38 for the 5-, 15-, and 30-min durations, respectively. Since there are no data from which to develop areal corrections, we apply the same ratio for all areas. It Is for this reason that we feel values for these shorter durations should be be limited only to area sizes of 200 mi or less. 85 10000 000 2S < llj cc < 00 10 DEPTH-DURATION RELATION FOR I -HR PMP (100) figure 28. amount. PERCENT OF I -HR I -Ml' -Depth-area relation for 1— hr PMP In percent of ixlaum point (1-nd ) 86 107 103 99 95 91 87 — I 1 — i i i ' i i' i — 100 100 200 300 400 KILOMETERS Figure 29. — 1-hr 10-nd 2 MP analysis for the eastern United States. 87 STATUTE MILES 100 100 200 300 ' i I I ' I '' i ' 100 100 200 300 400 KILOMETERS Figure 30. — 1-hr 100-nri/ PMP analysis for the eastern United States. 88 Figure 31. — 1-hr 200-ni MP analysis for the eastern United States. 89 107 103 99 95' 91 87 83* 79* 75* ^ 71* 100 190 200 39 000 100 200 300 400 KILOMETERS Figure 32. — 1-hr 1,000-nl MP analysis for the eastern United States. 90 100 100 200 300 400 KILOMETERS Figure 33. — 1-hr 5,000-nd 2 MP analysis for the eastern United States. 91 107 103 STATUTE MILES 100 200 300 -i 1 1— 3 —! r 1 — I 1 100 100 200 300 400 KILOMETERS figure 34. —1-hr 10,000-ai 2 MP analysis for the eastern United States. 92 300 400 Figure 35. — 1-hr 20,000-nd z MP analysis for the eastern United States. 93 100 100 200 300 ' -< 1 1 T i H — I — J 100 100 260 300 400 KILOMETERS Figure 36. — Ratio analysis of 5- to 60-mln precipitation used to obtain 5-nln MP. (Applicable to area sizes < 200 nd 2 .) 94 Figure 37. — Ratio analysis of 15- to 60-ndn precipitation used to obtain 15-nrLn MP. (Applicable to area sixes < 200 mi 2 .) 95 107 103 99 95 91 STATUTE MILES 100 200 -i >— — i — i-T 1' I 100 100 200 300 400 KILOMETERS W ^ e 3 f;— Batio analysis of 30- to 60-ndn precipitation used to obtain 30-ndn mP. (Applicable to area sixes < 200 mi .) 96 6.5 Isohyet Values for Durations Less Than 1-hr As in chapter 5, where a procedure vas given to compute isohyet values for each 6-hr isohyetal pattern of the 72-hr IMP, it is also important to provide a procedure to distribute the precipitation for durations within the greatest 6-hr increment. Such information has not been included in any previous study. Also, since little depth-duration data were available for the durations less than 6 hr in the major storms, it was not possible to pursue an approach similar to that used in chapter 5. Furthermore, one finds that by plotting the isohyet values for each 6-hr period, it is possible to fit the short durations (<6 hr) by any number of smooth curves. Especially for large values of 6-hr PMP the depth- duration relation for durations less than 6 hr has the greatest curvature and therefore the greatest flexibility in curve fitting, depending upon the individual analyst. As a consequence, a procedure was adopted that allowed answers to be obtained with an accuracy of ± 10 percent. This tolerance was judged acceptable considering the approximations involved in the procedure. Sections 6.5.1 and 6.5.2 describe the procedure to obtain isohyet values for isohyets in the PMP portion of the pattern as applied to short durations within the greatest 6-hr increment. Residual isohyet values are discussed in section 6.5.3. The discussion and example in chapter 7 are meant to further clarify the application of this procedure. 6.5.1 Description of procedure Only a brief description of the procedure has been provided here. Following the procedure in chapter 5, it is possible to determine the isohyet values for the greatest 6-hr increment relative to a specific drainage application. It was noted in . some sample applications that the 6/12-hr ratios obtained for each Isohyet decreased with increasing isohyets (area). This result implies that the 1/6-hr or 15-min/6-hr ratios will also vary between isohyets. The adopted procedure recognizes this variation and was developed as follows. Depth-duration curves were drawn for each isohyet from data for the 4 greatest 6-hr increments of PMP. Values for 1 hr were interpolated from these curves and 1/6-hr ratios determined. These ratios were plotted against area size (area enclosed by respective isohyets) and a smooth curve drawn through the points. A comparison was then made by computing the area-averaged precipitation obtained from distributing the precipitation according to the smooth curve and determining the area -averaged depth taken directly from the D.A.D data based on figures 24, and 29 to 35. The smooth curve was then adjusted to correct for any discrepancies. Determining the ratio curves at a number of locations throughout the region and for a number of pattern area sizes showed a regional and a real variation in the results. To account for the regional variation, it was decided to prepare an index map for the 1-hr 20,000-mi ratios of the 6-hr labels for the A isohyet. This particular choice was based on a number of trials and this area size was selected because it had the greatest regional variation. Figure 39 shows the 1/6-hr ratio index map. In this map the ratios increase from the southeast to the northwest through most of the region. To show the areal variation, a regionally averaged nomogram was developed, as shown in figure 40. The abscissa is based on a scale of percent of the corresponding 6-hr isohyet value. It was necessary to omit every other isohyet (B, D, F, H) from these nomograms for clarity, but simple Interpolation will 97 1 00 100 200 30 100 100 260 300 400 KILOMETERS 9 figure 39. — Index nap for 1- to 6-hr ratios for 20,000-nd. "A" isohyet. provide values for the missing isohyets. The nomogram does not include information for the residual isohyets. 6.5.2 Application of nomogram for short duration isohyets The use of the relations in figure 40 is simple. One locates the center of the drainage being considered (for which 6-hr isohyet values have been determined as directed in chapter 5) on figure 39 and interpolates the 1/6-hr ratio. This ratio then represents the label of the 1-hr 20,000-mi A isohyet on the nomogram in figure 40. The user must then make a copy of the scale provided with the nomogram and place the scale on the nomogram to correspond to the value determined from the index map. Having adjusted the scale, all isohyet values 98 CJ ex. < £-4- n 44- | i i [ — m 4-f — ! i i i 4-h ■ j i itit 1 1 w p ■Li- i i i"1 — MM — i ) M ISOHYETS ONMLKJIGECA - — — 4^ =- r I i . -x _ — 1 j - ^"^- 4 "? 44— — - •> A m i i i i i r i ii . . i - EfE i_ - — - 4= — ^_ H- -x — t— .. 1 t - i /// zt ■Mi //// fill ± 0000 - ULIUA -t4 - ----- t- .... 4 — ! — \— — 4— ! 1 — 1 — 1 — 1 — — 1- 1 ^o.fll Percent of 1 st 6-hr isohyet value 20 25 30 35 40 7 1 : 1 1 1 1- : : . f ■ i : iu\ f r •" i 1 fi VI!. fill I ! i J r HI Iff fH'tt : J S t Y mm ! M NOTE: SCALE MUST BE ADJUSTED __ HORIZONTALLY TO KEY THE "A" ISOHYET __ AT 20,000 Ml 2 INTO THE VALUE DETER- a. ~m\ wmw ! : 3 t\ i -;:"-' •.-':- Ftp W t\\ : ? . .. :•■:.]__ M- 4 l-i L -4-1- — , 1 ! 1 . | MINI — t — t — | 4=r :d FROM FIGU 44^r =?E 4= 39. -: - - — H- 1 — i — _~ 4- 4444 _ 1 It m ijjCvv. — i 1— ^T^ 4- — . - — — #4± .!_ 4~ J ~- .j_l! _ i ' •> '$t? > V -h 1 000 - ] 3 . - i "";-'■-■ ; f : i ! i -j ■ j |-Tvs^ fc< 1 ]_ j } . « ,. i- ' M 4 ; 1 - MM MM i-: ! ! tX 44 L. !!{_.}' K J f ^ 'i-i ' .r^ 4= =.=-4-^ it t : " 4!|| f _ 4 -r M- Hi 7 K .. ! i [ i ..! 1 -j i4-r44 — r44 — 4 -, ■. i : *v 4 ' ; ; ; 4 : 5 1- mm* -1 ! Mi£p- wi ^^ 4-_j_ j 4~ i 1 14 ^m^ 1 1 i !— 4 t -T i. j r 44 Jt - 1 r : : : : i i i ! 4 , i | -.4 ! t ■ It! 1 p ■ !--( f 4 ! "H — m~i — j-t 44-444-x I 1 j i f ?p & 1 } 1 =t^4~ 14-. ! i 1 t -4 — i — i — \ — MM M 1 i ; H 7 4| — f — i — i — : — — 3 m44X44 -— — 4 J_ { -l-TtTi H i : r l~ L-j L-- - = i— - L44 4^4 \Vk; • Li .M — 4 — 4— -1- — ~ rX- M- -4444 m^ 4 XX t u +: ^ : ~ =p4Et44 ---Tt|4-fa ..J - _l_ 4444 m : _L._|_ 4^:4=z 44 —I— — i — 1 — 1 1 1 -IX. —4- — — [ — • 4r 4 - u 4 =t= 4- ■1- =X _4-h "PIT 4444 - — -r 1 _L. 1 1 I ' 1 1 1 1 iii Ml i ! 4. ! 1 1 ! i -i 1-LL. 1 _ 1 1 DO Mi 1 | i i i ! 1 i . 1 ! 1 ; • i ! ; i f ~ { ■ | j 4 ! ! 1 ; j 1 8 ?r-H TV fgp=Xfl i~ . -L. j i i IS i {- j-ii ! ' ■ 4 4 ~n^- L j -i X i . j ' MM 7 6 4iJ : - -ir.-r r E5= n4^ — -- Wf MM ..J. ! 1 -! *K 1 1 1 1: 5 -.Sri-*.-- "._- : — r-rq — ?r£ — r ■ ? i t - 'vi ■ i j . = i 4 i ; : i j 1 w t J ' 1 t — ! — ! — c : : : 1 MM : 4 :• • \'3 : i 1 i p M ; • ; : t -. i V i 4 M . j ! i : j I : ttsa frlli ~|~l~ -ff- p* 3 • ; ': ; . • i r- : 1 ? 4-±4M= 44 4^ — H gpffffl 43444^ ; . l. 1 Hi _i_l — — 1— j — : —I — 44= 44" • - - M Ml _!_ -H-h— H — i — 'iii — 1 I 1 — H— — -j— _ -fH — i- i j j 1 j 1 iii 1 i j i ! ! : ! i 1 1 1 1 ill \ 1 0- 1 . . , , 1 1 i : • 4 Figure 40. — Regionally-averaged nomogram for 1-hr Isohyet values in percent of 1st 6-hr isohyet values. 99 may be read directly from the nomogram as percents of the corresponding 6-hr isohyet values. Once all isohyet values have been read, the ratios are multiplied by the greatest 6-hr isohyet values to get the 1-hr isohyet values. Because of the areal limitations discussed in section 6. A, we suggest that isohyet values for any durations less than 1 hr also be limited to small pattern areas (< 200 mi ). For such cases, short duration isohyet values can be interpolated from smooth curves connecting the 1-, 6-, 12-, 18- and 24-hr values to zero. Following this procedure for areas larger than 200 mi will result in pattern- averaged depths that are less than that of IMP determined from figures 36-38. 6.5.3 Isohyet values for short duration residual isohyet s Attempts were made to obtain values for isohyets describing residual precipitation along similar lines as discussed above. However, the results were confusing and the procedure abandoned. It was decided that the alternative was to allow interpolation from smoothed depth-duration curves drawn through isohyet values for the 6-, 12-, 18- and 24-hr durations connected to zero. These curves are relatively more flat than those for isohyets in the PMP portion of the pattern, especially those enclosing the smaller areas. Flatter curves allow the least flexibility in fitting the curve for durations less than 6 hr, and therefore the error involved in this decision is minimized. 7. PROCEDURE AND EXAMPLE APPLICATION Chapters 2 through 6 describe the development of guidance for distributing storm-area averaged PMP from HMR No. 51 over a specific drainage. Since much of this material and the considerations involved in its application are unique to this study and represent a relatively complex computational process, it is believed useful to summarize the results of the study in the form of a stepwise procedure. To further emphasize the meaning of each of the steps, two examples are fully detailed as additional insight into the methods recommended. Because of the complexity involved in the use of these procedures and the acknowledged length of time required to complete one application, it is recommended that the procedure be automated by those users having access to such capability. 7.1 Stepwise Procedure The following stepwise procedure is recommended for distributing storm-area averaged PMP over a drainage. In addition, some guidance considerations are provided to aid the user when a subjective decision is required. A. 6-B.r Incremental PMP (refer to BUR No. 51) Step 1. Obtain depth-area-duration (D.A.D) data from figures 18 through 47 in HMR No. 51 for the location of the drainage. Location is customarily judged at or near the center of the drainage. For particularly large drainages in which isohyetal pattern placements may be made at considerable 100 distance from the drainage center, the location of the pattern center should be used to obtain the appropriate D.A.D data. 2. Plot the data in step Al on semi -logarithmic paper (area on the log scale) and join points of common duration with curves. When drawing a smooth set of curves, we recommend that the curves be adjusted to assure that they are either parallel or show slight convergence with increasing area size; i.e., the largest incremental differences occur at 10 mi , and the smallest incremental differences occur at 20,000 mi 2 in HMR No. 51. 3. From the curves in step A2, read off D.A.D values for a set of standard isohyet area sizes* both larger and smaller than the area size of the specific drainage. Where possible, it is recommended that at least 4 pattern area sizes larger and smaller be used to adequately enclose the area size corresponding to maximum precipitation volume (see step Cll). 4. For each of the pattern area sizes selected in step A3, plot the depth-duration data (at least to 48 hr) on linear paper and fit a smooth curve to enable interpolation of values for the 18-hr duration. 5. Obtain incremental differences for each of the first three 6-hr periods (0 to 6, 6 to 12, and 12 to 18 hr) through successive subtraction for each area size considered in step A4. Because of possible inaccuracies in reading the map analyses, plotting, and drawing for the data in the preceding steps, the 6-hr incremental values should also be plotted (on semi-log paper) and smoothed to insure a consistent data set. Incremental data should decrease or remain constant with increases in both duration and pattern area size. In drawing these final smoothing curves choose a scale for the abscissa (incremental depths) that allows values from curves to be read off to the nearest hundredth. B. Isohyetal Pattern Step 1. A tracing of the drainage should be placed over the isohyetal pattern in figure 5, drawn at comparable map scales. Placement of the pattern (or adjustment of the drainage axis) is a subjective consideration. Placement is generally regarded as that which inputs the maximum *The standard isohyet area sizes are those of: 10, 25, 50, 100, 175, 300, 450, 700, 1,000, 1.500, 2,150, 3,000, 4,500, 6,500, 10,000, 15,000, 25,000, 40,000, and 60,000 mi 2 . 101 precipitation to the drainage. In most cases this consideration is met by drainage-centering the isohyetal pattern, that is, the isohyetal and drainage patterns have approximately the same center and axial orientation (see section 4.4.4 for exception). Judgment is guided by trying to place the greatest number of whole isohyets completely within the drainage, since the isohyets that enclose smaller area sizes contain proportionately higher rain amounts. This guidance is subject to consideration of the relative orientations preferred for PMP-type patterns discussed in the following steps. 2. Determine the orientation (to nearest whole degree) of the pattern when placed on the drainage, in terms of degrees from north. If this orientation does not fall between 135° and 315°, add 180° so that it does. 3. Determine the orientation preferred for PMP conditions from figure 8 at the location of the pattern center. If the difference between orientations from step B3 and B2 is less than 40 degrees, then for the isohyetal pattern as placed over the drainage there is no reduction factor to consider. If the orientation differences exceed 40 degrees, then a decision must be made whether the pattern is to be placed at some angle to the drainage at which no reduction to isohyet values is required, or aligned with the drainage and a reduction made to the isohyet values. A truly ob- jective decision on the orientation of the pattern yielding maximum volume would require numerous applications. As guidance, the area size of the drainage, the shape of the drainage, and the differences in orientations (preferred PMP and pattern placed on the drainage) have the greatest bearing on the volume of precipitation determined. Only the experience gained from numerous trials will enable the user to reduce the effort involved in making these decisions. An illustration of the effects of alternative placements is demonstrated in the examples. 4. Skip this step if no adjustment for orientation is needed. Having settled on a placement of the isohyetal pattern, de- termine the appropriate adjustment factors due to orienta- tion for the isohyets involved from the model shown in figure 10 (read to tenths of percent). Note that the amount of reduction is dependent upon area size (only pattern areas larger than 300 mi need to be reduced) and the difference between orientations. Multiply the adjustment factor times the corresponding 6-hr incremental amounts from step A5 for each pattern area size to obtain incremental values reduced as a result of pattern orientation. C. Maximum Precipitation Volume Determine the maximum volume of precipitation for the three largest 6-hr incremental periods resulting from placement of the 102 pattern over the drainage. To do this, it is necessary to obtain the value to be assigned to each isohyet in the pattern that occurs over the drainage during each period. Guidance for this determination is given in the following steps related to the format presented in figure 41. It is suggested that an ample number of copies of this figure be reproduced to serve in the computation procedure. Step Start by determining the maximum volume for the 1st 6-hr incremental period. 1. Fill in the name of the drainage, drainage area, date of computation, and increment (either 1st, 2nd or 3rd) in the appropriate boxes at top of form (fig. 41). 2 2. Put the area size (mi ) from step A3 for which the first computation is made under the heading at the upper left of form. 3. Column I contains a list of isohyet labels. Use only as many isohyet s as needed to cover the drainage. 4. For the area size in step C2, list in column II the corresponding percentages read from table 15 or the nomogram in figure 16 (first 6-hr period) for those isohyets needed to cover the drainage; use table 16 or figure 18 and table 17 or figure 19 for the 2nd and 3rd 6-hr periods, respectively, when determining step CIO. 5. Under the heading amount (Amt.) in column III place the value from step B4 corresponding to area size and increment of computation. Multiply each of the percentages in column II by the Amt. at the head of column III to fill column III. 6. Column IV represents the average depth between adjacent isohyets. The average depth of the "A" isohyet is taken to be the value from column III. The average depth between all other isohyets which are totally enclosed by the drainage is the arithmetic average of paired values in column III. For incomplete isohyets covering the drainage, it is necessary to make a weighted estimate of the average depth if a portion of the drainage extends beyond a particular isohyet. The average depth for the extended portion of the drainage may be taken as 0.5 to 1.0 times the difference between the enclosing isohyets plus the lower isohyet. The weighting relation is given by: F (X-Y) + Y where X and Y are adjacent isohyet values, X > Y, and the weight factor, F, may be between 0.5 and 1.0. If only a small portion of the drainage extends beyond X, then the 103 Figure 41. — Example of computation sheet shoving typical format. Drainage: Area : Increment: Date: I II III IV V VI I II Ill IV V VI Area size Iso. Nome Amt . Avg. depth AA AV Area size Iso. Nomo. Amt. Avg. depth AA AV A B C D E F G H I J K L M N P A B C D E F G H I J K L M N P Sum = Sum = Area size Amt. A B C D E F G H I J K L M N P Area size Amt A B C D E F G H I J K L M N P Sum = Sum = Area size Amt. A B C D E C H I J K L M N P Area size Amt. A B C D E G H I J K L M N P Sum = Sum 104 weight factor may be taken closer to 1.0, and if the drainage extends nearly to Y, then a weight factor close to 0.5 is appropriate. 7. Column V lists the incremental areas between adjacent isohyets. For the isohyets enclosed by the drainage, the incremental area can be obtained from table 8. For all other isohyets it will be necessary to planimeter the area of the drainage enclosed by each isohyet and make the appropriate successive subtractions. The sum of all the incremental areas in column V should equal the area of the drainage. If the computation in step 5 results in the zero isohyet's crossing the drainage, the appropriate total area is that contained within the zero isohyet, and not the total drainage area . 8. Column VI gives the incremental volume obtained by multiplying values in column IV times those in column V. The incremental volumes are summed to obtain the total volume of precipitation in the drainage for the specified pattern area size in the 6-hr period. 9. Steps C2 to C8 are repeated for all the other pattern area sizes selected in step A3. 10. The largest of the volumes obtained in steps C8 and C9 represents the preliminary maximum volume for the 1st 6-hr incremental period and specifies the pattern area to which such volume relates. The area of maximum volume can be used a 8 guidance in choosing pattern areas to compute volumes for the 2nd and 3rd 6-hr incremental period. Presumably, this guidance narrows in on the range of pattern area sizes considered and possibly reduces in some degree the number of computations. Compute the 2nd and 3rd 6-hr incremental volumes by repeating steps CI to C9, using the appropriate tables or nomograms. 11. Sum the volumes from steps C8 to CIO at corresponding area sizes and plot the results in terms of volume vs. area size (semi -log plot). Connect the points to determine the area size for the precipitation pattern that gives the maximum 18-hr volume in the drainage. 12. It is recommended, although not always necessary, that the user repeat steps C2 through Cll for one or two supplemental area sizes (area sizes other than those of the standard isohyetal pattern) on either side of the area size of maximum volume in step Cll. This provides a check on the possibility that the maximum volume occurs between two of the standard isohyet area sizes. To make this check, an isohyet needs to be drawn for each supplemental area size in the standard isohyetal pattern and positioned on the drainage so that the corresponding incremental areas between isohyets can be determined (planimetered). In addition, supplemental cusp points need to be determined in figures 105 16, 18 and 19 for each of the area sizes considered. To find the appropriate cusp position, enter the ordinate at the supplemental area size, and move horizontally to intersect a line between the two most adjacent cusps. This intermediate point will be the percentage for the supplemental isohyet when reading the other isohyet percentages in step C4; otherwise follow the computational procedure outlined. 13. The largest 18-hr volume obtained from either step Cll or C12 then determines the final pattern area size of maximum volume for the pattern placement chosen in step Bl. D. Distribution of Storm-Area Averaged IMP over the Drainage Step 1. For the pattern area size for IMP determined in step C13, use the data in step A3 to extend the appropriate depth- duration curve in step AA to 72-hr, and read off values from the smoothed curve for each 6 hr (6 to 72 hr). 2. Obtain 6-hr incremental amounts for data in step Dl for the 4th through 12th 6-hr periods in accordance with step A5, and follow procedural steps Bl to B4 to adjust these incremental values for isohyetal orientation, if needed. 3. Steps Dl and D2 give incremental average depths for each of the 12 6-hr periods in the 72-hr storm. To obtain the values for the isohyet s that cover the drainage, multiply the 1st 6-hr incremental depth by the 1st 6-hr percentages obtained from table 15 or the nomogram (fig. 16) for the area size determined in step C13. Then multiply the 2nd 6- hr incremental depth by the 2nd 6-hr percentages from table 16 or the nomogram (fig. 18) for the same area size, and similarly for the 3rd 6-hr increment (table 17 or fig. 19). Finally, multiply each remaining 6-hr incremental depth by the 4th through 12th percentages in table 18 or the nomogram (fig. 20). As a result of this step, a matrix of the following form can be completed (to the extent of whichever isohyets cover the drainage). Isohyet (In.) A 6-hr periods 5 6 7 8 9 10 11 12 B C Isohyet Values (in.) etc. 4. To obtain incremental average depths for the drainage, compute the incremental volumes for the area size of the PMP 106 pattern determined in step CIO. Divide each incremental volume by the drainage area (that portion covered by precipitation) . 5. Should it be of interest to determine the isohyetal values for durations less than 6 hr within the greatest 6-hr increment, the procedure discussed in section 6.3 gives the following steps. a. Interpolate the 1/6-hr ratio at the drainage location from figure 39. b. Adjust an overlay of the scale given in figure 40 along the abscissa of the figure such that the 20,000-mi "A" isohyet equals the ratio read in step D5a . c. At the area size for the IMP pattern found in step CIO, read from the nomogram (fig. 40) percentages of the 6-hr isohyet values. These isohyet s cover only the PMP portion of the pattern. d. Multiply the ratio in step D5c by the corresponding 6-hr isohyet values in step D3 to obtain 1-hr isohyet values. e. Plot the values from step D5d along with the 6-, 12-, 18-, and 24-hr isohyet values for each isohyet from step D3. Draw a smooth curve of best fit through points for each isohyet to include the origin. f.. Read off isohyet values for any other intermediate duration of interest. Note that the values interpolated from these smooth curves, 5-, 15-, and 30-mLn durations, will result in somewhat lower drainage-averaged PMP estimates than obtained from figures 36-38. g. To obtain isohyet values for any isohyet of residual precipitation in the PMP pattern, plot the 6-, 12-, 18- and 24-hr isohyet values from step D3 and fit a smooth curve through the points to include the origin. Read off isohyet values for any intermediate duration. (Note in step D5f is also valid for 1-hr values in this step.) E. Temporal Distribution In the matrix in step D3, storm^area averaged PMP has been distributed according to increasing 6-hr period. The discussion in chapter 2 provides guidance on distributing these incremental periods with time. A number of distributions are possible, with the choice being left to the user, depending on which is most appropriate for the drainage under study. Whatever distribution is selected must be applied to all isohyets. An example of one possible distribution is reordering the 6-hr incremental periods in step D3 as follows: 107 6-hr periods 1 2 3 4 5 6 7 8 9 10 11 12 11 10 851234679 12 F. Subdrainages Should it be necessary to determine the areal distribution of PMP across subdrainages of a particular drainage, consider the following steps: Step 1. With the pattern placed across the entire drainage as given in step Bl, and incremental isohyet values as determined in step D3 and/or D5, planimeter the incremental areas contained between isohyets within each subdrainage. 2. Follow the computational procedure outlined in steps C5 to C8 to obtain the incremental subdrainage volumes for 6-hr periods 1 through 12. 3. The subdrainage volumes divided by the subdrainage areas yield the average depths across the subdrainage for each 6- hr increment . Note: If the subdrainage is crossed by the zero isohyet, the appropriate area for consideration is the subdrainage area inside the zero isohyet, not that of the total subdrainage. 4. If it is hydrologically critical to rearrange the temporal sequence of the incremental amounts determined in step F3 for a particular subdrainage, then it is necessary that the same arrangement be applied to all other subdrainages. This requirement is important and must be observed without exception. Demonstration of a subdrainage application is given in example 2a . 7.2 Example No. la The first example demonstrates the computational procedure, and shows the affect on maximum volume determination that results from consideration of orientation of the isohyetal pattern. The drainage used in this example is that of the Leon River in Texas above Belton Reservoir (approximately 3,660 mi ) shown in figure 42, drawn to a scale of 1:1,000,000. Drainage center is about 31°45'N, 98°15'W. The following steps correspond to those outlined in section 7.1 leading to determination of the area size of the isohyetal pattern that gives maximum volume, from which we then assign isohyet values. 108 4) 60 B * I t 4) CO 41 cd «s o X > 4) *3" 0) 60 109 Step Al. For the Leon River drainage above Belton Reservoir (31°45°N, 98°15'W) we obtain storm-area averaged IMP data from HMR No. 51, figures 18 through 47 as, Duration (h o 2 Area (mi ) 6 12 24 48 72 10 29.8 36.2 41.8 46.7 49.8 200 22.3 27.4 33.0 37.5 41.4 1000 16.2 21.2 26.8 31.0 34.5 5000 9.3 13.1 18.1 22.6 25.9 10000 7.2 10.4 14.9 18.8 21.0 20000 5.2 8.2 11.7 15.4 18.4 A2. The depth-area -duration data in step Al is plotted in figure 43, and smooth curves drawn. The decision on how to smooth these curves to the data points is left to the user, although it is cautioned they are to be parallel or converge slightly with increasing area size. A3. From figure 43, we can read off values for the standard areas of isohyets area (3,660 mi 2 ). areas of isohyets both larger and smaller than the drainage Duration (hr) 2 Area (mi ) 6 12 24 48 72 1000 16.1 20.7 26.1 30.5 34.1 1500 14.4 18.9 24.1 28.5 32.0 2150 12.9 17.2 22.3 26.7 30.2 3000 11.5 15.7 20.6 25.0 28.5 4500 9.8 13.9 18.6 22.8 26.4 6500 8.5 12.4 16.7 21.0 24.3 10000 7.1 10.6 14.8 18.8 22.0 15000 5.9 9.3 13.0 16.8 20.0 A4. The data in step A3 are plotted on linear paper and smooth depth-duration curves drawn as shown in figure 44. From these curves we interpolate 18-hr values: 2 18 ' hr Area (mi ) Dura ti on 1000 23.7 1500 21.8 2150 20.0 3000 18.5 4500 16.5 6500 14.8 10000 13.0 15000 11.3 110 40000, 30000 20001 10001 5000 4000 3000 2001 I I ' I | I I I I | | | I I I I I I DURATION (hr) I I I I I I I I I I I I I l I I I I I I I I I I < UJ a. < I 000 — 500 40< 30( 200 I0( 50 40 3< 2 01- I 01 l__J I l_ Figure 43. — Depth-area -duration curves for 31°45 , N, 98°15'W applicable to the Leon River, TX drainage. A5. Incremental differences for the 1st three 6-hr periods are obtained by successive subtraction of the values contained in steps A3 and A4. 6-hr periods Area (mi ) 1000 16.1 4.6 3.0 1500 14.4 4.5 2.9 2150 12.9 4.3 2.8 3000 11.5 4.2 2.8 4500 9.8 4.1 2.6 6500 8.5 3.9 2.4 10000 7.1 3.5 2.4 15000 5.9 3.4 2.0 ill I I I I I P IT 30 25 20 I I- o. q I 5 I I I I I I I I I 'I I I I ' I 2 I 8 24 30 DURATION (hr) 36 ' ' 42 48 i i ■ i Figure 44. — Depth-duration curves for selected area sizes at 31 45 f N, SS'IS'W. Plotting each set of 6-hr values against area and fitting the points by smooth lines as shown in figure 45 gives the following set of incremental data (read to hundredths). 112 "i < < 20000 I OOOi 5000 400 3000 2000 I 000 500 400 300 200 I 00 t 1 — ' — i r 1 — ■— r i r LEGEND nt nt nt 1 I I I 2 3 4 5 2nd AND 3rd 6-hr AVERAGE DEPTHS (in.) I l _L 5 I 1st 6-hr AVERAGE DEPTHS (in.) Figure 45. — Smoothing curves for 6-hr Incremental values at selected area sizes for Leon River, TX drainage. 6-hr peri ods 2 Area (mi ) 1 2 3 1000 16.10 4.60 3.01 1500 14.35 4.42 2.89 2150 12.82 4.27 2.79 3000 11.40 4.14 2.70 4500 9.80 3.96 2.58 6500 8.50 3.82 2.48 10000 7.05 3.66 2.36 15000 5.80 3.50 2.25 113 Note that wLthin each column as a result of this smoothing, the values consistently decrease with increasing area size. Bl. The isohyetal pattern is then drainage-centered over the Leon River drainage drawn to 1:1,000,000 scale as shown in figure 46. Our judgment of best fit enclosed the "H" isohyet within the narrow outline of the drainage. The "N" isohyet encloses almost all the drainage. B2. The orientation of the pattern, when fit as in figure 46 is roughly 134°/314°. The 134° misses by 1° our preferred range (135° to 315°) and we accordingly added 180° to get an orientation of 314°. B3. For the location of the drainage center at 31°45'N and 98°15'W, figure 8 gives the H4P orientation of 208°. The angular difference is 314°-208°, or 106°. Since this difference, or its supplement, 74°, exceeds our range of ±40° for which no reduction to PMP is applied, we must adjust the storm-area averaged PMP for orientation of the pattern when aligned with the drainage. B4. Figure 10 gives the following reductions for the various isohyet areas considered in step A3 and the orientation difference from PMP given in step B3. Pattern Adjustment area (mi ) factor (%) 1000 96.1 1500 93.3 2150 89.7 3000 85.0 4500 85.0 6500 85.0 10000 85.0 15000 85.0 Multiply each of the final smoothed 6-hr incremental values in step A5 by the adjustment factors of step B4 to get the adjusted incremental values, 6-hr periods Pattern area (mi ) 1000 15.47 4.42 2.89 1500 13.39 4.12 2.70 2150 11.50 3.83 2.50 3000 9.69 3.52 2.30 4500 8.33 3.37 2.19 6500 7.22 3.25 2.11 10000 5.99 3.11 2.01 15000 4.93 2.98 1.91 114 / -r*> 0) I o > § 1-1 4J U 01 a. 0) > •a. o 4J 01 60 a •H 8 X H > 0) 0) d o u 3 0) w a H g, j= o 01 60 115 C. Determine the maximum volume of precipitation for the HIP patterns corresponding to the 8 area sizes used in the previous steps. To do this, we recommend filling in the computation sheets as shown in table 22. Some preliminary considerations have been made regarding the fit of the isohyetal pattern over the drainage. First, the small (^10-mi ) area of the drainage outside the N isohyet has been disregarded as insignificant to overall volume. Second, weight factors of 0.6 and 0.75 have been assigned (arbitrary judgment) to the average depth calculation for the L to M and M to N isohyetal areas, respectively (see step C6). Following the procedure outlined in section C, we find the greatest volume for the 1st 6-hr increment occurs at 1,500 mi . We should then check the volumes obtained for the 2nd and 3rd 6-hr increments before accepting 1,500 mi as our answer. For these additional increments it is not necessary to calculate volumes for all the areas considered in the 1st 6-hr increment, only those in the vicinity of the presumed area of maximum volume (1,500 mi ). Thus, we have limited our calculations to areas between 1,000 and 3,000 mi 2 (table 22). Addition of the incremental volumes at corresponding area sizes shows, however, that the maximum volume has shifted from 1,500 mi to 2,150 mi for these accumulated volumes. (The sum of the 1st to 3rd volumes is shown by the solid line in fig. 47.) It is of interest to narrow in on this maximum as to area size, and we chose to evaj.ua te two supplementary PMP pattern areas at 1,900- and 2,400 mi . Isohyets for these area sizes have been added to figure 46 as dotted lines. The results from table 23 (dashed lines in figure 47) show a maximum volume occurs at an area size slightly less than that for the 2,150-mi area pattern in the Leon River drainage. Because of the shift of area size between the 1st and the sum of the 1st three increments, it has been recommended that the three greatest increments be determined in the computation procedure. This significantly increases the number of computations required. Step_ Dl. Having concluded that the maximum volume occurs for a PMP pattern near 2,150 mi when placed over the Leon River, we can now determine the values for each isohyet for all twelve 6-hr increments. Return to the smooth depth-duration curve for 2,150 mi in step A4, and extend this curve to 72 hr before reading off the 6-hr values. Duration (hr) 6 12 18 24 30 36 42 48 54 60 66 72 Increm. PMP (in.) 12.9 17.2 20.0 22.3 23.8 25.0 26.0 26.8 27.7 28.5 29.2 29.9 116 Table 22. — Completed computation sheets for 1st, 2nd and 3rd 6-hr increments for Leon River, TX drainage Increment: 1 Drainage: Leon I River II , TX III IV V VI Area : 3 I 660 mi 2 II Da III te: IV V VI Area Amt. Avg. Area Amt . Avg. size Iso. No mo . 15.47 depth AA av size Iso. Nomo. 9.69 depth AA AV A 149 23.05 23.05 10 230.5 A 191 18.51 18.51 10 185.1 B 140 21.66 22.36 15 335.4 B 179 17.93 17.93 15 258.9 1000/1 C 131 20.27 20.97 25 524.2 3000/1 C 166 16.09 16.72 25 418.0 D 122 18.87 19.57 50 978.5 D 154 14.92 15.51 50 775.5 E 113 17.48 18.18 75 1363.5 E 142 13.76 14.34 75 1075.5 F 104 16.09 16.79 125 2098.8 F 132 12.79 13.28 125 1660.0 G 97 15.01 15.55 150 2332.5 G 122 11.82 12.31 150 1846.5 H 89 13.77 14.39 250 3597.5 H 112 10.85 11.34 250 2835.0 I 82 12.69 13.23 271 3585.3 I 102 9.88 10.37 271 2810.3 J 60 9.28 10.99 393 4319.1 J 92 8.91 9.39 393 3690.3 K 44 6.81 7.69 488 3752.7 •K 83 8.04 8.48 488 4138.2 L 32 4.95 5.88 582 3422.2 L 74 7.17 7.61 582 4429.0 (.60 X )* M 21 3.25 4.27 737 3146.9 (.60 X ) M 44 4.26 6.01 737 4428.4 (.75 X ) N 12 1.85 3.09 489 Sum = 1511.0 31198.1 (.75 X ) N 25 2.42 3.80 489 Sum = 1858.2 30418.9 Area Amt. Area Amt. size 13.39 size 8.33 A 162 21.69 21.69 10 216.9 A 212 17.66 17.66 10 176.6 B 152 20.35 21.02 15 315.8 B 198 16.49 17.08 15 256.1 1500/1 C 142 19.01 19.68 25 492.0 4500/1 C 184 15.33 15.91 25 397.8 D 132 17.67 18.34 50 917.0 D 170 14.16 14.75 50 737.5 E 122 16.33 17.00 75 1275.0 E 157 13.08 13.62 75 1021.5 F 112 14.99 15.66 125 1957.5 F 146 12.16 12.62 125 1577.5 G 105 14.06 14.52 150 2178.0 G 135 11.25 11.71 150 1756.5 H 96 12.85 13.46 250 3365.0 H 124 10.33 10.79 250 2697.5 I 88 11.78 12.32 271 3338.7 I 113 9.41 9.87 271 2674.8 J 80 10.71 11.24 393 4417.3 J 103 8.58 9.00 393 3537.0 K 56 7.50 9.10 488 4440.8 K 93 7.75 8.16 488 3982.1 L 41 '5.49 6.50 582 3783.0 L 83 6.91 7.33 582 4266.1 (.60 X ) M 26 3.48 4.69 737 3456.5 (.60 x ) M 71 5.91 6.51 737 4797.9 (.75 X ) N 16 2.14 3.14 489 Sum = 1535.5 31689.0 (.75 x ) N 37 3.08 5.20 489 Sum = 2542.8 30421.7 Area Amt. Area Amt. size 11.50 size 7.22 A 176 20.24 20.24 10. 202.4 A 233 16.82 16.82 10 168.2 B 165 18.98 19.61 15 294.2 B 218 15.74 16.28 15 244.2 2150/1 C 154 17.71 18.35 25 458.6 6500/1 C 203 14.66 15.20 25 380.0 D 142 16.33 17.02 50 851.0 D 187 13.50 14.08 50 704.0 E 131 15.07 15.70 75 1177.5 E 174 12.56 13.03 75 977.3 F 122 14.03 14.55 125 1818.8 F 160 11.55 12.06 125 1507.5 G 113 12.99 13.51 150 2026.5 G 148 10.69 11.12 150 1668.0 H 103 11.58 12.42 250 3105.0 H 137 9.89 10.29 250 2572.5 I 95 10.93 11.39 271 3086.7 I 125 9.03 9.46 271 2563.7 J 86 9.89 10.41 393 4091.1 J 113 8.16 8.59 393 3375.9 K 77 8.86 9.38 488 4577.4 K 103 7.44 7.80 488 3806.4 L 52 5.98 7.42 582 4318.4 L 93 6.71 7.08 582 4120.6 (.60 X ) M 33 3.80 5.11 737 3766.1 (.60 X ) M 81 5.85 6.37 737 4694.7 (.75 X ) N 20 2.30 3.42 489 Sum = 1672.4 31446.3 (.75 X ) N 70 5.05 5.65 48«> Sum =■ 2762.8 29545.7 * Weighting factor F (see text Section 7.1 Step C6) 117 "Bible 22. — Completed computation sheets for 1st, 2nd and 3rd 6-hr Increments for Leon River, TX drainage - Continued age: Leon I River, II TX III IV V VI Area : 3 I ,660 mi^ II In Da III crement te: 1,2 Drain IV V VI Area Amt . Avg. Area Amt. Avg. size Iso. Nomo. 5.99 depth AA AV size Iso. Nomo. 4.93 depth AA AV A 262 15.69 15.69 10 156.9 A 290 14.30 14.30 10 143.0 B 243 14.56 15.12 15 226.8 B 271 13.36 13.83 15 207.4 10000/1 C 227 13.60 14.08 25 352.0 15000/1 C 253 12.47 12.92 25 323.0 D 209 12.52 13.06 50 653.0 D 232 11.44 11.96 50 598.0 E 194 11.62 12.07 75 905.2 E 214 10.55 11.00 75 825.0 F 178 10.66 11.14 125 1392.5 F 196 9.66 10.10 125 1262.5 G 166 9.94 10.30 150 1545.0 G 183 9.02 9.34 150 1411.0 H 152 9.10 9.52 250 2380.0 H 168 8.28 8.65 250 2162.5 I 140 8.39 8.74 271 2368.5 I 156 7.69 7.98 271 2162.6 J 128 7.67 8.03 393 3155.8 J 143 7.05 7.37 393 2896.4 K 117 7.01 7.34 488 3581.9 K 131 6.46 6.76 488 3298.9 L 107 6.41 6.71 582 3905.2 L 120 5.92 6.19 582 3602.6 (.60 X ) M 93 5.57 6.07 737 4473.6 (.60 X ) M 106 5.22 5.64 737 4156.7 (.75 X ) N 82 4.91 5.40 489 Sum = 2640.6 27737.0 (.75 X ) N 94 4.63 5.07 489 Sum = 2479.2 25518.8 Area Amt. Area Amt. size 4.42 size 4.12 A 116 5.13 5.13 10 51.3 A 117 4.82 4.82 10 48.2 B 112 4.95 5.04 15 75.6 B 113 4.66 4.74 15 71.1 1000/2 C 108.5 4.80 4.88 25 121.9 1500/2 C 110 4.53 4.60 25 114.9 D 105 4.64 4.72 50 236.0 D 107 4.41 4.47 50 223.5 E 103 4.55 4.60 75 345.0 E 105 4.33 4.37 75 327.8 F 101 4.46 4.51 125 563.8 F 103 4.24 4.29 125 535.6 G 99 4.38 4.42 150 663.0 G 100.5 4.14 4.19 150 628.5 H 97 4.29 4.34 250 1085.0 H 99 4.08 4.11 250 1027.5 I 95 4.20 4.25 271 1151.8 I 97 4.00 4.04 271 1094.8 J 76 3.36 3.78 393 1485.5 J 95.5 3.93 3.97 393 1560.2 K 63 2.78 3.07 488 1498.2 K 75.5 3.11 3.52 488 1717.8 L 51 2.25 2.52 582 1466.6 L 605 2.49 2.80 582 1629.6 (.60 X ) M 38 1.68 2.02 737 1488.7 (.60 X ) M 45 1.85 2.23 737 1643.5 (.75 X ) N 24 1.06 1.52 489 Sum = 743.3 10975.7 (.75 X ) N 31 1.28 1.71 489 Sum = 836.2 11459.2 Area Amt. Area Amt. size 3.83 size 3.52 A 118.5 4.54 4.54 10 45.4 A 119.5 4.21 4.21 10 42.1 B 114.5 4.39 4.47 15 67.0 B 116 4.08 4.15 15 62.2 2150/2 C 110.5 4.25 4.32 25 108.0 3000/2 C 112.5 3.96 4.02 25 100.5 D 108.5 4.16 4.21 50 210.5 D 110 3.87 3.92 50 196.0 E 106.5 4.08 4.12 75 309.0 E 108 3.80 3.84 75 288.0 F 104.5 4.00 4.04 125 505.0 F 106 3.77 3.77 125 471.2 G 102 3.91 3.96 150 594.0 G 104 3.66 3.70 150 555.0 H 100 3.83 3.96 250 967.5 H 102 3.59 3.63 250 907.5 I 99 3.79 3.81 271 1032.5 I 100.5 3.54 3.56 271 964.8 J 97 3.72 3.76 393 1477.7 J 99 3.48 3.51 393 1379.4 K 96 3.68 3.70 488 1805.6 K 97 3.41 3.45 488 1683.6 L 73 2.80 3.24 582 1885.7 L 96 3.38 3.40 582 1978.8 (.60 X ) M 54 2.07 2.62 737 1930.9 (.60 X ) M 67 2.36 2.97 737 2188.9 (.75 X ) N 37.5 1.44 1.91 489 Sum = 934.0 11872.8 (.75 X ) N 45 1.58 2.17 489 Sum = 1061.1 11879.1 118 Table 22. — Completed computation sheets for 1st, 2nd and 3rd 6-hr Increments for Leon River, TZ drainage - Continued Leon I River, II TX III IV V VI Area : 3 I ,660 mi 2 II In( Eat III :rement : :e: 3 Drainage: IV V VI Area Amt. Avg. Area Amt . Avg. size Iso. Nomo. 2.89 depth AA AV size Iso. Nomo. 2.70 depth AA aV A 104.6 3.02 3.02 10 30.2 A 105 2.84 2.84 10 28.4 B 103.3 2.98 3.00 15 45.0 B 103.8 2.80 2.82 15 42.3 1000/3 C 102.3 2.96 2.97 25 74.2 1500/3 C 102.7 2.77 2.785 25 69.6 D 101.3 2.93 2.945 50 147.2 D 101.7 2.74 2.755 50 137.8 E 100.6 2.91 2.92 75 219.0 E 101 2.73 2.735 75 205.1 F 100.3 2.90 2.905 125 393.1 F 100.7 2.72 2.725 125 340.6 G 99.9 2.89 2.895 150 434.2 G 100.3 2.71 2.715 150 407.2 H 99.6 2.88 2.885 250 721.2 H 100 2.70 2.705 250 676.2 I 99.3 2.87 2.875 271 779.1 I 99.7 2.69 2.695 271 730.3 J 82.5 2.38 2.70 393 1061.1 J 99.4 2.68 2.685 393 1055.2 K 67 1.94 2.16 488 1054.1 K 81 2.19 2.44 488 1190.7 L 54 1.56 1.75 582 1018.5 L 65.5 1.77 1.98 582 1152.4 (.60 X ) M 43 1.24 1.43 737 1053.9 (.60 X ) M 51.5 1.39 1.62 737 1193.9 (.75 X ) N 31 .90 1.16 489 567.2 (-75 X ) N 38 1.03 1.30 489 635.7 Sum 7598.0 Sum = 7865.4 Area Amt. Ar ea Amt . size 2.50 si ze 2.30 A 105.3 2.63 2.63 10 26.3 A 105.7 2.43 2.43 10 24.3 B 104.2 2.60 2.615 15 39.2 B 104.6 2.41 2.42 15 36.3 2150/3 C 103.2 2.58 2.59 25 64.8 3000/3 C 103.5 2.38 2.40 25 60.0 D 102 2.55 2.565 50 128.2 D 102.5 2.36 2.37 50 118.5 E 101.3 2.53 2.54 75 190.5 E 101.7 2.34 2.35 75 176.3 F 101 2.52 2.525 125 315.6 F 101.3 2.33 2.345 125 293.1 G 100.6 2.52 2.52 150 378.0 G 100.9 2.32 2.335 150 350.2 H 100.3 2.51 2.515 250 628.8 H 100.5 2.31 2.315 250 578.8 I 100 2.50 2.505 271 678.8 I 100.2 2.30 2.305 271 624.6 J 99.7 2.49 2.495 393 980.5 J 99.9 2.30 2.30 393 903.9 K 99.5 2.49 2.49 488 1215.1 K 99.6 2.29 2.295 488 1120.0 L 80.5 2.01 2.25 582 1309.5 L 99.3 2.28 2.285 582 1329.9 (.60 X ) M 61 1.52 1.81 737 1334.0 (• 60 X ) M 76 1.75 2.07 737 1525.6 (.75 X ) N 46.5 1.16 1.43 489 Sum = 699.3 7988.6 (• 75 X ) N 57 1.31 1.64 489 Sum = 802.0 7943.5 119 liable 23. — Completed computation sheet for the 1st to 3rd 6-hr Increments for supplemental lsohyets on the Leon River, TX drainage Drainage: Leon River, TX Area : 3,660 mi' Increment : Date: 1 to 3 II III IV VI II III IV VI Area size Amt . Iso. Nomo. 12.12 Avg. depth aa AV Area size Iso. Nomo. Amt. 10.86 Avg. depth AA AV A 171 20.72 20.72 10 207.2 A 181 19.66 19.66 10 196.6 B 160 19.39 20.06 15 300.9 B 169 18.35 19.00 15 285.0 1900/1 C 149 18.06 18.72 25 468.0 2400/1 C 158 17.16 17.76 25 444.0 D 138 16.73 17.40 50 870.0 D 146 15.86 16.51 50 825.5 E 128 14.51 16.12 75 1209.0 E 134 14.55 15.20 75 1140.0 F 118 14.30 14.90 125 1862.5 F 125 13.58 14.06 125 1757.5 G 110 13.33 13.82 150 2073.0 G 116 12.60 13.09 150 1963.5 H 100 12.12 12.72 250 3180.0 H 106 11.51 12.06 250 3015.0 I 93 11.27 11.70 271 3170.7 I 97 10.53 11.02 271 2986.4 J 84 10.18 10.72 393 4213.0 J 88 9.56 10.04 393 3945.7 - 78 9.45 9.82 345 3387.9 K 79 8.98 9.07 488 4426.2 K 68 8.24 8.84 143 1264.1 - 76 8.25 8.42 211 1776.6 L 48 5.82 7.03 582 4091.5 L 58 6.30 7.28 371 2700.9 (.60 X ) M 30 3.64 4.95 737 3548.2 (.60 X ) M 36 3.91 5.34 737 3935.6 (.75 X ) N 18 2.18 3.28 489 Sum = 1603.9 31449.9 (.75 X ) N 21 2.28 3.50 489 Sum = 1711.5 31110.0 Area Amt. Area Amt. size 3.93 size 3.73 A 118 4.64 4.64 10 46.4 A 119 4.44 4.44 10 44.4 B 116 4.56 4.60 15 69.0 B 115 4.29 4.36 15 65.4 1900/2 C 111 4.36 4.46 25 111.5 2400/2 C 112 4.18 4.24 25 106.0 D 108 4.24 4.30 50 215.0 D 109 4.06 4.12 50 206.0 E 106 4.16 4.20 75 315.0 E 107 3.99 4.025 75 301.9 F 104 4.09 4.125 125 515.6 F 105 3.92 3.955 125 494.4 G 102 4.01 4.05 150 607.5 G 103 3.84 3.88 150 582.0 H 100 3.93 4.97 250 1242.5 H 101 3.77 3.805 250 951.2 I 98 3.85 3.89 271 1054.2 I 99 3.69 3.73 271 1010.8 J 96. 5 3.79 3.82 393 1501.3 J 97. 5 3.64 3.665 393 1440.3 - 95. 5 3.75 3.77 345 1300.6 K 96. 5 3.60 3.62 488 1766.6 K 86 3.38 3.57 143 510.5 - 96 3.58 3.59 211 757.5 L 68 2.67 3.03 582 1763.5 L 78 2.91 3.25 371 1205.8 (.60 X ) M 50. 5 1.98 2.39 737 1761.4 (.60 X ) M 57. 5 2.14 2.60 737 1916.2 (.75 X ) N 37 1.48 1.86 489 Sum = 909.5 11923.5 (-75 X ) N 40 1.49 1.98 489 Sum = 968.2 11816.7 Area Amt. Area Amt. size 2.56 size 2.43 A 105. 2 2.69 2.69 10 26.9 A 105. 4 2.56 2.56 10 25.6 B 104. 1 2.66 2.675 15 40.1 B 104. 3 2.53 2.545 15 38.2 1900/3 C 103 2.64 2.65 25 66.2 2400/3 C 103. 3 2.51 2.52 25 63.0 D 102 2.61 2.625 50 131.2 D 102. 3 2.48 2.495 50 124.8 E 101. 2 2.59 2.06 75 195.0 E 101. 5 2.47 2.475 75 185.6 F 100. 8 2.58 2.585 125 323.1 F 101. 2.45 2.46 125 307.5 G 100. 5 2.57 2.575 150 386.2 G 100. 7 2.45 2.45 150 367.5 H 100. 2 2.56 2.565 250 641.2 H 100. 3 2.44 2.445 250 611.2 I 99. 8 2.55 2.555 271 692.4 I 100. 2.43 2.435 271 659.9 J 99. 6 2.55 2.55 393 1000.2 J 99. 8 2.42 2.425 393 953.0 - 99. 4 2.54 2.545 345 878.0 K 99. 4 2.42 2.42 488 1181.0 K 92 2.36 2.45 143 350.4 - 99. 3 2.41 2.415 211 509.6 L 75 1.92 2.14 582 1245.5 L 86 2.09 2.25 371 834.8 (.60 X ) M 58 1.48 1.74 737 1285.3 (.60 X ) M 66 1.60 1.89 737 1392.9 (.75 X ) N 43 1.10 1.39 489 Sum = 679.7 7940.5 (.75 X ) N 49. 5 1.20 1.50 489 Sum = 733.5 7988.1 120 4000 3000 — E < Id tr. < 2000- VOLUME (xl0 3 mi 2 -in.) figure 47. — Volume vs. area curve for 1st three 6-hr Increments for Leon River, TX drainage. D2. Successively subtract the 6-hr values in step Dl. 6-hr periods 123456789 10 11 12 Increm. PMP (in.) 12.9 4.3 2.8 2.3 1.5 1.2 1.0 0.8 0.9 0.8 0.7 0.7 We read slightly different values (read to hundreths) in smoothed data from figure 45 for the 1st three 6-hr increments, which we substitute here, for consistency. Note that to assure a series of decreasing values it was necessary to reverse the values for the 8th and 9th increment. This does not cause any problem for our computations. 6-hr periods 123456789 10 11 12 Increm. PMP (in.) 12.82 4.27 2.79 2.30 1.50 1.20 1.00 0.90 0.80 0.80 0.70 0.70 Multiply each of these 6-hr incremental PMP by 89.7% to reduce them for orientation. 121 6-hr periods 5 6 7 8 10 11 12 Adj. IMP (in.) 11.50 3.83 2.50 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 D3. Isohyet values are then obtained by multiplying the 1st 6-hr value in step D2 by the percentages for 2,150 mi from table 15 or the 1st 6-hr nomogram (fig. 16), the 2nd 6-hr value by the percentages in table 16 or figure 18, the 3rd 6-hr value by the percentages in table 17 or figure 19, and the fourth through 12th 6-hr values by the percentages in table 18 or figure 20 as shown in table 24. In section 3.5.3, we have explained that the fourth through 12th 6-hr increments are assumed uniform. Thus, a constant value is used through the extent of the area size of PMP, 2,150 mi in this example. Table 24. — Isohyet values (in.), Leon River, TX, for example la 6-hr periods Isohyet 1 2 3 4 5 6 7 8 9 10 11 12 A 20.24 4.54 2.63 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 B 18.98 4.39 2.61 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 C 17.17 4.25 2.58 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 D 16.33 4.16 2.56 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 E 15.07 4.08 2.53 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 F 14.03 4.00 2.53 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 G 12.99 3.91 2.52 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 H 11.85 3.83 2.51 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 I 10.93 3.77 2.50 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 J 9.89 3.72 2.49 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 K 8.86 3.68 2.48 2.06 1.34 1.08 0.90 0.81 0.72 0.72 0.63 0.63 L 5.98 2.80 2.03 1.66 1.08 0.87 0.72 0.65 0.58 0.58 0.51 0.51 M 3.80 2.07 1.55 1.26 0.82 0.66 0.55 0.49 0.44 0.44 0.38 0.38 N 2.30 1.44 1.16 0.96 0.62 0.50 0.42 0.38 0.33 0.33 0.29 0.29 Note: The results shown in this matrix emphasize the fact that for the fourth through 12th 6-hr period the distribution of PMP is uniform across the PMP portion of the pattern (A through K) for each increment. However, isohyets L to N represent residual precipitation for the 2,150-mi' are assigned decreasing values. pattern and these isohyets D4. The values in table 24 represent the incremental isohvetal values for the Leon River drainage with the 2,150-mi PMP pattern placed as shown in figure 46. To obtain incremental average depths (PMP) for this drainage it is necessary to compute the incremental volumes as determined from the tabulated isohyetal values according to the procedures described for figure 41, and then divide each incremental volume by the drainage area. This results in the following incremental average depths. (See computations in table 25.) 122 Table 25. — Completed computation sheets shoving typical format to get Incremental drainage-average depths, Leon River, TX lage: Leon River I II , TX III IV V VI Area : 3 I ,660 mi 2 II In Da III crement te: : 1 to 6 Dralr IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 11.50 depth aA aV size Iso. Nomo. 2.06 depth aA AV A 20.24 20 .24 10 202.4 A 100 2.06 2.06 10 20.6 B 18.98 19 .61 15 294.2 B 100 2.06 2.06 15 30.9 2150/1 C 17.71 18 .35 25 458.8 2150/4 C -100 2.06 2.06 25 51.5 D 16.33 17 .02 50 851.0 D 100 2.06 2.06 50 103.0 E 15.07 15 70 75 1177.5 E 100 2.06 2.06 75 154.5 F 14.03 14 55 175 1818.8 F 100 2.06 2.06 125 257.5 G 12.99 13 51 150 2026.5 G 100 2.06 2.06 150 309.0 H 11.85 12 42 250 3105.0 H 100 2.06 2.06 250 515.0 I 10.93 11 39 271 3086.7 I 100 2.06 2.06 271 558.3 J 9.89 10 41 393 4091.1 J 100 2.06 2.06 393 809.6 K 8.86 9 38 488 4577.4 K 100 2.06 2.06 488 1005.3 L 5.98 7 42 582 4318.4 L 80.5 1.66 1.86 582 1082.5 (.60 X ) M 3.80 5 11 737 3766.1 (.60 X ) M 61 1.26 1.46 737 1076.0 (.75 X ) N 2.30 3. 42 489 1672.4 (.75 X ) N 46.5 .96 1.11 489 542.8 Total = 3660 Sum = 31446.3 Sum = 6516.5 Avg ,. depth = 8.59 Avg. d spth = 1.78 Area Amt. Area Amt. size 3.83 size 1.34 A 10 45.4 A 100 1.34 1.34 10 13.4 B 15 67.0 B 100 1.34 1.34 15 20.1 2150/2 C 25 108.0 2150/5 C 100 1.34 1.34 25 33.5 D 50 210.5 D 100 1.34 1.34 50 67.0 E 75 309.0 E 100 1.34 1.34 75 100.5 F 125 505.0 F 100 1.34 1.34 125 167.5 G 150 594.0 G 100 1.34 1.34 150 201.0 H 250 967.5 H 100 1.34 1.34 250 335.0 I 271 1032.5 I 100 1.34 1.34 271 363.1 J 393 1477.7 J 100 1.34 1.34 393 526.6 K 488 1805.6 K 100 1.34 1.34 488 653.9 L 582 1887.5 L 80.5 1.08 1.21 582 704.2 (.60 X ) M 737 1930.9 (.60 X ) M 61 0.82 0.95 737 700.2 (.75 X ) N Avg ;. d 489 Sum = =pth = 934.0 11872.8 3.24 (.75 X ) N 46.5 0.62 0.72 Avg. 489 Sum = lepth = 352.1 4238.1 1.16 Area Amt . Area Amt . size 2.50 size 1.08 A 10 26.3 A 100 1.08 1.08 10 10.8 B 15 39.2 B 100 1.08 1.08 15 16.2 2150/3 C 25 64.8 2150/6 C 100 1.08 1.08 25 27.0 D 50 128.2 D 100 1.08 1.08 50 54.0 E 75 190.5 E 100 1.08 1.08 75 81.0 F 125 315.6 F 100 1.08 1.08 125 135.0 G 150 378.0 G 100 1.08 1.08 150 162.0 H 250 628.8 H 100 1.08 1.08 250 270.0 I 271 678.8 I 100 1.08 1.08 271 292.7 J 393 980.5 J 100 1.08 1.08 393 424.4 K 488 1215.1 K 100 1.08 1.08 488 527.0 L 582 1309.5 L 80.5 0.87 0.98 582 570.4 (.60 X ) M 737 1334.0 (.60 X ) M 61 0.66 0.77 737 567.5 (.75 X ) N 489 Sum = 699.3 7988.6 (.75 X ) N 46.5 0.50 0.58 489 Sum = 283.6 3421.6 — _ • Avg. d apth = 2.18 123 • Avg. depth = 0.93 Table 25. — Completed computation sheets showing typical format to get Incremental drainage-averaged depths, Leon River, TX. - Continued Increment : 7 to 12 Drain age: Leon I River, II TX III IV V VI Area : 3 I ,660 mi 2 II Da III te: IV V VI Area Amt . Avg. Area Amt. Avg. size Iso. Nomoo 0.90 depth AA AV size Iso. Nomo. 0.72 depth AA AV A 100 0.90 0.90 10 9 A 100 0.72 0.72 10 7.2 B 100 0.90 0.90 15 13.5 B 100 0.72 0.72 15 10.8 2150/7 C 100 0.90 0.90 25 22.5 2150/10 C 100 0.72 0.72 25 18.0 D 100 0.90 0.90 50 45.0 D 100 0.72 0.72 50 36.0 E 100 0.90 0.90 75 67.5 E 100 0.72 0.72 75 54.0 F 100 0.90 0.90 125 112.5 F 100 0.72 0.72 125 90.0 G 100 0.90 0.90 150 135.0 G 100 0.72 0.72 150 108.0 H 100 0.90 0.90 250 225.0 H 100 0.72 0.72 250 180.0 I 100 0.90 0.90 271 243.9 I 100 0.72 0.72 271 195.1 J 100 0.90 0.90 393 353.7 J 100 0.72 0.72 393 282.9 K 100 0.90 0.90 488 439.2 K 100 0.72 0.72 488 351.4 L 80.5 0.72 0.81 582 471.4 L 80.5 0.58 0.65 582 378.3 (.60 X ) M 61 0.55 0.64 737 471.7 (.60 X ) M 61 0.44 0.51 737 375.9 (.75 X ) N 46.5 0.42 0.49 Avg. d 489 Sum = epth = 239.6 2849.5 0.78 (.75 X ) N 46.5 0.33 0.39 Avg. d 489 Sum = =pth = 190.7 2278.3 0.62 Area Amt. Area Amt. size 0.81 size 0.63 A 100 0.81 0.81 10 8.1 A 100 0.63 0.63 10 6.3 B 100 0.81 0.81 15 12.2 B 100 0.63 0.63 15 9.5 2150/8 C 100 0.81 0.81 25 20.3 2150/11 C 100 0.63 0.63 25 15.8 D 100 0.81 0.81 50 40.5 D 100 0.63 0.63 50 31.5 E 100 0.81 0.81 75 60.8 E 100 0.63 0.63 75 47.3 F 100 0.81 0.81 125 101.3 F 100 0.63 0.63 125 78.8 G 100 0.81 0.81 150 121.5 G 100 0.63 0.63 150 94.5 H 100 0.81 0.81 250 202.5 H 100 0.63 0.63 250 157.5 I 100 0.81 0.81 271 219.5 I 100 0.63 0.63 271 170.7 J 100 0.81 0.81 393 318.3 J 100 0.63 0.63 393 247.6 K 100 0.81 0.81 488 395.3 K 100 0.63 0.63 488 307.4 L 80.5 0.65 0.73 582 424.9 L 80.5 0.51 0.57 582 331.7 (.60 X ) M 61 0.49 0.57 737 420.1 (.60 X ) M 61 0.38 0.45 737 331.7 (.75 X ) N 46.5 0.38 0.44 Avg. de 489 Sum = pth = 215.2 2560.4 0.70 (.75 X ) N 46.5 0.29 0.34 Avg. d 489 Sum = epth = 166.3 1996.6 0.54 Area Amt. Area Amt. size 0.72 size 0.63 A 100 0.72 0.72 10 7.2 A 100 0.63 0.63 10 6.3 B 100 0.72 0.72 15 10.8 B 100 0.63 0.63 15 9.5 2150/9 C 100 0.72 0.72 25 18.0 2150/12 C 100 0.63 0.63 25 15.8 D 100 0.72 0.72 50 36.0 D 100 0.63 0.63 50 31.5 E 100 0.72 0.72 75 54.0 E 100 0.63 0.63 75 47.3 F 100 0.72 0.72 125 90.0 F 100 0.63 0.63 125 78.8 G 100 0.72 0.72 150 108.0 G 100 0.63 0.63 150 94.5 H 100 0.72 0.72 250 180.0 H 100 0.63 0.63 250 157.5 I 100 0.72 0.72 271 195.1 I 100 0.63 0.63 271 170.7 J 100 0.72 0.72 393 282.9 J 100 0.63 0.63 393 247.6 K 100 0.72 0.72 488 351.4 K 100 0.63 0.63 488 307.4 L 80.5 0.58 0.65 582 378.3 L 80.5 0.51 0.57 582 331.7 (.60 X ) M 61 0.44 0.51 737 375.9 (.60 X ) M 61 0.38 0.45 737 331.7 (.75 X ) N 46.5 0.33 0.39 Avg . d 489 Sum = epth = 190.7 2278.3 0.62 (.75 X ) N 46.5 0.29 0.34 Avg. d 489 Sum = jpth = 166.3 1996.6 0.54 124 6-hr periods 4 5 6 7 8 9 10 11 12 Avg. PMP (in.) 8.59 3.24 2.18 1.78 1.16 0.93 0.78 0.70 0.62 0.62 0.54 0.54 These give a 72-hr total drainage-averaged RIP of 21.68 in., which can be compared to 27.4 in. for 3,660 mi (from fig. 43), or a 21 percent reduction from HMR No. 51. The reduction is due to orientation and basin shape factors. D5. a. At Sl^'N, 98°15'W, we read a 1/6-hr ratio of 0.306 from figure 39. b. We adjust the scale for the that the abscissa for the 20 0.306. nomogram in figure 40 such ,000-mi "A" isohyet reads c. With the scale set as in step D5b, we read ratios for the following isohyets. 1/6-hr Isohyet ratio A .299 B .298* C .297 D .295* E .293 F .2915* G .290 H .2875* I .285 J .282 K .279 ♦interpolated isohyet on nomogram d. Multiply the ratios in step D5c by the corresponding values from table 24 (1st 6-hr period only) to get the 1-hr isohyet values. Isohyet A B C D E F G H I J K 1-hr isohyet values 6 .05 5 .66 5 .10 4 .82 4 .42 4 .09 3 .77 3 .73 3 .12 2 .78 2 .47 125 e. Plot the values in step D5d and those for the 4 greatest increments from table 24 and draw a smooth curve of best fit through these points with the origin as the starting point as shown in figure 48. f . From figure 48, we can read isohyet values for any other duration less than 6 hr (see note in procedure step 7D5f). g. The 4 greatest 6-hr incremental isohyet values for the M isohyet have also been plotted on figure 48 as an example of residual precipitation. It is apparent that this curve is flatter than those for the PMP portion of the pattern. Lesser errors are therefore likely in interpolating short duration isohyet values for residual precipitation than for those within the PMP area. (Note in procedure step 7D5f applies here and to 1-hr values for residual precipitation.) 7.3 Example lb As a comparison to the results of example la, we will now evaluate the maximum volume for the Leon River, Texas drainage when no adjustment for orientation is applied. In step B3, we obtained the orientation for PMP from figure 8 as 208° for 31°45'N, 98°15'W. Figure 10 indicates that within 40° of PMP orientation, no reduction need be applied to isohyets values. Subtracting 40° from 208°, we get an orientation of 168°. Thus, if we place the isohyetal pattern at an orientation of 168° on the Leon River drainage, as shown in figure 49, no adjustment is necessary. We must planimeter the areas between each of the incomplete isohyets, and then refer to step C in the procedure. C. Complete the computational process of figure 41 for the area sizes considered in example la. We have omitted the 1,000- and 15,000-mi areas based on the outcome of example la. Note that the nomogram percentages will be the same as those used in example la, but the amount heading column III is now unadjusted for orientation; i.e., smoothed values from figure 45. Table 26 presents completed computations for this example. The preliminary maximum volume for the first 6-hr increment appears to occur between 6,500 and 10,000 mi . To check on this outcome, the 15,000-mi area pattern volume was determined and was found to be significantly less than that at 10,000 mi . Computation of the 2nd and 3rd 6-hr increments for the standard isohyet areas between 4,500 and 15,000 mi resulted in 18-hr volumes ranging between 45,000 and 49,000 mi -in. Note that by not adjusting the isohyets for orientation, the PMP pattern area of maximum volume has greatly increased from 2,150 mi in example la to 10,000 mi in this example, but the total volume as decreased. This occurs because some of the larger isohyets become more effective as the isohyet values increase with increasing area, and combine with proportionately larger incremental areas. At the same time the volume contributed by the isohyets enclosing smaller areas has been markedly reduced. 126 s § Jl s Cfi 0) 3 4J ! n I i P CO 49 a P 01 w a o 4J CO fl CO 0) C"i) eamvA sisahosi 127 73 T> 4) A 4J 6 • 03 0) 60 1 t a 00 ■H «* fl OJ T3 fl* X 60 H 4J I s CD cd o a 4J M H a cu a •H 8 •o x H 0) > 53 8 •J 6 4J a 128 Table 26. — Completed computation sheets for 1st three 6-hr increments for alternate placement of pattern on Leon River, TX drainage Leon I River II , TX III IV V VI Area : 3 I ,660 mi II In 2 » III crement te: 1 Drainage: IV V VI Area Amt . Avg. Area Amt. Avg. size Iso. Nomo. 14.35 depth aA AV size Iso. Nomo. 9.80 depth aA AV A 162 23.25 23.25 10 232.5 A 212 20.78 20.78 10 207.8 B 152 21.81 22.53 15 338.0 B 198 19.40 20.09 15 301.4 1500/1 C 142 20.34 21.08 25 527.0 4500/1 C 184 18.03 18.72 25 468.0 D 132 18.94 19.64 50 982.0 D 170 16.66 17.34 50 867.0 E 122 17.54 18.22 75 1366.5 E 157 15.39 16.02 75 1201.5 F 112 16.07 16.79 125 2098.8 F 146 14.31 14.85 125 1856.2 G 105 15.07 15.57 125 1946.2 G 135 13.23 13.77 125 1721.2 H 96 13.78 14.42 125 1802.5 H 124 12.15 12.69 125 1586.2 I 88 12.68 13.20 150 1980.0 I 113 11.07 11.61 150 1741.5 J 80 11.48 12.06 240 2894.4 J 103 10.09 10.58 240 2539.2 K 56 8.04 9.76 340 3318.4 K 93 9.11 9.60 340 3264.0 L 41 5.88 6.96 240 1670.4 L 83 8.13 8.62 240 2068.8 M 26 3.73 4.80 525 2520.0 M 71 6.96 7.54 525 3958.5 N 16 2.30 3.02 505 1525.1 N 37 3.63 5.30 505 2676.5 7 1.00 1.65 535 882.8 18 1.76 2.70 535 1444.5 (.60 X ) P 0.0 0.60 445 267.0 (.60 X ) P 8 0.78 1.37 445 609.6 (.70 X ) Q 0.0 0.0 130 Sum = 0.0 24251.6 (.70 X ) Q 0.0 0.55 130 Sum = 71.5 26583.4 Area Amt. Area Amt. Size 12.82 Size 8.50 A 176 22.56 22.56 10 225.6 A 233 19.80 19.80 10 198.0 B 165 21.15 21.86 15 327.9 B 218 18.53 19.16 15 287.5 2150/1 C 154 19.74 20.44 25 511.0 6500/1 C 203 17.26 17.90 25 447.4 D 142 18.20 18.97 50 948.5 D 187 15.90 16.58 50 829.0 E 131 16.79 17.50 75 1312.5 E 174 14.79 15.34 75 1150.5 F 122 15.64 16.22 125 2027.5 F 160 13.60 14.20 125 1775.0 G 113 14.49 15.06 125 1882.5 G 148 12.58 13.09 125 1636.2 H 103 13.20 13.84 125 1730.0 H 137 11.64 12.11 125 1513.8 I 95 12.18 12.69 150 1903.5 I 125 10.62 11.14 150 1671.0 J 86 11.02 11.60 240 2784.0 J 113 9.60 10.11 240 2426.4 K 77 9.87 10.44 340 3549.6 K 103 8.76 9.18 340 3121.2 L 52 6.67 8.27 240 1984.8 L 93 7.90 8.33 240 1999.2 M 33 4.23 5.45 525 2861.2 M 81 6.88 7.39 525 3879.8 N 20 2.56 3.40 505 1717.0 N 70 5.95 6.42 505 3242.1 9 1.15 1.86 535 995.1 29 2.46 4.20 535 2247.0 (.60 X ) P 2 0.26 0.79 445 351.6 (.60 X ) P 13 1.10 1.92 445 854.4 (.70 X ) Q 0.0 0.18 130 Sum = 23.4 25135.7 (.70 X ) Q 1 0.08 0.79 130 Sum = 102.7 27381.2 Area Amt. Area Amt. size 11.40 size 7.05 A 191 21.77 21.77 10 217.7 A 262 18.47 18.47 10 184.7 B 179 20.41 21.09 15 316.4 B 243 17.13 17.80 15 267.0 3000/1 C 166 18.92 19.66 25 491.5 10000/1 C 227 16.00 16.56 25 414.1 D 154 17.56 18.24 50 912.0 D 209 14.73 15.36 50 768.0 E 142 16.89 16.88 75 1266.0 E 194 13.68 14.20 75 1065.0 F 132 15.05 15.62 125 1952.5 F 178 12.55 13.11 125 1638.8 G 122 13.91 14.48 125 1810.0 G 166 11.70 12.12 125 1515.6 H 112 12.77 13.34 125 1667.5 H 152 10.72 11.21 125 1401.2 I 102 11.63 12.20 150 1830.0 I 140 9.87 10.30 150 1544.2 J 92 10.49 11.06 240 2654.4 J 128 9.02 9.44 240 2265.6 K 83 9.46 9.98 340 3393.2 K 117 8.25 8.64 340 2937.6 L 74 8.44 8.95 240 2148.0 L 107 7.54 7.90 340 1894.8 M 44 5.02 6.73 525 3533.2 M 93 6.56 7.05 525 3701.2 N 25 2.85 3.94 505 1989.7 N 82 5.78 6.16 505 3110.8 12 1.37 2.11 535 1128.8 68 4.79 5.28 535 2824.8 (.60 X ) P 4 0.46 1.01 445 449.4 (.60 X ) P 27 1.90 3.63 445 1615.4 (.70 X ) Q 0.0 0.32 130 Sum = 41.6 25808.3 (.70 X ) Q 7 0.49 1.48 130 Sum = 192.4 27341.2 129 Table 26. — Completed computation sheets for 1st three 6-hr Increments for alternate placement of pattern on Leon River, TX drainage - Continued age: Leon I River, II TX III IV V VI Area : 3 I ,660 mi 2 II Inc Dat III •.rement: e: 1 to 3 Drair IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 5.80 depth AA aV size Iso. Nomo. 3.66 depth AA AV A 290 16.82 16.82 10 168.2 A 122 4.54 4.54 10 45.0 B 271 15.72 16.26 15 243.9 B 120. 5 4.41 4.48 15 67.2 15000/1 C 253 14.67 15.20 25 379.9 10000/2 C 117 4.28 4.34 25 108.5 D 232 13.46 14.06 50 703.0 D 115 4.21 4.245 59 212.2 E 214 12.41 12.94 75 970.5 E 113 4.14 4.175 75 313.1 F 196 11.37 11.89 125 1486.2 F 111 4.06 4.10 125 512.5 G 183 10.61 10.99 125 1373.8 G 109 3.99 4.025 125 503.1 H 168 9.74 10.18 125 1272.5 H 107 3.92 3.96 125 494.4 I 156 9.05 9.40 150 1410.0 I 105. 5 3.86 3.89 150 583.5 J 143 8.29 8.67 240 2080.8 J 104 3.81 3.84 240 920.5 K 131 7.60 7.94 340 2699.6 K 102. 5 3.75 3.78 340 1285.2 L 120 6.99 7.30 240 1752.0 L 101 3.70 3.72 240 894.0 M 106 6.21 6.60 525 3465.0 M 99 3.62 3.66 525 1921.5 N 94 5.45 5.83 505 2944.2 N 97 3.55 3.58 505 1810.4 80 4.64 5.04 535 2696.4 95 3.48 3.52 535 1880.5 (.60 X ) P 65 3.77 4.29 445 1909.0 (.60 X ) P 50 1.83 2.82 445 1254.9 (.70 X ) Q 18 1.04 2.95 130 Sum = 383.5 25938.5 (.70 X ) Q 14 .51 1.43 130 Sum = 185.9 12992.4 Area Amt. Area Amt. size 3.96 size 3.50 A 121 4.79 4.79 10 47.9 A 125 4.38 4.38 10 43.8 B 117 4.63 4.71 15 70.6 B 122 4.27 4.33 15 64.9 4500/2 C 114 4.51 4.57 25 142.2 15000/2 C 119 4.17 4.22 25 105.5 D 112 4.44 4.48 50 224.0 D 117 4.10 4.14 50 207.0 E 109. 5 4.34 4.39 75 329.2 E 115 4.03 4.07 75 305.0 F 108 4.28 4.31 125 538.8 F 113 3.96 4.00 125 500.0 G 105. 5 4.18 4.23 125 528.8 G 111 3.89 3.93 125 491.2 H 103. 5 4.10 4.14 125 517.5 H 109 3.82 3.86 125 482.5 I 102 4.04 4.07 150 610.5 I 107 3.75 3.79 150 568.5 J 100. 5 4.00 4.02 240 964.8 J 106 3.71 3.73 240 895.2 K 99 3.92 3.96 340 1346.4 K 104 3.64 3.68 340 1251.2 L 97. 5 3.86 3.89 240 933.6 L 102. 5 3.59 3.62 240 868.8 M 96 3.80 3.83 525 2010.8 M 101 3.54 3.57 525 1874.2 N 59 2.34 3.07 505 1550.4 N 99 3.47 3.51 505 1772.6 39 1.54 1.94 535 1037.9 97 3.40 3.44 535 1840.4 (.60 X ) P 17 0.67 1.19 445 529.6 (.60 x ) P 96 3.36 3.38 445 1504.1 (.70 X ) Q 00 0.00 0.47 130 Sum = 61.1 11416.1 (.70 x ) Q 34 1.19 2.71 130 Sum = 332.3 13127.4 Area Amt. Area Amt. size 3.82 size 2.58 A 122 4.66 4.66 10 46.6 A 106 2.73 2.73 10 27.3 B 119 4.54 4.60 15 69.0 B 105 2.72 2.72 15 40.8 6500/2 C 115. 5 4.41 4.48 25 112.0 4500/3 C 104 2.68 2.695 25 67.4 D 113 4.32 4.36 50 218.0 D 103. 1 2.66 2.67 50 133.5 E 111 4.24 4.28 75 321.0 E 102. 1 2.63 2.645 75 198.4 F 109 4.16 4.20 125 525.0 F 101. 7 2.62 2.625 125 328.1 G 107 4.08 4.12 125 515.0 G 101. 2 2.61 2.615 125 326.9 H 105 4.01 4.045 125 505.6 H 100. 9 2.60 2.605 125 325.6 I 104 3.97 3.99 150 598.5 I 100. 6 2.60 2.60 150 390.0 J 102 3.90 3.94 240 945.6 J 100. 2 2.59 2.595 240 622.8 K 100. 5 3.84 3.87 340 1315.8 K 99. 9 2.58 2.585 340 878.9 L 99 3.78 3.81 240 914.4 L 99. 6 2.57 2.575 240 618.0 M 97. 5 3.72 3.75 525 1968.8 M 99. 3 2.56 2.565 525 1346.6 N 95. 5 3.65 3.68 505 1858.4 N 76 1.96 2.26 505 1141.3 52. 5 2.02 2.82 535 1508.7 (.60 x ) 49 1.26 1.61 535 861.4 (.60 X ) P 27. 5 1.07 1.64 445 729.8 (.70 x ) P 21 0.54 0.97 445 431.6 (.70 X ) Q 1. 0.04 0.76 130 98.8 Q 0.00 0.38 130 49.4 Sum ■ 12251.0 Sum = 7788.0 130 Table 26.— Completed computation sheets for 1st three 6-hr Increments for alternate placement of pattern on Leon River, TX drainage - Continued Leon I River, II TX - III IV V VI Area : 3 I ,660 mi II Ii 2 r, in lcrement : te: 3 > } Drainage: IV V VI Area Amt . Avg. •Area Amt . Avg. size Iso. Nomo. 2.48 depth AA AV size Iso. Nomo. 7.70 depth AA 6V A 106.4 2.64 2.64 10 26.4 A 247 18.98 18.98 10 189.8 B 105.5 2.62 2.63 15 39.4 B 230 17.71 18.34 15 275.1 6500/3 C 104.5 2.59 2.605 25 65.1 8000/1 C 214 16.48 17.10 25 427.5 D 103.5 2.57 2.58 50 129.0 D 198 15.17 15.82 50 791.0 E 102.5 2.54 2.555 75 191.6 E 183 14.09 14.63 75 1097.2 F 102 2.53 2.535 125 316.9 F 169 12.97 13.53 125 1691.2 G 101.5 2.52 2.525 125 315.6 G 157 12.01 12.49 125 1561.2 H 101.2 2.51 2.515 125 314.4 H 144 11.09 11.55 125 1443.8 I 100.9 2.50 2.505 150 375.8 I 132 10.16 10.62 150 1593.0 J 100.5 2.49 2.495 240 598.8 J 120 9.28 9.72 240 2332.8 K 100.2 2.48 2.485 340 844.9 K 110 8.43 8.86 340 3012.4 L 99.8 2.48 2.48 240 595.2 L 99 7.62 8.02 240 1924.8 M 99.5 2.47 2.475 525 1299.4 M 87 6.70 7.16 525 3759.0 N 98.9 2.45 2.46 505 1242.3 N 75 5.81 6.26 505 3161.3 65 1.60 2.02 535 1080.7 - 69 5.31 5.56 320 1779.7 (.60 X ) P 34.5 0.86 1.30 445 578.5 40 3.08 4.20 215 903.0 (.70 X ) Q 1 0.02 0.61 130 79.3 (.60 X ) P 18 1.39 2.40 445 1068.0 (.70 X ) Q 4 0.31 1.07 130 139.1 Sum 8093.3 Sum = 27149.6 Area Amt. Area Amt. size 2.36 size 7.35 A 106.8 2.52 2.52 10 25.2 A 2 54 18.67 18.67 10 186.7 B 106 2.50 2.51 15 37.6 B 237 17.42 18.04 15 270.6 10000/3 C 105 2.48 2.49 25 62.2 9000/1 C 221 16.24 16.83 25 420.8 D 104 2.45 2.465 50 123.2 D 203 14.92 15.58 50 779.0 E 102.8 2.43 2.44 75 183.0 E 189 13.89 14.40 75 1080.0 F 102.4 2.42 2.425 125 303.1 F 174 12.79 13.34 125 1667.5 G 101.9 2.41 2.415 125 301.9 G 161 11.83 12.31 125 1538.8 H 101.6 2.40 2.405 125 300.6 H 148 10.88 11.36 125 1420.0 I 101.3 2.39 2.395 150 359.2 I 136 10.00 10.44 150 1566.0 J 100.9 2.38 2.385 240 572.4 J 124 9.15 9.58 240 2299.2 K 100.5 2.37 2.375 340 807.5 K 113 8.30 8.72 340 2964.8 L 100.2 2.36 2.365 240 567.6 L 103 7.57 7.94 240 1905.6 M 99.8 2.36 2.36 525 1239.0 M 90 6.65 7.11 525 3732.8 N 99.2 2.34 2.35 505 1186.8 N 78 5.77 6.21 505 3136.0 98.7 2.33 2.335 535 1249.2 - 68 5.00 5.38 435 2340.3 (.60 X ) P 59 1.37 1.95 445 867.8 51 3.75 4.38 100 438.0 (.70 X ) Q 18 0.42 1.08 130 140.4 (.60 X ) P 22 1.62 2.90 445 1290.5 (.70 X ) Q 5 0.37 1.24 130 161.2 Sum 8326.7 Sum = 27197.8 Area Amt. Area Amt. size 2.25 size 6.40 A 107.2 2.41 2.41 10 24.1 A 274 17.54 17.54 10 175.4 B 106.5 2.40 2.405 15 36.1 B 255 16.32 16. 93 15 254.0 15000/3 C 105.5 2.37 2.385 25 59.6 12000/1 C 238 15.23 15.78 2S 394.5 D 104.4 2.35 2.36 50 118.0 D 219 14.02 14.62 50 731.0 E 103.3 2.32 2.335 75 175.1 E 203 12.99 13.50 75 1012.5 F 102.8 2.31 2.315 125 289.4 F 186 11.90 12.44 125 1555.0 G 102.3 2.30 2.305 125 288.5 G 174 11.14 11.52 125 1440.0 H 102 2.30 2.30 125 287.5 H 159 10.18 10.66 125 1332.5 I 101.7 2.29 2.295 150 344.2 I 147 9.41 9.80 150 1470.0 J 101.2 2.28 2.285 240 548.4 J 135 8.64 9.02 240 2164.8 K 100.8 2.27 2.275 340 773.5 K 123 7.87 8.26 340 2808.5 L 100.5 2.26 2.265 240 543.6 L 113 7.23 7.55 240 1812.0 M 100.1 2.25 2.255 525 1183.9 M 99 6.34 6.78 525 3559.5 N 99.5 2.24 2.245 505 1133.7 N 87 5.57 5.96 505 3009.8 99 2.23 2.235 535 1195.7 73 4.67 5.12 535 2739.2 P 78 2.21 2.22 445 987.9 - 67 4.29 4.48 220 985.6 (.60 X ) Q 42 0.95 1.83 130 237.9 (.60 X ) P 38 2.43 3.55 225 798.8 (.70 X ) (.70 x ) Q 11 0.70 1.86 130 241.8 Sum 8226.7 Sum = 26484.8 131 "fable 26. — Completed computation sheets for 1st three 6-hr Increments for alternate placement of pattern on Leon River, TX drainage - Continued Drainage: Leon River, TX Area: 3,660 mi' Increment: Date: 2 to 3 I II Ill IV V VI I II Ill IV V VI Area size Iso. Nomo. Amt. 3.75 Avg. depth M AV Area size Iso. Nomo. Amt. 2.41 Avg. depth AA AV A 123 4.61 4.61 10 46.1 A 106.6 2.57 2.57 10 25.7 B 120 4.50 4.56 15 68.4 B 105.7 2.55 2.56 15 38.4 8000/2 C 116. 5 4.37 4.44 25 110.9 8000/3 C 104.8 2.52 2.535 25 63.4 D 114 4.28 4.32 50 216.0 D 103.7 2.50 2.51 50 125.5 E 112 4.20 4.24 75 318.0 E 102.7 2.48 2.49 75 186.8 F 100 4.12 4.16 125 520.0 F 102.2 2.46 2.47 125 308.8 G 108 4.05 4.085 125 510.6 G 101.7 2.45 2.455 125 306.9 H 106 3.98 4.015 125 501.9 H 101.4 2.44 2.445 125 305.6 I 104. 5 3.92 3.95 150 492.5 I 101.1 2.44 2.44 150 366.0 J 103 3.86 3.89 240 933.6 J 100.7 2.43 2.435 240 584.4 K 101. 5 3.81 3.835 340 1303.9 K 100.3 2.42 2.425 340 824.5 L 100 3.75 3.78 240 907.2 L 100 2.41 2.415 240 579.6 M 98. 5 3.69 3.72 525 1953.0 M 99.6 2.40 2.405 525 1262.6 N 96 3.60 3.63 505 1833.2 N 99 2.38 2.39 505 1207.0 - 95 3.56 3.58 320 1145.6 - 99 2.38 2.38 320 761.6 66 2.48 3.02 215 649.3 79 1.90 2.14 215 460.1 (.60 X ) P 37 1.39 2.04 445 907.8 (.60 X ) P 45 1.08 1.57 445 698.6 (.70 X ) Q 6 0.22 1.04 130 Sum = 135.2 12653.2 (.70 X ) Q 8 0.19 0.81 130 Sum = 105.3 8210.8 Area Amt. Area Amt. size 3.70 size 2.37 A 123. 5 4.57 4.57 10 45.7 A 106.7 2.53 2.53 10 25.3 B 120 4.44 4.50 15 67.5 B 105.8 2.51 2.52 15 37.8 9000/2 C 117 4.33 4.38 25 109.5 9000/3 C 104.9 2.49 2.50 25 62.5 D 115 4.26 4.30 50 215.0 D 103.8 2.46 2.475 50 123.8 E 113 4.18 4.24 75 318.0 E 102.7 2.43 2.445 75 183.4 F 110. 5 4.09 4.135 125 516.9 F 102.3 2.42 2.425 125 303.1 G 108. 5 4.01 4.05 125 506.2 G 101.8 2.41 2.415 125 301.9 H 106. 5 3.94 3.975 125 496.9 H 101.5 2.40 2.405 125 300.6 I 104. 5 3.87 3.905 150 585.8 I 101.2 2.40 2.40 150 360.0 J 103. 5 3.83 3.85 240 924.0 J 100.8 2.39 2.395 240 574.8 K 102 3.77 3.80 340 1292.0 K 100.5 2.38 2.385 340 810.9 L 100. 5 3.72 3.745 240 898.8 L 100 2.37 2.375 240 570.0 M 99 3.66 3.69 525 1937.2 M 99.7 2.36 2.365 525 1241.6 N 97 3.59 3.625 505 1830.6 N 99.1 2.35 2.355 505 1189.3 - 95 3.52 3.56 435 1548.6 - 99 2.35 2.35 435 1022.2 79 2.92 3.22 100 322.0 88 2.08 2.215 100 221.5 (.60 X ) P 43 1.59 2.39 445 1063.6 (.60 X ) P 52 1.23 1.74 445 774.3 (.70 X ) Q 10 0.37 1.22 130 Sum = 158.6 12836.9 (.70 X ) Q 12 0.28 0.94 130 Sum = 122.2 8225.2 Area Amt. Area Amt. size 3.58 size 2.30 A 124. 5 4.46 4.46 10 44.6 A 107 2.46 2.46 10 24.6 B 121 4.33 4.40 15 66.0 B 106.2 2.44 2.45 15 36.8 12000/2 C 118 4.22 4.28 25 107.0 12000/3 C 105.3 2.42 2.43 25 60.8 D 116 4.15 4.18 50 209.0 D 104.2 2.40 2.41 50 120.5 E 114 4.08 4.12 75 309.0 E 103.0 2.37 2.385 75 178.9 F 112 4.01 4.04 125 505.0 F 102.6 2.36 2.365 125 295.6 G 110 3.94 3.98 125 497.5 G 102.1 2.35 2.355 125 294.4 H 108 3.87 3.90 125 487.5 H 101.8 2.34 2.345 125 293.1 I 106. 5 3.81 3.84 150 576.0 I 101.5 2.33 2.335 150 350.2 J 105 3.76 3.78 240 907.2 J 101 2.32 2.325 240 558.0 K 103 3.69 3.72 340 1264.8 K 100.7 2.32 2.32 340 788.8 L 102 3.65 3.67 240 880.8 L 100.3 2.31 2.315 240 555.6 M 100 3.58 3.62 525 1900.5 M 99.9 2.30 2.305 525 1210.1 N 98 3.50 3.54 505 1787.7 N 99.3 2.28 2.29 505 1156.4 96 3.44 3.47 535 1856.4 98.8 2.27 2.275 535 1217.1 - 95 3.40 3.42 220 752.4 - 98.3 2.26 2.265 220 498.3 (.60 X ) P 64 2.29 2.96 225 666.0 (.60 X ) P 71.5 1.64 2.01 225 452.2 (.70 X ) Q 21 0.75 1.83 130 Sum ■ 237.9 13055.3 (.70 X ) Q 27.5 0.63 1.34 130 Sum « 174.2 8265.6 132 In view of this result, and considering the elongated shape of the drainage, greater volume might have been obtained had the pattern in figure 49 been centered at one of the fatter parts of the drainage. By doing so, it appears possible that the H isohyet could be totally enclosed in the drainage when compared with the F Isohyet as placed in figure 49. However, there would be proportionately lower volumes contributed from the rest of the drainage. We will not carry this example beyond this point, as to do so would repeat the procedure demonstrated in example la. The objective of this example has been to show that, particularly for a long drainage, alignment of the isohyetal pattern (isohyets reduced for orientation) with the drainage axis will generally give greater volume than will a non-aligned pattern of unreduced isohyets. 7.4 Example No. 2a The second example describes the effect of a drainage-centered pattern vs. a pattern placement that may be considered for obtaining peak discharge. Also considered in this example will be the evaluation of subdrainages. For this example we chose the Ouachita River, Arkansas, above Rennel Dam, a drainage encompassing about 1,600 mi . The drainage outline drawn to a map scale of 1:1,000,000 is shown in figure 50 and includes four typical subdrainages. The areas within the four subdrainages are: 2 Area (mi ) 1. Above Pine Ridge 300 2. Between Pine Ridge and Washita 278 3. Between Washita and Blakely Mt. Dam 604 4. Between Blakely Mt . Dam and Rennel Dam 418 As in example la we will concern ourselves with determining the storm area sizj of the PMP pattern that provides the maximum volume within the entire 1,600 mi' drainage. The following steps correspond to those outlined in section 7.1. Step Al. The drainage center for the Ouachita River above Rennel Dam is roughly 34°36'N, 93°27'W. At this location, the following table of values is obtained from figures 18 through 42 of HMR No. 51. 133 + + 35* 93* RENNEL DAM MILES SCALE 1:1,000,000 + 34* 94* + 34* 93* figure 50. — Ouachita River, AR (1,600 ml ) above Rennel Dam showing drainage. Dura ti on (hr) Area (ml ) 6 12 24 48 72 10 30.0 35.9 40.6 44.6 47.1 200 22.2 27.0 31.2 34.7 37.7 1000 16.3 21.0 25.3 29.0 31.2 5000 9.5 13.5 17.7 21.6 24.2 10000 7.3 10.7 14.0 18.0 20.8 A2. The storm-area averaged PMP depths in step Al are plotted in figure 51 and smooth curves drawn. Notice that to obtain a consistent set of curves, it has not been possible to draw through all the data points. 134 < UJ K < !000( 500< 400( 300( 2000 I 000 — 500 40 300 200 — I0< 5( 4( 30 20 i r i i l i | i i i i | l l i l | i i I i DURATION (hr) 12 24 48 72 I I I I I I I I I I I I I I I I I I I IO J I I I I 50 Figure 51. — Depth-area -duration curves for 34°36*N, 93°27*W applicable to the Ouachita River AR, drainage. A3. From figure 51 we read off the data for at least 4 standard isohyet area sizes larger and smaller than the area of the drainage. We have chosen the areas in the following table. Duration (hr) Area (mi ) 12 24 48 72 450 19.3 24.0 28.2 31.2 34.3 700 17.7 22.3 26.3 29.5 32.6 1000 16.3 20.8 24.9 28.0 31.1 1500 14.7 19.1 23.1 26.4 29.4 2150 13.3 17.5 21.5 24.8 27.8 3000 12.0 16.0 20.0 23.4 26.4 4500 10.4 14.2 18.2 21.5 24.6 6500 8.9 12.6 16.5 19.8 23.0 135 0. u Q 3 5| | | | | | I | | | | | 30 2 5 20 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 5 6 I I I I I I I I I I 12 18 I I I i I 1 I I i i I I I I I I I i I I I i I I I I i I I I i I i 24 30 36 42 48 54 DURATION (hr) figure 52. — Depth-duration curves for selected area sizes at 34°36'N, 93°27 , W. A4. A smooth depth-duration curve is drawn for each of the eight area sizes listed in step A3, as shown in figure 52. From these curves, values are interpolated for 18-hr durations. Area (mi ) 18-hr Dura ti on 450 700 1000 1500 2150 3000 4500 6500 26.5 24.9 23.2 21.6 20.0 18.6 16.8 15.2 A5. Incremental differences are obtained for the 1st three 6-hr periods through subtraction of successive 6-hr values. 136 6-hr periods Area (ml ) 1 2 3 450 19. J 4.7 2.5 700 17.7 4.6 2.6 1000 16.3 4.5 2.4 1500 14.7 4.4 2.5 2150 13.3 4.4 2.5 3000 12.0 4.0 2.6 4500 10.4 3.8 2.6 6500 8.9 3.7 2.6 These values should then be plotted and fit by smooth curves as demonstrated In figure 53. The results from this figure provide smooth incremental values read to hundredths. 2 Area (mi ) 6-hr periods 1 2 3 450 19.32 4.73 2.54 700 17.70 4.63 2.54 1000 16.34 4.51 2.54 1500 14.79 4.36 2.54 2150 13.40 4.21 2.53 3000 12.05 4.05 2.52 4500 10.35 3.86 2.51 6500 8.80 3.67 2.50 Note that within each column, the values consistently decrease as com- pared to the unsmoothed values. Bl. The isohyetal pattern from figure 5 is placed over the drainage outline drawn to a scale of 1:1,000,000 as shown in figure 54. It was judged that the best fit of the isohyetal pattern was to enclose the H isohyet by the drainage outline. B2. For the isohyetal pattern placement in figure 54, the orientation is 095°. Since this orientation does not fall between the specified range of 135° and 315°, we add 180° to get an orientation of 275° (effectively the other end of the orientation line). B3. From figure 8, the orientation for PMP at 34°36'N, 93°27'W is about 235°. The difference between the orientation of the pattern laid over the drainage and that of PMP from figure 8 is 40°. On the basis of the model shown in figure 10, no adjustment need be made to the values in step A5 . B4. This step is skipped as no reduction is required. C. Now we can determine the maximum volume for PMP isohyetal pattern areas given in step A5. This computation is performed using the form provided in figure 41 and is completed for the 137 O) CO CO 10 Q. UJ o UJ CO < or UJ > < I CO ro Q z < CVJ rO 0L UJ Q UJ o < or UJ > < l CM ♦* 0) o o o o O o o o o o o o o o o O o o o o o o o o o o O io *■ ro CVJ o m *- ro CVJ — ( 2 !"0 V3UV 138 ORIENTATION 095°/275° ______ _ M + 34'36'n 93°27'w 10 20 30 40 ■ 50 MILES SCALE 1:1,000,000 34 # +. 94' + 34* 9 3* Figure 54. — Isohyetal pattern placed on the Ouachita River, AR drainage to give uaxlnum precipitation volume. 1st 6-hr incremental period as shown in table 27, following the steps outlined in section 7.1c In this computation, it was decided that the average depth of rainfall over the small portion of the drainage between isohyets L and M was insignificant to the volume computation, and therefore only the volume within the L isohyet has been determined. we find with the When computing the 2nd and Following the computation through the 1st 6-hr period, volumes that range between 19,000 and 22,000 mi -in. maximum between 1,500 and 2,150 ml 3rd 6-hr increments, we can narrow in on the range of areas to those areas between 1,000 and 4,500 mi (table 27). The results from summation of the incremental volumes at corresponding area sizes indicates that the maximum volume occurs at 2,150 mi . 139 ■Bible 27.— Completed computation sheets for 1st three 6-hr Increments for Ouachita River, AR drainage Oua chi ta I II River, AR III IV V VI Area : 1 I ,600 ml II Ir 2 Da III lcrement te: 1 Drainage: IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 19.32 depth aA AV size Iso. Nomo. 14.79 depth AA AV A 132 25.50 25.50 10 255.0 A 162 23.88 23.88 10 238.8 B 124 23.96 24.73 15 371.0 B 152 22.40 23.14 15 347.1 450/1 C 116 22.41 23.18 25 579.6 1500/1 C 142 20.93 21.66 25 541.5 D 108 20.87 21.64 50 1082.0 D 132 19.52 20.22 50 1011.0 E 101 19.52 20.20 75 1515.0 E 122 18.04 18.78 75 1408.5 F 93 17.97 18.74 125 2342.5 F 112 16.51 17.28 125 2160.0 G 86 16.62 17.30 150 2593.0 G 105 15.53 16.02 150 2403.0 H 63 12.17 14.90 250 3725.0 H 96 14.15 24.84 250 3710.0 I 50 9.66 10.92 242 2642.6 I 88 13.02 13.59 242 3288.8 J 38 7.34 8.50 242 2057.0 J 80 11.79 12.40 242 3000.8 K 30 5.80 6.57 224 1471.7 K 56 8.25 10.02 224 2244.5 L 23 4.44 5.12 192 Sum ■ 983.0 19617.4 L 41 6.06 7.16 192 Sum = 1374.7 21728.7 Area Amt. Area Amt. size 17.70 size 13.40 A 140 24.78 24.78 10 247.8 A 176 23.58 23.58 10 235.8 B 132 23.36 24.12 15 361.8 B 165 22.11 22.84 15 342.6 700/1 C 124 21.95 22.66 25 566.5 2150/1 C 154 20.64 21.38 25 534.5 D 115 20.36 21.16 50 1058.0 D 142 19.03 19.84 50 992.0 E 107 18.94 19.65 75 1473.8 E 131 17.55 18.29 75 1371.8 F 98 17.35 18.14 125 2267.5 F 122 16.35 16.05 125 2006.2 G 92 16.28 16.82 150 2523.0 G 113 15.14 15.74 150 2361.0 H 84 14.87 15.58 250 3895.0 H 103 13.80 14.47 250 3617.5 I 63 11.15 13.01 242 3148.4 I 95 12.73 13.26 242 3208.9 J 48 8.50 9.82 242 2376.4 J 86 11.52 12.12 242 2933.0 K 36 6.37 7.44 224 1666.6 K 77 10.32 10.92 224 2446.1 L 27 4.78 5.58 192 Sum = 1071.4 20656.2 L 52 5.97 8.64 192 Sum = 1658.9 21708.3 Area Amt. Area Amt. size 16.34 size 12.05 A 149 24.35 24.35 10 243.5 A 191 23.02 23.02 10 230.2 B 140 22.88 23.58 15 353.7 B 179 21.57 22.30 15 334.5 1000/1 C 131 21.41 22.12 25 553.0 3000/1 C 166 20.00 20.78 25 519.5 D 122 19.93 20.67 50 1033.5 D 154 18.56 19.28 50 964.0 E 113 18.46 19.20 75 1440.0 E 142 17.11 17.84 75 1338.0 F 104 16.99 17.72 125 2215.0 F 132 15.91 16.51 125 2063.8 G 97 15.85 16.42 150 2463.0 G 122 14.70 15.30 150 2295.0 H 89 14.54 15.20 250 3800.0 H 112 13.50 14.10 250 3525.0 I 82 13.40 13.97 242 3380.7 I 102 12.29 12.90 242 3121.8 J 60 9.80 11.60 242 2807.2 J 92 11.09 11.69 242 2829.0 K 44 7.19 8.50 224 1904.0 K 83 9.88 10.48 224 2347.5 L 32 5.23 6.21 192 Sum » 1192.3 21385.9 L 74 8.92 9.40 192 Sum ■ 1804.8 21373.1 140 "Bible 27.— Completed computation sheets for 1st three 6-hr Increments for Ouachita River, AR drainage — Continued Increment: 1, 2 Drainage: Ouachita River, AR Area: 1,600 ml Date: II III IV VI II III IV VI Area size Iso. Nomo. Amt . 10.35 Avg. depth AA AV Area size Iso. Nomo. Amt. 4.36 Avg. depth &A aV 4500/1 Area size 6500/1 Area size 1000/2 A 212 21.94 21.94 10 219.4 B 198 20.49 21.22 15 318.3 C 184 19.04 19.76 25 494.0 1500 D 170 17.60 18.32 50 916.0 E 157 16.25 16.92 75 1269.0 F 146 15.11 15.68 125 1960.0 G 135 13.97 14.54 150 2181.0 H 124 12.83 13.40 250 3350.0 I 113 11.70 12.26 242 2966.9 J 103 10.66 11.18 242 2705.6 K 93 9.63 10.14 224 2271,4 L 83 8.59 9.11 192 1749.1 Sum = 20409.7 Amt. Area 8.80 size A 233 20.50 20.50 10 205.0 B 218 19.18 19.84 15 297.6 C 203 17.86 18.52 25 463.0 2150 D 187 16.46 17.16 50 858.0 E 174 15.31 15.88 75 1191.0 F 160 14.08 14.70 125 1837.5 G 148 13.02 13.55 150 2032.5 H 137 12.06 12.54 250 3135.0 I 125 11.00 11.53 242 2790.3 J 113 9.94 10.47 242 2533.7 K 103 9.06 9.50 224 2128.0 L 93 8.18 8.62 192 Sum = 1655.0 19126.6 Amt. 4.51 Area size A 116 5.23 5.23 10 52.3 B 112 5.05 5.14 15 77.1 C 108.5 4.89 4.97 25 124.3 3000 D 105 4.74 4.82 50 241.0 E 103 4.65 4.70 75 352.5 F 101 4.56 4.61 125 576.2 G 99 4.46 4.51 150 676.5 H 97 4.37 4.42 250 1105.0 I 95 4.28 4.33 242 1047.9 J 76 3.43 3.86 242 934.1 K 63 2.48 3.14 224 703.4 L 51 2.30 2.57 192 Sum = 493.4 6383.7 A 117 5.10 5.10 10 51.0 B 113 4.93 5.02 15 74.2 C 110 4.80 4.87 25 121.8 D 107 4.67 4.74. 50 237.0 E 105 4.58 4.63 75 347.2 F 103 4.49 4.54 125 567.5 G 100.5 4.38 4.44 150 666.0 H 99 4.32 4.35 250 1087.5 I 97 4.23 4.28 242 1035.8 J 95.5 4.16 4.20 242 1016.4 K 75.5 3.29 3.73 224 835.5 L 60 2.62 2.96 192 Sum = 568.3 6608.2 Amt . 4.21 A 118.5 4.99 4.99 10 49.9 B 114.5 4.82 4.91 15 73.7 C 111 4.67 4.75 25 118.8 D 108.5 4.57 4.62 50 231.0 E 106.5 4.48 4.53 75 339.8 F 104.5 4.40 4.44 125 555.0 G 102 4.29 4.35 150 652.5 H 100 4.21 4.25 250 1062.5 I 98.5 4.15 4.18 242 1011.6 J 97 3.08 4.12 242 997.0 K 95 4.00 4.04 224 904.9 L 73 3.07 3.54 192 679.7 Sum 6676.4 Amt. 4.05 A 119.5 4.84 4.84 10 48.4 B 116 4.70 4.77 15 71.6 C 112.5 4.56 4.63 25 115.8 D 110 4.46 4.51 50 225.5 E 108 4.37 4.42 75 331.5 F 106 4.29 4.33 125 541.3 G 104 4.21 4.25 150 637.5 H 102 4.13 4.17 250 1042.5 I 100 4.05 4.09 242 989.8 J 99 4.01 4.03 242 975.3 K 97 3.93 3.97 224 889.3 L 96 3.89 3.91 192 750.7 Sum = 6619.2 141 liable 27. — Completed computation sheets for 1st three 6-hr Increments for Ouachita River, AR drainage — Continued Drainage: Ouachita Ri I II ver, AR III IV V VI Area : 1 I ,600 mi 2 II Inc Dat III ;rement: e: 2 , 3 IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. No mo. 3.86 depth aA AV size Iso. Nomo. 2.53 depth AA AV A 121 4.67 4.67 10 46.7 A 105.3 2.66 2.66 10 26.6 B 117 4.52 4.60 15 68.9 B 104.2 2.64 2.65 15 39.8 4500/2 C 114 4.40 4.46 25 111.5 2150/3 C 103.2 2.61 2.625 25 65.6 D 112 4.32 4.36 50 218.0 D 102 2.58 2.595 50 129.8 E 109.5 4.23 4.28 75 321.0 E 101.3 2.56 2.57 75 192.8 F 108 4.17 4.20 125 525.0 F 101 2.56 2.56 125 320.0 G 105.5 4.07 4.12 150 618.0 G 100.6 2.54 2.55 150 382.5 H 103.5 4.00 4.04 250 1010.0 H 100.3 2.54 2.54 250 635.0 I 102 3.94 3.97 242 960.7 I 100 2.52 2.53 242 612.3 J 100.5 3.88 3.91 242 946.2 J 99.7 2.52 2.52 242 609.8 K 99 3.82 3.85 224 862.4 K 99.5 2.52 2.525 224 565.6 L 97.5 3.76 3.79 192 Sum = 727.7 6416.1 L 80.5 2.04 2.28 192 Sum = 437.8 4017.6 Area Amt. Area Amt. size 2.54 size 2.51 A 104.6 2.66 2.66 10 26.6 A 105.7 2.65 2.65 10 26.5 B 103.3 2.62 2.64 15 39.6 B 104.6 2.63 2.64 15 39.6 1000/3 C 102.3 2.60 2.61 25 65.3 3000/3 C 103.5 2.60 2.62 25 65.4 D 101.3 2.57 2.59 50 129.5 D 102.5 2.57 2.59 50 129.5 E 100.6 2.56 2.57 75 192.8 E 101.7 2.55 2.56 75 192.0 F 100.3 2.55 2.56 125 320.0 F 101.3 2.54 2.55 125 318.8 G 99.9 2.54 2.55 150 382.5 G 100.9 2.53 2.54 150 381.0 H 99.6 2.53 2.54 250 635.0 H 100.5 2.52 2.53 250 632.5 I 99.3 2.52 2.53 242 612.3 I 100.2 2.52 2.52 242 609.8 J 82.5 2.10 2.31 242 559.0 J 99.9 2.51 2.52 242 609.8 K 67 1.70 1.90 224 425.6 K 99.6 2.50 2.51 224 562.2 L 54 1.37 1.54 192 295.7 L 99.2 2.49 2.50 192 480.0 Sum = 3683.9 Sum 4046.8 Area Amt. Area Amt. size 2.54 size 2.51 A 105 2.67 2.67 10 26.7 A 106 2.66 2.66 10 26.6 B 103.8 2.64 2.66 15 39.8 B 105 2.64 2.65 15 39.8 1500/3 C 102.7 2.61 2.63 25 65.8 4500/3 C 104 2.61 2.63 25 65.8 D 101.7 2.58 2.60 50 130.0 D 103.1 2.59 2.60 50 130.0 E 101.0 2.57 2.58 75 193.5 E 102.1 2.56 2.58 75 193.5 F 100.7 2.56 2.57 125 321.2 F 101.7 2.55 2.56 125 320.0 G 100.3 2.55 2.56 150 384.0 G 101.2 2.54 2.55 150 382.5 H 100 2.54 2.55 250 637.5 H 100.9 2.53 2.54 250 635.0 I 99.7 2.53 2.535 242 613.5 I 100.6 2.53 2.53 242 612.3 J 99.4 2.52 2.525 242 611.0 J 100.2 2.52 2.53 242 612.3 K 81 2.06 2.29 224 513.0 K 99.9 2.51 2.52 224 564.5 L 65.5 1.66 1.86 192 357.1 L 99.6 2.50 2.51 192 481.9 Sum = 3893.1 Sum = 4064.2 142 "Bible 27.— Completed computation sheets for 1st three 6-hr Increments for Ouachita River, AR drainage - Continued Ouachita I II River, AR III IV V VI Area : 1 I ,600 mi II In< Eat III ;rement : :e: 1 . 2 Drainage: IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 14.30 depth AA AV size Iso. Nomo. 4.30 depth AA AV A 167 23.88 23.88 10 238.8 A 117.5 5.05 5.05 10 50.5 B 156 22.31 23.10 15 346.4 B 114 4.90 4.98 15 74.6 1700/1 C 145 20.74 21.52 25 538.1 1700/2 C 110.5 4.75 4.83 25 120.8 D 135 19.30 20.02 50 1001.0 D 107.5 4.62 4.69 50 234.5 E 125 17.88 18.59 75 1394.2 E 105 4.52 4.57 75 342.8 F 116 16.59 17.24 125 2155.0 F 103.5 4.45 4.49 125 561.2 G 107 15.30 15.94 150 2391.0 G 101 4.34 4.40 150 660.0 H 98 14.01 14.52 250 3630.0 H 99 4.26 4.30 250 1075.0 I 91 13.01 13.51 242 3269.4 I 97 4.17 4.22 242 1021.2 J 82 11.73 12.37 242 2993.5 J 96 4.13 4.15 242 1004.3 - 79 11.30 11.52 87 1002.2 - 95.5 4.10 4.12 87 358.4 K 62 8.87 10.08 137 1381.0 K 80 3.44 3.77 137 516.5 L 44 6.29 7.58 192 1455.4 L 64 2.74 3.07 192 589.4 Sum = 21796.0 Sum 6609.2 Area Amt. Area Amt. size 13.85 size 4.25 A 171 23.68 23.68 10 236.8 A 118 5.02 5.02 10 50.2 B 160 22.16 22.92 15 343.8 B 116 4.93 4.98 15 74.6 1900/1 C 149 20.64 21.40 25 535.0 1900/2 C 111 4.72 4.83 25 120.8 D 138 19.11 19.88 50 994.0 D 108 4.59 4.66 50 233.0 E 128 17.73 18.42 75 1381.5 E 106 4.51 4.5 75 341.3 F 118 16.34 17.03 125 2128.8 F 104 4.42 4.47 125 558.8 G 110 15.24 15.79 150 2368.5 G 102 4.34 4.38 150 657.0 H 100 13.85 14.54 250 3635.0 H 100 4.25 4.30 250 1075.0 I 93 12.88 13.36 242 3233.1 I 98 4.17 4.21 242 1018.8 J 84 11.63 12.26 242 2966.9 J 96.6 4.10 4.14 242 1001.9 - 78 10.80 11.22 144 1615.7 - 95.5 4.06 4.08 144 587.5 K 68 9.42 10.11 80 808.8 K 86 3.66 3.86 80 308.8 L 48 6.65 8.04 192 Sum = 1543.7 21791.6 L 68 2.87 3.28 192 Sum = 629.8 6657.5 Area Amt. Area Amt. size 12.94 size 4.15 A 181 23.42 23.42 10 234.2 A 119 4.94 4.94 10 49.4 B 169 21.87 22.64 15 339.6 B 115 4.77 4.86 15 72.8 2400/1 C 158 20.44 21.16 25 528.9 2400/2 C 112 4.65 4.71 25 117.8 D 146 18.89 19.66 50 983.0 D 109 4.52 4.59 50 229.3 E 134 17.34 18.12 75 1359.0 E 107 4.44 4.48 75 336.0 F 125 16.18 16.76 125 2095.0 F 105 4.36 4.40 125 550.0 G 116 15.01 15.60 150 2340.0 G 103 4.27 4.32 150 647.3 H 106 13.72 14.36 250 3590.0 H 101 4.19 4.23 250 1057.5 I 97 12.55 13.14 242 3179.9 I 99 4.11 4.15 242 1004.3 J 88 11.39 11.97 242 2896.7 J 97.5 4.05 4.08 242 987.4 K 79 10.22 10.77 224 2412.5 K 96.5 4.00 4.025 224 901.6 - 76 9.83 10.80 70 756.0 - 96 3.98 3.99 70 279.3 L 58 7.50 8.67 122 1057.7 L 78 3.24 3.61 122 440.4 Sum 21772.5 Sum 6613.1 143 "Cable 27. — Completed computation sheets for 1st three 6-hr Increments for Ouachita River, AR drainage - Continued Drainage: Ouachita River, AR Area: 1,600 ml' Increment : Date: I II Ill IV V VI I II Ill IV V VI Area size Iso. Nomo. Amt. 2.54 Avg. depth AA AV Area size Iso. Nomo. Amt. Avg. depth AA AV A 105.1 2.67 2.67 10 26.7 B 104 2.64 2.66 15 39.8 1700/3 C 102.8 2.61 2.63 25 65.8 D 101.9 2.59 2.60 50 130.0 E 101.1 2.57 2.58 75 193.5 F 100.7 2.56 2.57 125 321.2 G 100.4 2.55 2.56 150 384.0 H 100 2.54 2.55 250 637.5 I 99.7 2.53 2.54 242 614.7 J 99.5 2.53 2.53 242 612.3 - 99.3 2.52 2.525 87 219.7 K 86 2.18 2.35 137 322.0 L 70 1.78 1.98 192 Sum = 380.2 3947.4 Area Amt. size 2.53 A 105.2 2.66 2.66 10 26.6 B 104.1 2.63 2.65 15 39.7 1900/3 C 103 2.61 2.62 25 65.5 D 102 2.58 2.60 50 130.0 E 101.2 2.56 2.57 75 192.8 F 100.8 2.55 2.56 125 320.0 G 100.5 2.54 2.55 150 382.5 H 100.2 2.54 2.54 250 635.0 I 99.8 2.52 2.53 242 612.3 J 99.6 2.52 2.52 242 609.8 - 99.4 2.51 2.525 144 363.4 K 92 2.33 2.42 80 193.6 L 75 1.90 2.12 192 407.0 Sum = 3978.2 Area Amt. size 2.52 A 105.4 2.66 2.66 10 26.6 B 104.3 2.63 2.65 15 39.7 2400/3 C 103.3 2.60 2.62 25 65.4 D 102.3 2.58 2.59 50 129.5 E 101.5 2.56 2.57 75 192.8 F 101 2.55 2.56 125 320.0 G 100.7 2.54 2.55 150 382.5 H 100.3 2.53 2.54 250 635.0 I 100 2.52 2.53 242 612.3 J 99.8 2.51 2.52 242 609.8 K 99.4 2.50 2.51 224 562.2 - 99.3 2.50 2.50 70 175.0 L 86 2.17 2.34 122 285.5 Sum = 4036.3 144 29 30 31 32 33 VOLUME (xl0 3 mi 2 -in.) Figure 55. — Volume vs. area curve for 1st three 6-hr increments for Ouachita River, AR drainage. As recommended in the procedure, we should compute volumes for supplemental area sizes on either side of 2,150 mi . We chose 1,700, 1,900 and 2,400 mi 2 (see table 27 for computations). Supplemental isohyets for these three area sizes have been added to figure 54 as the dotted isohyets. The additional computations result in the conclusion that the 1,900-mi area pattern provides the greatest volume (about 32,400 mi -in.). (See the dashed line in figure 55.) Step 2 Dl. For an area size of 1,900 mi , it is necessary to return to figure 51 and read off depth-duration values as follows: Duration (hr) 12 24 48 72 1,900 mi/ PMP (in.) 13.8 18.1 22.1 25.4 28.1 145 Plotting these data on a linear depth-duration diagram, we read off the following 6-hr values. Duration (hr) 6 12 18 24 30 36 42 48 54 60 66 72 1,900-mi 2 PMP (in.) 13.8 18.1 20.5 22.1 23.1 23.9 24.6 25.4 26.1 26.8 27.4 28.0 D2. Subtract the 6-hr value in step Dl from the 12-hr value, the 12-hr from the 18-hr, etc., to get the 12 incremental values. 6-hr periods 5 6 7 8 9 10 11 12 Increm. PMP(in.) 13.8 4.3 2.4 1.6 1.0 0.8 0.7 0.8 0.7 0.7 0.6 0.6 Now the values for the 1st three increments can be replaced by the smoothed values obtained from figure 53, read to hundreths. Note, that to maintain a consistently decreasing set of values with increasing period it is necessary to interchange the incremental values for the 7th and 8th period to get a final smooth set of depth-duration values of: 6-hr periods 5 6 7 8 9 10 11 12 Increm. PMP(in.) 13.85 4.25 2.53 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 D3. Form the matrix of isohyet values shown in table 28 by multiplying the 1st 6-hr value in step D2 times the isohyet percentages for 1,900 mi from the 1st 6-hr nomogram (fig. 16), the 2nd 6-hr value in step D2 times the percentages for 1,900 mi from figure 18, etc., and each of the fourth through 12th 6-hr values times the percentages from figure 20. D4. Incremental average depths for the Ouachita River drainage with the 1,900-mi PMP storm pattern placed as shown in figure 54 can be obtained using the incremental isohyetal labels in step D3 and the 6-hr incremental depths from step D2, as was done for example la. These results (computations shown in table 29) are, 6-hr periods 123456789 10 11 12 Drainage avg. PMP 13.62 4.16 2.49 1.55 0.98 0.78 0.78 0.68 0.68 0.68 0.59 0.59 (in.) 146 "Cable 28. — Isohyet values (in.), Ouachita River, AR, for example 2a 6 -hr periods (Isohyet) 1 2 3 4 5 6 7 8 9 10 11 12 A 23.68 5.02 2.66 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 B 22.16 4.93 2.63 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 C 20. 6A 4.72 2.61 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 D 19.18 4.59 2.58 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 E 17.73 4.51 2.56 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 F 16.41 4.42 2.55 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 G 15.24 4.34 2.54 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 H 13.92 4.25 2.54 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 I 12.88 4.17 2.52 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 J 11.63 4.10 2.52 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.60 1900 ml Z 10.80 4.06 2.51 1.60 1.00 0.80 0.80 0.70 0.70 0.70 0.60 0.65 K 9.35 3.66 2.33 1.47 0.92 0.74 0.74 0.64 0.64 0.64 0.55 0.55 L 6.58 2.89 1.90 1.19 0.74 0.60 0.60 0.52 0.52 0.52 0.45 0.45 Note the results shown In this matrix of isohyet values emphasize the fact that for the fourth through 12th 6-hr period the distribution of IMP is uniform across the PMP portion of the pattern (A through 1,900 mi ) for each increment. However, isohyets outside the 1,900-mi isohyet (K and L) represent the residual precipitation for the 1,900-mi' decreasing values. pattern, and these isohyets are assigned These give a 72-hr total drainage-averaged PMP of 27.59 in. and can be compared to the 29.2 in. from figure 51 for 1,600 mi , or a 6 percent reduction from HMR No. 51. This small reduction is in part caused by the fact that no adjustment was made for orientation and the fact that the basin shape is relatively elliptical. D5. In this example, isohyetal values for durations less than 6 hr were not required. If they were needed, they would be computed at this point. E. Temporal Distribution The isohyet values listed in the matrix of step D3 may be reordered according to the limitations given in section 2.3. Remember that if reordering is done, it must be done consistently for all isohyets covering the drainage. F. Subdrainage Average Depths Figure 56 shows the four subdrainages within the Ouachita River Drainage (above Rennel Dam) covered by the isohyetal pattern. It is often of interest to determine the incremental average depths of precipitation applied to each subdrainage. For this example we will demonstrate the steps to determine average depth 147 •Bible 29. — Completed conputation sheets shoving typical format to get lncrc Ouachita River, AR ■ental drainage-average depths, Increment: 1 to 7 Drainage: Ouachita River, AR Area: 1,600 ml Date: I II Ill IV V VI I II Ill IV V VI Area size Iso. Nomo. Amt. 13.85 Avg. depth A V Area size Iso. Nomo. Amt. 1.60 Avg. depth A V A 10 236.8 A 100 1.60 1.60 10 16.0 8 15 343.8 B 100 1.60 1.60 15 24.0 1900/1 C 25 535.0 1900/4 C 100 1.60 1.60 25 40.0 D 50 994.0 D 100 1.60 1.60 50 80.0 E 75 1381.5 E 100 1.60 1.60 75 120.0 F 125 2128.4 F 100 1.60 1.60 125 200.0 G 150 2368.5 G 100 1.60 1.60 150 240.0 H 250 3635.0 H 100 1.60 1.60 250 400.0 I 242 3233.1 I 100 1.60 1.60 242 387.2 J 242 2966.9 J 100 1.60 1.60 242 387.2 - 144 1615.7 - 100 1.60 1.60 144 230.4 K 80 808.8 K 92 1.35 1.48 80 118.4 L Total 192 = 1600 Sum = 1543.7 21791.6 L 74.5 1.19 1.27 192 Sum = 243.8 2487.0 Avg. depth = 13.62 Avg. depth = 1.55 — — — — — — — — — — — — — Area Amt. Area Amt. size 4.25 size 1.00 A 10 50.2 A 100 1.00 1.00 10 10.0 B 15 74.6 B 100 1.00 1.00 15 15.0 1900/2 C 25 120.8 1900/5 C 100 1.00 1.00 25 25.0 D 50 233.0 D 100 1.00 1.00 50 50.0 E 75 341.3 E 100 1.00 1.00 75 75.0 F 125 558.8 F 100 1.00 1.00 125 125.0 G 150 657.0 G 100 1.00 1.00 150 150.0 H 250 1075.0 H 100 1.00 1.00 250 250.0 I 242 1018.8 I 100 1.00 1.00 242 242.0 J 242 1001.9 J 100 1.00 1.00 242 242.0 - 144 587.5 - 100 1.00 1.00 144 144.0 K 80 308.8 K 92 0.92 0.96 80 76.8 L 192 Sum = 629.8 6657.5 L 74.5 0.74 0.83 192 Sum = 159.4 1564.2 Avg. depth = 4.16 Avg. depth = .98 Area Amt. Area Amt. size 2.53 size 0.80 A 10 26.6 A 100 0.80 0.80 10 8.0 B 15 39.7 B 100 0.80 0.80 15 12.0 1900/3 C 25 65.5 1900/6,7 C 100 0.80 0.80 25 20.0 D 50 130.0 D 100 0.80 0.80 50 40.0 E 75 192.8 E 100 0.80 0.80 75 60.0 F 125 320.0 F 100 0.80 0.80 125 100.0 G 150 382.5 G 100 0.80 0.80 150 120.0 H 250 635.0 H 100 0.80 0.80 250 200.0 I 242 612.3 I 100 0.80 0.80 242 193.6 J 242 609.8 J 100 0.80 0.80 242 193.6 - 144 363.4 - 100 0.80 0.80 144 115.2 K 80 193.6 K 92 0.74 0.77 80 61.6 L 192 Sum = 407.0 3978.2 L 74.5 0.60 0.67 192 Sum = 128.6 1252.6 Avg. depth ■ 2.49 Avg. depth = .78 148 Table 29. -Completed computation sheets showing typical format to get Incremental drainage-average depths, Ouachita River, AR - Continued Drainage: Ouachita River, AR II III IV VI Increment: Area: 1,600 ml 2 Date: I II III IV 8 to 12 VI Area size Iso. Nomo. Amt. 0.70 Avg. depth aA av Area size Amt, Is o . Nomo . Avg. depth AA AV A 100 0.70 0.70 10 7.0 B 100 0.70 0.70 15 10.5 1900/8,9, C 100 0.70 0.70 25 17.5 10 D 100 0.70 0.70 50 35.0 E 100 0.70 0.70 75 52.5 F 100 0.70 0.70 125 87.5 G 100 0.70 0.70 150 105.0 H 100 0.70 0.70 250 175.0 I 100 0.70 0.70 242 169.4 J 100 0.70 0.70 242 169.4 - 100 0.70 0.70 144 100.8 K 92 0.64 0.67 80 53.6 Area L 74.5 0.52 Amt. 0.58 Avg. d 192 Sum = epth = 111.4 1094.6 .68 size 100 0.60 A 100 0.60 0.60 10 6.0 B 100 0.60 0.60 15 9.0 1900/11,12 C 100 0.60 0.60 25 15.0 D 100 6.60 0.60 50 30.0 E 100 0.60 0.60 75 45.0 F 100 0.60 0.60 125 75.0 G 100 0.60 0.60 150 90.0 H 100 0.60 0.60 250 150.0 I 100 0.60 0.60 242 145.2 J 100 0.60 0.60 242 145.2 - 100 0.60 0.60 144 86.4 K 92 0.55 0.58 80 46.4 L 74.5 0.45 0.50 192 Sum = 96.0 939.2 Avg. depth = .59 149 -h35 - 93* ®L S / 10 _i_ 20 30 _L_ 40 _l_ 50 _l MILES SCALE*. 1:1,000 000 + 34' 94* (D— PINE RIDGE (2)_WASHITA (3)-BLAKELY MI DAM ®— RENNEL DAM 93* Figure 56. — Isohyetal pattern placed on the Ouachita River, AR drainage relative to suhdralnages. 2 over the subdrainage between Pine Ridge and Vfeshita (278 mi ). From figure 56 we see that this subdrainage is covered by isohyets B through K. Step Fl. Planimeter the areas between isohyets for each isohyet that crosses the subdrainage to obtain the areas used in column V of the computation sheet shown in table 30. F2. Use the isohyet values in step D3 to fill in column III in table 30. Follow the computational procedure outlined in steps C5 to C8 to obtain the subdrainage incremental volumes. Note that for the fourth through 12th 6-hr periods it is not necessary to formally compute the volumes, since the subregion Is not covered by residual precipitation, and 150 Table 30. — Completed computation sheet for determining average depths for 1st three 6-hr increments over subdralnage between Blakely Nt. Dam and Washita, AR Increment: 1 to 3 Drainage: Ouachita River, AR Area : Eate: I II Ill IV V VI I II Ill IV V VI Area Size Iso. Nomo. Amt. Avg. depth 6A AV Area size Iso. Nomo. Amt. Avg. depth AA AV 1900/1 Area size 1900/2 A B C D E F G H I J K A B C D E F G H I J K 22.16 20.64 21.40 7.7 164.8 19.18 19.91 15.8 314.6 17.73 18.46 40.7 751.3 16.41 17.07 21.4 365.3 15.24 15.82 25.7 406.6 13.92 14.58 47.0 685.3 12.88 13.40 59.8 801.3 11.63 12.22 55.6 679.4 9.35 10.49 4.3 45.1 Total - 278.0 Sum ■ 4213.7 Avg. 6 epth = 15.2 in Amt, 4.93 4.72 4.82 7.7 37.4 4.59 4.66 15.8 73.6 4.51 4.55 40.7 185.2 4.42 4.46 21.4 95.4 4.34 4.38 25.7 112.6 4.25 4.30 47.0 202.1 4.17 4.21 59.8 251.8 4.10 4.14 55.6 230.2 3.66 3.88 4.3 16.7 Sum = 1205.0 Avg. d epth = 4.3 in Area Amt. size A B 2.63 1900/3 C 2.61 2.62 7.7 20.2 D 2.58 2.595 15.8 41.0 E 2.56 7.57 40.7 104.6 F 2.55 2.555 21.4 54.7 G 2.54 2.545 25.7 65.4 H 2.54 2.54 47.0 119.4 I 2.52 2.53 59.8 151.3 J 2.52 2.52 55.6 140.1 K 2.33 2.42 4.3 Sum ■ Avg. depth - 10.4 707.1 2.5 in 151 thus the average depths for these increments will be the same as the incremental PMP amounts. F3. The average depths for the subdrainage between Pine RLdge and Washita are thus, 6-hr periods 123456789 10 11 12 Subdrain- age. avg. 15.2 4.3 2.5 1.6 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 depth (in.) 7.5 Example No. 2b In this example we want to suggest that a placement of the isohyetal pattern closer to the outlet may be advantageous to bring about a greater peak discharge, however, the result is a lower volume than the drainage-centered placement considered in example 2a. Figure 57 shows the displacement of our standard pattern toward the drainage outlet. One might judge that a somewhat better placement is possible than that shown. However, for the purpose of illustration, it was believed necessary not to change the original orientation in order to show that any reduction in volume was due to difference other than orientation. For this example, it is not necessary to start over by obtaining new values from HMR NO. 51.* Therefore, we can proceed directly to the computation of volume previously determined in table 27, and it is only necessary to change the incremental areas as a result of planimetering figure 57. The computations for the 1st three 6-hr increments for the standard isohyetal areas as recomputed in table 31 are shown to be roughly 10 percent lower than those for the drainage- centered placement (fig. 54). In table 31, we find that unlike the result from example 2a, the area of PMP determined by maximum .volume In the drainage has increased from 1,900 mi to the vicinity of 3,000 mi . This result implies a less intense storm has been considered. Although not shown, a reduction in volume would also have occurred had we applied the same isohyet values from table 28 to the pattern shown in figure 57. These results support our claim that a placement that may be advantageous to obtaining a maximum peak discharge in general will give less than maximum volume. Although relocation of a PMP storm pattern closer to the drainage outlet results in a a smaller drainage volume, one should consider the impact of concentrating a more intense storm pattern near the dam. A more intense storm here means a PMP storm pattern area less than that giving the maximum volume of precipitation in the drainage, but which contains greater central depths. For the example storm shown in figure 54, we might consider a PMP storm pattern for 450 ml or 1,000 mi and compute the peak discharge. Since we do not have sufficient information to compute the peak discharge, it is left to the user to make such tests. From these tests the user can determine whether other more *The user may need to redetermine these if the pattern is moved a significant distance. 152 93- , ^35 9* 3 5-4" L 10 _i 20 i 30 _i *S. IP MILES SCALE: 1:1,000,000 93 + 34 94* Figure 57. — Alternate placement of isohyetal pattern on Ouachita River, AR drainage typical of determination of peak discharge. Intense storms or pattern repositions will yield more critical peak flows. It should be noted again that drainage-averaged depths from any PMP pattern smaller than that which gives maximum volume in the drainage, will be less than drainage- averaged PMP. ACKNOWLEDGMENTS The authors express their appreciation to Mr. John Riedel, former Chief, Hydrometeorological Branch, Office of Hydrology, National Weather Service; Dr. Donald Jensen, and Mr. Arthur Cudworth, Bureau of Reclamation, Denver; and Messrs. Eugene Stallings and Ron Hula, U. S. Army Corps of Engineers for their helpful comments and suggestions during the preparation of this report. We appreciate the large amount of technical assistance provided by Keith Bell, Marion Choate, Roxanne Johnson, and Teresa Nero of the Hydrometeorological Branch. The many drafts and final versions of this manuscript were typed by Helen Rodgers, Kathryn Carey and Clara Brown. 153 Table 31. — Completed computation sheets for 1st three 6-hr Increments for alternate placement of pattern on Ouachita River, AR drainage Ouachita I II River, AR III IV V VI Area : 1 I ,600 mi II Ir 2 ft III lcrement te: 1 Drainage: IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 17.70 depth aA AV size Iso. Nomo. 13.40 depth aA aV A 140 24.78 24.78 10 247.8 A 176 23.58 23.58 10 235.8 B 132 23.36 24.07 15 361.0 B 165 22.11 22.84 15 342.6 700/1 C 124 21.95 22.66 25 566.5 2150/1 C 154 20.64 21.38 25 534.5 D 115 20.36 21.16 50 1058.0 D 142 19.03 19.84 50 992.0 E 107 18.94 19.65 75 1473.8 E 131 17.55 18.29 75 1371.8 F 98 17.35 18.14 125 2267.5 F 122 16.35 16.95 125 2118.8 G 92 16.28 16.82 140 2354.8 G 113 15.14 15.74 140 2203.6 H 84 14.87 15.58 140 2181.2 H 103 13.80 14.47 140 2025.8 I 63 11.15 13.01 115 1496.2 I 95 12.73 13.26 115 1524.9 J 48 8.50 9.82 160 1571.2 J 86 11.52 12.12 160 1939.2 K 36 6.37 7.44 210 1562.4 K 77 10.32 10.92 210 2293.2 L 27 4.78 5.58 260 1450.8 L 52 6.97 8.64 260 2246.4 M 18 3.19 3.98 225 895.5 M 33 4.42 5.70 225 1282.5 N 10 1.77 2.48 50 Sum = 124.0 16310.7 N 20 2.68 3.55 50 Sum = 177.5 19288.6 Area Amt. Area Amt. size 16.34 size 12.05 A 149 24.35 24.35 10 243.5 A 191 23.02 23.02 10 230.2 B 140 22.88 23.62 15 354.3 B 179 21.57 22.30 15 334.5 1000/1 C 131 21.40 22.14 25 553.5 3000/1 C 166 20.00 20.78 25 519.5 D 122 19.93 20.66 50 1033.0 D 154 18.56 19.28 50 964.0 E 113 18.46 19.20 75 1440.0 E 142 17.11 17.84 75 1338.0 F 104 16.99 17.73 125 2216.2 F 132 15.90 16.50 125 2062.5 G 97 15.85 16.42 140 2298.8 G 122 14.70 15.30 140 2142.0 H 89 14.54 15.20 140 2128.0 H 112 13.50 14.10 140 1974.0 I 82 13.40 13.97 115 1606.6 I 102 12.29 12.90 115 1483.5 J 60 9.80 11.60 160 1856.0 J 92 11.09 11.69 160 1870.4 K 44 7.19 8.50 210 1785.0 K 83 10.00 10.54 210 2213.4 L 32 5.23 6.21 260 1614.6 L 74 8.92 9.46 260 2459.6 M 21 3.43 4.33 225 974.2 M 44 5.02 6.97 225 1568.2 N 12 1.96 2.70 50 Sum = 135.0 18238.7 N 25 3.01 4.02 50 Sum = 201.0 19360.8 Area Amt. Area Amt. size 14.79 size 10.35 A 162 23.96 23.96 10 239.6 A 212 21.94 21.94 10 219.4 B 152 22.48 23.22 15 348.3 B 198 20.49 21.22 15 318.3 1500/1 C 142 21.00 21.74 25 543.5 4500/1 C 184 19.04 19.76 25 494.0 D 132 19.52 20.26 50 1013.0 D 170 17.60 18.32 50 916.0 E 122 18.04 18.78 75 1408.5 E 157 16.25 16.92 75 1269.0 F 112 16.56 17.30 125 2162.5 F 146 15.11 15.68 125 1960.0 G 105 15.53 16.04 140 2245.6 G 135 13.97 14.54 140 2035.6 H 96 14.20 14.86 140 2080.4 H 124 12.83 13.40 140 1876.0 I 88 13.02 13.61 115 1565.2 I 113 11.70 12.26 115 1409.9 J 80 11.83 12.42 160 1987.2 J 103 10.66 11.18 160 1788.8 K 56 8.28 10.06 210 2112.6 K 93 9.62 10.14 210 2129.4 L 41 6.06 7.17 260 1864.2 L 83 8.59 9.10 260 2366.0 M 26 3.84 4.95 225 1113.8 M 71 7.35 7.97 225 1793.2 N 16 2.37 3.10 50 Sum ■ 155.0 18839.4 N 37 3.83 5.59 50 Sum ■ 279.5 18855.1 154 Table 31. — Completed computation sheets for 1st three 6-hr increments for alternate placement of pattern on Ouachita River, AR drainage - Continued Oua I chita Rl II ver, AR III IV V VJ Area : 1 I ,600 ml 2 II In( Dat III :rement: e: 2 Drainage: IV V VI Area Amt . Avg. Area Amt. Avg. size Iso. Nomo. 4.63 depth aA aV size Iso. Nomo. 4.21 depth AA AV A 114.5 5.30 5.30 10 53.0 A 118.5 4.99 4.99 10 49.9 B 110 5.09 5.20 15 78.0 B 114.5 4.82 4.90 15 73.5 700/2 C 107 4.95 5.02 25 125.5 2150/2 C 111 4.67 4.74 25 118.5 D 104 4.81 4.88 50 244.0 D 108.5 4.57 4.62 50 231.0 E 101 4.68 4.74 75 355.0 E 106.5 4.48 4.52 75 339.0 F 99 4.58 4.63 125 578.8 F 104.5 4.40 4.44 125 555.0 G 97 4.49 4.54 140 635.6 G 102 4.29 4.34 140 607.6 H 95 4.40 4.445 140 622.3 H 100 4.21 4.25 140 595.0 I 78 3.61 4.005 115 460.6 I 99 4.17 4.19 115 481.8 J 65.5 3.03 3.32 160 531.2 J 97 4.08 4.12 160 659.2 K 54 2.50 2.76 210 579.6 K 96 4.04 4.06 210 852.6 L 44 2.04 2.27 260 590.2 L 73 3.07 3.56 260 925.6 M 32 1.48 1.76 225 396.0 M 54 2.27 2.67 225 600.8 N 19.5 0.90 1.19 50 59.5 N 37.5 1.58 1.92 50 96.0 Sum 5309.3 Sum = 6185.5 Area Amt. Area Amt. size 4.51 size 4.05 A 116 5.23 5.23 10 52.3 A 119.5 4.84 4.84 10 48.4 B 112 5.05 5.14 15 77.1 B 116 4.70 4.77 15 71.6 1000/2 C 108.5 4.89 4.97 25 124.2 3000/2 C 112.5 4.56 4.64 25 115.0 D 105 4.74 4.82 50 241.0 D 110 4.46 4.51 50 225.0 E 103 4.64 4.69 75 351.8 E 108 4.37 4.42 75 331.5 F 101 4.56 4.60 125 575.0 F 106 4.29 4.33 125 541.2 G 99 4.46 4.51 140 631.4 G 104 4.21 4.25 140 595.0 H 97 4.37 4.42 140 618.8 H 102 4.13 4.17 140 483.8 I 95 4.28 4.32 165 496.8 I 100.5 4.07 4.10 115 471.5 J 76 3.43 3.86 160 617.6 J 99 4.01 4.04 160 646.5 K 63 2.84 3.14 210 659.4 K 97 3.93 3.97 210 833.7 L 51 2.30 2.57 260 668.2 L 96 3.89 3.91 260 1016.6 M 38 1.71 2.01 225 452.2 M 67 2.71 3.30 225 742.5 N 24 1.08 1.40 50 70.0 N 45 1.82 2.26 50 113.0 Sum 5635.8 Sum = 6336.7 Area Amt. Area Amt. size 4.36 size 3.86 A 117 5.10 5.10 10 51.0 A 121 4.67 4.67 10 46.7 B 113 4.93 5.02 15 75.0 B 117 4.52 4.60 15 69.0 1500/2 C 110 4.80 4.86 25 121.5 4500/2 C 114 4.40 4.46 25 111.5 D 107 4.66 4.73 50 236.5 D 112 4.32 4.36 50 218.0 E 105 4.58 4.62 75 346.5 E 109.5 4.23 4.28 75 321.0 F 103 4.49 4.54 125 567.5 F 108 4.17 4.20 125 525.0 G 100. 5 4.38 4.44 140 621.6 G 105.5 4.07 4.12 140 576.8 H 99 4.32 4.35 140 609.0 H 103.5 4.00 4.04 140 565.6 I 97 4.23 4.28 115 492.2 I 102 3.94 3.97 115 456.6 J 95. 5 4.16 4.20 160 672.0 J 100.5 3.88 3.91 160 625.6 K 75. 5 3.29 3.72 210 781.2 K 99 3.82 2.85 210 808.5 L 60. 5 2.64 2.96 260 769.6 L 97.5 3.76 3.79 260 985.4 M 45 1.96 2.30 225 517.5 M 96 3.71 3.74 225 841.5 N 31 1.35 1.66 50 83.0 N 59 2.28 3.00 50 150.0 Sum 5944.1 Sum = 6301.2 155 ■^ Table 31. — Completed computation sheets for 1st three 6-hr Increments for alternate placement of pattern on Ouachita River, AR drainage - Continued Oua I chita Ri II ver, AR III IV V VI Area : 1 I ,600 mi 2 II Inc Dal III :rement: :e: 3 Drainage: IV V VI Area Amt. Avg. Area Amt. Avg. size Iso. Nomo. 2.54 depth AA AV size Iso. Nomo. 2.53 depth aA AV A 104.2 2.65 2.65 10 26.5 A 105.3 2.66 2.66 10 26.6 B 102.9 2.61 2.63 15 39.3 B 104.2 2.64 2.65 15 39.8 700/3 C 101.7 2.58 2.595 25 64.9 2150/3 C 103.2 2.61 2.625 25 65.6 D 100.8 2.56 2.57 50 128.5 D 102 2.58 2.595 50 129.8 E 100.2 2.54 2.55 75 191.2 E 101.3 2.56 2.57 75 192.8 F 99.9 2.54 2.54 125 317.5 F 101 2.56 2.56 125 320.0 G 99.6 2.53 2.535 140 354.9 G 100.6 2.54 2.55 140 357.0 H 99.2 2.52 2.525 140 353.5 H 100.3 2.54 2.54 140 355.6 I 85 2.16 2.34 115 269.1 I 100 2.53 2.535 115 291.5 J 70.5 1.79 1.98 160 316.8 J 99.7 2.52 2.525 160 404.0 K 58.5 1.48 1.64 210 344.4 K 95.5 2.42 2.47 210 518.7 L 47 1.19 1.34 260 348.4 L 80.5 2.04 2.23 260 579.8 M 37 0.94 1.06 225 238.5 M 61 1.54 1.79 225 402.8 N 25.5 0.65 0.80 50 Sum = 40.0 3033.5 N 46.5 1.18 1.36 50 Sum = 68.0 3752.0 Area Amt . Area Amt. size 2.54 size 2.52 A 104.6 2.66 2.66 10 26.6 A 105.7 2.66 2.66 10 26.6 B 103.3 2.62 2.64 15 39.6 B 104.6 2.64 2.65 15 39.8 1000/2 C 102.3 2.60 2.61 25 65.2 3000/3 C 103.5 2.61 2.625 25 65.6 D 101.3 2.57 2.585 50 129.2 D 102.5 2.58 2.595 50 129.8 E 100.6 2.56 2.565 75 192.4 E 101.7 2.56 2.57 75 192.8 F 100.3 2.55 2.555 125 319.4 F 101.3 2.55 2.555 125 319.4 G 99.9 2.54 2.545 140 356.3 G 100.9 2.54 2.545 140 356.3 H 99.6 2.53 2.535 140 354.9 H 100.5 2.53 2.535 140 354.9 I 99.3 2.52 2.525 115 290.4 I 100.2 2.52 2.525 115 290.4 J 82.5 2.10 2.31 160 369.6 J 99.9 2.52 2.52 160 403.2 K 67 1.70 1.90 210 399.0 K 99.6 2.51 2.515 210 528.2 L 54 1.73 1.16 260 301.6 L 99.3 2.50 2.505 260 651.3 M 43 1.09 1.23 225 276.8 M 76 1.92 2.21 225 497.2 N 31 0.79 0.94 50 47.0 N 57 1.44 1.68 50 84.0 Sum = 3168.0 Sum = 3939.5 Area Amt. Area Amt. size 2.54 size 2.51 A 105 2.67 2.67 10 26.7 A 106 2.66 2.66 10 26.6 B 103.8 2.64 2.655 15 39.8 B 105 2.64 2.65 15 39.8 1500/3 C 102.7 2.61 2.625 25 65.6 4500/3 C 104 2.61 2.625 25 65.6 D 101.7 2.58 2.595 50 129.8 D 103.1 2.59 2.60 50 130.0 E 101 2.56 2.57 75 192.8 E 102.1 2.56 2.575 75 193.0 F 100.7 2.56 2.56 125 320.0 F 101.7 2.55 2.555 125 319.4 G 100.3 2.55 2.555 140 357.7 G 101.2 2.54 2.545 140 356.3 H 100 2.54 2.545 140 356.3 H 100.9 2.53 2.535 140 354.9 I 99.7 2.53 2.535 115 291.5 I 100.6 2.52 2.525 115 290.4 J 99.4 2.52 2.525 160 404.0 J 100.2 2.52 2.52 160 403.2 K 81 2.06 2.29 210 480.9 K 99.9 2.51 2.515 210 528.2 L 65.5 1.66 1.86 260 483.6 L 99.6 2.50 2.505 260 651.3 M 51.5 1.31 1.48 225 333.0 M 99.3 2.49 2.495 225 591.4 N 38 0.96 1.14 50 57.0 N 76 1.91 2.20 50 110.0 Sum 3548.7 Sum = 4030.2 156 REFERENCES American Meteorological Society, 1959. Glossary of Meteorology. Boston, Mass. , 638 pp. Canadian Department of Transport (ongoing publication). Canadian Storm Rainfall . 315 Bloor Street West, Toronto, Ontario, Canada. Frederick, R.H., V.A. Myers, and E.P. Auciello, 1977. Five- to 60-Minute Precipitation Frequency for the Eastern and Central United States. NOAA Technical Memorandum NWS HYDRO-35, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, Silver Spring, Md., 36 pp. Goodyear, Hugo V. and John T. Riedel, 1965. Probable Maximum Precipitation Susquehanna River Drainage Above Harrisburg, Pennsylvania. Hydrometeorological Report No. 40, Weather Bureau, U.S. Department of Commerce, Washington, D.C., 70 pp. Hershfield, D.M., 1961. Rainfall Frequency Atlas of the United States for Durations 30 Minutes to 24 Hours and Return Periods from 1 to 100 Years. Technical Paper No. 40, Weather Bureau, U.S. Department of Commerce, Washington, D.C., 115 pp. Huff, Floyd A., 1967. Time Distribution of Rainfall in Heavy Storms. Water Resources Research , 3, pp. 1007-1019. Huff, Floyd A. and John L. Vogel, 1976. Hydrometeorology of Heavy Rainstorms in Chicago and Northeastern Illinois, Phase I - Historical Studies. Illinois State Water Survey Report of Investigation 82, Urbana, 111 . , 63 pp. Lott, George A. and Vance A. Myers, 1956. Meteorology of Flood-Producing Storms in the Mississippi River Basin. Hydrometeorological Report No. 34. Weather Bureau, U.S. Department of Commerce, Washington, D.C., 226 pp. Maddox, R.A., C.F. Chappell and L.R. HoxLt, 1979. Synoptic and Meso-Scale Aspects of Flash Flood Events. Bulletin of the American Meteorological Society, 60, 2, pp. 115-123. Miller, J.F., R.H. Frederick, and R.J. Tracey, 1973. Precipitation Frequency Atlas of the Western United States. NOAA Atlas 2, tfetional Oceanic and Atmospheric Administration, U.S. Department of Commerce, Silver Spring, Md., 11 Vols. Myers, Vance A., 1959. Meteorology of Hypothetical Flood Sequences in the Mississippi River Basin. Hydrometeorological Report No. 35. Weather Bureau, U.S. Department of Commerce, Washington, D.C., 46 pp. National Weather Service, 1914- . Climatological Data. NOAA, teitional Climatic Center, Asheville, N.C. 157 Neumann, C.J., G.W. Cry, E.L. Caso and B.R. Jarvinen, 1978. Tropical Cyclones of the North Atlantic Ocean 1871-1977. National Weather Service, National Climatic Center, Asheville, N.C., 170 pp. Newton, C.W. and S. Katz, 1958. Movement of large Convective Rainstorms in Relation to Winds Aloft. Bulletin of the American Meteorological Society , 39, 3, pp. 129-136. Paulhus, J.L.H. and CS. Gilman, 1953. Evaluation of Probable Maximum Precipitation Transactions, American Geophysical Union, 34, 5, Washington, D.C., pp. 701-708. Riedel, John T., 1973. Probable Maximum Precipitation and Snowmelt Criteria for the Red River of the North above Pembina, and Souris River above Minot, North Dakota. Hydrometeorological Report No. 48. National Weather Service, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, Washington, D.C., 69 pp. Schwarz, Francis K. , 1961. Meteorology of Flood-Producing Storms in the Ohio River Basin. Hydrometeorological Report No. 38. Weather Bureau, U.S. Department of Commerce, Washington, D.C., 67 pp. Schwarz, Francis K. , 1973. Meteorological Criteria for Extreme Floods for Four Basins on the Tennessee amd Cumberland River Watersheds. Hydrometeorological Report No. 47. National Weather Service, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, Silver Spring, Md., 59 pp. Schwarz, F.K., and N.F. Helfert, 1969. Probable Maximum and TVA Precipitation for Tennessee River Basins up to 3,000 Square Miles in Area and Durations to 72 Hours. Weather Bureau, Hydrometeorological Report No. 45, Environmental Science Services Administration, U.S. Dept. of Commerce, Silver Spring, Md., 166 pp. Schreiner, Louis C. and John T. Riedel, 1978. Probable Maximum Precipitation Estimates, United States East of the 105th Meridian. Hydrometeorological Report No. 51. National Weather Service, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, Washington, D.C., 87 pp. U.S. Army Corps of Engineers, 1945- Storm Rainfall in the United States. Washington, D.C. World Meteorological Organization, 1973. Manual for Estimation of Probable Maximum Precipitation. Operational Hydrology Report No. 1 , WMO No. 332, Geneva, Switzerland, 190 pp. 158 APPENDIX The 53 storms listed in the Appendix to HMR 51 were chosen as the sample of storms to be used initially in this study. However, in the study of storm shapes and orientations it was found that this sample was particularly small when questions of regional variation, regional averages, or statistical distributions were considered. For this reason a subordinate storm sample was created to provide additional guidance in some of these discussions. The subordinate sample of storms was derived from the major storms listed in "Storm Rainfall" (U.S. Army Corps of Engineers 1945- ). This file includes storms from as early as the 1870's and is continually updated as new storms are studied. Some additional storm data are available from other agencies and from storms studied by the Hydrometeorplogical Branch. We concentrated on the 253 storms whose areas were 10,000 mi or larger and whose durations were 60 hr or longer, since we believe the larger /longer storms were more useful in pointing up possible differences. We also imposed a controlling factor in our storm selection, that only storms whose 72-hr depth was 90 percent or more of the total-storm depth (20,000 mi , 72 hr) would be used, because we wanted storms that basically represented extreme 3-day rains. These are listed in table A.l. The distribution of the 253 storms according to area and duration classes is shown in table A. 2. The regional distribution of this sample is shown in figure A.l, which includes the orientation of the respective rainfall patterns. One feature shown in this figure is that even in this sample of 253 storms, there are local regions for which no storms satisfying the areal and durational criteria of our sample occur. That is not to say that storms of these magnitudes have not occurred in these regions, but rather that we have no records of such storms. The distribution of the 253 storms relative to area size and shape ratio classes is given in table A. 3. These results can be compared to those in table 7 for the 53 storm sample. 159 Table A.l - 253 Major storms (listed in Storm Rainfall, >_ 10,000 mi and >_ 60 hr; 2 72 hr > 90% total storm amount at 20,000 ml , arranged in chronological order) 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. st. area (mi 2 ) amt . Date center (°) (') (°) (') dur. (hr) (in.) 9/10-13/1878 Jefferson, OH 41 45 80 46 84 90,000 11.0 9/20-24/82 Rater son, NJ 40 55 74 10 108 40, 000 7.9 7/27-31/87 Union Pt. , GA 33 37 83 04 114 100 ,000 9.0 9/8-12/88 Greenwood, SC 34 12 82 10 120 120, 000 8.4 5/30-6/1/89 Wellsboro, PA 41 45 77 17 60 82 ,000 8.3 3/5-9/91 Kosciusko, MS 33 05 89 35 114 185, 000 7.2 6/23-27/91 Larrabee, IA 42 52 95 30 96 30 ,000 9.3 7/24-28/92 Minneapolis, MN 45 04 93 18 108 20, 000 6.4 5/25-29/93 Marianna, AR 34 44 90 49 96 175 ,000 7.7 8/26-28/93 Manning, SC 33 14 80 12 66 54, 000 11.1 9/6-10/93 Franklin, LA 29 47 91 30 114 40 ,000 10.4 3/17-20/84 Washington, AR 33 48 93 40 72 112, 000 6.0 5/17-22/94 Bridgeton, MS 39 26 75 14 120 57 000 5.1 5/29-31/94 Ward District, CO 40 04 105 32 60 25, 300 4.6 8/3-6/94 Felkland, NC 35 34 77 38 96 72 ,800 6.4 12/16-20/95 Phillipsburg, M0 37 34 92 47 96 110, 000 6.5 12/31-1/3/96 Pine Bluff, AR 34 12 92 00 78 118 ,000 5.7 6/4-7/96 Greeley, NE 41 33 98 32 78 84, 000 9.2 7/6-8/96 Greenwood, SC 34 11 82 09 66 118 ,000 6.0 9/27-30/96 Bloomery, WV 39 23 78 22 66 50, 000 6.8 7/12-14/97 Southington, CT 41 39 72 53 60 44 ,000 6.7 7/18-22/97 Lambert, MN 47 47 95 55 102 80, 000 5.8 7/25-27/97 Butternut, Wl 46 00 90 30 66 15 ,000 8.6 7/26-29/97 Jewell, MD 38 46 76 34 96 32, 000 6.2 12/1-4/97 Jackson, MS 32 17 90 11 96 70 ,000 6.6 5/2-6/98 Norman, OK 35 13 97 18 84 68, 000 6.0 6/2-6/98 Pine River Dam, MN 46 41 94 07 102 30 ,000 5.7 8/26-29/98 St. Andrews Bay, FL 30 10 85 45 96 64, 000 7.0 8/30-9/3/98 Port Royal, SC 32 23 80 42 120 42 ,000 9.6 9/28-10/1/98 Sikeston, M0 30 25 87 13 84 75, 500 8.1 10/2/-4/98 Highlands, NC 35 02 83 12 66 60 ,000 5.9 6/27-7/1/99 Hearne, TX 30 52 96 37 108 78, 000 21.1 12/8-11/99 Port Gibson, MS 31 58 90 59 66 30 ,000 7.3 4/15-18/1900 Eutaw, AL 32 47 87 50 84 75, 000 11.3 7/14-17/00 Primghar, LA 43 05 95 38 78 100 000 9.1 9/7-11/00 - 42 41 96 40 102 50, 000 6.1 10/27-30/00 La Crosse, WI 43 48 91 15 78 15 200 6.7 5/18-22/01 Lumber ton, NC 34 32 79 00 108 79, 600 6.2 7/1-6-01 New Folden, MN 48 22 96 20 108 50 000 6.1 3/25-29/02 Ripley, MS 34 42 88 57 114 100, 000 8.6 160 Table A.l - 253 Major storms (listed In Storm Rainfall, >^ 10,000 mi and >^ 60 hr; 9 72 hr > 90% total storm amount at 20,000 mi , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long . Tot. st. area (mi 2 ) amt . Date center (°) (') (°) C) dur. (hr) (in.) 9/20-24/02 Wakeeney, KS 39 01 99 53 108 81,600 5.3 9/24-27/02 Colora , MD 39 40 76 06 72 40 000 5.6 8/24-28/03 Wood burn, IA 40 57 93 35 96 59 ,000 10.3 9/7-10/03 Burlingotn, KS 38 12 95 45 72 40 ,900 5.7 9/28-10/1/03 Gainesville, TX 33 37 97 08 90 50 ,000 7.5 10/7-11/03 Paterson, NJ 40 55 74 10 96 35, 000 10.9 5/1-3/04 Boxelder, CO 40 59 105 11 66 21 ,200 3.4 6/1-5/04 Hartshorne, OK 34 51 95 33 84 66, 000 7.2 6/2-5/04 Spearfish, SD 44 29 103 47 78 12 ,300 3.4 9/12-15/04 Friesburg, NJ 39 35 75 25 66 35, 000 6.7 9/26-30/04 Rociada, m 35 52 105 20 90 70 ,000 5.4 2/10-13/05 Putman, GA 32 14 84 25 72 80, 000 5.8 6/3-8/05 Medford, WI 45 08 90 20 120 67 ,000 7.0 7/18-21/05 Hartshorne, OK 34 51 95 33 84 100, 000 6.8 10/16-19/05 New Haven, M0 38 38 91 13 69 26 ,000 6.6 8/21-25/06 Hartington, NE 42 37 97 16 96 33, 900 4.7 8/22-26/06 Warsaw, MO 38 15 93 21 102 24 ,300 6.6 5/7-10/07 Lafayette, LA 30 14 91 59 96 49, ,000 9.0 5/28-31/07 Sugarland, TX 29 36 95 38 90 80 ,000 8.7 7/13-16/07 Nema ha , NE 40 20 95 41 96 40, ,000 7.9 5/21-25/08 Sabinal, TX 34 25 98 39 108 175 ,000 5.3 7/28-31/08 New Bern, NC 35 07 77 03 72 29 ,000 5.9 8/23-28/08 Monroe, NC 36 26 80 28 120 69 ,600 9.5 9/16-20/08 Cameron, LA 29 45 93 20 102 22 ,000 10.1 10/19-24/08 Meeker, OK 35 30 96 54 126 80 ,000 8.6 5/24-28/09 Shoccoa , MS 32 39 89 53 114 70 ,000 7.2 7/4-7/09 Bethany, M0 40 15 94 02 66 27 ,000 7.3 7/18-23/09 Iron wood, Ml 46 27 90 11 108 50 ,000 10.0 9/6-9/09 Topeka , KS 39 09 95 37 78 39 ,000 6.9 9/19-22/09 St. Francisville, LA 30 46 91 22 66 31 000 10.2 6/6-11/10 Boon vi lie, MO 38 58 92 45 120 70 ,000 2.9 10/3-6/10 Golconda, IL 37 22 88 29 90 70, 000 7.4 2/16-18/11 Woodward (nr), OK 36 27 99 23 60 44 ,000 4.5 4/12-15/11 Benton, AR 34 33 92 37 60 75, 000 4.9 8/23-31/11 St. George, GA 30 30 82 02 84 39 ,000 13.5 4/11-14/12 Arnegard, ND 47 48 103 25 90 10 ,700 2.0 5/19-22/12 Gladwin, MI 43 59 84 29 72 37 ,156 4.6 6/14-18/12 Johnstown, PA 40 20 78 55 120 50 ,000 4.0 9/22-25/12 Emmitsburg, Md 39 41 77 21 72 40 ,000 4.6 9/22-25/12 Camden, SC 34 15 80 37 72 16 ,000 5.5 161 Table A.l - 253 Major storns (listed In Storm Rainfall, _> 10,000 nd and >_ 60 hr; 2 72 hr y_ 90% total storm amount at 20,000 mi , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. st. area (mi 2 ) amt . Date center (°) (') (°) (') dur. (hr) (in.) 7/12-15/13 Toboso, OH 40 03 82 13 72 17,000 5.9 12/1-5/13 San Marcos (nr), TX 29 52 97 51 96 70 ,000 9.3 3/24-28/14 Merryville, LA 30 46 93 32 96 125 ,000 10.7 4/24-28/14 Merryville, LA 30 46 93 32 96 100 ,000 8.1 4/29-5/2/14 Clayton, M 36 20 103 06 66 36 ,500 7.9 6/25-28/14 Hazelton, ND 46 29 100 17 90 66 ,000 6.8 6/25-28/14 Morris, MN 45 35 95 55 60 45 ,000 4.7 2/12-14/15 Onida, SD 44 42 100 04 60 50 ,000 3.1 6/2-7/15 Henrietta, TX 33 48 98 12 138 60 ,000 4.7 9/6-9/15 Moran, KS 37 56 95 10 96 24 ,000 7.6 5/14-19/16 York, NY 42 52 77 52 120 21 ,400 3.8 7/13-17/16 New Ulm, MN 44 19 94 28 96 30 ,000 5.6 7/15-17/16 Altapass, NC 35 53 82 01 108 37 ,000 15.0 9/10-12/16 Cunningham, KS 37 39 98 24 60 44 ,000 4.4 9/14-16/17 Hatteras, NC 35 15 75 40 60 25 ,000 6.5 3/12-15/18 Hoi comb, WV 38 15 80 34 66 17 ,200 4.0 5/9-13/18 Mountain Home, AR 36 20 92 30 78 70 ,000 5.7 8/19-22/18 Maryville, ND 47 30 97 19 78 24 ,000 4.8 10/24-27/18 Tryon, NC 35 13 82 14 72 17 ,200 7.1 10/26-31/18 Highlands, NC 35 02 83 12 120 107 ,000 6.7 11/6-8/18 Neosha , M0 36 52 94 22 72 34 ,500 4.5 3/14-16/19 Atchison, KS 39 34 95 07 60 33, 000 5.0 6/22-24/19 Clinton, IL 40 08 88 58 66 20 ,000 5.1 8/25-29/19 Warrensburg, M0 38 46 93 44 102 19, 900 9.3 9/16-19/19 Bruning, NE 40 20 97 34 66 58 ,350 7.4 10/7-12/19 Little Rock AR 29 47 94 40 120 60 , 000 7.2 10/25-28/19 Steelville, M0 37 59 91 22 60 84 ,000 6.8 12/6-10/19 Selma , AL 32 25 87 02 90 116, 000 7.5 1/21-24/20 Pontotoc, MS 34 15 89 00 84 100 ,000 2.8 2/3-6/20 Runnymede, VA 37 01 76 39 60 20, 000 — 5/9-12/20 Vale, SD 44 37 103 24 78 54 ,000 3.8 6/15-18/20 W. Newport, PA 40 13 79 36 84 30, 000 3.8 9/6-9/20 Memphis, TN 35 09 90 03 66 24 000 3.7 3/11-14/21 Magnolia , MS 31 06 90 28 72 42, 000 10.1 6/2-6/21 Pueblo (nr), CO 38 27 105 04 114 144 ,000 7.8 6/17-21/21 Springbrook, MT 47 18 105 35 108 52, 600 11.3 10/29-11/2/21 Marion, NC 35 41 82 01 96 24 000 4.6 11/16-19/21 Searcy, AR 35 15 91 44 78 130, 000 7.4 2/19-23/22 West Branch, Mt . 44 19 84 17 114 35, 000 3.5 4/24-27/22 Weatherford, TX 32 45 97 48 66 65, 700 7.6 162 Table A.l - 253 Major storms (listed in Storm Rainfall, >^ 10,000 mi and >^ 60 hr; 9 72 hr >_ 90Z total storm amount at 20,000 mi , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. st. area amt . Date center (°) (') (°) C) dur. (hr) (mi 2 ) (in.) 6/8-11/22 Wright st own, WI 44 20 88 12 84 45,000 6.1 6/9-12/22 Syracuse (nr), NY 43 04 76 16 84 20 000 4.2 7/9-12/22 Grant City, M0 40 29 94 25 78 113 ,500 9.3 9/27-10/1/23 Savageton, WY 43 52 105 47 108 95 ,000 6.6 7/11-14/24 Fort Scott, KS 37 51 94 42 72 35 ,000 5.6 8/3-6/24 West Bend, WI 43 25 88 11 90 50 000 6.7 9/13-17/24 Beaufort, NC 34 44 76 39 96 100 ,000 11.5 12/4-8/24 Brownsville, KY 37 13 86 15 108 32 ,400 6.2 5/27-29/25 Eagle Pass, TX 28 43 100 30 60 47 ,100 7.1 6/1-3/25 St. Joseph, M0 39 46 94 55 66 64 ,000 4.9 9/23-26/25 Freeman Springs, AR 35 40 93 06 90 75 ,000 3.9 3/20-22/26 St. Francisville, LA 30 46 91 22 66 28 ,200 5.9 8/23-26/26 Dona ldsonvi lie, LA 30 06 90 58 72 50 ,000 11.5 9/2-5/26 Columbus, KS 37 15 94 52 78 50 ,000 5.9 9/17-21/26 Bay Minette, AL 30 53 87 47 120 35 ,700 13.7 9/25-30/26 Eufaula, OK 35 35 95 35 108 40 000 6.6 2/11-14/27 Clinton, LA 30 52 91 00 72 50 ,000 7.0 3/17-20/27 Tuscumbia, M0 38 15 92 27 60 32, 000 4.2 4/12-16/27 Jefferson, LA 29 40 90 05 108 250 ,000 14.7 5/5-9/27 Belvidere, SD 43 50 101 16 108 150, 000 3.7 5/20-23/27 Kaplan, LA 30 01 92 19 72 12 500 8.1 7/12-15/27 Ardmore, OK 34 12 97 08 96 33, 000 8.6 8/11-14/27 Bison, KS 38 31 99 12 72 34 000 6.6 11/2-4/27 Kinsman Notch, NH 44 03 71 45 60 60, 000 7.8 5/14-16/28 Woodville, MS 31 06 97 18 60 33 000 8.0 6/12-17/28 Crystal Sprngs, MS 31 59 90 26 108 20, 000 8.6 6/28-30/28 Clinton, TN 36 06 84 08 66 70 000 7.7 7/5-8/28 Berthold, ND 48 20 101 46 72 20, 000 5.8 7/18-21/28 Mt. Ayr, IA 40 43 94 14 84 19, 500 3.8 8/9-13/28 Settle, NC 36 01 80 46 96 24, 000 7.0 8/10-13/28 Cheltenham, MD 34 44 76 51 66 35, 000 8.8 8/13-17/28 Caesars Head, SC 35 07 82 38 102 77, 300 9.4 9/4-7/28 Marion, SC 34 11 79 23 72 19, 600 4.9 9/16-19/28 Darlington, SC 34 17 79 02 96 100, 000 10.8 11/15-17/28 Lebo, KS 37 55 95 26 60 60, 000 8.1 3/11-16/29 Elba, AL 31 25 86 04 114 100, 000 16.1 7/16-18/29 Woodville, MS 31 09 91 18 66 24 000 5.4 9/20-23/29 Gallinas (nr), N4 35 09 105 39 72 17, 000 2.6 9/23-28/29 Glenville, GA 31 56 81 56 120 70 000 13.1 9/29-10/3/29 Vernon, FL 30 38 85 43 84 103, 000 9.3 163 Table A.l - 253 Major storms (listed in Storm Rainfall, >^ 10,000 nri/ and >^ 60 hr; o 72 hr >^ 90Z total storm amount at 20,000 nd. , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. st. area (mi 2 ) amt . Date center (°) C) (°) C) dur. (hr) (in.) 1/6-11/30 Arkadelphia, AR 34 07 93 03 114 70,000 5.4 5/15-19/30 Camden, AR 33 36 92 49 108 116,000 7.3 6/12-15/30 Washington, IA 41 17 91 41 63 70,000 7.7 10/9-12/30 Porter, M 35 12 103 17 60 27,700 7.2 7/20-25/31 Conklingville, NY 43 19 73 56 120 17,000 3.1 6/2-6/32 Tribune, KS 35 30 96 54 84 70,000 8.7 7/3-8/32 Clay, WV 38 28 81 05 120 36,000 5.6 7/31-8/3/32 Lexington, KY 38 02 84 36 72 23,300 5.8 9/5-7/32 Abilene, TX 32 26 99 41 60 20,400 4.5 10/4-6/32 Elka Park, NY 42 10 74 14 66 60,000 7.4 10/4-7/32 Elka Park, NY 42 10 74 14 96 29,000 6.9 10/14-18/32 Tuscaloosa, AL 33 14 87 37 90 70,000 6.8 10/15-18/32 Rock House, NC 37 00 79 54 72 50,000 7.4 12/21-24/32 Sulphur, OK 34 30 96 58 66 100,000 6.7 4/11-14/33 Durham, NH 43 08 70 56 60 20,000 5.0 7/22-27/33 Logansport, LA 31 58 94 00 126 100,000 14.8 8/20-24/33 Peekamoose, NY 41 56 74 23 108 66,000 8.2 2/27-3/4/34 De Ridder, LA 30 50 93 16 126 200,000 7.2 6/6-8/34 Akron, IA 42 49 96 33 66 53,400 5.2 9/4-9/34 Beaufort, NC 34 44 76 39 108 19,000 7.3 11/19-21/34 Millry, AL 31 38 88 19 66 130,000 9.0 11/28-12/1/34 Southport, NC 33 55 78 01 84 90,000 6.4 1/18-21/35 Hernando, MS 34 50 90 00 84 98,500 7.9 5/2-7/35 Mellville, LA 30 41 91 44 126 133,000 11.1 5/16-20/35 Simmesport, LA 30 59 91 48 102 75,000 10.4 7/6-10/35 Hector, NY 42 30 76 53 90 38,500 8.6 9/2-6/35 Easton, MD 38 46 76 01 114 48,469 10.8 12/5-8/35 Satsuma (nr), TX 29 54 96 37 60 56,500 13.9 7/29-8/2/36 Blountstown, FL 30 26 85 02 102 100,000 6.7 9/14-18/36 Broome, TX 31 47 100 50 96 70,000 13.8 9/25-28/36 Hillsboro, TX 32 01 97 08 90 157,000 9.9 4/24-28/37 Clear Springs, MD 39 40 77 54 114 20,000 6.1 5/26-30/37 Ragland, Ntf 34 49 103 44 84 37,000 3.3 6/11-13/37 Circle, MT 47 30 105 34 60 62,000 4.0 8/31-9/3/37 Wolverton, MI 45 17 84 37 72 19,000 7.0 9/6-10/37 Bentonville, AR 36 22 94 13 84 42,750 6.1 9/30-10/4/37 New Orleans, LA 29 57 90 04 114 20,000 11.3 10/17-20/37 Caesars Head, SC 35 07 82 38 72 15,000 6.1 3/28-31/38 Ford's Ferry, KY 37 28 88 06 84 25,000 6.0 4/5-9/38 Lock No. 2, AL 32 08 88 02 108 95,000 7.9 164 Table A.l - 253 Major storms (listed in Storm Rainfall, >^ 10,000 nri/ and >^ 60 hr; o 72 hr >^ 90Z total storm amount at 20,000 mi , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. St. area (mi 2 ) amt . Date center (°) (') (°) C) dur . (hr) (in.) 6/26-28/38 Odessa, DE 39 28 75 40 60 10 8/12-15/38 Roll, LA 30 20 92 45 90 34 8/30-9/4/38 Loveland (nr), CO 40 23 105 04 126 21 9/17-22/38 Buck, CT 41 40 72 40 120 67 3/9-12/39 Charleston, IL 39 29 88 11 72 70 8/6-9/40 Miller's Island, LA 29 45 92 10 84 36 9/2-6/40 Hallett, OK 36 15 96 36 90 20 11/22-25/40 Hempstead, TX 30 08 96 08 78 78 5/26-31/41 Jennings, LA 30 13 92 39 120 54 8/28-31/41 Hayward, WI 46 00 91 28 78 60 9/20-23/41 McColleum Ranch, M 32 10 104 44 78 38 10/17-22/41 Trenton, FL 29 48 82 57 138 193 10/18-22/41 Lindsborg, KS 38 34 97 40 96 16 4/17-21/42 Kenton (nr), OK 36 55 102 58 102 54 5/19-23/42 Carbondale, PA 40 48 76 08 72 12 6/23-26/42 Clifton Hill, MO 39 25 92 42 72 35 7/2-6/42 Spring Branch, TX 29 55 98 25 96 52 8/7-10/42 Charlottesville, VA 38 02 78 30 96 24 8/29-9/1/42 Rancho Grande, M 34 56 105 06 84 35 10/11-17/42 Big Meadows, VA 38 31 78 26 156 25 12/27-30/42 Ashville, AL 33 51 86 20 79 30 1/16-19/43 River Falls, AL 31 21 86 32 66 40 5/6-12/43 Warner, OK 35 29 95 18 144 212 5/12-20/43 Mounds (nr), OK 35 52 96 03 192 200 7/27-29/43 Devers, TX 30 02 94 35 60 33 6/10-13/44 Stanton, NE 41 52 97 03 78 16 6/2-5/44 Colony, WY 44 56 104 12 72 36 9/12-15/44 New Brunswick, NJ 40 29 74 27 96 50 8/26-29/45 Hockley, TX 30 02 95 51 72 34 5/25-28/46 Renovo, PA 41 20 77 45 78 16 8/12-15/46 Cole Camp (nr), MO 38 40 93 13 78 45 8/12-16/46 Collingsville, IL 38 40 89 59 114 20 5/25-30/47 Plattsmouth, NE 41 01 95 53 132 300 6/2-7/47 Browning (nr), MO 40 03 93 06 120 306 6/10-13/47 Earlham, IA 41 28 94 07 78 300 6/18-23/47 Holt (nr), MO 39 27 94 20 120 306 6/23-26/47 Annapolis, MD. 37 22 90 40 66 306 6/26-30/47 Lathrop, M0 39 33 94 20 96 306 8/10-13/47 Plentywood, MT 48 45 104 30 72 64 8/24-27/47 Dallas, TX 32 51 96 51 72 30 500 000 500 000 000 200 000 000 000 000 000 000 000 500 000 000 800 500 600 000 950 000 000 000 000 000 000 000 000 800 000 400 000 000 000 000 000 000 329 000 5.3 12.0 3.1 7.7 3.9 18.4 13.6 14.2 5.6 9.1 6.3 18.2 7.9 3.1 5.0 6.9 6.9 5.3 6.8 9.1 9.7 8.7 11.1 8.5 13.7 9.3 3.4 5.6 13.4 4.7 8.3 9.0 4.8 5.6 2.3 4.1 3.9 9.3 165 Table A.l - 253 Major storms (listed In Storm Rainfall, > 10,000 mi 2 and >_ 60 hr; 2 72 hr 2. 90Z total storm amount at 20,000 ml , arranged in chronological order) - Continued 1000-mi 2 Tot. st. 24-hr Station nearest Lat. Long. Tot. st. area (mi 2 ) amt . Date center (°) C) (°) ( r ) dur. (hr) (in.) 4/22-25/50 Monmouth (nr), IL 40 55 90 43 60 20,000 4.6 9/3-7/50 Yankeetown, FL 29 03 82 42 96 43,500 30.2 8/9-13/51 Council Grove, KS 38 40 96 30 108 57,000 6.6 6/23-28/54 Vic Pierce, TX 30 22 101 23 120 27,900 18.4 8/10-15/55 New Bern, NC 35 07 77 03 126 69,000 8.9 8/11-15/55 Slide Mt., NY 42 01 42 25 120 81,000 6.0 8/15-19/55 Big Meadows, VA 38 31 78 26 96 50,000 5.5 8/17-20/55 Westfield, MA 42 07 72 45 72 35,000 12.4 5/18-21/60 New Prague, MN 44 35 93 35 85 10,000 4.4 9/10-13/61 Bay City, TX 28 58 95 57 90 101,000 9.6 9/11-13/61 Shelbina, M0 39 41 92 03 60 121,000 7.1 3/2-5/66 Courtenay (nr), ND 47 14 98 35 72 35,000 3.1 6/19-23/72 Zerbe, PA 40 37 76 32 96 130,000 12.3 166 Table A.2. — Distribution of 253 ma jor storms by duration and area size classes Area (mi 2 ) 10- <20 20- <30 30- <40 40- <50 50- <60 60- <70 70- <80 80- <90 90- <100 100- <120 120- <140 140- 160- 189- 200- <160 <180 <200 <300 >300 Total Dur. (hr) 60 1 7 4 5 2 3 2 2 • 1 • • • • 27 66 2 7 5 1 4 4 1 • 2 1 • • • • 1 28 72 10 3 10 4 3 1 1 1 • • • • • 34 78 4 1 3 1 2 1 2 3 1 • • • • 1 20 84 2 2 5 2 • 2 3 3 3 • • • • • 22 90 1 1 2 • 2 1 4 2 • 1 15 96 1 5 6 3 3 1 4 4 2 1 1 31 102 1 2 1 • 2 • 2 1 • • • • • 10 108 1 2 2 2 4 1 2 2 1 • 11.1 21 114 • 3 1 2 • • 2 3 • 1.1. 13 120 1 2 2 1 3 4 2 1 1 2 20 126 1 1 1 1 1 6 132 • • • • • 1 1 138 • 1 • • • 1 2 144 . • • • • 1 1 >150 1 • • • • 1 2 Total 24 37 41 21 25 20 25 9 5 22 7 3 2 2 4 6 253 Table A.3. — Shape ratios of 253 major storm sohyetal patterns relative to area size classes Area size Total no. category (10 J mi z ) Shape ratio of storms 1 2 3 4 5 6 7 8 % of total storms in category 10 to < 20 17 33 29 8 4 4 4 24 20 to < 30 8 24 35 11 11 3 7 36 30 to < 40 2 41 22 17 12 5 41 40 to < 50 24 33 19 19 5 21 50 to < 60 8 38 8 15 19 8 4 26 60 to < 75 6 28 25 19 6 11 3 3 36 75 to <100 22 22 26 17 9 23 100 to <125 9 17 30 26 4 4 9 23 > 125 4 35 39 4 17 23 Tot< il 253 167 V 107 103 99 95 91 87 100 tOO 200 300 V KILOMETERS Figure A.l. — Regional distribution of 253 major storms listed in table Al showing orientation of total-storm precipitation patterns. *U.S. GOVERNMENT PRINTING OFFICE: 1982-0-522-017/4257 168 No. 45. No. 46. No. 47. (Continued from inside front cover) Probable maximum and TVA precipitation for Tennessee River Basins up to 3,000 square miles in area and durations to 72 hours. 1969. Probable maximum precipitation, Mekong River Basin. 1970. Meteorological criteria for extreme floods for four basins in the Tennessee and Cumberland River Watersheds. 1973. No. 48. Probable Maximum Precipitation and Snowmelt Criteria For Red River of the North Above Pembina, and Souris River Above Minot, North Dakota. 1973. No. 49. Probable Maximum Precipitation Estimates, Colorado River and Great Basin Drainages. 1977. No. 50. The Meteorology of Important Rainstorms in the Colorado River and Great Basin Drainages. 1982 (PB82 185414) No. 51. Probable Maximum Precipitation Estimates, United States East of 105th Meridian. 1978. (PB287925) No. 52. Application of Probable Maximum Precipitation Estimates — United States East of the 105th Meridian. 1982. No. 53. Seasonal Variation of 10-Square-Mile Probable Maximum Precipitation Estimates, United States East of the 105th Meridian. 1980. (NUREG/CR-1486) PENN STATE UNIVERSITY LIBRARIES 1111 ADODD I II II I ADD0D33ES : 176^ NOAA--S/T 82-153