HYDROMETEOROLOGICAL REPORT NO. 49 Probable Maximum Precipitation Estimates, Colorado River and Great Basin Drainages U.S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION U.S. DEPARTMENT OF ARMY CORPS OF ENGINEERS Silver Spring, Md. September 1977 Digitized by the Internet Archive in 2013 http://archive.org/details/probablemaximumpOOhans U.S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION U.S. DEPARTMENT OF THE ARMY CORPS OF ENGINEERS HYDROMETEOROLOGICAL REPORT NO. 49 Probable Maximum Precipitation Estimates, Colorado River and Great Basin Drainages Prepared by E. Marshall Hansen, Francis K. Schwarz, and John T. Riedel Hydrometeorological Branch Office of Hydrology National Weather Service Silver Spring, Md. September 1977 >. a o u o a 0) a For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 Stock No. 003-017-00408-2 CONTENTS Page Abstract 1 1. Introduction 1 1.1. Purpose of report 1 1.2. Authorization 2 1.3. Scope 2 1.4. Definition of probable maximum precipitation 2 1.5. Methods of this report 4 1.6. Organization of report 4 2. Convergence component of PMP 5 2.1. Introduction 5 2.1.1. Method of determining general-storm PMP 5 2.1.2. Definition of convergence PMP 5 2.1.3. General storm relation to local storm 5 2.1.4. Convergence PMP for adjoining regions 6 2.1.5. Summary of procedure 6 2.2. Mid-month 1000-mb (100-kPa) convergence PMP maps, 24 hrs, 10 mi 2 (26 km 2 ) 7 2.2.1. Envelopment of maximum observed rainfalls 7 2.2.2. Enveloping 12-hr persisting dew points 11 2.2.3. Regional patterns 11 2.2.4. Seasonal variation 12 2.2.5. PMP storm prototypes 18 2.2.6. Development of 10-mi 2 (26-km 2 ) 24-hr convergence PMP 19 2.3. Effect of barrier and elevation 34 2.3.1. Effective barrier and elevation map 34 2.3.2. Reduction for effective barrier and elevation .... 34 2.4. Depth-duration variation 36 2.4.1. Data 36 2.4.2. Depth-duration relation 39 2.4.3. Seasonal variation 41 2.4.4. Regional variation 45 2.5. Areal reduction for basin size 50 3. Orographic component of PMP 53 3.1. Introduction 53 3.1.1. Methods for determining orographic effects on rainfall 53 3.1.2. Definition of orographic precipitation 53 3.1.3. Detail in orographic PMP 55 3.2. Orographic index map 56 3.2.1. Development of first approximation 57 3.2.2. Guidance to modification 58 3.2.2.1. Rain ratios for line segments 58 3.2.2.2. Rain ratios for central Arizona 62 3.2.2.3. Effects to lee of ridges .63 3.2.2.4. Summary 65 in Page 3.2.3. Modifications to index map 67 3.2.3.1. In areas of most-orographic effects 67 3.2.3.2. In areas of least-orographic effects 68 3.2.3.3. In areas of intermediate-orographic effects 68 3.2.3.4. Other modifications 69 3.2.4. Modified orographic PMP index map 69 3.3. Seasonal variation 69 3.3.1. Introduction 69 3.3.2. Boundary regions 70 3.3.3. Indices within the region 79 3.3.3.1. Maximum precipitation at high elevations 79 3.3.3.2. Maximum winds and moisture 79 3.3.3.3. Orographic model computations 79 3.3.4. Smoothed maps 80 3.3.5. Supporting evidence 80 3.4. Variation with basin size . , 88 3.4.1. Introduction 88 3.4.2. Storm data 90 3.4.3. Adopted variation 92 3.5. Durational variation 92 3.5.1. Background 92 3.5.2. Variation of maximum winds 93 3.5.3. Variation of maximum moisture 94 3.5.4. Variation of relative humidity 95 3.5.5. Orographic model computation 95 3.5.6. Guidance from observed precipitation 97 3.5.7. Adopted variation ^ 99 4. Local-storm PMP for the Southwestern Region and California 103 4.1. Introduction 103 4.1.1. Region of interest 103 4.1.2. Definition of local storm 105 4.2. Storm record 105 4.3. Development of 1-hr PMP 108 4.3.1. Introduction 108 4.3.2. Data adjustments 109 4.3.2.1. Application of adjustments to data Ill 4.3.3. Analysis Ill 4.4. Durational variation 116 4.4.1. Duration of local-storm PMP 116 4.4.2. Data and analysis for durations from 1 to 6 hours . . . 116 4.4.3. Data and analysis for less than 1-hr duration 119 4.5. Depth-area relation 120 4.6. Distribution of PMP within a basin 122 4.7. Time distribution of incremental PMP 122 4.8. Seasonal distribution 127 5. Checks on the general level of PMP 129 5.1. Introduction • • • • 129 5.2. Comparisons with greatest known general-storm areal 1 OQ rainfalls x ^ IV Page 5.3. Comparisons with greatest known local-storm rainfalls. . . 133 5.4. Comparisons with estimates from a previous study 135 5.5. Comparisons with 100-yr return period rainfalls 135 5.6. Mapped ratios of 100-yr to PMP values over the Western States 137 5.7. An alternate approach to PMP 139 5.8. Statistical estimates of PMP 140 5.8.1. Background 140 5.8.2. Computations 141 5.8.3. Discussion 141 5.9. Hypothesized severe tropical cyclone 142 5.9.1. Transposition and adjustment of PMP based on the Yankee- town, Fla. storm of September 5-6, 1950 143 5.10. Conclusion on PMP checks 145 6. Procedures for computing PMP 146 6.1. Introduction 146 6.2. Steps for computing general-storm PMP for a drainage . . . 146 6.3. Steps for computing local-storm PMP 148 Acknowledgements 156 References 157 TABLES 2.1. Most extreme general-storm convergence rainfalls 9 2.2. Stations within least-orographic regions for which daily precipitation was available for 20 years or more before 1970 13 2.3. Seasonal variations of 1000-mb (100-kPa) convergence PMP for 24 hours, from HMR No. 43 (USWB 1966a) 18 2.4. Stations within least-orographic regions for which hourly precipitation data were available for the period 1948 through 1972 38 2.5. Nonsummer storms in the Southwest and the number of stations with relatively large rainfalls in least-orographic regions used in duration analysis of convergence PMP 39 2.6 Comparison of 6/24-hr ratios in the Northwest and Southwest studies at 42°N, 113°W 46 2.7. Durational variation of convergence PMP 50 3.1. Summary of average rain ratios 61 3.2. Average rain ratio for 9 selected upslope segments in Arizona (B, D, E, F, G, H, I, J, K in fig. 4.5) 61 3.3. Seasonal variation east of Cascade Ridge in Northwest States as percent of August 70 Page 3.4. Seasonal variation in Pacific drainage of California as percent of August 70 3.5. Data analyzed for determining depth-area variation of orographic PMP 91 3.6. Durational variation of maximum moisture of the Southwest 94 3.7. Computation of durational variation of orographic precipita- tion for the Southwest States using a simplified oro- graphic model 98 3.8. Durational variation in major storms in orographic locations; Southern California and Arizona 100 3.9. Durational variation of orographic PMP 103 4.1. Major short-period rains of record in the Southwestern States and all of California 106 4.2. Adjustment to most critical local-storm rainfalls. . . . 113 4.3. Depth-duration relations of severe local storms 119 ? 2 4.4. Durational variation of 1-mi (2.6-km ) local-storm PMP in percent of 1-hr PMP 120 4.5. Isohyetal labels for the 4 highest 15-min PMP increments • and for 1-hr PMP 124 4.6. Isohyetal labels for second to sixth hourly incremental PMP in percent of 1-hr 1-mi 2 (2.6-km 2 ) PMP 125 4.7. Time sequence for hourly incremental PMP in 6-hr storm . 126 4.8. Time sequence for 15-min incremental PMP within 1 hr . . 127 4.9. Seasonal distribution of thunderstorm rainfalls 127 5.1. Comparison of storm areal rainfall depths with general- storm PMP for the month of the storm 130 5.2. Adjustment of tropical storm PMP for distance-f rom-coast 145 6.1. General-storm PMP computations for the Colorado River and Great Basin 150 6.2. Example computation of general-storm PMP 151 6.3. Local-storm PMP computations, Colorado River, Great Basin and California drainages 152 vi Page 6.4. Example computations, of local storm PMP 154 FIGURES 1.1. Primary study area, Colorado River and Great Basin Drainages. 3 2.1. Location of stations used in studies of 1- and 3-day rainfall 8 2.2. Location of most extreme general-storm convergence rainfalls in the Southwest 10 2.3. Examples of schematic diagrams depicting moisture sources (arrows) implied by gradients of 12-hr persisting 1000-mb (100-kPa) dew points, January and August 14 2.4. Seasonal variation of convergence PMP and supporting data for least-orographic subregions; a. Southwest Arizona, b. north- east Arizona 15 2.4. Seasonal variation of convergence PMP and supporting data for least-orographic subregions; c. western Utah, d. southern Nevada 16 2.4. Seasonal variation of convergence PMP and supporting data for least-orographic subregions; e. northwest Nevada. ... 17 2.5. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for January 22 2.6. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for February 23 2.7. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for March 24 2.8. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for April 25 2.9. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for May 26 2.10. 1000-mb QOO-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 kaT) for June 27 2.11. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for July . 28 DO-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for August 29 vii Page 2 2.13. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi (26 km 2 ) for September 30 2 2.14. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi (26 km 2 ) for October 31 2 2.15. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi (26 km ) for November 32 2.16. 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for December 33 2.17. Effective barrier and elevation heights (1000* s of feet) for Southwestern States 35 2.18. Percent of 1000-mb (100-kPa) convergence PMP resulting from effective elevation and barrier considerations 37 2.19. Relation between 6/24-hr and 72/24-hr ratios for within-storm cases of 3 consecutive day rainfall for all stations listed in table 2.4 40 2.20. Idealized depth-duration curves in percent of 24-hr amount. . 42 2.21. Adopted 6/24-hr vs. 72/24-hr convergence PMP ratios 43 2.22. Seasonal variation of 6/24-hr ratios at least-orographic sub- region midpoints 44 2.23. Seasonal variation of 6/24-hr durational rainfall ratios for Southwest and adjacent regions 44 2.24. Smoothed variation of 6/24-hr ratios at subregional midpoints 45 2.25. Regional variation of 6/24-hr ratios by month (percent); Jan- uary to April 47 2.26. Regional variation of 6/24-hr ratios by month (percent); May to August 48 2.27. Regional variation of 6/24-hr ratios by month (percent); September to December 49 2.28 Depth-area variation for convergence PMP for first to fourth 6-hr increments; January to July 51 2.29. Depth-area variation for convergence PMP for first to fourth 6-hr increments; August to December 52 vm Page 3.1. Areas of minimum orographic effects in Southwest States. . . 54 3.2. Schematic of orographic PMP index map development 56 3.3. A first approximation to the orographic PMP (inches) for 10 mi^ (26 km^) 24 hr in southeast Arizona 57 3.4. Segments across major ridges in Southwest States used in rain ratio study 59 3.5. Segments across major ridges in Arizona superimposed on analysis of 100-yr 24-hr precipitation (in tenths of an inch) 60 3.6. Generalized topography and station locator map in vicinity of Workman Creek, Arizona 62 3.7. Rainfall-elevation relation for August 1951 storm, and rain- fall for September 1970 storm 63 3.8. Leeward isohyetal patterns; a. 100-yr 24-hr rainfall, b. August 1951 storm 64 3.8. Leeward isohyetal patterns; c. September 1970 storm 65 3.9. Leeward rainfalls in percent of ridge value for major storms and 100-yr 24-hr rains 66 3.10. Example of profiles of several rainfall indices (in percent of maximum values) 67 2 2 3.11a. 10-mi (26-km ) 24-hr orographic PMP index map (inches), northern section 71 2 2 3.11b. 10-mi (26-km ) 24-hr orographic PMP index map (inches), north-central section 73 2 2 3.11c. 10-mi (26-km ) 24-hr orographic PMP index map (inches), south-central section 75 2 2 3. lid. 10-mi (26-km ) 24-hr orographic PMP index map (inches), southern section 77 2 2 3.12. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); January, February 81 2 2 3. IS. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); March, April 82 ix Page 2 2 3.14. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); May, June 83 2 2 3.15. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); July, August 84 2 2 3.16. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); September, October 85 2 2 3.17. Seasonal variation in 10-mi (26-km ) 24-hr orographic PMP for the study region (in percent of values in figure 3.11); November, December 86 3.18. Months of maximum total general-storm PMP for Southwest States, 10 mi 2 (26 km 2 ) 24 hr 87 3.19. Season and month of maximum and secondary maximum 24-hr station precipitation, after Pyke (1972) 87 3.20. Variation of orographic PMP with basin size 89 2 2 ? 3.21. 1000-mi (2590-km ) storm depths relative to 10-mi (26-km ) depths for 72-hr rainfalls 90 3.22. Durational variation of maximum winds at Tucson, Arizona compared with variations for adjoining regions 93 3.23. Durational variation of precipitable water 95 3.24. Adopted durational variation in relative humidity and supporting data 96 3.25. Durational variation in orographic precipitation near north- ern and southern borders of Southwest region (from oro- graphic model) 97 3.26. Ratios of 72/24-hr rains at high elevations from major storms in southern California and Arizona 102 3.27. Adopted durational variation in orographic PMP 102 4.1. Location of short-duration extreme rainfalls 104 4.2. Variation of maximum 6-hr summer recorder rainfall with elevation (period of record is 1940-1972) 110 4.3. Variable depth-duration curves for 6-hr PMP in the Southwest States and all of California 112 x Page 4.4. Maximum clock-hour rainfalls at stations with records for period 1940-1972 114 4.5. Local-storm PMP for 1 mi 2 (2.6 km ) 1 hr . . . 115 4.6. Criteria of clock-hour rainfall amounts used for selection of storms at recorder stations for depth-duration analysis 117 4.7. Analysis of 6/1-hr ratios of averaged maximum station data (plotted at midpoints of 2° latitude-longitude grid) . 119 4.8. Depth-area relations adopted for local-storm PMP in the Southwest and other data 121 4.9. Adopted depth-area relations for local-storm PMP 123 4.10. Idealized local-storm isohyetal pattern 126 4.11. Regional variation of month of maximum local-storm rainfall . 128 5.1. Comparison between observed rainfall depths and general- storm PMP for 100 mi (259 km ) 24 hr 133 5.2. Comparison between observed rainfall depths and general- storm PMP for 5000 mi 2 (12,950 km 2 ) 24 hr 134 5.3. Comparison between observed rainfall depths from local storms and local-storm PMP for the duration of the storm. . 134 5.4. General-storm PMP for 10 mi 2 (26 km 2 ) 24 hr in inches (upper number) and local-storm PMP for 10 mi 2 (26 km2) 6 hr in inches (lower number) at 1° grid points 136 5.5. Comparison between PMP from Technical Paper No. 38 (U.S. Weather Bureau 1960) and from this study 136 5.6. Comparison between 100-yr rainfall (Miller et al. 1973) and PMP 137 5.7. Ratios of 100-yr point rainfall (Miller et al. 1973) to highest PMP for 10 mi 2 (26 km 2 ) 24 hr 138 5.8. Ratios of PMP determined from an alternate approach (see section 5.7) to that of this study for 10 mi 2 (26 km 2 ) 24 hr 140 XI Page 5.9. Comparison between statistical PMP (Hershfield 1965) and the highest PMP for 10 mi 2 (26 km 2 ) 24 hr at stations with records exceeding 50 years 141 5.10. Distance-from-coast reduced tropical storm nonorographic PMP compared with 1000-mb (100-kPa) convergence PMP for August, 10 mi 2 (26 km 2 ) 24 hr , 144 XII PROBABLE MAXIMUM PRECIPITATION ESTIMATES, COLORADO RIVER AND GREAT BASIN DRAINAGES E. Marshall Hansen, Francis K. Schwarz, and John T. Riedel Hydrometeorological Branch Office of Hydrology NOAA, National Weather Service, Silver Spring, Md. ABSTRACT. This study gives general-storm probable maximum precipitation (PMP) estimates for durations between 6 and 72 hours and for area sizes between 10 and 5,000 mi 2 (26 and 12,950 km 2 ), for any location in the Colorado River and Great Basin drainages. Total PMP is determined as the sum of convergence and orographic PMP components. Esti- mates are given for each month. The study also provides estimates for local-storm PMP. In addition to the above drainages these estimates are provided for all of California. The estimates cover durations between 15 minutes and 6 hours and drainage areas between 1 and 500 mi 2 (2.6 and 1,295 km2) . Local- storm PMP is applicable to the warm season between May and October. Comparisons are given between PMP estimates and the greatest observed rainfalls of record, 100-yr fre- quency rainfall and statistically derived PMP. A step- by-step outline of the procedure for computing PMP estimates is presented with examples for both the general and local storm. 1 . INTRODUCTION 1 .1 Purpose of Report The purpose of this report is to present the material necessary to compute estimates of probable maximum precipitation for any watershed up to 5,000 mi 2 (12,950 km 2 ) for durations up to 72 hours in the Colorado River or Great Basin drainages. The material for preparing an estimate makes up only a small portion of this text; the bulk of the report consists of data and studies required to develop the criteria. The local-storm criteria presented in this report also cover the Pacific Ocean drainage of California. 1.2 Authorization Authorization for the study was given in a memorandum from the Office of Chief of Engineers, Corps of Engineers, dated July 8, 1971. In conferences between representatives of the Corps of Engineers and the National Weather Service it was agreed the study should cover the Colorado River drainage and interior drainages of Nevada, Utah, and California. As thunderstorm PMP had not been previously considered for the Pacific Ocean drainages in California, it was subsequently agreed to expand this portion of the study. 1.3 Scope Estimates of general-storm probable maximum precipitation (PMP) in this re- port cover the region between the crest of the Sierra Nevadas on the west and the Continental Divide on the east. To the north, the region extends to the southern limits of the Columbia River drainage and to the south to the U. S. border. This study region is shown in figure 1.1. The shaded portion of the study region in figure 1.1 is a zone (to the west of the Continental Divide) where the PMP values are considered least certain. Detailed generalized PMP estimates including seasonal variation are not avail- able for the slopes immediately east of the Continental Divide. PMP gradients in this region can influence PMP estimates west of the Divide. A future PMP study covering the area east of the Divide is needed before there will be comparable confidence in PMP over the contiguous portion of the Southwestern States. General-storm PMP estimates may be obtained for basin sizes from 10 to 5,000 mi^ (26 to 12,950 km^) for durations from 6 to 72 hours. Values can be computed for each month. Intense local summer thunderstorms can produce rain for short durations over small basins that exceed the rain potential from general storms. Chap- ter 4 gives these criteria for durations from 15 minutes to 6 hours covering basin sizes up to 500 mi^ (1,295 km2) . The thunderstorm PMP estimates cover not only the primary study region defined above but also the remainder of California except a small section of the northern coastal region. The meteorological background and discussions have been kept to a minimum. A companion report (Schwarz and Hansen 1978) contains detailed descriptions of the meteorology of storms and other major meteorological analyses. 1.4 Definition of Probable Maximum Precipitation Probable maximum precipitation (PMP) is defined (American Meteorological Society 1959) as "...the theoretically greatest depth of precipitation for a given duration that is physically possible over a particular drainage basin at a particular time of year." We recognize there are yet unknowns in the complicated atmospheric processes responsible for extreme rainfalls. Thus, methods used for deriving PMP include making judgments based on record storms and meteorological processes related to them. Results of studies are con- sidered estimates because changes are likely as our understanding increases. Figure 1.1.-- Primary study area, Colorado River and Great Basin drainages, Criteria for shaded "portion are considered of lesser reliability. In this derivation of PMP we assume that the record storms during the past 80 or so years are representative of the climate of extreme precipitation. PMP estimates therefore do not allow for changes in climate. Experience gained from PMP studies in other regions gives additional guid- ance to procedures and methods used. This then points to an operational de- finition of PMP; i.e., estimates by hydrometeorologists of Upper limits of rainfall, supplied to engineers for use in hydrologic design. Quoting from Operational Hydrology Report No. 1 (World Meteorological Organization 1973), "Whatever the philosophical objection to the concept, the operational defini- tion leads to answers that have been examined thoroughly by competent meteor- ologists and engineers and judged as meeting the requirements of a design criterion." 1.5 Methods of This Report Estimation of general storm PMP of this report uses basically the same pro- cedure used in two studies for adjoining regions; to the west (U. S. Weather Bureau 1963) and to the north (U.S. Weather Bureau 1966a). First, essentially nonorographic PMP, also termed convergence PMP (precipitation due to atmos- pheric processes), is estimated. Then orographic PMP (precipitation from moist air forced upward by mountain slopes and the triggering of rainfall near first upslopes) is estimated. The two components of PMP are then added to- gether. The convergence PMP is based on moisture-maximized rains of record, reduced for mountain barriers and elevations. Consideration was given to convergence PMP from the adjoining studies. Orographic PMP, for the most part, was not based on the orographic precipitation computation model used in adjoining regions (U. S. Weather Bureau 1961 and 1966a). Reasons for this departure are spelled out in chapter 3. The model is not suited for the meteorological conditions accompanying the main PMP storm prototype for much of the Southwest, partly because the topography is too complicated. Alter- nate methods for estimating orographic PMP are discussed in chapter 3. The method used for local or thunderstorm PMP was to adjust the most in- tense storm values for maximum moisture and develop a 1-hr PMP map for 1 mi z (2.6 km^) . The regional pattern of this map took into account maximum 1-hr rainfalls from recorder stations and broad-scale terrain features. Depth- duration and depth-areal variations to extend the estimates to other dur- ations and larger areas were based on record storms. 1.6 Organization of Report General-storm convergence PMP estimates are developed in chapter 2 and gen- eral storm orographic PMP in chapter 3. PMP for small areas from intense thunderstorms is covered in chapter 4. Checks on the general level of PMP are discussed in chapter 5; while chapter 6 gives procedures for and examples of use of the developed criteria. We at times refer to the study region as the Southwest or the Southwestern States. Frequent reference will be made to studies for two adjoining regions. These are the Columbia River drainage, Hydrometeorological Report No. 43 (U. S. Weather Bureau 1966a) and the Pacific Ocean drainages of California, Hydrometeorological Report No. 36 (U.S. Weather Bureau 1961). Hereafter they will be referred to as HMR No. 43 and HMR No. 36, respectively. 2. CONVERGENCE COMPONENT OF PMP 2.1 Introduction 2.1.1 Method of Determining General-Storm PMP We noted in chapter 1 that the method for determining general-storm PMP in this study was to make separate estimates of orographic and nonorographic PMT ; to judge the regional, seasonal, depth-area, and depth-duration variations of each component; and then to add the components for an estimate of total PMP. This method is comparable to that used for general-storm PMP estimates to the west and north (HMR No. 36 and No. 43). Development of nonorographic PMP, or convergence PMP, is the subject of this chapter. 2 1.2 Definition of Convergence PMP Nonorographic precipitation can be defined as precipitation resulting from atmospheric processes not affected by terrain. Lifting and therefore cooling of moist air are necessary for major precipitation. Lifting or vertical motion can be produced by horizontal convergence of air at lower levels; hence, the term "convergence" for nonorographic precipitation. Under this definition all precipitation in regions with no abrupt changes in elevation is classified as convergence. Convergence and orographic precipitation can occur simultaneously. 2.1.3 General Storm Relation to Local Storm In the United States east of approximately the 105th meridian, many extreme small area rainfalls have occurred within longer storm periods in which gen- eral rains cover larger areas. In contrast, experience has shown that the greatest short-duration rainfalls over small areas in the intermountain region come from intense local storms (thunderstorms) as opposed to general- storm situations. For the Southwestern States, therefore, separate estimates of local-storm PMP are given in chapter 4. While most extreme point rain- falls of record in the Southwest States have been isolated with regard to space and time, this does not negate the occurrence of lesser thunderstorm rains imbedded in the general PMP storm prototype. The point to be empha- sized is that the local thunderstorm, the greatest potential rainfall threat for small areas and short durations, is an isolated event in time and space in the Southwestern States, while less intense thunderstorm occurring within general-storm rains are the key for general-storm convergence PMP. 2.1.4 Convergence PMP for Adjoining Regions The Southwest States Region is bounded on the west by the Pacific Ocean drainage of California. Convergence PMP estimates for that drainage (HMR No. 36) were based on multiplying greatest observed ratios of P/M by M (observed precipitation, P, divided by storm moisture, M , multiplied by maxi- mum moisture, M )'. The P/M ratios were associated with rains at least-oro- graphic locations such as on the floor of the Central Valley of California. Enveloping values of P/M and a regional pattern of M were used to determine a basic convergence PMP xndex map for 10 mi 2 (26 km 2 ) for 6 hours duration. For the Columbia River drainage to the north (HMR No. 43), similar proce- dures for estimating convergence PMP were used. The major difference from HMR No. 36 was that regional patterns of convergence PMP were determined for each month, October through June. These monthly maps incorporated the sea- sonal variations of maximum observed 1-day precipitation at groups of least- orographic stations as well as the seasonal variation of maximum moisture. In developing convergence PMP for the present study, reasonable consistency was maintained with values for the two adjoining regions. Also of some interest are PMP estimates for the United States east of the 105th meridian (Schreiner and Riedel 1978, and Riedel et al. 1956). For these studies, the effects of steepening slopes near the 105th meridian in Colorado and New Mexico were not taken into account. Thus, the PMP estimates to the east of the steep slopes of the Rocky Mountains should be considered nonorographic. The steep slopes east of the Continental Divide separate by distances up to 300 miles (483 km) , the region of those studies from that of the present study. Sharp gradients in precipitation potential are expected in this intervening region that do not allow detailed comparisons of PMP be- tween the two studies. Some overall general consistency checks can be made, such as the effect of moisture sources on PMP patterns, etc. Checks of this nature have been considered in this study. 2.1.5 Summary of Procedure The approach for convergence PMP in this study follows after but is not identical with that for HMR Nos. 36 and 43. Instead of developing P/M s ratio envelopes, the greatest moisture-maximized observed rainfalls for least-oro- graphic locations were enveloped. This is equivalent to the previous studies [(P/M s ) envelope x M x = (P x M x /M s ) envelope]. Monthly patterns of highest moisture and seasonal trends in maximum observed precipitation were used as guides in interpolating between locations of- highest moisture-maximized rain- falls. The resulting patterns are consistent with patterns of convergence PMP in HMR No. 43 and No. 36. The 1000-mb (100-kPa) convergence PMP esti- mates were then reduced for effective elevation and barrier. Depth-duration (from 6 to 72 hours) and depth-area (from 10 to 5,000 mi 2 , 26 to 12,950 km 2 ) relations were based on maximum observed precipitation in least-orographic areas of the Southwestern States and those from eastern states data respec- tively. These procedures are in general agreement with those used in HMR No. 36 and HMR No. 43. 2.2 Mid-Month 1000-mb (100-kPa) Convergence PMP Maps, 24 hrs, 10 mi 2 (26 km 2 ) 2.2.1 Envelopment of Maximum Observed Rainfalls Record storm rainfall is the underpinning to any PMP study. We need two restrictions to our data sample. First, extreme isolated thunderstorm values are not appropriate for development of general-storm convergence PMP. Such values rather are the basis for the local-storm PMP estimates of chapter 4. Secondly, in this section we are concerned with only the convergence com- ponent of record storm amounts. No consistent method has been found for separating total observed storm precipitation into convergence and orographic components; however, we can restrict the data to observed maxima in least- orographic regions of the Southwest. Least-orographic regions are subjectively determined zones (shown in fig. 2.1) outlined on a 1:2,000,000 scale topographic map. The boundary of each subregion depicted on the figure is not significant other than to enclose a group of at least five stations whose precipitation we believe to be least influenced by orography. An appreciation for the complex terrain and an aid in determining general limits for these subregions was gained by two of the authors (Riedel and Hansen) during a 2-day series of overflights in 1972. We recognize that some substantial orographic features remain within the least- orographic boundaries shown in figure 2.1 but stations selected within these subregions were judged not to be significantly influenced by orography. An attempt was made to obtain an equal number of stations in each subregion, but this was difficult to maintain. Station storm totals exceeding 5 inches (127 mm) in 24 hours or less in the subregions were extracted from the histor- ical records. The five storms meeting this criterion are listed in table 2.1. One other storm for Porter, N.M.,east of the region of interest, is listed for comparison. Meteorological descriptions of each of the events is given in the companion report (Schwarz and Hansen 1978). Each storm total is the result of thunderstorms sustained over a period of 6 hours or more within a more general precipitation storm. This distinguishes them from the isolated thunderstorm events used for local- storm PMP. The locations of storms listed in table 2.1 are shown in figure 2.2. San Luis, Mexico lies just south of the study region. Since the exact duration of the San Luis 1-day storm amount (Secretaria de Recursos Hydrolicos 1970) could not be determined, a duration of 24 hours was used. Two of the 5 values in table 2.1, at Bug Pt., Utah and Dove Ck. 10 SW, Colo. , occurred in the September 4-6, 1970 storm. These stations near the edge of an outlined least-orographic region (see fig. 2.1) reported rainfalls of 6.50 inches (165 mm) and 6.00 inches (152 mm), respectively. They are on a high plateau at elevations of 6600 and 6900 feet (2012 and 2103 m) respec- tively. Analysis of orographic PMP in the following chapter shows that some minimum-orographic effect is necessary over this subregion. Analyses of other notable general storms for the region (i.e. the September 4-7 and 11-13, 1939 and August 28-30, 1951 Arizona storms), disclosed that maximum precipitation for these storms occurred primarily in orographic regions. Total storm amounts were all less than 3 inches (76 mm) at least-orographic stations. Figure 2.1. — Location of stations used in studies of 1- and 3-day rain- fall. Numbered stations listed in table 2.2. Letters by X-stations refer to additional stations listed in table 2.4. Least-orographio regions considered for grouping stations into subregions enclosed by solid lines. Double circles indicate approximate midpoints for each subregion discussed in section 2.2.1. e u o CO < en •r- 1 • O u 0) i-J o W < S o o 6 PI ^ •— s r-l O ^ vO O •H v *-^ 4-1 4-1 co i CO > CO ^H 4-1 o S-i W 14-4 CN 0) 3 cu 60 3 O 1) •H e 4-1 S-i (U CO rfl vT> r-l r-l 4-1 3 tt Q 00 CM CO o en CN O O ^D O l m I ON O m - U~> IS o CO 00 o o o m dJ o > r-. O en CN CN SO O O CN en CN O O rH in rH O CN CM CN O O o o o o ON \£> rH \0 vD <-\ 4-t o u m o en T3 OJ •H 14-4 •H J-i > 3 fj e 2.2. — Location of most extreme general-storm convergence rain- falls in the Southwest. 11 The major nonsummer general storms such as February 3-8, 1937, November 25-28, 1905 and December 14-17, 1908, also indicated less than 3 inch (76 mm) total storm amounts for least-orographic stations. Taken collectively, and excluding the Porter storm, the amounts listed in table 2.1 are the greatest known general-storm convergence point rainfalls for the Southwest. The storm values were adjusted to a common elevation and duration, and to optimum moisture conditions. The adjustments are as follows: a. Adjustment for elevation. The events of table 2.1 were adjusted to sea level (assumed 1000 mb, 100 kPa) . This adjustment is the ratio of the avail- able precipitable water above 1000 mb (100 kPa) to that available above the surface. Where adjustments were necessary, the precipitable water was de- termined using the storm 12-hr persisting 1000-mb (100-kPa) dew point and assuming a pseudo-adiabatic saturated atmosphere ( U. S. Weather Bureau 1951a). b. Adjustment for duration. A generalized durational variation determined for convergence PMP was applied to obtain a common duration of 24 hours for all the storms. Reference is made to figures and tables discussed in section 2.4 for the generalized relation. A monthly 6/24-hr ratio was interpolated from the appropriate map (figs. 2.25 to 2.27) at the location of storm rain- fall. Entering table 2.7 or figure 2.20 with the 6/24-hr ratio and the dura- tion of the rain amount gives the factor by which the rain amount needs to be adjusted to provide an estimated amount for the 24-hr duration. c. Adjustment for maximum moisture. One of the steps in estimating PMP is to adjust observed storms to the maximum moisture potential for the storm location and date. Maximum 12-hr persisting 1000-mb (100-kPa) general- storm dew points (Schwarz and Hansen 1978) were used in this adjustment. The ad- justment assumes a pseudo-adiabatic lapse rate with a saturated atmosphere and is the ratio of precipitable water for the maximum 1000-mb (100-kPa) dew point to that for the storm dew point at a location representative of the inflow moisture. A further maximization was made by allowing the maximum 12-hr persisting 1000-mb (100-kPa) dew point to be read 15 days toward the seasonal maximum. 2.2.2 Enveloping 12-hr Persisting Dew Points Enveloping 12-hr persisting dew points have been developed and presented in HMR Nos. 36 and 43 and on a national basis in the Climatic Atlas Environment- al Science Services Administration 1968) . The companion volume to the present study (Schwarz and Hansen 1978) updates the data for the Southwest and develops both general- and local-storm 12-hr maximum persisting 1000-mb (100-kPa) dew points. 2.2.3 Regional Patterns The adjusted storm amounts in the last column of table 2.1 were plotted at their respective locations on a map (not shown) . The few data points pro- vided the lowest level of convergence PMP to be considered at these locations but were insufficient to define a regional pattern. 12 One approach to regional patterns was based on maximum 1-day precipitation for each month in the least-orographic regions in the Southwest. All long- record (>20 years) stations considered least-orographic within each subregion are listed in table 2.2 and are located by numbered dots in figure 2.1. Max- imum monthly 1-day rains were obtained from Technical Paper No. 16 (Jennings 1952) and supplemented by recent records through 1970. Averaged maximum values, by month within each subregion, were helpful but not sufficient to define regional patterns, due primarily to the small number of data points. A further step of adjusting . the data to a common elevation and for upwind barriers did not help materially. Additional guidance for regional patterns of 1000-mb (100-kPa) convergence PMP came from analysis of moisture potential. The Climatic Atlas (Environ- mental Science Services Administration 1968) presents charts of maximum persisting 12-hr 1000-mb (100-kPa) dew points covering the 48 conterminuous states. These charts were used because they portray the broadscale moisture patterns influencing the Southwest. The use of revised moisture charts for the Southwest would not affect the conclusions on moisture patterns based on that Atlas. Figure 2.3 shows examples of schematic charts adapted from the January and August dew point charts from the Atlas. These schematics sug- gest the source of atmospheric moisture for the region. The solid lines are used to imply moisture from the Gulf of Mexico, while the dashed lines sug- gest moisture from Pacific Ocean sources. The change in orientation of the dashed lines between January and August reflects a change from mid- latitude storms in winter and spring to moisture surges from tropical lati- tudes in late summer. The dotted lines represent smoothing in the transition zone between the two moisture sources. The moisture patterns for each of the months give guidance to the pattern of regional variation but not to magnitude of precipitation. They show that the tropical Pacific moisture source has its greatest influence over the southwest region from May through October. The Gulf of Mexico is recognized by many researchers as a source for much of the day-to-day precipitation over the Southwest. However, such rainfall occurrences are not representative of conditions for extreme precipitation (Hansen 1975a, 1975b). Precipitation climatology studies of the Southwest by Schwarz and Hansen (1978) supports this interpretation. 2.2.4 Seasonal Variation Clues to regional patterns of 1000-mb (100-kPa) convergence PMP for each month can also be obtained from analyses of seasonal trends in precipitation data at various locations. Therefore, the seasonal variations of the maximum 1-day precipitation for the stations in least-orographic subregions shown in figure 2.1 and listed in table 2.2 were analyzed. Seasonal charts, figures 2.4a to 2.4e, show monthly averages within each subregion by open circles, along with an eye-smoothed curve (short dashes). In figure 2.4a to 2.4e the regionally averaged 1-day maximum precipitation curves have a summertime maximum in all five regions except northwest Nevada, which shows a summer minimum and bimodal winter and late spring maximum. 13 Table 2.2. — Stations within least-orographic regions for which daily pre- cipitation was available for 20 years or more before 1970. Years of Stat ion Southwest Arizona *1. Ajo, Ariz. 2. Buckeye, Ariz. 3. Casa Grande, Ariz 4. Gila Bend, Ariz. 5. Maricopa, Ariz. 6. Phoenix, Ariz 7. Yuma, Ariz 8. Blythe, Calif. 9. Brawley, Calif. 10. Calexico, Calif. 11. Indio, Calif. 12. Iron Mt. , Calif. # rec. thru Elevation 1970 Latitude Longitude ft. (m) 66 32°22 112°52 1763 ( 537) 70 33°22 112°35 888 ( 271) 63 32°53 111°45 1390 ( 424) 70 32°57 112°43 737 ( 225) 59 32°57 112°00 1242 ( 379) 72 33°28 112°04 1083 ( 330) 100 32°44 114°36 138 ( 42) 58 33°37 114°36 268 ( 82) 58 32°59 115°32 -119 (- 36) 47 32°40 115°30 3 ( 1) 71 33°43 116°14 20 ( 6) 22 34°08 115°08 922 ( 281) Northeast Arizona 13. Jeddito, Ariz. 14. Leupp, Ariz. 15. Tuha City, Ariz. 16. Winslow, Ariz. 17. Bluff, Utah 18. Green River, Utah 19. Hanksville, Utah 20. Crownpoint, N.Mex 21. Farmington, N. Mex. 35 35°46 110°08 6700 (204 2) 22 35°17 110°58 4700 (1433) 46 36°08 111°15 4936 (1504) 55 35°01 110°44 4880 (1487) 59 37°17 109°33 4320 (1317) 64 39°00 110°09 4087 (1246) 45 38°25 110°41 4456 (1358) 63 35°40 108°13 6978 (2127) 64 36°43 108°12 5300 (1615) Western Utah 22. Black Rock, Utah 23. Deseret, Utah 24. Dugway, Utah// 25. Enterprise B.Jct. 26. Kelton, Utah 27. Lucin, Utah 28. Milford, Utah 29. Wendover, Utah 30. Malad, Idaho Utah# 48 77 20 30 52 45 49 66 57 38°45 39°18 40°10 37°43 41°45 41°22 38°25 40°44 42°11 113°02 4860 (1481) 112°38 4541 (1384) 113°00 4359 (1329) 113°39 5220 (1591) 113°08 4225 (1288J) 113°50 4413 (1345) 113°01 5029 (1533) 114°02 4239 (1292) 112°16 4420 (1347) Southern Nevada 31. Beatty, Nev. 32. Caliente, Nev. 33. Goldfield, Nev. 34. Las Vegas, Nev. 35. Logandale, Nev. 36. Searchlight, Nev. 37. Tonopah, Nev. 38. Needles, Calif. 34 36°54 116°45 3314 (1010) 29 37°37 114°31 4402 (1342) 45 37°43 117°13 5700 (1737) 47 36°10 115°09 2006 ( 611) 30 36°35 114°25 1400 ( 427) 35 35°28 114°55 3540 (1079) 44 38°04 117°14 6101 (1860) 22 34°46 114°38 913 ( 278) Northwest Nevada 39. Battle Mt. , Nev. 81 40°37 116°52 4528 (1380) 40. Elko, Nev. 109 40°50 115°47 5075 (1547) 41. Fallon Exp. Sta. , Nev. 73 39°27 118°47 3965 (1209) 42. Lovelock, Nev. 73 40° 12 118°28 3977 (1212) 43. Sand Pass, Nev. 49 40°19 119°48 3900 (1189) 44. Sulphur, Nev. 34 40°54 118°40 4044 (1233) 45. Winnemucca , Nev . 82 40°54 117°4& 4314 (1316) 46. McDermitt, Nev.# 20 42°00 117°43 4427 (1349) ^Location identification number in figure 2.1. [Station information from Technical Paper No. 16 (Jennings 1952) except when noted by # from hourly precipitation records.] 14 JANUARY GULF OF MEXIC( I SOLID LINES) TROPICAL PACIFIC (DASHED LINES) AUGUST GULF OF MEXICO (SOLID LINES) LEGEND CONTINENTAL DIVIDE TRANSITION LINES Figure 2.3. — Examples of schematic diagrams depicting moist- ure sources (arrows) implied by gradients of 12-hr persis- ting 1000-mb (100-kPa) dew points 3 January and August. 15 100 80 60 40- 20 1 1 1 1 1 1 1 1 1 r PHOENIX. ARJZ t r AVERAGE OF -DAY MAX. PRECIPITATION J I I L J L J F M A M J JASON MONTH i -L-l0 100 80 -60 -40 20 a. Southwest Arizona 100 80- 60 20- i 1 1 1 1 1 1 1 1 1 1 r AVERAGE OF 1-DAY MAX. PRECIPITATION MAX. 3-DAY PRECIPITATION OF RECORD IGREEN RIVER. UTAH. WINSLOW. ARIZ.) J I I L J L J L M A M J JASON MONTH J L 100 80 60 40 -20 b. Northeast Arizona ^ Maximum precipitable water at subregion midpoint "Eye" smoothed 1-day station average (stations listed in table 2.2) 0.02 probability level of 3-day maximum rains 1000-mb (100-kPa) convergence PMP at subregion midpoint taken from analyses in figures 2.5 to 2.16 Figure 2.4. — Seasonal variation of convergence PMP and supporting data for least-orographic subregions. All values given in percent of the maximum monthly value for that parameter. 16 o. Western Utah 100- "i 1 1 1 1 1 1 r -i 1 1 r MAX. 3-DAY PRECIPITATION OF RECORD MILFORD. UTAHI 100 80 60 40 20 o< i i I I i l I i 1 i 1 1 1 — 'o J FMAMJ J ASONDJ MONTH 100- 80- 60- d. Southern Nevada 5 o I K®' 5 \ • \ . . 1 I \ \ \ 1 1 i 9.0 ) \ \ ^_ 1 \ • • 1- • 35 S^\ \ 1 I " 1 • • . i • -35° \ - i *> 1 / • ) • • f > '9.0 NN) [MM) \jT ■400 \l ' 15- J ' • • » * . •J l ( 1 •300 115° - 1 / 10- - DISTANCE SCALE 1 / •200 100 200 300 Ml. | (9.2) ■ i i i i K ' 1 10° ■ 5- . • 1 i i 1 100 200 300 400 KM. 0- ■100 ■0 METRIC co SCALE Figure 2.6. — 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for February. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 24 110° {7 A 120° 1 115° 8.0 \ {-> j^- . — _L sJ 8- 3 X 1 • j. (8.9T*^) ■ • • I. v i -35° ^ 1 \ • j • • • f J 1 y 1 j 9.0 (IN) 15- « (MM) •400 ■ -300 1^^ 115° ^ • >^ ' \ f ■ / 10- . DISTANCE SCALE 100 200 1 i i i i \ 300 Ml. J 9^0^ I / ■ ■200 - \ (9.2) 1 1 i i \ 100 200 300 400 KM. 110° 5' 0- MET CONV SO -100 *° RIC | ERSION UE Figure 2.7 '.—1000-mb (100-kPa) 24-hr> convergence PMP (inches) for 10 mi 2 (26 hn 2 ) for March. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 25 110° 1 120° 9.0 J $\5 (8.21 715° 8.5 if 1 J-'\ / ^^"""^ • . 1 \ ' \ C / 1 i ( . __ \ \(9.9) J\ i • • \ • • . \ . J— 40° • 1 1 l\ i y i. \ 1* (8.2) , i \ \ \ • \ . \ 1 ' i i i ' c^- 5 \ | i \ i i 8.5J x i • • / • . i- i J • y ' 1 • * ' 1 ' i / \ —35° V \" i • / i / \l ) (IN) (MM) I 15 ' ■400 • • * , i ( •300 1^^ 175° ■ '/ \ / 10- DISTANCE SCALE i / . •200 •100 100 ■ ill 200 i 1 300 Ml. 1 9.0 | 110° 5- 1 i i 100 200 1 \ 300 400 KM. 0- MET CONVI SC/ ■0 RIC :RSION M.E Figure 2.8.—1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for April. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 26 110° 12.0 1 120° 1 8.0/1 8.5 1CL0/ 115° jr\ Sa y 40bA. • • 1 \ . 1 \ i \.~'~~\^ r \(14j0) J\ \ 1 ' \ \ x *\ * \ ' \ ' \ \ • \ • \ 1—40° \ 1 \ \ Z0 ■ A- 1 \ i A \ \ i A • 1 • ^o.o -J . \ \ • v • • 1 - • / • • / • • : 1 —35° (IN) (MM) 8 A • • l / • A ) i -400 | ( \/ /■ < ■300 DISTANCE SCALE 100 ■ ill 200 115° ^*<^ • 300 Ml. .1 • ' f 10- ■ -200 •100 p.o 1 i i 100 200 1 1 300 400 KM. 110° 3 ; 0- MEl CONV SC ■0 rRic ERSION ALE Figure 2.9. — 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi% (26 hn^) for May. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 27 110° 1 120° 1 ' 8.5 8-0/ \ 11.0. /< 9.0 | J^K — \ \ 1 \ _L \. 3 1 X \ \ X 16 - C \ \ J\ \ V \ (7.7K \ • v \ x • • x \ ' \ l\ v 1 \ \ ' \ \ ' \ \ V \ . y UQ6.7) 16.0 \ \ \ \ x \ \ ■ A- \ \ \ \ \ ' \ \l \ <4£o 14.0 35^-x • . j aor • n * r x 1 • 1 ■ w • • 1 * 1) di.o — 35 {IN) IMW , • ) 1 / » * hi* • * 1 1 / 15- ■ 10- ■400 ■300 l8V5\ 115° DISTANCE SCALE 100 200 1 1 1 1 1 y 5- -200 -100 300 Ml. .,..J y.o | 10.0 110° 1 1 J 1 100 200 300 \ 40C KM. 0- MET CONVt so -0 RIC IRSJON Figure 2.10.—1000-rrib (100-kPa) 24-hr convergence PMP (inches) for \ 10 mi 21 (26 1e limiting values and are to facilitate extrapolation beyond the indicated gradient. 28 110* 400 KM . (MM) 400 ■-100 0-LO METRIC CONVERSION SCALE Figure 2. 11. —1000-mb (100-kPa) 24-hr convergence PMP (inches) for\10 mi 2 (26 km 2 ) for July. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 29 110° 1 14 *5H 720° '8.0 115° 11.0, ^\V 1 / / " \9.0 P°-0 La ^ - • \- l V v (7.8^-^y . • / • ll \ V \ v^^N 5 - 4*4 . / i / ' / i 1 \ \ \~\~ HJ6.0) J\ /' ' J ' i * \ * \ A • \ •1—40° • / * 1 * '" • \ • ( J5.0 *K\ x"- ■ / • • 1 jf P y v x^ r 10.01 35°--}. X-<-> X N >X y' v. • ' / \ -3f i° 11.0 i2.o| xy i X ^ ^ — • \^J^ ! h 5.0 (IN) 15- (MM) ■400 ■300 ■200 ■100 13.0 |iKl, 1 15° 15.0^ 200 300 Ml. 1 \ ' DISTANCE SCALE 100 iiii i.O \ /f6.0 .4) 10- 5- | (16 1 1 i 100 200 1 1 300 400 KM . 110° - 0- MET CONV SC •0 RIC ERSION ALE Figure 2.12. — 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 hn^J for August. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 30 110° 13.0 | 720° (air. 9^0 ii5° 11.0 12.0 |\\ i ~1 no.o r^ / 1 1 )— • -\ \ 1 \ \ 1 ^v 1 4oK' / /' 1 " •• / 1 I 1 \ \ I ^^1 s(16j0) • r * 1 * * \ "I * i \- 40° 9.0V / f • 1 • ' I - '• * 1 * L \ N • X\ i IJM \ v^ yT- * • 1 • - 1 *J io.oV. N N ^/^ \ \<^ '" •— • ^ . - * — 7* — — • /— — -4- — -^ 35°--jA ^ s>^ rs^ ^^0^^^ | / 1 —35° 12.0 ) v"? • r > 15.0 (IN) 15. 10- 5- (MM) ■400 -300 -200 -100 13.0 14 '°|C C ]6 -o 3) 1 J 5 ° 15 -°^ 1 DISTANCE SCALE 100 200 300 Ml. 1 i i i i i i 6.0^ h | (16.: 1 i i i i 100 200 300 400 KM. 110° c 0- MET ONVI SO -0 RIC ERSION M.E Figure 2.13. — 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 hn2) for September. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 31 110° 1 17.0/, 1 120° 1 10.0 /\A •\ (8.4)' 715° /I s?.0 ■ J' X^jJ^f r • / • . 1 J-'-\ L / i • y\ 2.0 S13.0 v. / / ' 1 1 - . _ . ~ t - - J— • ■ — — T — "A 40^.' ^X ; \ 1 I H33.7) 9 -°v ' . / * / • | • /• 1—40° \ • • • • y / 1 1. v ^^ ' 1 / V s • . ^^ i i i / j */ * , . /•/ \ ^^^ /l io.oV 7 ^ ' 1 \ N | > 1 V N is l < \s^ y/ • h / • 35?- A ^\' 1 >^ • j\ — 35° i C • /js^^ # • • / i f (. A n UN) (MM) /I4.U >^ • • 1 / - 15- • ■400 -300 '^^ H5° i 3 ^r V ' ' . \ 1 10- DISTANCE SCALE 100 200 300 Ml. 1 ii • ill 1 / .3) • 5- ■200 ■TOO 14.0 110° (14 1 1 i i i 100 200 300 400 KM. 0- ■0 METRIC CONVERSION SCALE Figure 2.14.—1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for October. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 32 110° 1 720° 1 aJ \9.0 • (8.5L 715° r. ^)\ I 9jO^- L . J 1 \. -^.9.5 C \ • 1 ^^ — • __ — • ™ ~J 40^' . i \10.0 9.0^ -r-^ \ 1 1 f / • ^T^ • • a ^r ^ / ^J— 40° \ ,N | / \ \ '/ ./ \ \ 9.5L 1 \ yS I 1 35^-/ . I X 1 \ • jr • |» • >/ /-..'. \ —35° 10.0C. • J ) ' * • * b Q0.5 (IN) 15- (MM) -400 1^. -300 115° ^v^ • y/r / 10- - DISTANCE SCALE 100 200 ■ i i i i \ 300 Ml. _J *• - 5- ■200 ■100 10.5 | 110° 1 i i i 100 200 300 1 400 KM. ( 0- MEl :onv so ■0 "RIC | ERSION Figure 2.15.—1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km 2 ) for November. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 33 110° (ai}l 120° 1 115° ^Jl \ d^r ^J. 1 \— •x \ 1 • ■ i >-4?- 1) 40^.' . 1 i J\ • ■ i " N. ' . i. 1—40° \\ 1 1 9.6^ • • 1 f • >. . i. . / \ xs. i 1 x. 1 X \ ^\. j • . ^^^k*. • •/ \ s ^v 1 1 " — <^5 I 1 \ \ v 1 \ • h - / 35°--/ . N 1 \ . *" -. l V-°— 35 o ^ * / • I • • f / (IN (MM) ' 1 15 " ■400 ) ' • • r A ■ - I 1 1 f -300 DISTANCE SCALE 115 O ^^""x 9^5*^^ ^ I io- —J- 9 - 5 -200 100 200 ■ i i i i I 300 J Ml. \ 1 1 i i \ 100 200 300 400 KM. 110° 5- o- ME1 •100 ■0 ■RIC CONVERSION SCALE Figure 2.16. — 1000-mb (100-kPa) 24-hr convergence PMP (inches) for 10 mi 2 (26 km^) for December. Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 34 2.3 Effect of Barrier and Elevation The adopted convergence PMP is for 1000 mb (100 kPa) or sea level. For lo- cations at higher elevations or to the lee of mountain barriers, the 1000-mb (100-kPa) convergence PMP must be decreased. This is accomplished by reduc- tions for barrier and elevation. 2.3.1 Effective Barrier and Elevation Map During strong inflow of saturated or near saturated air, moisture is de- pleted on windward slopes by the higher elevations. Moisture is depleted for areas to the lee of upwind barriers by the effect of the barrier. Elevations used in this study were based on smoothed elevation contours of a 1:1,000,000 scale topographic map. The smoothing moved the actual terrain elevation slightly upwind. This "effective" elevation, as differentiated from the actual elevation, provided for greater moisture into a region be- cause precipitation particles can be carried along by the wind to higher elevations. The "effective" barrier for the lee areas was determined from the height of the upwind barrier. These effective barriers may differ from the maximum elevation of the barrier since allowance was made for moisture flow through substantial breaks in the ridgeline. Inflows from southwest through south-southeast were of prime importance in deriving the effective barrier and effective elevation chart for a large por- tion of the Southwestern States. Winds from westerly to northwesterly direc- tions were involved near the northwest corner of the region. A reasonable, tie-in was maintained with the effective barrier and elevation charts of studies for adjoining areas. Also, inflow into southwestern Wyoming and northeastern Utah from the east to northeast resulted from the prototype storm for this portion of the study region. This is consistent with extreme rains to the east of the Continental Divide caused by easterly flow in late spring storms. With some variability permitted in the direction of moist inflow, isolated mountains and ridges less than 10 miles (16 km) long (measured at the base relative to the wind direction) are not effective in reducing moisture. The effective barriers were in many instances phased out, downwind, at a distance about 1 to 1.5 times their length, implicitly allowing recharge of moisture behind such obstacles. The amount of recharge is similar to that of border- ing generalized reports (HMR Nos. 36 and 43). Recharge toned down or eliminated effects of ridges somewhat longer than the initial 10-mi (16-km) criterion. Figure 2.17 shows the combined barrier/elevation map for the for the Southwest. 2.3.2 Reduction for Effective Barrier and Elevation Variation of nonorographic PMP with barrier height and elevation has been made proportional to the variation with elevation of precipitable water in a saturated column. It is the same as that used for convergence PMP in HMR No. 36 for California and for some of the variation in HMR No. 43 for the 35 ELEVATIONS FOR EVEN 1000'S OF FEET ARE DASHED Figure 2.17. — Effective barrier and elevation heights (1000's of feet) for Southwestern States. 36 Columbia River drainage. The adopted variation with elevation, which is proportional to the variation in precipitable water, is consistent with the method used for moisture-maximizing the greatest observed least-orographic rains for guidance in setting the level of 1000-mb (100-kPa) convergence PMP. The maximum 12-hr persisting 1000-mb (100-kPa) dew points for August gen- eral storms (Schwarz and Hansen 1978) of 73° (23°C) were used for determining the percent reduction due to effective barriers and elevations. The August dew points tend to give less reduction than winter dew points. High-eleva- tion rainfall would be unreasonably reduced if winter dew points were used, particularly because the use of a single moisture chart does not allow for the high wind and therefore higher rainfall capability at the higher eleva- tion in the cool season. Figure 2.18 shows the reduction (in percent) of 1000-mb (100-kPa) conver- gence PMP for effective barrier and elevation over the Southwestern States. There is agreement between the patterns shown in figures 2.17 (barrier/eleva- tion) and 2.18 (reduction of 1000-mb (100-kPa) convergence PMP) with one exception. Figure 2.18 contains a large area of 45% reduction in north- eastern Arizona, to the lee (northeast) of the Mogollon Rim. A continuous approximate 8,000-ft (2,440-m) barrier does not exist to support the 45% feature directly. We believe this factor is justified, since the effect of downslope motion behind the major barrier is to produce additional drying of the air which is equivalent to a higher effective barrier. Further downwind, the 45% reduction line has been closed off to indicate the gradual influence of recharge of moisture below 8,000 ft (2,440 m) . When using figure 2.18 to determine a percent of convergence PMP for a specific basin, interpolate between the isopleths. However, for locations that lie within closed contours or at the end of gradients, (within the 95% con- tour in southern California, and within the 50% contour in north-central Nevada. for example), the correct value is that of the last identified contour, i.e., do not extrapolate . 2.4 Depth-Duration Variation The 24-hr mid-month convergence PMP values can be extended to other dura- tions through application of rainfall depth-duration relationships. Durations between 6 and 72 hours are required. Relationships were developed from 6/24- hr, 48/24-hr and 72/24-hr ratios of rainfall in selected severe storms and from maximum rainfalls of record at recorder stations. Seasonal and regional variations of depth-duration relations are given. 2.4.1 Data Hourly precipitation data for up to 25 years (1948-72) were available on magnetic tapes for recorder stations listed in table 2.4. These stations are located in the least-orographic regions shown in figure 2.1. Stations A, B, C, D, and F in table 2.4 are geographically close to stations 3, 10, 11, 13, and 23, respectively, in table 2.2. An additional station at Baker, Cali- fornia (station E in table 2.4) was included in the southern Nevada subregion. Although some of these stations (A to F) had records exceeding 20 years, only 37 Pigure 2.18. — Percent of 1000-mb (100-kPa) convergence PMP resulting from effective elevation and barrier considerations. Isolines drawn for every five percent. 38 Table 2.4. — Stations within least-orographic regions for which hourly precipitation data were available for the period 1948 through 1972. Elevation Station Latitude Longitude ft (m) Southwest Arizona , Ajo, Ariz. 33°22 112°52 1763 ( 537) A* Casa Grande Ruins, Ariz. 33°00 110°32 1419 ( 433) Phoenix, Ariz. 33°28 112°04 1083 ( 330) Yuma, Ariz. 32°44 114°36 138 ( 42) Blythe, Calif. 33°37 114°36 268 ( 82) B El Centro, Calif. 32°46 115°34 - 37 (- ID Iron Mt. , Calif. 34°08 115°08 922 ( 281) C Thermal, Calif. 33°38 116°10 - 112 (- 34) Northeast Arizona D Keems Canyon, Ariz. 35°49 110°12 6205 (1893) Winslow, Ariz. 35°01 110°44 4880 (1487) Green River , Utah 39°00 110°09 4087 (1246) Hanksville, Utah 38°25 110°41 4456 (1358) Crownpoint, N. Mex. 35°40 108°13 6978 (2128) Farmington, N. Mex. 36°43 108°12 5300 (1615) Western Utah F Delta, Utah 39°20 112°35 4626 (1410) Dugway, Utah 40°10 113°00 4359 (1329) Enterprise B. Jet., Utah 37°43 113°39 5220 (1598) Milford, Utah 38°25 113°01 5029 (1535) Wendover , Utah 40°44 114°02 4239 (1292) Malad , Idaho 42°11 112°16 4420 (1347) Southern Nevada Beatty, Nev. 36°54 116°45 3314 (1010) Caliente, Nev. 37°37 114°31 4402 (1342) Las Vegas, Nev. 36°10 115°09 2006 ( 611) Searchlight, Nev. 35°28 114°55 3540 (1079) E Baker, Calif. 35°16 116°04 940 ( 287) Needles, Calif. 34°46 114°38 913 ( 278) Northwest Nevada Elko, Nev. 40°50 115°47 5075 (1548) Lovelock, Nev. 40°12 118°28 3977 (1212) McDermitt, Nev. 42°00 117°43 4427 (1349) Winnemucca, Nev. 40°54 117°48 4314 (1315) *Locators in figure 2.1, 39 the longer record station was used in the studies for determining the magni- tude and regional and seasonal variation of convergence PMP. Additional data were sought from major storms of record for which there were large rainfalls in least-orographic regions. Almost all major storms in the Southwest have their centers in orographic regions; thus, it is difficult to obtain large amounts (more than one inch in 24 hours) in least-orographic regions. Data from the August 1951 and the northern center of the September 1970 storms along with seven lesser nonsummer storms were considered for guid- ance in establishing the seasonal variation of durational relations. The latter storms are listed in table 2.5. Table 2.5. — Nonsummer storms in the Southwest and the number of stations with relatively large rainfalls in least-orographic regions, used in duration analysis of convergence PMP. Date No. of stations Location Dec. 14-17, 1908 Dec. 17-24, 1914 Jan. 14-20, 1916 Feb. 01-07, 1905 Feb. 10-22, 1927 Mar. 11-17, 1941 Apr. 05-10, 1926 W. Cent. Arizona S. Arizona S. Arizona SE Calif. , S. Ariz, S. Utah SE Calif. , S. Ariz S. Arizona 2.4.2 Depth-Duration Relation A depth-duration relation of PMP for an area size indicates the relation- ship between PMP values for various durations. It can be specified by a smooth curve of duration vs. depth (either in inches or percent of the value for a selected duration) or mathematically by ratios of the depths for var- ious durations to that say of 24 hours. A PMP depth-duration relation is based on the concept that the average intensity of rainfall decreases with increasing duration. This concept is analogous to that in depth-area rela- tions of PMP in which precipitation decreases with increasing area size. It might be well to point out that a depth-duration relation of PMP does not specify the time sequence in which incremental rain will fall. A smooth depth-duration relation can be quite well defined by the 6/24- and 72/24-hr ratios of rainfall. Some regional PMP studies have used one depth-duration relation for the en- tire region. From preliminary examination of 6/24-hr ratios of rainfall, it was apparent that seasonal and regional variations precluded use of a single relation for the Southwestern States. As an alternative, a concept of a family of smooth depth-duration relations was envisioned that would cover the range of probable relations required. When expressed in percent of the 24-hr amount, the concept of a smooth family of curves that require a continually decreasing rate of rainfall intensity in- volves an inverse relationship: Where the short-duration value is high, the long-duration value with which it is associated is low, and vice versa. In effect, this implies that high 6/24-hr ratios relate to low 72/24-hr ratios, and that low 6/24-hr ratios relate to high 72/24-hr ratios. 40 A tendency to support the inverse relation can be seen in the data plotted in figure 2.19. These ratios are selected within-storm (paired 6/24- and 72/24-hr ratios from the same storm) values from the stations in table 2.4. All storms were used where the 24-hr amount equalled or exceeded 1.0 inch (25 mm) . To aid in understanding seasonal variations the data were stratified according to winter (Jan. and Feb.) and summer (Jul. and Aug.) months. An attempt was made to reduce the influence of thunderstorms by purging the data to eliminate 6/24-hr ratios greater than or equal to 0.90 and 72/24-hr ratios less than or equal to 1.10. An envelopment of the data in figure 2.19 sup- ports an inverse relation. Similarly, a rough average through all the points, aside from the wide scatter, supports an inverse relation. 200 181 u DC o < CM V. CM 160 — 140 121 100 I • JAN. FEB (WINTER) \ x-RJL. AUG (SUMMER) \ OWINTER AVERAGE * D SUMMER AVERAGE \ A.B -SEE DISCUSSION. X SECTION 2.4.3 \ \ * X\ \ X x x"x X \ ENVELOPING \ LINE -| V x A - X •B 20 40 60 80 6/24 - HR RATIO (PERCENT) 100 Figure 2.19. — Relation between 6/24-hr and 72/24-hr ratios for within- storm oases of 2 consecutive day rainfall for all stations listed in table 2.4 (see text for criteria for selection). Points identified as winter or summer. 41 A family of depth-duration curves that would cover the range required in the Southwest was then developed. First, a base depth-duration curve was es- tablished using all recorder data for least-orographic stations in the August 1951 and September 1970 storms. These storms are the closest to the proto- type PMP storm for most of the Southwest. Averages of 6/24-, 12/24-, 18/24-, 48/24-, and 72/24-hr ratios are shown by the large dots in figure 2.20. The 72-hr dot is based solely on August 1951 data. A smooth line was drawn through these dots. Next, we expanded this base depth-duration curve to a family of curves constrained by the limits: a. Contant rainfall rate. A straight line from to 100% at 24 hours to 300% at 72 hours. b. All rain in the first instant, or 100% at all durations. These two constraints are represented by the straight lines in figure 2.20. There is great flexibility in how to draw additional curves between these two lines. We selected 6/24-hr ratios at increments of 30, 40,..., 90% and drew smooth curves between and 24 hours that were consistent with the curvature of the basic relation and somewhat symmetrical about a perpendicular bisector to the curves . The 6 additional curves were then extended to 48 and 72 hours as smooth (not necessarily straight) lines. Further adjustments were made to the in- crements between curves beyond 24 hours in order to maintain a gradual in- crease (smooth gradient) in the increment between successive curves as the 72/24-hr ratios increased. The control for this gradient was the range in individual recorder durational curves for the stations used in the August 1951 and September 1970 storms. Although the family of curves in figure 2.20 suggests a broad range of 72/24-hr ratios, a much smaller range is ap- plicable to the Southwest as discussed under seasonal and regional variations. The PMP study for the Northwestern States, HMR No. 43, used a similar gen- eralized set of depth-duration relations for convergence PMP. While not de- veloped in the same manner as in the present study, the results are similar. Adopted smooth relations from the two studies are compared in figure 2.21. 2.4.3. Seasonal variation It is to be expected that the 6/24-hr ratio should have a seasonal varia- tion, i.e., because of greater convective activity ratios should be higher in summer than in winter. In figure 2.19, a check was made of two points (labelled A and B) that ap- pear to be extremes relative to the seasonal distribution of points indicated in this figure. Hourly precipitation records and synoptic weather analyses indicate that point A is the result of 3 days of isolated afternoon thunder- showers. Thus, it is not representative of a general-storm summer rainfall. Point B results from one-day rainfall associated with a rapidly moving and dissipating low-latitude cold front with light post-frontal showers on the 42 ' I ■ I ' I ' I ' T T — T 1~ r o o oo tJ ^ "Xj i v ■ - i i . i i ■ ■ - i i . r / 60 115' DISTANCE SCALE 100 200 300 Ml 1 — '. ' i ' ,' 't— » 200 400 KM. 110° 1 -\ J69) 110° March 155) 40^ DISTANCE SCALE 100 200 300 Ml I — V ' i ' i 1 1 — ■ 200 400 KM . 70 (71) | 70 110° April Figure 2.25.— Regional variation of 6/24-hr ratios by month (percent) Values in parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 48 157) 40- DISTANCE SCALE 100 200 300 Ml I ' ■ ' I ' I 1 T ' 200 400 KM. 110° -40° 110° DISTANCE SCALE 100 200 300 Ml * — 'i ■ i ' i 1 — i — ' 200 400 KM 110° May June DISTANCE SCALE 100 200 300 Ml \ — ■■ ' i ■ i 1 \ — ' 200 400 KM 110° -40° 110° 40^ DISTANCE SCALE 100 200 300 Ml ♦ — 'i ■ . ■ i 1 — I — ' 200 400 KM 110" -40° July August Figure 2.26. — Regional variation of 6 /24-hr ratios by month, (-percent) Values in -parentheses are limiting values and are to facilitate extrapolation beyond the indicated gradient. 49 no e DISTANCE SCALE 100 200 300 Ml I h ' I ' I 1 1 j [X Y-JASh "Ouuy x^ \ 3! I l(XX>l======i^========A^lt=iL ^l y**T i — rr" EEEEEE==ESEEEEE=E = 5*rS = = 3 \ 1 ^ At \ \ \ 1000 \ ) \ _____ _ N _± it. r r\r\ & 1 I rl_ \t \ V 1 1 100" = =- ^=-=M: L — m 3r — \4|p EEEEEEEEEzEEEEEE EEEEKEEEH t \ 11 1 X M ijV ^B ■100 \ Vjj til y i\j] \] |0 , | M . ! 1 1 11 i i N 40 50 60 70 80 90 IOC ) 50 60 70 80 90 100 Percent of 6-hr, 10 mi 2 (26 km 2 ) amount Figure 2.28. — Depth-area variation for convergence PMP for first to fourth 6-hr increments. 52 5000- 1000 D © 40 50 60 70 80 90 100 50 60 70 80 90 100 Percent of 6-hr, 10mi 2 (26km 2 ) amount 5000- 1000 o a> 40 50 60 70 80 90 100 Percent of 6-hr, 10mi 2 (26km 2 ) amount Figure 2.29.— Depth-area variation for convergence PMP for first to fourth 6-hr increments. 53 3. OROGRAPHIC COMPONENT OF PMP 3.1 Introduction 3.1.1 Methods for Determining Orographic Effects on Rainfall Recent PMP studies in mountainous terrain have used one of two methods for determining the orographic effects on precipitation magnitude and distribu- tion. One computes precipitation with a numerical orographic windflow model based on physical principles. Examples of the use of this method are HMR No. 36 and HMR No. 43. The other, used where the windflow model does not apply is a more empirical approach in which observed rains on slopes and in nearby least orographic areas (fig. 3.1, see discussion in 3.2.3.2) are compared and the differences are assumed to be orographic. This procedure was used in studies for the Hawaiian Islands (Schwarz 1963) , the Yukon River in Alaska (U. S. Weather Bureau 1966b), and the Tennessee River drainage (Schwarz and Helfert 1969). The western slopes of California mountains (HMR No. 36) are one of the better locations for use of the orographic windflow model for estimating PMP in winter. The Sierras form a barrier to stable moist air. A large number of representative rainfall measurements are available for checking the model. The west slopes of the Cascades (HMR No. 43), are almost as suitable for model calculations but have fewer rainfall measurements. Using the model in the interior of the Northwest, resulted in problems stemming mainly from short mountain ridges and complicated terrain. In major storms, moisture transport into the Southwestern States involves less stable air than in the Northwestern States and the orographic model with its assumed laminar flow is less applicable. Much rainfall, as in the Sep- tember 4-6, 1970 storm in Arizona and Colorado, results mainly from an ef- fect called "stimulation" in earlier reports, that is, the initiation of non-laminar convection, including thunderstorms, by mountain slopes. Because of these factors the orographic windflow model has limited use in estimating PMP for the Southwestern States, where it is more practical to base the estimation of orographic effects primarily on observed variations in precipitation and terrain. 3.1.2 Definition of Orographic Precipitation In this report orographic precipitation for the general storm is defined as the excess over nonorographic precipitation, and includes stimulation. In this report orographic PMP also includes some local details that were omitted from the smooth convergence PMP index maps. 54 11 O c —40° Figure 3.1. — Areas of mini-mum orographic effects in Southwest States. 55 3.1.3 Detail in Orographic PMP Mean annual precipitation (MAP) charts and rainfall frequency maps (Miller et al. 1973) show details quite closely related to terrain. This close a relation to terrain features may not be warranted for PMP. As the magnitude of a storm increases, the energy involved in the dynamic processes also in- creases and the effect of terrain features is less important. Inadequate knowledge of the complex mechanisms involved in precipitation in mountainous regions also must be considered. Many of these problems were highlighted in papers presented at a symposium on precipitation in mountain- ous regions (World Meteorological Organization 1972) . In generalized PMP studies, effects of many wind directions, moisture sources, and storm types must be evaluated. This may be particularly im- portant when small terrain features are considered. Factors pertinent to judging the proper amount of detail follow. a. A single orographic index map was developed. This is a simplifying step that does not take completely into account differences in terrain ef- fects due to month-to-month variation in moisture, wind, and height of freezing level. Use of a single index map using near highest moisture is a slight maximizing factor. b. With a condensation level near the surface for the PMP storm, differ- ences between lower and upper reaches of slopes become less than in ordinary storms. This reduces the detailed response to elevation. c. From several empirical terrain-rainfall studies, discussed later, we concluded that in extrapolation to the general-storm PMP prototype, rainfall is intensified more on large, steep slopes than on smaller, gentler slopes. On the other hand, some regions (with minimum upwind barriers) where condi- tions are particularly favorable for orographic rainfall, the stimulation of rain at low levels (with a low condensation level in the PMP) may tend to decrease the gradient of rainfall on the slope. Throughout development of orographic PMP several forms of topographic charts were used to identify primary terrain features. This information was transferred to, and final smoothing made on a 1:2,000,000 scale map. This scale was adopted for the final orographic index map. ICharts considered were: a. Normal Annual Precipitation (NAP) for New Mexico (State of New Mexico) , Arizona (State of Arizona) , Utah (State of Utah) , and Colorado (State of Colorado) prepared by National Weather Service, NOAA for data period 1931- 1960. b. NAP for Upper Colorado River drainage (U. S. Geological Survey 1964) for data period 1921-1950. c. MAP for southeastern Idaho prepared jointly by Soil Conservation Serv- ice and U. S. Weather Bureau (1965). 56 3.2 Orographic Index Map Rainfall frequency analyses for the Western States have recently been de- veloped by Miller et al. (1973). These analyses were based on multiple cor- relations relating precipitation to physiographic factors. The resulting charts thus qualitatively show variations that will also be present in the PMP. Following this reasoning, a first approximation of the 24-hr lO-mi^ (26-km2) orographic component to PMP was based on an estimate of the oro- graphic component of the 100-yr 24-hr rainfall values. The first approximation orographic index map was modified by considering a number of other precipitation/terrain effects to arrive at a finalized map. Figure 3.2 is a schematic of the procedure. FIRST APPROXIMATION TO OROGRAPHIC PMP INDEX (EXAMPLE: FIG. 3.3) AID TO MODIFICATIONS: CLASSIFICATION OF REGION BY MOST-, LEAST-, AND INTERMEDIATE-OROG. EFFECTS GENERALIZED RAIN-ELEVATION ' ■ OROGRAPHIC GRADIENT TWICE 100-YR. GRAD. ON MAIN UPSLOPES DETAILED PROFILE STUDIES SUBJECTIVE MODIFICATIONS OROGRAPHIC CENTERS MOVED 2.5-5 Ml (4-8 KM) DOWNSLOPE (UPWIND FROM RIDGE) • OROGRAPHIC EFFECTS SPREAD OUT • SMALL-SCALE HIGH VALUES ELIMINATED • SMOOTH ANALYSIS RELATIVE TO 100-YR / CHECKS ON GENERAL LEVEL OF PMP FINAL OROGRAPHIC PMP INDEX MAP (FIG. 3.11) Figure 3.2. — Schematic of orographic PMP index map development. 57 3.2.1 Development of First Approximation The 100-yr 24-hr rainfall of 4.0 inches (102 mm) over the nearly flat area of southwestern Arizona and southern California was assumed to be entirely convergence rainfall. Comparable convergence, values over the entire South- western States were estimated by first applying reductions for effective bar- rier and elevation^. The total 100-yr 24-hr rainfall was then expressed as a percent of this convergence component. These percents (minus 100) are a preliminary approximation to orographic effects. The convergence component of PMP has been shown to have a regional gradient (See section 2.2.6, and figures 2.5 to 2.16). An adjustment to the pre- liminary approximation to orographic effects incorporated a regional gradient. For the sake of simplicity, the August 1000-mb (100-kPa) convergence PMP was used as a single index map. This month was selected since a decadent tropi- cal storm is the PMP prototype over much of the region. The preliminary ap- proximation values were multiplied by the convergence PMP values adjusted for effective barrier and elevation. Figure 3.3 shows an example of the first approximation of the orographic PMP for central Arizona. 6 6 68 10 10 8 8 10 12 10 Figure 3.3. — A first approximation to the orographic PMP (inches) for 10 mi 2 (26 km 2 ) 24 hr in southeast Arizona. The effective barrier-elevation chart used was less smooth than the final version shown in figure 2.17. 58 Implicit in the procedure is the assumption that the orographic and con- vergence components of PMP have the same relation to each other as the rela- tion between the orographic and convergence components of the 100-yr 24-hr rainfall each appropriately adjusted for elevation and barrier. We have thus estimated the orographic component of PMP utilizing the equation: PMP = PMP 10 °- yr o o c 100-yr J c where subscript "o" denotes the orographic component and "c" the convergence component of precipitation. Numerous departures from this assumption were made through modifications discussed in the following sections. 3.2.2 Guidance to Modification . The result of several studies using various data gave guidance to modify- ing the first approximation to the orographic PMP index. 3.2.2.1. Rain Ratios for Line Segments. We first cover the variations of rainfall along lines or segments across major ridges. Figure 3.4 shows the segments selected for the study region and figure 3.5 shows the segments for Arizona. This last figure also shows the 100-yr 24-hr rainfall. In addi- tion to 100-yr and 2-yr 24-hr values, storm rainfall and normal annual precipitation were considered. For each of the line segments, we determined the rain ratio or the change in rainfall per 1000 feet (305 m) , divided by the low-elevation rainfall. For example, if along a line segment the 100-yr 24-hr rainfall is 2.0 inches (51 mm) at the base and 4.0 inches (102 mm) at the ridge with a 4,000-foot (1,219-m) difference in elevation, the rain ratio is 0.25, or 4.0-2.0 /9 4 This rain ratio is an index of the variation of rainfall with elevation, re- lated to the low-elevation value. Various rain ratios for this study region and the Northwest States (HMR No. 43) were determined. These ratios are summarized in table 3.1. Rain ratios for the Northwest States in table 3.1a were computed for the orograph- ic PMP index values and 100-yr 24-hr rainfall for various regions with signi- ficant orographic effects. The rain ratios for the segments in figure 3.4 are summarized in table 3.1b, for two rainfall categories; 100-yr 24-hr, and mean annual precipitation. The high 100-yr 24-hr average ratio for southeast California implies low values of rainfall at the beginning point of many of the segments. The large rain ratios from the mean annual precipitation, compared to those for the 100-yr rainfall, are due to the greater frequency of rains at higher eleva- tions. Adjustment of the mean annual precipitation rain ratios for frequency would make them more nearly similar to those for the 100-yr 24-hr rainfall. The comparisons with HMR No. 43 indicate that PMP ratios ought to be larger than 100-yr rain ratios for areas of significant upslope. 59 110° 1 120° 1 1 1 "5° ~^H ' s V 1 _>• L • / J/ ^ Xpjs-Vv^ ' i A ~ (T / > ■ • -< I . ' • I \-> 4^i-. " -/ „•.. X. -f'"[— -'TV \ -x ; ^ - ^/. ,. . . 1 ^.v V \ ^ ' -- -- ' i /xT V^ * ^ ■ . . ' ' i < ' ^\ 35^/. ■ ^^'^ // • / -'•''/ • /// • '• \ -35° / V „ . / * 1 S V / ' / //' ) i<. / ' i^ 7 1 15° ^^ • ' > f ^\/ /'/ DISTANCE SCALE 100 200 300 400 KM. 1 T I : i . . _« '160' 260 ' 3b0 Ml. ' IU SUPPLEMENTARY SEGMENTS FOR DETAILED PROFILE STUDY IN SELECTED AREAS Figure 3.4. — Segments across major ridges in Southwest States used in rain ratio study. 60 32 RAINFALL CONVERSION SCALfc DISTANCE SCALE 0-Lo I 114 2D 40 6^ 90 km. I 113 L 109 Figure 5.5. — Segments across mag or ridges in Arizona superimposed on analysis of 100-yr 24-hr precipitation (in tenths of an inch) 61 Table 3.1.— Summary of average rain ratios [change in rainfall per 1000-ft (305-m) elevation difference divided by low-elevation rainfall] State or portion of State Average ratio for segments in indicated region for: Mean annual precipitation Northwest States Montana (W. of Continental Divide) Western Washington Eastern Washington Southwest Idaho Northern Idaho 100-yr Orog. PMP 24-hr index (HMR No. 43) .13 .34 .15 .61 .21 .47 .09 .82 .14 .98 b. Southwest States Arizona Utah Nevada* Western New Mexico Southeast California* Western Colorado Mean 26 .07 46 .10 — .12 56 .10 — .22 39 .12 42 .12 *The available MAP chart for Nevada did not provide an isohyetal analysis that could be used for computing rain ratios. The southeast California MAP was considered too uncertain in orographic areas for computing reliable ratios. One other set of rain ratios is shown in table 3.2. This compares the av- erage rain ratios (as previously defined) for 9 selected segments (B, D, E, F, G, H, I, J, K in fig. 3.5) which had considerable rain in the August 1951 and September 1970 storms, with the ratios for the 100-yr 24-hr rainfall. These data show that rainfall from the 2 storms was affected more by the slopes than the 100-yr 24-hr rainfall (rain ratios of 0.31, 0.21 and 0.11, respectively, for the September 4-6, 1970, August 25-30, 1951 and 100-yr 24-hr rainfalls). Table 3.2. — Average rain ratios for 9 selected upslope segments in Arizona (B, D, E, F, G, H, I, J, K in fig. 3.5). Source Ratio 100-yr 24-hr rainfall August 25-30, 1951 rainfall September 4-6, 1970 rainfall .11 .21 .31 62 3.2.2.2 Rain Ratios for Central Arizona. Other sets of data analyzed were for the prominent slopes north and east of Phoenix. Figure 3.6 is a map of the region with generalized contours and precipitation stations. Figure 3.7 shows the rainfall for these stations during the August 25-30, 1951 and September, 4-6 1970 storms, plotted vs. station elevation. An eye-fitted curve is shown for the August 1951 storm data. If one computes the rain ratio of the curve in figure 3.7, a value of 0.28 is obtained (1.05 in. per 1000 ft/ 3.7 in.) Rains of one month or longer could be useful for guidance on rain-elevation relations for this same region (fig. 3.6.) We used mean July to September rainfall after adjusting it by a f requency-of-rain vs. elevation relation (not shown). The resulting rain ratio was 0.18, not greatly different from the approximate 0.28 of figure 3.7 for the August 1951 storm and the average rain ratio of 0.21 in table 3.2 for the same storm. GENERALIZED ELEVATION (1000'S FEET) p^ \#6. PAYSON rJ. V 51 / Wtih STATION NUMBER (SEE FIGURE 3.7) . YOUNG 5100' ~>vL dL'8. WORKMAN CREEK 6790'. /"J \Vt/"V ^- 9 - t J pp E R PARKER CREEK 550 7- 5- 4- 3- 2- 1- LEGEND 1. PHOENIX 2. BARUETT DAM 3. SUNFLOWER 4. SIERRA ANCHA 5. YOUNG 6. PAYSON RS 7. SUPERIOR SMELTER 8. WORKMAN CREEK 9. UPPER PARKER CREEK (STATIONS LOCATED IN FIGURE 3.61 • AUGUST, 1951 STORM DATA ^SEPTEMBER, 1970 STORM DATA -1 RAIN-ELEVATION RELATION FOR AUGUST. 1951 STORM DATA 10 I 1 1 12 , I (IN.) 50 100 150 200 250 300 (MM) RAINFALL Figure 3.7. — Rainfall- elevation relation for August 1951 storm 3 and rainfall for September 1970 storm. For maximum monthly rains in the same region, the variation with elevation is not as closely tied to the frequency of rains. The air in such months would tend to be more nearly saturated at low elevations, (as with the rains for the PMP-type storm), in comparison to mean monthly rainfall cases. With the above in mind, a relation between rain increases and elevation for warm- season maximum monthly rain was developed. These rains give a rain ratio of about 0.19. This appears to give reasonably good agreement with the rain ratio from major storms that are the prototype for the PMP in this portion of the study region. 3.2.2.3 Effects to Lee of Ridges. The decrease of rainfall to the lee of a major ridge in Arizona for each of the two important warm-season PMP-proto- type storms of August 1951 and September 1970 was compared to the decrease in the 100-yr 24-hr rainfall. The rainfall along a line through the rainfall centers extending leeward normal to the ridge is the basis for the compari- son. Figures 3.8a to 3.8c show the analyzed isohyets and figure 3.9 shows the comparisons. 64 4^ <>v> * ro && *■ O 8-rS o Oi t-H CO »-Q ft Jh I Si I 0) « o CO I i oo to — CO z UJ ex. 00 1 o (N o >■ CO o < UJ o o o_ UJ co X O CO 00. CN CN O. CN 0_ CN_ O CN O .CN Q o UJ Z < 00 CO s o +i o '9 s G o +i . S co 0) . c^ 0) . Gj Gi s » 6 e? ^ g G •^ pq G Sh •Xj CO is £ G V 3 G 0) Sh ^ Sh 1 r« I I . Ml 0} C\] CO 6h I JJN3Da3d 67 c. Mean monthly or mean annual precipitation maps exaggerate orographic effects because of a greater frequency of rains at higher elevations. Such maps should be used with caution as guidance to PMP distribution. 3.2.3 Modifications to Index Map The guidelines summarized above and other aids, were used to modify the first approximation to the orographic PMP index. For such modifications it was expedient to first classify the region into three terrain categories: areas with (1) most- (2) least- and (3) intermediate-orographic effects. 3.2.3.1 In Areas of Most-Orographic Effects. The most important guideline for these areas was to try to make the gradient of total PMP about twice that of the 100-yr 24-hr rainfall. Additional detailed analyses in prominent upslope regions (see example in fig. 3.10) resulted in the rule of moving orographic rainfall centers from 2.5 miles (4.0 km) to 5.0 miles (8.0 km) downslope from the ridgelines. This helped meet the criterion for the grad- ient of PMP to be twice that of the 100-yr 24-hr rainfall. In some terrain, i.e., where the ridges are small or close together such rules do not apply. (FT X ltniKMI 100 90- 80 70 uj 50 40 30 20 -20 -1.5 I -iO "T -20 (KM) 10 DISTANCE FROM RIDGE Figure 3.10. — Example of profiles of several rainfall indices (in per- cent of maximum values). 68 The objective procedure of moving the orographic center downslope was also, in some instances, largely negated by the subjective increases for nearby slopes facing differing directions. Maintaining an allowance for stimula- tion on the lower slopes also tended to negate the initial aim of doubling the upslope gradients of the 100-yr 24-hr precipitation. 3.2.3.2 In Areas of Least-Orographic Effects. A map of least-orographic areas was useful in establishing limits to orographic precipitation gradients, delineating sheltering effects, and providing guidance in modifying the first approximation orographic index map. Figure 3.1 integrates the independent interpretation of least-orographic areas by three meteorologists in accord with the following guidelines: a. Areas where mean annual precipitation was less than 8 inches. b. Areas where the first approximation to an orographic index map showed less than 10% increase over the convergence component developed for August in chapter 2. c. Areas where the orographic component of total PMP from the method de- scribed in section 5.7 was less than 50% greater than the convergence compo- nent. For the Southwest States a lower limit of 1.0 inch (25 mm) orographic PMP in 24 hours was set in least-orographic regions. Such rainfall in these regions is attributed to either spillover from upwind ridges or to a general- izing (spreading out of the influences of small ridges or hills that make up a part of most areas classified as least-orographic. Within portions of the outlined least-orographic areas, the threshold of 1.0 inch (25 mm) in 24 hours was increased. For example, rainfall gradients to the lee of upwind ridges at times suggested higher values. In effect, the original areas of least-orographic rainfall, figure 3.1, were decreased in size and their bounds smoothed. 3.2.3.3 In Areas of Intermediate-Orographic Effects. Intermediate orograph- ic areas were those remaining after areas of most- and least-orographic ef- fects were considered. The intermediate areas are usually a mix of nearly flat areas with enough small orographic features to preclude classification as least orographic. The following factors should be kept in mind in connection with the inter- mediate areas. a. With light winds predominating in ordinary rain situations (producing values contributing significantly to MAP charts and lesser values in the series of precipitation amounts used in developing frequency maps), the effect of small orographic features are overly emphasized relative to what one can expect from strong winds in a PMP storm situation. Note that figure 3.1 differs somewhat from least-orographic regions of fig- ure 2.1. The latter was influenced by availability of station rainfal data. 69 b. With the varying wind directions possible in PMP storms, orographic effects can be spread out in numerous directions from small areas that act as foci (or stimulation points) for rainfall. To get away from the overemphasis of orographic effects (point a.)) the overall orographic precipitation increase for a particular orographic feature was reduced by 50%. However, a compensating feature stemming from point b. was to spread influences from foci or orographic increases over a larger area. We increased by fourfold the area influenced by small orographic fea- tures . 3.2.3.4 Other Modifications a. Isohyetal peak rainfall centers in the most-orographic regions, cover- ing areas of up to about 100 mi 2 (260 km2), were eliminated. Most indices of rainfall have a built-in increase with elevation derived from depending too closely on MAP. Where peak MAP values over small areas are supported by data, we feel they must be due to ordinary rains as compared with the strong diversion of air that must take place in major storms. b. Additional smoothing was done in areas where 100-yr 24-hr rain values were low and had a small range (2.2 to 2.8 inches, 56 to 71 mm). We believe the small range in 100-yr values indicated such smoothing as realistic. This was done regardless of orographic classification. 3.2.4 Modified Orographic PMP Index MAP Figures 3.11 a, b, c and d are the adopted orographic PMP index maps cover- ing the Southwest States. Figure 3.11a covers the northernmost portion (down to latitude 40°N) while figure 3. lid covers the southernmost portion with figures 3.11b and 3.11c covering the intervening region. The maps overlap by one degree of latitude. This index is for 24 hr 10 mi 2 (26 km 2 ). Linear interpolation may be used between the isolines for obtaining an average index over a basin. However, within any closed high or low center, the value of the last enclosed isoline should be used. The remainder of this chapter covers extension of orographic PMP to all 12 months, to durations from 6 to 72 hours and basin sizes from 10 to 5000 mi2 (26 to 12,950 km 2 ). 3.3 Seasonal Variation 3.3.1 Introduction Seasonal variation of PMP is always difficult to define because the rain- fall sample is increasingly limited. For the Western States the problem is especially difficult because of com- plicated terrain influences which do not permit direct transposition of storms. The approach adopted for the Southwest States was to tie into the seasonal variations of HMR No. 43 and 36 near the boundaries and utilize various rainfall indices within the region. 70 3.3.2 Boundary Regions Seasonal variation for the Northwest States (HMR No. 43) is given for the months October through June. A separate variation was determined for each of four zones, three of which border our study region. Elevation plays a part in differentiating among the zones. By analysis of station maximum observation-day precipitation of record, the seasonal variations for the three zones were smoothly extended through the remaining 3 months. Percent of the August values for each month are shown in table 3.3. Table 3.3. — Seasonal variation east of Cascade Ridge in Northwest States as percent of August Zone in HMR No. 43 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec B 91 91 95 87 74 67 84 100 107 108 107 104 C (5000 ft) (1524 m) D The seasonal variations of HMR No. 43 stress winter maximum values west of the Cascade Ridge and in a region to the east of the ridges (Zone B) . May through October are the maximum months near the eastern borders of the Columbia River drainage (Zone D) . Between these is a transition zone with a maximum from late summer to early winter; the importance of winter maximum increasing with elevation in zone C. From HMR No. 36, the seasonal variation for the west slopes of the Sierras is adopted for use at the western border of the Southwest Region. Again it was necessary to extend the seasonal variation given there throughout the year or over the months of May through September. Maximum observation -day precipitation amounts for high elevation orographic stations were used for this extension. The results in percent of August are shown in table 3.4. Table 3.4. — Seasonal variation in Pacific drainage of California as percent of August Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 106 106 102 97 91 91 96 100 103 104 104 105 92 92 91 94 98 97 98 100 100 100 99 96 90 90 90 95 100 100 100 100 100 98 97 94 71 >5 50 -i ' 1- 50 100 DISTANCE SCALE 75 100 -J 150 (IN) 10 - 200 6 — 4 — - 100 (26-km 2 ) 24-hr orographic PMP index map (inches), northern section. 70 3.3.2 Boundary Regions Seasonal variation for the Northwest States (HMR No. 43) is given for the months October through June. A separate variation was determined for each of four zones, three of which border our study region. Elevation plays a part in differentiating among the zones. By analysis of station maximum observation-day precipitation of record, the seasonal variations for the three zones were smoothly extended through the remaining 3 months. Percent of the August values for each month are shown in table 3.3. Table 3.3. — Seasonal variation east of Cascade Ridge in Northwest States as percent of August Zone in HMR No. 43 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec B 91 91 95 87 74 67 84 100 107 108 107 104 C (5000 ft) (1524 m) D The seasonal variations of HMR No. 43 stress winter maximum values west of the Cascade Ridge and in a region to the east of the ridges (Zone B) . May through October are the maximum months near the eastern borders of the Columbia River drainage (Zone D). Between these is a transition zone with a maximum from late summer to early winter; the importance of winter maximum increasing with elevation in zone C. From HMR No. 36, the seasonal variation for the west slopes of the Sierras is adopted for use at the western border of the Southwest Region. Again it was necessary to extend the seasonal variation given there throughout the year or over the months of May through September. Maximum observation -day precipitation amounts for high elevation orographic stations were used for this extension. The results in percent of August are shown in table 3.4. Table 3.4. — Seasonal variation in Pacific drainage of California as percent of August Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 106 106 102 97 91 91 96 100 103 104 104 105 92 92 91 94 98 97 98 100 100 100 99 96 90 90 90 95 100 100 100 100 100 98 97 94 FIGURE 3.11a-10-mi 2 (26-km 2 ) 24-hr orographic PMP index map (inches), northern section. 73 100 6-km 2 ) 24-hr arographic PMP index map (inches), north-central section. 3 4 5 5 4 3 3 4 5 6 10 8 6 665445 5432 2 3443 3 3 3 3 3 4 5 NW1 Mexico FIGURE 3.11b.-10-mi 2 (26-km 2 ) 24 hr arographic PMP index map (inches), north-central section. 75 25 l • 37 c 106° (IN) (MM) 28 - -800 24 _ -600 • 20" -500 16" -400 12- -300 8- -200 4- -100 • 35° 0- -0 107° 50 75 i l 50 100 DISTANCE SCALE 100 I 150 km 2 ) 24-hr orographic PMP index map (inches), south-central section. ISTANCE SCALE FIGURE 3.11c.-10-mi 2 (26km 2 ) 24-hr orographic PMP index map (inches), south-central sectic i (26-km 2 ) 24-hr orographic PMP index map (inches), southern section. 35°. 119' ST. Ml. DISTANCE SCALE f — 5 6 8 FIGURE 3.11d.-10-mi 2 (26-km 2 ) 24-hr orographic PMP index map (inches), southern section. ■^M 79 3.3.3 Indices Within the Region 3.3.3.1 Maximum Precipitation at High Elevations. On the mountain slopes north and east of Phoenix, Ariz, the maximum observation-day rainfalls of record for seven stations for each month of record were averaged. Highest average values were equal for August and September, Lowest values (61% of highest) were in May. Use of these data as an index to seasonal variation of orographic precipitation assumes either that the precipitation is entirely orographic or that the seasonal variation is the same as that for convergence precipitation. Probably these stations come closer to being an index to orographic variation than any other stations in the Southwestern States where the terrain is more broken and complex. It would also assume no regional variation in the pattern of seasonal variation. The seasonal variation of maximum observation-day precipitation (by month) was further evaluated at high-elevation stations at various locations in the Southwest States. In northern Nevada, a seasonal plot of the data showed a fall maximum with relatively little variation through the winter. In south- western Wyoming and extreme northeastern Utah, spring maximums predominate with a secondary maximum in early fall. Stations in Colorado north of about 39° N indicate a broad summertime maximum extending from June through September. These data, when averaged, gave an estimate of seasonal varia- tion near the center of the region (the northern border of Arizona.) July, August, and September gave about equally high values. The lowest values, in May and June, averaged 80% of summer. 3.3.3.2 Maximum Winds and Moisture. A physical index of intensity of oro- graphic precipitation at a given location is the product of the strength of the horizontal wind normal to the mountain and the moisture content of the air column. This index was evaluated seasonally from upper-air observations at Tucson, Ariz. From the twice-a-day observations (1956-69) a series of maximum southerly wind components were determined for each month for the 900- , 700- , 500- , and 300-mb (90-, 70-, 50-, and 30-kPa) levels. The 0.01 probability southerly components were then computed using the log-normal distribution. These monthly wind components were then expressed in percent of the highest value of the 12 months for each level. Precipitable water through' the 300 mb level associated with the maximum 12-hr persisting 1000-mb (100-kPa) dew points assuming a saturated pseudo- adiabatic atmosphere for each month at Tucson were also expressed in percent of the highest value. Multiplication of the percentages of wind and moisture for each month gives an index to the magnitude of moisture transport. The highest value of this index was about the same for August through October. December through May averaged 78%. 3.3.3.3 Orographic Model Computations. The detailed orographic precipita- tion computation model described in HMR Nos. 43 and 36 was applied to 10 80 profiles in a steep upslope region. Five of these were north-south slopes north of Phoenix; the others were SW-NE slopes near the same location. In- put to the model were maximum winds at Tucson described previously and mois- ture based on maximum 12-hr persisting 1000-mb (100-kPa) dew points. The computed precipitation for the 10 slopes was used as another seasonal index to orographic PMP . September gave the highest orographic precipitation of the 12 months followed by October (92% of September) and July (81%). Decem- ber and January were the months of lowest values (68% of September) . 3.3.4 Smoothed Maps Recommended seasonal variation of orographic PMP is provided by mid-month maps, figures 3.12 to 3.17, showing isolines of percent of the orographic index. The several different indices discussed were used as guidance in these analyses. The maps have been adjusted to yield smooth seasonal curves at grid points covering the region. 3.3.5 Supporting Evidence Division of total storm precipitation into two components (convergence and orographic) is uncertain; therefore, direct use of rainfall data to check the seasonal variation of orographic PMP was not attempted. We prefer to evaluate the seasonal variation of total PMP as determined from the criteria developed. 2 2 Twenty -four-hr 10-mi (26-km ) PMP for each month was computed for each point on a 1° grid covering the Southwestern States. The regional pattern of month of maximum is shown in figure 3.18. June gives maximum total PMP for a small portion of the northeast corner of the Southwest. Winter or fall months dominate the northwest portion. The tropical cyclone during August and September dominates three-fourths of the Southwestern States. In recorded history only a small number of such storms have had important effects on the Southwestern States, mainly Arizona. The storms of September 1939, October 1911, August 1951, and September 1970 were most intense. A map was plotted (not shown) that presented a composite of all pertinent tropical storm rainfalls greater than 2.0 inches (51 mm), regardless of duration. A large void in tropical cyclone rainfall existed across most of Nevada eastward to the Wasatch Mountains in Utah. Yet, composite weather maps for some of the tropical storm situations suggest that at some time in the future, only slight changes in synoptic features could bring tropical cyclone-related rainfall into nearly all of Utah and much of Nevada. The infrequency of this storm type means a very long record is needed to delin- eate the effects of such storms. Checks were also made from more commonly observed precipitation. One analysis of the month of maximum 24-hr station precipitation in the Western States appears in a study by Pyke (1972). His analysis of these data re- vealed that much of the Southwest experienced a bimodal distribution of precipitation. Figure 3.19 shows Pyke's results, where the season and 81 o o r to o , ^ // 1 i 00 o o iO CO v 1 y i / CI \ '1 V ' / V 1 o \ CO i / <^~~"^ o O °o *"" — "s*'*^ ' / l /• * • • » i— /-p- i _ -i V • ■O ~N f CD \_l i r | V - -' - -- ' — J — ~> . . . 5 • j ~ i . ■^ ^ ^ " J 7." 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C \ J ^-T — -*o o \ 1 ^ \. co -^ 1 s. - • — 3 O 1 ^»^ i I °o ^~ — 'r^^ ' 1 ^*> 1 » 1— -f- 1 f \ i 1 _ -J 1 I i r i r i ' -*— ■X.O 00 "t J ~) . /Os 5 ^^*i^ o / / > "■—i^ "* "■" / o -f in ex o O-i n o -o / Jio UJ O o- CN o -o ( ° < CO o o o l/> -o o ~~ """""^r -" — i LU u z O o- CN Vii* -o o 1 3 V TD •— CO Q o — -o xr O -<* 1 - o V v> ^TiSw i \ 1 °o m / ! — ' - -• ' — "i ■ i ■ i ' _ _ o o I™* "■"V^^ • — r— o - 1 - 1 1 • i i i ■ i i i t • i ! ' • / / / "^ ^1 Ao o o- $ tt *9 o St •^ « M s toi o 5s o ?H r« ■* C\l — N T~H CK] rs r2 tyj to 05 CN3 ^ ^- s <33 CK1 -^ V «K I s to V V-H to £ 0) V 3 t<> £ « O » •^ . ■P ^ « o •^ G S Pi s s ion ( 0) IN- C^ t-h Q5 • 5s ^5 0) ^ 5s S S-fS tn co •^> &s 87 O o -I- o CO O 1 / 1 \s I \ 1 / I ' II ' °o o — ^^ » >^ • ^ uj • CO I O CN - ' o .1 en CO UJ z < to Q o o— -o CN _o o 1 -o T CtjCN] 88 month of primary maximum is indicated, and the secondary maximum is given in parenthesis. There is general agreement between month of maximum shown in figure 3.19 and that of this PMP study shown in figure 3.18, particularly considering the need to extend beyond the raw data, which necessarily has in it much bias toward showers. August has a maximum on the southeastern third of the region in Pyke ' s study and is a secondary maximum through much of the remainder except the northwestern corner. The month of May dominates along the northeast to north-central border of the region, while April appears to dominate in central Nevada to northwestern Utah. The winter maxima of 24-hr precipitation in January and February along the western portion of the South- west differ from the month of maximum PMP in a similar way. While both areal and point storm rainfall show a winter or spring maximum, the latent pos- sibility of tropical storms, so infrequent in the storm data shifts the PMP to late summer . An analysis of season of maximum monthly precipitation over the Great Ba- sin was made by Houghton (1969). While monthly precipitation is not a good index to PMP for durations up to 3 days, the comparisons with PMP may be of interest. His conclusions apply to the Great Basin, roughly the northwest- ern half of the Southwestern States. There is general correspondence be- tween Houghton's results and those of Pyke. The larger expanse of spring maximum in Houghton's work is the major disagreement with the PMP analysis. The seasonal analysis of PMP shown in figure 3.18 is considered justified on the basis of the PMP storm prototypes and the relative potential for precipitation in the various months. 3.4 Variation With Basin Size 3.4.1 Introduction The orographic PMP index (figures 3.11 a to d) is for the 24-hr duration and a lO-mi^ (26-km2) area. For application to specific basins, it is necessary to define a depth-area relation. Depth-area relations for the orographic PMP index maps are controlled by the steepness, height, length, orientation, and exposure of each slope re- lative to moisture bearing winds. There is a limit to the lateral extent over which moisture can be transported over mountain slopes without some decrease in intensity. This was assessed for the Sierra Mountains in HMR No. 36 by a study of the variation of pressure gradients with distance be- tween stations that take pressure observations. Figure 3.20 shows this variation by the dashed curve. An additional factor is required for the present orographic index. This is the way the index was developed. Inflow from several directions was considered in determining the magnitude and gradient of orographic PMP. However, for any particular 6-hr period of the PMP storm over a given drainage, the winds would generally be from one direction and thus have an orographic influence for slopes normal to that direction only. 89 *i2 OO < UJ OH U LU o o o * / CN CN o . o z O o o o H o o o o < X 1 CM / U / < lot- Zu \%\ ' CN Of o u_ — 1— z LU u Q£ LU a. Z LU o z < Of — _L 1 1 <- 1 ->■ 1 o o o — o o o o o o o o o -<* o go ° o CN % o o o o CN o •o o o -< o o o CN ^ 0£ < CO < 0) CO K CO « 3 53 o o o I o o o o o 00 o o •o o 2 W>I93) 2 IW0l dO !N3Dci3d 90 An approximate method was used to take into account both the reduction due to lateral extent of a basin and the fact that at a given time slopes orient- ed in only one direction can be effective. This was to analyze the depth- area relations of most orographically-inf luenced rainfalls for major storms of record in the Southwestern States. The approximation is that we assume precipitation at high elevations is mostly orographic. 3.4.2 Storm Data. The storms used in the analysis are listed in table 3.5 along with the 10-mi 2 (26-km 2 ) precipitation for 24 and 72 hours. The 1000-mi 2 (2590 km 2 ) values for 24 and 72 hours are given in percentages of the 10-mi 2 (26-km 2 ) values. Some storms with centers at lower elevations, such as the September 3-9, 1939 storm in California, were omitted from the storm sample. If the duration of the storm is less than 72 hours, the actual duration is aster- isked in the right-hand column of table 3.5. All storms occurred within the southwest study region. 2 2 Figure 3.21 shows 1000-mi (2590-km ) 72-hr precipitation expressed in percent of the 10-mi 2 (26-km 2 ) value. The data do not suggest a simple re- lation between magnitude of rainfall at 10 mi 2 (26 km 2 ) , and the percent at 1000 mi 2 (2590 km 2 ) . A similar plot (not shown) for 24-hr durations 100 - u- 90 O 70 60 50 40 60 • (•) • • (•)« (•) !•) !•>• (•)• • 13.5- 343MM" (•) 80 T - r - 140 — — 100 120 10 Ml 2 (26 KM 2 ) 72-HR PRECIPITATION NOTE: DOT IN PARENTHESIS (•) IS FOR A STORM OF SHORTER DURATION 6 I 160 7\ 180 200 1 9 (IN) 220 (MM) Figure 3.21.— 1000-mi (2590-hm ) storm depths relative to 10-mi 2 (26-km 2 ) depths for 72-hr rainfalls. 91 CO cd <4-l 3 3 rH •H CO CO > U CM -K * * * * * * CM •H o vfj O CO Cn 00 CTi 00 CTi CT\ 00 CT» r^- r^ r~ CTi 00 00 CTi m vO o o 4-1 ■H rH O X O. 5-1 B^S cO ,3 5-i 1 s 60 CM •H o u o r*» 4-1 CM o ■H •-\ e rH •--\ r^ en CT\ -d" o O o r^ r^ cr\ co m m o CO CO CM < r^ vo en H r^ co o r^ vo oo O rH O o CO g rH rH ^ rH rH rH rH rH rH rH rH rH rH rH CO CM rH rH CM Vw' H H v-'v^v^h rH •H lH 4-1 \_^ v^/ 4-> 3 co 5-1 •H •H .3 cfl • 00 CO en en rH CO CT> oo oo r-» so co m co m o vO rH CM 00 CO r~- rH CD M rH CO 1 CO a) X m 3 4-) s rH ex •H CO T3 5-1 CM 00 CN •H 3 •H £ o o 00 CM in o r^ CM CO 00 o\ »d- o r-^ rH > g r-l /■^ 00 vO rH CM CT\ On en o\ CM CM cr> rH H v_^ n-' CM N— ' »_• v_^ v.^ v_x \_^ \_^ ^-^ o 3 c rH 4-1 v—' v_^ S/ N— / **s V-' v— y ^^" v—* Vw* o aj CO U 3 •H rH 43 4-J CO ,3 CO • CO o cm «d- r-- Cn rH r^ O O CO o\ 00 CO ct. r^ r~- CT» rH vO oo j m co M3 r» r^ rH rH O 00 OS rH CM r^ r- cm rH co II 3 rH O o o o O o H rH rH CM CM CO " ~* m r^ o O rH rH CM CM " co CD CTi en Cn Cn ON OA CTi CTi CT» 0\ CT» CTv CTi CTi o> c?\ 5-i •> ^ CO #V a * « oO *^ *» X 3 5-i N r. O CO 00 n r^ St O O " CM ». CO !>• CM 00 S rH rH ~ 5-1 r^ #* * rH en o 3 en co •> CO 3 o 3 e •H t^> CM rH CM co r-^ O rH l-~ vO CM CM rH j O CO M3 rH v£5 CO o vo vo r^- m oo rH rH & 4-1 rH CM rH r-l rH CM H CM rH CM CJ rH rH CM CM CM rH CO • • u CO 4-J • 0) 4-J **, .4->Q) CU 4-1 O o 4-1 CO x> 5-1 U > u a u C C 5-1 43 J3 ^1 5J oo a, O CX 4-1 5-i 3 O- rH M ft C >n 3 •K CD 3 ex o 0) CD a) co co a, a; cu cj to Fn Pn fe S 3 CD 0) QJ CJ S 3 Q) 3 3 OJ 3 Pn < !Z5 a Q Q •-> >-5 < < CO Q CO O O en o < to o s 92 2 2 indicates a slight trend of lower percents for the greater 10-mi (26-km ) values; however we do not believe this trend is significant. We chose to use a depth-area relation not related to magnitude of the 10-mi 2 (26-km 2 ) value o Another aspect of depth-area variation is whether one relation can be used for all months of orographic PMP. The 1000-mi 2 (2590-km 2 ) 'rainfall for 24 hours, in percent of 10-mi 2 (26-km 2 ) values, column 2 of table 3.5, were averaged for each month. The results did not show a clear-cut seasonal trend. Similar analysis of 7 2-hr values was also inconclusive. The limited number of storms and their uneven seasonal distribution are handicaps in defining seasonal trends. Without data to indicate otherwise, and to avoid unduly complicating one aspect of the PMP criteria, we recommend use of one depth-area relation for all months. 3.4.3 Adopted Variation An average depth-area relation was developed from the 17 storms in table 3.5 with 10-mi 2 (26-km 2 ) 24-hr amounts _> 3.0 inches (76 mm). These averages are shown in figure 3.20 separately for the 24- and 72-hr durations along with the range in ratios from the two durations indicated by arrow points. The averages are somewhat less than the adopted areal variation used in the adjoining Northwest Region (HMR No. 43). Considering the ranges in the data, and that nonorographic precipitation in the data would tend to lower the ratios, we recommend the same areal variation as in the Northwest Region. This is the solid curve shown in figure 3.20. 3.5 Durational Variation 3 - 5 c 1 Background Variation of orographic precipitation with duration depends on the duration- al variation of winds and moisture,, The measure of moisture used in this study is surface dew point. During major storms there are periods when depth of the moist layer is limited by drier air aloft. In a study for the Northwest (HMR No. 43) a variation in relative humidity with duration during the 3-day PMP storm was introduced, based upon some recent storms of record. For com- putations of PMP with the orographic model on the Sierra slopes of California (HMR No. 36) an equivalent procedure was used for taking into account the variation of relative humidity. This was to calibrate the computed oro- graphic precipitation by comparison with observed values. The longer the duration, the lower the calibration factor. We postulated that the lowering in relative humidity was responsible for variation of the calibration factor with duration. In this section durational variation of winds, moisture, and relative humidity for data in the Northwest and California study areas will be com- pared with similar data for the Southwest. Finally, an adopted variation will be described. 93 3.5.2 Variation of Maximum Winds The variation with duration of maximum 6-hr incremental winds for 500- and 900-mb (50- and 90-kPa) pressure levels is shown for Tucson, Ariz, by the solid curves in figure 3.22. These variations are the average of 10 windy periods for each level that contained the highest instantaneous winds at 100 o 90 80 70 O 60 50 40 30 _ HMR NO. 36 (HG. 5-25) HMR NO. 43 (RG. 4-35) THIS STUDY - I ■ I 1 I 1 6 8 6-HR PERIOD 10 12 Figure 3.22. — Durational variation of maximum winds at Tucson, Arizona compared with variations for adjoining regions. Tucson (1956-69) . While the instantaneous winds were definitely greater during the winter months, the amount of variation with duration did not show a consistent correlation with time of year. For each of the windy periods, the highest average wind for consecutive observations was determined, and each durational average expressed in percent of its instantaneous highest value. From twice-a-day observations, 2 consecutive observations were con- sidered for a 12-hr average, etc., to 7 consecutive observations for a 72-hr average. The durational decay of winds was then converted to give the dura- tional variation of 6-hr incremental winds. The 10 cases were then averaged. 94 For comparison the durational variations for these same two levels for the Northwest (HMR No. 43, fig. 4-35) and California (HMR No. 36, fig. 5-25) are shown in figure 3.22 by long and short dashes, respectively. The variations for the two adjoining regions are quite similar because most of the basic data was the same. The Tucson winds have a decidedly greater decrease with duration. This is reasonable from the standpoint that the Tucson winds were restricted to the southerly component, the important direction to moisture inflow for most of the Southwest study region. Extreme westerly winds are stronger and longer lasting. 3.5.3 Variation of Maximum Moisture Highest 12-hr persisting 1000-mb (100-kPa) dew points are used as the index to moisture assuming a pseudo-adiabatic lapse rate. For the Southwest States, 12-hr persisting 1000-mb (100-kPa) dew points for durations extending out to 3 days (U. S. Weather Bureau 1948) were considered at 7 stations well spaced over the region. The maximum persisting dew points for 6, 12, 24, 36, 48, 60 and 72 hours for each of the 12 months at each station were expressed in inches of pre- cipitable water assuming a saturated psuedo-adiabatic atmosphere and then in percent of the 12-hr values. Smooth seasonal curves (not shown) of these percents for each duration were then constructed. These curves showed small random fluctuations in percents for each station not forming a discernible regional pattern. Table 3.6 lists the 7 stations and the 12-month average 3-day moisture in percent of the 12-hr moisture. One durational curve was adopted, as shown in figure 3.23. Similar curves for California and the Northwest are shown for comparison in the figure. Table 3. 6. — Durational variation of maximum moisture of the Southwest 3-day moisture in percent of Station max. 12-hr moisture Grand Junction, Colo. 84 Salt Lake City, Utah 82 Winnemucca, Nev. 80 Tonopah, Nev. 80 Yuma, Ariz. 84 Phoenix, Ariz. 82 Modena, Utah 79 95 no 100 90 80 — 70 ADOPTED FOR SOUTHWEST HMR #36 HMR #43 12 24 36 48 DURATION (HRS) 60 72 Figure 3.23. — Durational variation of preoipitable water. 3.5.4 Variation of Relative Humidity Four recent storms in Arizona (two in winter and two in summer) were selec- ted for analysis of relative humidity (RH) from the surface to 500 mb (50 kPa) . The average surface to 500-mb relative humidity for each of two sound- ings was plotted on a time graph for each storm. From a smooth curve join- ing these data, the maximum 6-, 12-, 18-, 24- . . . hr relative humidity for the surface to 500 mb was determined and expressed in percent of the 6-hr value. The storms considered and the durations averaged are shown in figure 3.24. An envelopment of these percents is given by the upper solid curve in this figure. For comparison with the variation used in HMR No. 43, the dura- tional curve was expressed in terms of 6-hr incremental RH values. This is shown by the lower solid curve. The comparable RH values from HMR No. 43 are given by the dashed curve. The variation based on four Arizona storms generally shows a greater decrease with succeeding 6-hr increments. 3.5.5 Orographic Model Computation One method of evaluating the durational variation of precipitation is to make computations with the orographic computation model. Tests of the de- tailed model (which includes consideration of the slope of the inflow wind profile) show that resulting durational variations are strongly dependent on the height and length of the slope so that a different durational variation would result for each different ground profile. 96 ¥ 80 — - . 1 1 1 1 1 1 - t nN. ^DURATIONAL VARIATION ARIZONA STORMS / (durational variation) N^ • ^ — , -^/ • AUG. 26-29. 1951 - + X SEP. 3-7, 1970 — t + DEC. 14-17. 1967 \> ^ • ^""*"— ■—, ^ i o MAR. 22-25. 1954 x\ ~~~— - -^ • _ X v—- _ ° 6-HR INCREMENTAL ^ \. \-HR INCREMENTAL VARIATION VARIATION ^^FROM HMR #43 (USWB 1966 b) ' 1 1 1 O 1 o o 1 1 24 36 48 DURATION IHRSI Figure 3.24. — Adopted durational variation in relative humidity and supporting data. A simplified orographic model (World Meteorological Organization 1973) was used to evaluate differences in precipitation with duration. This is Ap R = V. (3.1) where : R = precipitation V = mean inflow wind W, , WT = inflow and outflow precipitable water Ap ,Ap»= inflow and outflow pressure differences Y"= horizontal distance. This model also yields somewhat different durational variations depending on the height of the terrain profile, but the differences are not as great with this simplified model since the inflow wind profile is given as one average value. We believe it is a satisfactory tool where only relative magnitudes are required. For the computations, the winds, moisture, and relative humidity for the northern border of the region were obtained from HMR No. 43. Near the south- ern border we used the values of parameters in Arizona described in 3.5.2 to 3.5.4. A lift of 150 mb (15 kPa) was assumed at both locations. For the southern location the slope is from 1000 mb (100 kPa) to 850 mb (85 kPa) . For the northern location it is from 850 mb (85 kPa) to 700 mb (70 kPa) . The Y distance is held constant. A nodal surface of 300 mb (30 kPa) is assumed. The mean inflow wind for the southern location is an average of the 900- , 97 700- , and 500-mb (90-, 70- and 50-kPa) winds. For the northern location, it is an average of the 700- and 500-mb (70- and 50-kPa) winds. Table 3.7 shows details of the computations made for the 1st, 4th, 8th and 12th 6-hr periods. Rainfall computations were made for January and August in both lo- cations. The 12th period averages 33% of the 1st for the southern border and 39% for the northern border (fig. 3.25). The southern location shows 6% more decrease in precipitation than the northern border region (relative to the first 6-hr value) for each of the 6-hr periods. T T T T 100 —J —I < z < £80 Q o "60 40 Z OJ U 20 T T T T NORTHERN BORDER AVERAGE SOUTHERN BORDER AVERAGE NORTH . JAN. . X AUG. SOUTH © JAN. 9 AUG. 6 8 6-HR PERIOD 10 12 Figure 3.25. — Durational variation in orographic precipitation near northern and southern borders of Southwest region (from orographic model). 3.5.6 Guidance from Observed Precipitation HMR No. 36 Rev. (U.S. Weather Bureau 1969) shows a tendency in more intense storms for less decrease in rain for longer durations in the north than in the south. This latitudinal variation in the durational variation of orographic PMP was based on observed precipitation along the Coastal and Sierra Mountains of California at high elevation stations during major storms. Since orographic precipitation is dependent on the strength of moisture- bearing winds flowing against the mountains, one could expect >a greater de- 98 CO cu ■u 3 •u c/1 CO CU rs 4-1 rH o M-l a o •H •U 3 4-J •H Cu •H a cu u ex r-l oo o rH o 14-1 o a o CO CO a o •H 4-1 CO U T3 o •H 4J 4-1 3 | o u I I en CO H cu rH CU o e o •H J3 a cO u 60 O r-l O T3 CU 3 •H CO 3 cu T3 o 3 CU .3 4J 3 o CO rH CO cu 3 CU rH o ,0 s u CU 4J 5h o (3 S-i CO CU cO Ch O o CO I o o e o o o o CO I o o o Ch < cO 52 m m o co l m oo o m m o o CO I o m oo Ch cO Ch M m in o ro l m oo ■i o m m o o oo l o m oo Ch < CO Ch o o en I o •i o o o o CO l o o CM Ch < c •H CU CO cO cu u CJ CU 00 3 •H rH CU •H CO 3 o o u cu 4J cO & CU rH ,Q CO 4-) •H (X •H a cu Sh Ch 4J CO 3 00 I CM cO 3 cO 4-> CO 3 00 u cO 3 3 CO g vo in vo cj\ g in N_^ V— ' V— ' . rH vO CM 00 c cn r» 3 o vo m co . 00 rH >~\ /"> /""N y—\ ^^ O 3 g m o oo oo m r-l w/ •3 o r3 H O 4-1 4J •H r~N •— \ /""s /-n ^^ 3 rH g cm r- r-l u • m t^ co cm CU 3 r3 3 oo vo m r-^ O 3< 4-1 3 r^- m >a- J3 rH 3 <3 g •d- . •H a • # w (X 3 CD r-l o g 3 3 O CM rH CO o r^ m co T3 O 3 iH /"S /'-v ^— \ /^N ^-\ 3 rH 3 g m cm o oo •H "4-4 •-> g rH lH rH v-* ^ s-^ v_> <<^> V— ' N-^ CU Pd • O r>. o> cm 00 3 VO «* CO CO 3 •H m • • • o U CU 4 rH *T3 3 O -H ^3 )H 1 cu vo a- rH 4-1 01 c CO CO a) 4-1 CO 4-1 co C J-i CD 4-1 Cfl 0) !3 £1 •u d o CO a) *c 4-) C •H O cj CD U MH o c ■H CO >h XI O •H 01 I 4-1 U o rG en to E 3 - - o 60 C 3 01 01 c c o o a o CO •H rH rH 10 tO 4-i o a C -H -H 3 a ex o o o B U rl < E-< H 0) 01 c d 0) 01 00 00 •H -H TJ TJ 01 01 -a tj •a tj 01 01 X XI E E o> d CTt CX» CM CO vd- LO •H rH rH 01 X - » 045 W W d CJ CJ tO CO CO JSP TJ \£> CM CO rH ^o ct> r^ 01 rH 00 fl -O 13 k h » -H CM CM X) >43l N 31 0\ CM rH r-H in tO CJ*t 00 CTt CJ> o rH 01 ■ <\) o 01 H o H c c l-i a rl 01 o 01 o MH 3 rH 4-J 3 4-1 O rH a co rH CO VJ MM >, MM 3 (1) C CJ rH c rH CO > a •H CO ■rH CO 0) C •H rH S-l u M 0) tO 01 CO CU <1) 0) 3 « 4J C o d c c PQ u t) •H cu o CU 01 rH a 00 rH 00 R C cj u U O C >> u c >. c IH ■H 3 CJ 4-1 •H u •H MH 4-1 CO d rH a) T1 rH TJ C R o tfl rH 01 m 01 O 01 •H CJ Xl TJ t) TJ •H rH 4-1 •H ■H TJ •H tj 4-1 C) CO CO. co 0) CA 01 tO 01 o O CO x> n X> u Qi o ^1 o H a Fi 3 r-l H a, M H Q CN cr, csl CM tjo-\ r^ en ^n -^ ^O dm CT\ CO o> CO a\ <■ o) r-. > aj q 3 J r- 01 > - CO O 01 O 3 ^i « M o a\ co oo co r- o O rH CM rH ^J-CTiO^OO^OlO-rJ-UOin CMOr-~CMOCOmrHCMOO CTt CO in CT» 00 CO rH 0O cMOcrvor-^o-tfrHi-Hinoo CT\CTirH0OCM-3-0O0O0Or~-OOrH CNfrHrHrHi-H j H CN O rH CO CM f- inmr-rHomcorHcM oiojoin o CO Ch H lA N in co oo <■ m o m o O Ch *j rs 00 rH CO o r~~ ai en rH 01 '•^ *> — ■^^ ~^ 4J rH CO CO CM CO rH CM CM CN H ' ^ — * ' — . r- co i-h \D O O O O ~-o o -i r^cocT\cT»cT»*j-mcTi-4-r^ cMcocococominin^Dvo rHOCMinvOCr*COCTlv£)0 rHrHOOi-HCMCMCM O . rH MJ3 CO N COOXOCOOllNCOlOOlOl oooomomooo coincMmLnooin-^-ino oomcNiinooOoocor^-tf oooooooooo ooooo<-ooino OHOHCOiOCO-J^'C ^Din-d-incMcocN<-cM^ O oo cm oo vo co m n io o in -i * HN* rHCMin CO o ■a -a T3 T3 T3 TJ •a -a TJ TJ TJ TJ TJ TJ TJ TJ rH cfl TJ X cfl CO i a (S 6 e c c c ^c C c c c £3 C C3 c 4-1 d d 4-1 ^ ^-^ ^r' ^^ ^^ ^^ ^^ ^^ N^ ' **S V-' 01 d ^^ Mm O i r-» 4-1 •rl 4-1 . TJ • 4-1 Cfl d Pm d rH i CO to M Xi •rl u c rH f"H CJ S 0) XI 00 o X CJ m CN CO 4-1 c CJ rH 3 3 CO MH c l-H CO cu rH •rl CO CO o X O TJ rH CU CO •rl MH o CU T3 4J tfl 0) C CO m ^ n_* ■H o O tfl MM rH 0) a 00 4J 4-> •H •H cfl Cu Vj CO o x: u 01 Crf CO X > ro 3 0) 00 CO C C -H > Mm 4-1 4J CO 4J 01 0) rH •H c >, o 01 CO tO X C O 4-1 •iH CO CO 4-1 rH rl c £ X O -H CJ O 10 •rl 4-1 X d CO > 4J rQ 4-4 o 01 s 01 C 1H u CJ OJ O a) 3 3 01 c 33 c o X PQ O ^ o CJ E 3 0) 4J rl d 01 CJ o 0) o CO CO rH XI S U co u 4J X 4-1 4-1 H C & 01 o & 00 a •H rH cfl CO O" rH Cfl 0) •rl d cfl 4-1 3, cfl d a o u • CO O 01 s 0) CO o rH C rH E o TJ CO ■H TJ E 3 cfl CO X O i-H •rl Ji CJ d X z CO 4-1 H o 3 cO 4-1 •rl M -H •H •H X r-{ 01 cfl CO 01 X M 01 •H CO M 0) CO cr > rS 01 3 CO CO X Cfl C 01 0) 01 CU o rJ H Pn fu pa CJ c/> Cm CO H O 3 CO 2 3 H Cm ►J in c O 3 OS u c« < H Url> o CQ W U H E= o s o a) (J TJ MH O Cfl O u 01 N rH CN co -a- m vd r^ CO CTi o H CM CO <■ in ^O r^ CO •H cn o rH CM CO ^r in vD r- oo o> o rH CN CO -i O O CU CO .5 03 O •H CU a 4-1 o en o CO CU H co S O T) H n ^0 r^ c C c^ H cr> CM as •» O ^H ^H ■H H c (0 — . >-. (U u CO c) U] CI) C3 c E= •a 3 M lit >-i c en CJ iH cfl 5 3 O 33 St VD CM o^ en m CM CO o> CO CO r^ 00 ro m co m CM H ? CO O H CM ? as U1 O H r- CO vO CO CD D> o o o o o in in O v£) \D in vo cm in - c o O O CO Jil C H HUH) W O B nj -o . . . . 5) N CO OS O > co co co •H u > i CU n rH u 4-1 X crt al u B S C •rH •H H H S U u o -a o> 3 H CO O CU CU 3 O c/l en cq Nan en » u 3 O U Q (O CO W C_> C_> CD S 3 43 a, a cu u u cu 4J O O 4J •u a, a. j-i cu cu cu o cu >J B! K i-l U J HNC1 to _ 5 X" ♦ 5 , / • m / • • /' • • • • • • •• • •• • • • S-' • • 2 _. < Z < I 3 X < o 5 < < > / / ' / /. /. / 3--~ 3-- / / NOI1YA313 Ill percent per 1,000 feet (305 m) of additional elevation is applied. This ad- justment was used to normalize all observations in table 4.1 for elevation. Similarly, this adjustment must be applied to PMP for elevations above 5,000 feet (see chapter 6). c. Adjustment for duration. The storms in table 4.1 had durations ranging between 15 and 210 minutes (except for the four relatively longer duration storms in California). All the durations in this table were adjusted to a common duration of 1 hour. Normalization for duration has been accomplished through use of the depth-duration relations shown in figure 4.3. These re- lations were developed from local-storm rainfalls for May through September in the study region (see discussion, section 4.4). 4.3.2.1 Application of Adjustments to Data. Of the 43 storms listed in table 4.1, the 16 most intense and widely distributed over the region were selected. Table 4.2 shows the results of moisture maximizing and normaliz- ing (for elevation and duration) the 16 storm amounts. Note in column 3 of table 4.2 that the effect of the elevation adjustment for those observations above 5,000 feet (1,524 m) is to increase the rain amount by 5% per 1,000 feet (305 m) above that elevation. The maximized, normalized values given in column 7 of table 4.2 were plotted on a map at their respective locations as the lower bounds to PMP for those locations. Data were insufficient to define a regional pattern. 4.3.3 Analysis Maximum 1-hr amounts from recorder stations (1940-72) were examined for guidance to a regional pattern of 1-hr PMP. Not all stations had complete 33-yr records. The largest 1-hr amounts at each station for the months May to September were plotted and an analysis made at 1-in. (25 mm) isohyetal interval (fig. 4.4). All amounts exceeding 1.5 inches (38 mm) have been underlined as an aid to locating zones of maxima. Noticeable are the number of underlined amounts extending SE-NW across Arizona. These observations reflect the interaction between the terrain and moist southerly flows from the Gulf of California. A much smaller zone of maxima occurs in southern California. Large zones of minimum amounts occur over portions of the Great Basin, the Central Valley of California, and along the Pacific coast. Further guidance was obtained from the shape of the maximum moisture pat- tern for August (see fig. 2.3). Lowest moisture occurs along the Pacific coast with a push of maximum values northward through east central Arizona. There is a tendency for lower values in northern New Mexico and western Colorado. The analysis in figure 4.4 has been influenced by knowledge of the terrain. This includes allowing for stimulation of convective activity which leads to triggering of rainfall in upslope areas. 112 Q. Q. I I o DC 200 180 - 160 - 140 - 120- 100 - Figure 4.3. — Variable depth-duration curves for 6-hr PMP in the Southwest States and all of California. 113 O H ^ 3 3 XI -H e on CM o CM CO CO rH O ^H -a- CM in CM in CM o H m CM r4 H ON rH CM rH m CM rH ■X> rH in CM VO rH 00 st in VO o o m on ^D CO VD ON 00 (U 3 rJ 0) 3 fc J-J .u 01 V) ■r4 3 C C_> ■H o O "-' CO Mh d ■H CO U e o 4-1 a: l .H cfl u o CO o •H 4-1 •H Sn a 4-1 CO o 6 o 4J 4-1 d CD e 4J CD 3 •i - ) j«Ttnn>£) en S>> 4J Jo mh rJ cO o cu O C O m % u o co H 01 4J X> C 3 CU It) 1 O ctj JS 4J M x: H I O ><: O 4J U MH a exi o CO o Q vt CM CO Ul 0\ O ^ CM ON O CO 00 00 rH rH<5-CMONCOCMONrHO NHCHcocooico-crrN T3 C ctj XI 1 cu -a g N CM CM^^H CM HH^^rlH'-'HCM rH > cu 4J CO o > c •u o XI rJ 3 C 4J cd 0) CO O i . * o in m -a- in co + en •H o TO CO X) CO a oo m m m i-h cm MnvoincMinminio 1 cu 0) a o •H CJ 3 o ■H oo r-H oo ci co r-~ oo \D R x co co co in. i^ r^ COOCOiOlOOCfiOOl rH rH o o T3 3 CO rJ 3 CTJ g 3 ON CU O •H O rH rH ■H • XI T3 in 4J , Colo Calif, o cd 3 r^. cd 4-1 3 cd > O 00 cu • )J •H X rH C MH O 4-1 ■H UH CU o •H ■H CO 3 o •H N • in . N rH MH I-l CU 0) Sh 4-1 Nev. if. , Ari N.P z. Call Flat, •H CO -H • 0, 3 O 4J O CO U O • rH UH . . cr x; 3 UH CJ -U U CJ tD 4J > CU CO U O 4J B c O U CO >-l -H *H CU *H *> CO « B c TO- M 4-1 o 4J xs CU -H > .« glH i< 41 C! -" ^ 3 Cl) x: CO 4J 4-1 - O > - CJ O C CO -H -r4 4-1 C C o O CO 1 3 en cu o S cu cu 4-) COCO -V4CCJ300 4-1 1 CO -cr •n gO. CO XI rH CO 604-1 O CU CU-H MH U C/3 pa CN -a rH B • tl O H H l-iCAiAiOCJ-HcOIS * •K + t < CO Cfl 4-1 CU rH CO X3 Oc0rHc0J3CrJ>l) * =fc D-i O ft, S o > O SmWpqd-iWS 10 inches, 254 mm) occurs at the north end of the Sacramento Valley in northern California because the northward-flowing moist air is increasingly channeled and forced upslope. Support for this PMP cen- ter comes from the Newton, Kennett, and Red Bluff storms (fig. 4.1). Although the analysis in this region appears to be an extension of the broad maximum through the center of the Southwestern Region, it does not indicate the direction of moist inflow. The pattern has evolved primarily as a result of attempts to tie plotted maxima into a reasonable picture while considering inflow directions, terrain effects, and moisture potential. 116 The last mentioned considerations were important in establishing the gradients through north-central Arizona and the northeastern quadrant of the region of interest. The Mogollon Rim, a range 5,000 to 7,000 feet (1,524 to 2,134 m) in elevation appears to be a prominent obstacle to the low-level moist flows coming northward from the Gulf of California. We believe this barrier is the principle reason why no large local-storm rainfall has been observed to the northeast, and that a sheltering effect is reasonable for the PMP analysis. To the south and southwest of the Mogollon Rim, the PMP in- creases to a maximum, to reflect the available moisture. 4.4 Durational Variation 4.4.1 Duration of Local-Storm PMP We postulated that the most extreme or PMP-type local storm could last for 6 hours. A large portion of the total storm should occur in the first hour and almost all within 3 hours. An exception lies in the coastal drainage areas of California where a more continuous inflow of moisture is possible, particularly when synoptic scale systems are involved. Thus, PMP of up to 6 hours probably comes from a moisture resupply that is more typical of the general-storm situation. 4.4.2 Data and Analysis for Durations from 1 to 6 Hours To obtain local-storm PMP for durations from 1 to 6 hours a number of types of rainfall data were studied. One source of data was recorder station maxi- ma (1940-72). Amounts for 1, 6 and 24 consecutive clock-hour amounts were chosen that met the following conditions. a. A criterion of minimum clock-hour amounts was established on a region- al basis as shown in figure 4.6. The criterion recognizes differences in the magnitude of extremes over the region. b. The 1-, 6-, and 24-hr consecutive clock-hour amounts at a station must occur on the same date. c. The 24-hr amount could not exceed the 6-hr amount by more than 0.1 inch (2.5 mm). This helped avoid general type storms. From data meeting the above criteria, 6/1-hr ratios of rainfall were determined. Averages of ratios for stations within 2° latitude-longitude grid units were used to smooth the data. An analysis of the grid averaged data is shown in figure 4.7. This analysis needed only slight adjustment to reflect anticipated shelter- ing influences of major terrain barriers. Especially noteworthy is the strong gradient along the eastern slopes of the Sierra Nevada. East of this gradient the ratios range between 1.10 and 1.40. A zone of minimum ratios (1.10 to 1.20) is centered in the plateau region of southeastern Utah and northeastern Arizona. This minimum can be ascribed to the sheltering effects of the Wasatch range on the west, the Mogollon Rim on the south, 117 Figure 4.6. — Criteria of clock-hour rainfall amounts used for selection of storms at recorder stations for depth- duration analysis. and the Rockies on the east. The apparent minimum in Nevada shown by the data is questionable since there are no broadscale topographic features blocking moisture flow. The result may be due to a deficiency of data. With the exception of the Mojave Desert, the analysis in California shows considerably higher ratios. The maximum along the coast and into the upper Central and Sacramento Valleys exceeds 1.80. Farther inland, terrain bar- rier effects reduce the ratios. The wide range of 6/1-hr ratios shown in figure 4.7 suggests that the en- tire region cannot be represented by a single depth-duration relation. The problem is similar to the depth-duration problem of general-storm PMP (see section 2.4) and we used a similar solution: Find a suitable relation to 118 123 121 119' 117 ° 115° 113° 1 1 1 CZJaverage OF <3 STATIONS ♦ NO DATA Figure 4.7. — Analysis of 6/1-hr ratios of averaged maximum station data (plotted at midpoints of a 2° latitude -longitude grid). establish the basic depth-duration curve, then structure a variable set of depth-duration curves to cover the range of 6/1-hr ratios that are needed. Three sets of data were considered for obtaining a base relation (see table 4.3 for depth-duration data). a. An average of depth-duration relations from each of 17 greatest 3-hr rains from summer storms (1940-49) in Utah (U. S. Weather Bureau 1951b) and in unpublished tabulations for Nevada and Arizona (1940-63) . The 3-hr amounts ranged from 1 to 3 inches (25 to 76 mm) in these events. b. An average depth-duration relation from 14 of the most extreme short- duration storms listed in Storm Rainfall (U. S. Army, Corps of Engineers 1945- ) . These storms come from Eastern and Central States and have 3-hr amounts of 5 to 22 inches (127 to 559 mm) . 119 Table 4.3. — Depth-duration relations of severe local storms Duration (hr) 12 3 6 Percent of 1-hr value 1. Average of 17 storms Utah, Nevada, and Arizona (recorder data) 100 125 133 152 2. Average of 14 most extreme short-duration storms in Storm Rain- fall (U. S. Corps of Engineers 1945- ) 100 125 135 166 3. March 3, 1945, Los Angeles storm (U. S. Corps of Engineers 1958) 100 118 128 (144) c. The depth-duration variation from one of the best documented thunder- storm rainfalls of record in the Southwest. This is the 3-hr, 3.3-in. (84-mm) fall in Los Angeles County, Calif, on March 3, 1943 (U. S. Army, Corps of Engineers 1958) . Even though this rainfall was imbedded in more general storm rains, March 3-6, 1943, covering parts of several states, the large amount of reliable data for the event make it useful. Most of the extreme local storms in the study region (table 4.1) lasted less than 3 hours and little depth-duration data are available for them. We would expect that a representative PMP depth-duration curve would have a lower 6/1-hr ratio than either of the first relations listed. We chose to adopt the relation for the March 3, 1943 storm as guidance for the basic depth-duration curve for the local-storm PMP. A smooth extension of this relation to 6 hours gave a 6-hr value that is 144% of the 1-hr amount. This relation is quite similar to the local storm depth-duration curve of HMR No. 43 in which major Southwest storms were considered. For a variable re- lation, a family of curves (fig. 4.3) was established where the 6-hr values were incrementally 10% greater than the 1-hr amount. A smooth curve was drawn between the 1-hr (100%) point and the 6-hr (110%) point. The remain- ing curves were determined by the ratio of the 6-hr value to the difference between 110% and the basic depth-duration (dashed line fig. 4.3) curve. 4.4.3 Data and Analysis for Less Than 1-Hr Duration Durational relationships for durations less than 1 hour were obtained from data at first-order stations in Utah, Arizona, Nevada and southern California for a period of record between 1954 and 1970. Tables of excessive precipita- tion at these stations are summarized in the Annual Summary of Climatological Data (U. S. Weather Bureau 1954- ) for durations of 5 to 180 minutes. These data showed that storms with low 3/1-hr rain ratios had higher 15-min to 1-hr 120 ratios than storms with high 3/1-hr ratios. The geographical distribution of 15-min to 1-hr ratios also were inversely correlated with magnitudes of the 6/1-hr ratios of figure 4.7. For example, Los Angeles and San Diego (high 6/1-hr ratios) have low 15-min to 1-hr ratios (approximately 0.60) whereas the 15-min to 1-hr ratios in Arizona and Utah (low 6/1-hr ratios) were generally higher (approximately 0.75). Depth-duration relations for durations less than 1 hour were then smoothed to provide a family of curves consistent with the relations determined for 1 to 6 hours, as shown in figure 4.3. Adjustment was necessary to some of the curves to provide smoother relations through the common point at 1 hour. We believe we were justified in reducing the number of the curves shown in figure 4.3 for durations less than 1 hour, letting one curve apply to a range of 6/1-hr ratios. The corresponding curves have been indicated by letter designators, A-D, on figure 4.3. As an example, for any 6-hr amount between 115% and 135% of 1-hr, 1-mi 2 (2.6-km 2 ) PMP, the associated values for durations less than 1 hour are obtained from the curve designated as "B", Table 4.4 lists durational variations in percent of 1-hr PMP for selected 6/1-hr rain ratios. These values were interpolated from figure 4.3. To determine 6-hr PMP for a basin, use figure 4.3 (or table 4.4) and the geographical distribution of 6/1-hr ratios given in figure 4.7. Table 4. 4. —Durational variation of 1-mi 2 (2.6-km 2 ) local-storm PMP in percent of 1-hr PMP (see figure 4.3) 6/1-hr Duration (hr) ratio 1/4 1/2 3/4 1 2 3 4 5 6 1.1 1.2 1.3 1.4 1.5 1.6 1.8 2.0 4.5 Depth-Area Relation We have thus far developed local-storm PMP for an area of 1 mi 2 (2.6 km 2 ). To apply PMP to a basin, we need to determine how 1-mi 2 (2.6-km 2 ) PMP should decrease with increasing area. We have adopted depth-area relations based on rainfalls in the Southwest and from consideration of a model thunderstorm. 86 93 97 100 107 109 110 110 110 74 89 95 100 110 115 118 119 120 74 89 95 100 114 121 125 128 130 63 83 93 100 118 126 132 137 140 63 83 93 100 121 132 140 145 150 43 70 87 100 124 138 147 154 160 43 70 87 100 130 149 161 171 180 43 70 87 100 137 161 175 188 200 121 Figure 4.8 is a plot of available depth-area data for major local storms listed in table 4.1. The durations given with the 7 storms are longer than for the point value because of the areal pattern. Most of the data from which areal patterns were drawn came from bucket surveys and other unofficial observations. 100 i — X^ 1 1 ( f 1 1 1 | i i i i i i i i | DURATION / 1 \ / 1 i HRS) 1 I r r | 1 'J ST - 80 CN - o\ as. ^^. - CN CM ! 60 U_ - * \ * - o LEGEND * \ + N^ 1— Z LU u c* LU 40 Q- STORMS (SEE TABLE 4.1) D MORGAN. UTAH < 1 )* ■f GLOBE, ARIZ. ( 1 ) \ N> - I * BAKERSRELD. CAUF. (1,5) * \\ \S ■ 1 — Q_ LU Q O -0 X SANTA RITA ARIZ. 12.31 VALLEOTO. CAUF. (4.5) PHOENIX. ARIZ. (6) o D O *«> + 20 A TEHACHAPt CAUF. (6.5) MODEL THUNDERSTORM AnOPTFD ax o x h - * TOTAL DURATION (HRS) OF AREAL PATTERN (Ml 2 ) o o 1 ? 5 1.0 i i i i i i i 1 20 i i 50 100 i i i i i i I 200 i 500 i iii I i 1 1 l' | i i t i ii 1 y i i 'i r |' i 1 III 1 ' 100 (KM 2 ) 1000 AREA Figure 4.8. — Depth-area relations adopted for local-storm PMP in the Southwest and other data. Also shown on figure 4.8 are 1- and 3-hr curves from a model thunderstorm. The following conditions comprised the model: 2 2v a. A depth-duration relation for 1 mi (2.6 km ) based on a 6-hr percent of 1 hr of 144% (fig. 4.3). b. Circular isohyets. c. A storm rate of travel of 4 mph (1.8 m/sec). d. A rate of change in storm intensity due to storm motion the same throughout the areal pattern as at a point. 122 Both the data and the model thunderstorm results were used in determining the adopted depth-area relations for 1 and 3 hours shown on figure 4.8. A first consideration is that the relation must envelop the data. The adopted 1-hr curve shown in figure 4.8 envelops the 1-hr rains (Globe, Morgan and Bakers field) by roughly 10%. Only data for the two 6-hr rains (Phoenix and Tehachapi) exceed the 1-hr curve. The adopted 3-hr curve envelops all the storm data. The model thunderstorm curves are also enveloped. In the model thunderstorm we assume that if the rate of travel were reduced, the model curves would approach the adopted curves. A depth-area curve for the Southwest for 6 hours was estimated from rela- tions given in HMR No. 43 based on selected storms for the Eastern United States. Using the curves for 1-, 3-, and 6-hr durations, relations were interpolated for intermediate durations. Depth-duration curves based on these relations and for a number of area sizes were used to obtain values to approximate curves for durations less than 1 hour. The adopted depth- area relations are shown in figure 4.9. 4.6 Distribution of PMP Within a Basin Idealized elliptically shaped isohyets patterned after the few available storms have been developed for distribution of PMP. The extreme storms at Globe and Vallecito were examples from which an isohyetal pattern having a 2:1 axial ratio was adopted for application throughout the Southwest. The pattern, shown in figure 4.10, is drawn to a 1:500,000 scale. Isohyets are shown on this idealized pattern labeled A (1 mi 2 , 2.6 km2) to J (500 mi 2 , 1,295 km 2 ). 7 7 Table 4.5 gives isohyets labeled in percent of 1-hr 1-mi (2.6-km ) PMP for the 4 highest 15-min incremental PMP values. Incremental labels are given for each of the four indexed 6/1-hr ratio categories (see fig. 4.3). These labels when multiplied by the 1-hr 1-mi (2.6-km 2 ) PMP for a specific drain- age give drainage PMP isohyetal labels for the 4 highest 15-min increments. Table 4.5 also gives isohyetal labels for 1-hr PMP. The resulting isohyetal values take into account the depth-duration relations of figure 4.9. For obtaining PMP out to 6 hours duration (remaining five lesser 1-hr in- crements of PMP), use the isohyetal values given in table 4.6. The 1-hr in- crements of PMP are listed in successively decreasing order of magnitude. The percents by which the 1-hr 1-mi 2 (2.6-km 2 ) PMP are to be multiplied to obtain isohyetal values are categorized by the 6/1-hr ratios. Steps outlin- ing the application of these percents are presented along with an example in chapter 6. 4.7 Time Distribution of Incremental PMP We have little information about the time sequence of incremental 1-hr rainfalls for intense local storms. A study of sequences of increments in each of 38 six-hr storms (U. S. Weather Bureau 1947) resulted in an average mass curve in which the maximum intensities occurred in the middle of the 123 o J !_=. o o- •o o o 7o o o- l93)jlW L JO lN3Da3d)Hld3Q 124 m o ON O CN ^ 4= O co I oc» o vo ^- 00 H CJ N_*" lj_, c o w ,—s 4-1 w mco c oo in in CN rH m o o in von o oo iH rH rH rH in rH 0O vO CN CN COCM H rl 00 CO N. N, CO O CD rH H H rH rH rH rH rH rH r-{ rH rH rH T-i rH rH 4-1 • . . 4-1 • . . 4-1 • . . 4-1 • . g Pm Fj CO T3 TJ 42 CO T3 T3 42 CO Tj T3 42 CO Hd X) 42 PM g 01 0) Pi (H ■u 01 c rl 4-1 0) f2 S-J 4-1 0) c M 4-1 PM o 42 CM 60 •H CO 1 ) t V 1 vO rH rH l vo CO A 125 Table 4.6. — Isohyetal labels for second to sixth hourly incremental PMP in perceont of 1-hr 1-mi (2.6-km 2 ) PMP 6/1-hr Isohyet ratio A B C D E F Second highest 1-hr PMP increment 1.1 7 7 7 7 7 7 6 4 4 4 1.2 11 11 11 11 10 8 7 5 5 5 1.3 14 14 14 12 If 9 7 5 5 5 1.4 17 17 16 14 12 10 8 6 6 6 1.5 21 20 18 16 13 11 8 6 6 6 1.6 24 23 20 18 15 12 9 7 7 6 1.7 27 26 23 20 16 13 10 7 7 7 1.8 30 29 25 21 17 14 10 8 8 7 1.9 34 32 27 23 18 14 11 8 8 8 Third highest 1-hr PMP increment 1.1 2 2 2 2 2 2 2 2 2 2 1.2 4 4 4 4 4 4 4 4 4 4 1.3 6 6 6 6 6 6 5 5 5 5 1.4 9 9 9 9 8 7 6 5 5 5 1.5 11 11 11 11 10 8 7 5 5 5 1.6 14 14 14 13 11 10 8 6 6 6 1.7 17 17 17 14 13 11 8 7 6 6 1.8 19 19 18 16 14 12 9 7 6 6 1.9 21 21 20 18 15 13 10 8 7 7 Fourth highest 1-hr PMP increment 1.1 1 1 1 1 1 1 1 1 1 1 1.2 3 3 3 3 3 3 3 3 3 3 1.3 5 5 5 5 5 5 5 4 4 4 1.4 6 6 6 6 6 5 5 4 4 4 1.5 7 7 7 7 7 6 5 4 4 4 1.6 8 8 8 8 7 6 5 5 5 5 1.7 10 10 10 9 8 7 6 5 5 5 1.8 12 11 11 10 9 8 7 6 5 5 1.9 14 13 12 11 10 9 7 6 6 6 Fifth highest 1-hr PMP increment 1.1 1 1 1 1 1 1 1 1 1 1 1.2 2 2 2 2 2 2 2 2 2 2 1.3 3 3 3 3 3 3 3 3 3 3 1.4 5 5 5 5 5 5 4 4 4 4 1.5 6 6 6 6 6 5 5 4 4 4 1.6 7 7 7 7 7 6 5 5 5 5 1.7 9 9 9 9 8 7 5 5 5 5 1.8 10 10 10 10 9 7 6 6 5 5 1.9 12 12 12 11 9 8 6 6 6 6 Sixth highest 1-hr PMP increment 1.1 1 1 1 1 1 1 1 1 1 1 1.2 1 1 1 1 1 1 1 1 1 1 1.3 2 2 2 2 2 2 2 2 2 2 1.4 4 4 4 4 4 4 4 4 4 3 1.5 5 5 5 5 5 5 4 4 4 4 1.6 6 6 6 6 6 5 5 5 5 5 1.7 7 7 7 7 7 6 5 5 5 5 1.8 8 8 8 8 8 6 5 5 5 5 1.9 9 9 9 9 9 8 6 6 5 5 126 Figure 4. 10. — Idealized loeal-storm isohyetal pattern. DHYET INCLOSED AREA . (SQ.MI.) (KM ) A 1 2.6 B 5 13 C 25 65 D 55 142 E 95 246 F 150 388 G 220 570 H 300 777 1 385 997 J 500 1295 SCALE 6 8 IMO 'l I ' 10 12 (KM) SCALE 1:500.000 storm period. The sequence of hourly incremental PMP for the Southwest 6-hr thunderstorm in accord with this study is presented in column 2 of table 4.7. A small variation from this sequence is given in Engineering Manual 1110-2-1411 (U. S. Army, Corps of Engineers 1965). The latter, listed in column 3 of table 4.7, places greater incremental amounts somewhat more toward the end of the 6-hr storm period. In application, the choice of either of these distributions is left to the user since one may prove to be more critical in a specific case than the other. Table 4.7. — Time sequence for hourly incremental PMP in 6-hr storm Increment HMR No. 5 EM1110-2-14ir Sequence Position Largest hourly amount 2nd largest 3rd largest 4th largest 5th largest least U. S. Weather Bureau 1947. 2U. S. Corps of Engineers 1952. Third Fourth Second Fifth First Last Fourth Third Fifth Second Last First 127 Also of importance is the sequence of the four 15-min incremental PMP values. We recommend a time distribution, table 4.8, giving the greatest intensity in the first 15-min interval (U.S. Weather Bureau 1947). This is based on data from a broad geographical region. Additional support for this time distribution is found in the reports of specific storms by Keppell (1963) and Osborn and Renard (1969) . Table 4.8. — Time sequence for 15-min incremental PMP within 1 hr . Increment Sequence Position Largest 15-min amount 2nd largest 3rd largest least First Second Third Last 4.8 Seasonal Distribution The time of the year when local-storm PMP is most likely is of interest. Guidance was obtained from analysis of the distribution of maximum 1-hr thunderstorm events through the warm season at the recording stations in Utah, Arizona, and in southern California (south of 37 °N and east of the Sierra Nevada ridgeline) . The period of record used was for 1940-72 with an average record length for the stations considered of 27 years. The month with the one greatest thunderstorm rainfall for the period of record at each station was noted. The totals of these events for each month, by States, are shown in table 4.9. Table 4.9. — Seasonal distribution of thunderstorm rainfalls. (The maximum event at each of 108 stations, period of record 1940-72.) Utah Arizona S. Calif.* Month M J J A S 1 5 9 14 5 4 16 19 4 14 10 7 No. of cases/mo. 1 23 35 40 No. of Cases 34 43 31 *South of 37°N and east of Sierra Nevada ridgeline, 128 This distribution, by months, agrees well with the month of occurrence of the extreme thunderstorm rainfalls for the Southwest listed in table 4.1. July and August have the greatest frequency of extreme rains in both sets of data. For the coastal drainages of California, most thunderstorms are associated with general-storm rainfalls (see discussion in the companion volume, Schwarz and Hansen 1978). The occurrence of these cool-season mid-latitude and tropical storm systems is apparently limited to the spring and fall months. Figure 4.11 presents the regional variation of the months of greatest potential for a 1-hr thunderstorm event approaching the magnitude of PMP. Figure 4.11. — Regional variation of month of maximum local- storm rainfall. (boundaries are not precise) 129 5. CHECKS ON THE GENERAL LEVEL OF PMP 5.1 Introduction All probable maximum precipitation estimates involve some degree of uncer- tainty. Decisions leading to a level that provides safety, while not intro- ducing unrealistically large estimates of precipitation amounts, requires experience and meteorological judgment. Guidance for such decisions includes evaluating maximum observed precipitation depths, and meteorological studies of storm characteristics such as moisture sources and storm mechanism. PMP must exceed the envelop of maximum observed values. For most regions, nature has not yet given us the biggest storm; rainfalls occasionally exceed the previous maximum from over 50 years of record by factors of 2 or 3. In this chapter PMP estimates are compared with known maximum precipitation amounts in the Southwest States. We also show comparisons of the general level of PMP in this study with values in an earlier study and with PMP estimates in adjoining regions. In chapters 2 and 3 we pointed out how con- vergence and orographic PMP index maps compare with similar maps in HMR Nos. 43 and 36 for adjoining regions to the north and west, respectively. These discussions will not be repeated here. Rather, the general level of total PMP will be compared. Comparisons are also made with 100-yr rainfall and with some statistically estimated PMP values. Finally, we evaluate the rain poten- tial from a hypothetical tropical cyclone, one that has the most extreme characteristics for producing rainfall for the Southwest States that such a storm might have. 5c 2 Comparisons with Greatest Known General -Storm Areal Rainfalls From a catalog of greatest known areal rainfall depths (Shipe and Riedel 1976) the greatest depths for various portions of the study region were extracted for the winter, spring, summer and fall seasons. Four standard areas: 100, 500, 1,000 and 5,000 mi 2 (259, 1,295, 2,590 and 12,950 km 2 ) for 6, 12, 18, 24, 48, and 72 hours were considered. Table 5.1 lists the storm date, latitude and longitude of rainfall center, general location by section of the State, and the ratio of observed to gen- eral-storm PMP for the month of the storm for the selected area sizes. Of these comparisons, the September 1970 rainfall center in southwestern Colorado and southeastern Utah stands out with a high ratio of observed to PMP of 0.88 for 6 hours over 100 mi 2 (259 km 2 ). [The local-storm PMP (chapter 4) at this location exceeds the general-storm values, for this size area and duration, giving a ratio of observed to PMP of 0.69.] The more intense rainfall center of the September 1970 storm in central Arizona (where the ratios of observed to PMP are smaller than at the northern center) is not as rare an event. Comparisons with mean annual precipitation and other rain- fall indices also lead to this conclusion. Examination of the variation of the ratios of observed to PMP with duration shows the ratios decrease with increasing duration. This trend is considered reasonable in that nature has given us a larger number of extreme short- duration storms than longer ones over any given basin. 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B O u 1 tH TJ • cu cu LO 3 +J C CO CU •H Q ^H 4-1 X c CO o ^£3 co CO CN CO ro o CO H CO o 00 CN CO CM CN co CO CO rH m CO CO CO CO CO tH in rH rH tH CO CN co CN CN m CN m o- CO CO CN CO CO co on co CO CN CO co m CO CN tH co H CO CO CN m CN CM CO CM tH CT\ co CO O CO o m tH ^o m m 00 VD CN CN co cn in o •o- m m -d- o vo r~- m -d- m -d- r-N CTi ON m o r^ o o o v£> d- co CM CM co r^ m o CO r-» m ON CO CO vO m cm r~~ O CM m co i^ CO r^ 00 CO CM ro m o- co m n «d- co co m m vo r^ CM CM CM CM CN CM CM CN vo m m o O (MOO m o o CT\ m o o on m o O in <^ m a> o m CTv m CT\ CTi m m ct\ o\ m o> cr\ m m CTN on m in CTi C7\ m CM CN CN CM m CN CN CM cn m CT\ cn cn m CM CM m on CN CN m a\ CM cm m ON ■^^ H N»X rH CN V— t tH ^^ H CM CN ^— ' rH CM v-^ r-i CM CM •>— ' l-\ CN CM ^HN CM s_/ N^ N«/ s.^ V^/ N*^ rH >w/ ■^ •^ tH ^ — ' v— ' v_/ rH 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 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 tH m rH m o tH H m rH m o o m tH m o H rH m o o tH m tH m o o tH m tH m o o m X > cfl CU 4-1 S3 & W 53 3 N •H U < tH X CO CO U 4-1 4-1 S3 G cu 53 u CO 4-> o u CO 4J 5=> ■a 4J C73 -d- m CN CN O m CM -J- v£> m CO •o- O H CO o o O o sr H v£> O CO CO o O r^ s3- CO o CO I CN H U CO CO I CN 00 CO CO CN CN 00 CO CO CN co ON I -d- — m CO v£3 I tH CO m I CN 132 0) 4= 4-1 LH O 4= ■y d i 0) •p VI o I o CO ■H IH o ^n o> 0\ 1^ CN LO m m x> 00 o 4= 00 ■H 00 O m o O g J m On o> •m m o> O^ m m CT> oo LO j_i CN CN m o> CN CM m cr\ CN CN m C^ o ed w ^-^ r-\ CN CN ^s^ <-{ CN CN w rH CN CN 4-> CU ^^ *^s rH •^^ ^^ rH ^s ^-^ <-\ CO 1 5-i Vw/ W ■^s H CN o o o o o o o o o O o o ed ■H o o o o o o o o o o o o U a H m o o r-i m o o rH LO o o cu rH m rH m rH LO d 0) 00 4= N N 4-> d •H •H •H rH O 5-1 5-1 5 ed -H 5-1 4-1 <3 , < CO 03 ed H o 43 cd rH 42 d o ed rH ed 4-J Q3 O 5-1 O 4J 5-i CU O H 4J o P 4-1 01 d d TJ (13 o 3 CO C/3 0) U H rH ed IH d •H cd u 03 T3 .. .. _ rH 3 rH ed 4-1 CN o m CO 3 M-l 4-1 O O 00 en CT> M-l •H w o o O 4-1 ed en en en d hJ • 03 m 3 d 0) -H rH 4-1 43 d cd o H O 03 4-1 ed O O en I m CN oo o m I en o> o r^ m I en <3\ 133 occasions when rains repeat or are continuous over a basin for a 3-day period. Continuation of an extreme inflow of moisture for longer durations is less likely, but yet a possibility. The August 1951 storm is an example of an event where a high level of moisture inflow and a continuation of the mechanism for causing rain produced an extreme rainfall event of 3-day duration. Figures 5.1 and 5.2 show scatter diagrams for two sets of data taken from table 5.1. The com- parison between maximum observed 100-mi 2 (259-km 2 ) 24-hr storm amounts and corresponding PMP estimates is shown in figure 5.1. Storms whose observed amounts come within 50% of PMP are iden- tified. Note that for 24 hours duration, a southwest Utah storm in October 1946 more closely approaches PMP than any other storm. Figure 5.2 shows the com- parison of known greatest rain- fall amounts to PMP for 5,000 mi 2 (12,950 km 2 ). Only one storm comes within 50% of PMP. The validity of the trend toward lower ratios with larger areas is supported by the fact that fewer large-area storm depths have been recorded than small- area storm depths. 1 T ■ l M 1 '1 (IN) IB (MM) "/ $/ 7 / f " /OBSERVED IN » OF ?lfo 7 16 -400 mb / / / / / / < y 14 / / / / f^ 12 ~300 / / / " 10 J / 3 / / 1 / 8 r 200 A / 7 '■ / / Identified Stormj 1. OCT. 27-29, 1946 ; SW UTAH 2. SEP. 3-5. 1970 . SW COlO . 3. NOV. 12-17. 1930: NE NEV 4. OCT. 4-6. 1911 i SW COLO. 5. FES. 1-5. 1907 , NE NEV. 4 -100 / 6. SEP. 3-5. 1970 i CENT. ASIZ. 7. DEC 14-17. 190B : SW COIQ 8. FE». 27-MAD. 4. 1938 i S UTAH. 2 " n r 100 ■1 • 200 (MM) ! 3 ?f OBSERVED BAINFAll Figure 5.1. — Comparison between observed rainfall depths and general-storm PMP for 100 mi (259 hrfi) 24 hr. 5.3 Comparisons with Greatest Known Local -Storm Rainfalls Local-storm PMP estimates were determined for the location of the 39 major local storms given in table 4.1. This does not include the four long-duration California storms. A scatter diagram of maximum observed total-storm amount vs. the PMP estimate for that duration is shown in figure 5.3. Envelopment of local-storm data by PMP is less than that for general-storm data. The Campo and Chiatovich Flat, California rains come within 15% of the local-storm PMP estimates. Because of the doubt that has been given to the Palmetto, Nev. observation (U.S. Weather Bureau 1960), a question mark has been placed at this point in figure 5.3. 134 to to COV^ q to o £^ TO S s 5 £ CO o +i CO Qj •^ TO 8 s^ I £ I '^ • « Ph (^ «K ^ ? ttj Sh O ^ 4^> i£j CO O -P TO CO r£ 1 +^ T-i « «K e> o t-i s? 0, •w V sf -^ a <3 CO 4^ "X5 TO Mh B f5 0) CO p rO !n • o TO £ e CO to 1 Vl TO r~^ CK1 a -^ TO cdcnj rO TO J s <3i o # T-i Q> U3 e CM ^LO TO £ £j •^ Sn *Je w ^ <35 S ^K g "X3 CO K 03 G fc to to CO os 03 s g G » 03 RQ PL, 03 . +i "G g s 03 -R ^ CO I V~J> to G t-H s ,o oj s--, G> CO 03 +i r-g g CO g o Cl, -P 3 ""G Oi V "K fc O a Gs cn E Cl 0) £ t~H Gs o ?H +i -P G CO G \~-i 1 -^ o) G "~ cq<3~ cjo'o' COOx CK OO' o."*o." oT oo" CO 'o o" "co* O n ■OCN cnTcJ 29 Oo io*n" CN — •a 2 _ — CO cx"~-* 5^ CD — oo'*2 CO I**" o-.o CK 00* to co ^3 o> m CN° Wi CN oo'^ O CN CD •"" cx"*^" N. ^ v — CO cn" io oo com : df§ ^.. ■** CO *~ cn r^ ex ^f~ i?2- 00 ^~ en _ ^" s co CX -o 1 ] co" "O ?0» k co' Z CO CN cod o- — Oo'cN* o - 12 i o Ot n i it •o N Lq o ""Tj" *o" •o — cv od «"2 CN ^ oo' — ' oo 00* O °2 ooZ CX — CO — 'iXi °1^ °*»< T^fO CX.1V/ CX to N - Cx"i5 CN-N ^S ^-.^ ** Cx— O O ^^TK CO — -**H Os -^ o* <^ cn cn 00 oo o o- CN o -o o -o ■d w — 5 •o" 2' OfN O CN K— ■ ~ A. 3/5 ^y .(V < L I- o -o CN o -o \ *^* ■— ro Z b < **-* C o - - o I G co to O 0) CM O ^S! £ G g to -s .O E to *+-. 3 _ S -^ ■ •U.IS.17J19 .14.16^19. "1 I + 300 < 9 - 3 °.3/.29/ 2 / : l/'r 100 300 500 400 700 ' 500 Too (HMD (KM) V •'6.15 J)9 - L 4 -l4.ll7 ■ A v. '/-*■' + / >/ J_ J_ \ Figure 5. 7. —Ratios of 100-yr point rainfall (Miller et al. 1973) to highest PMP for 10 mi 2 (26 ten 2 ) 24 hr. Underlined ratios are -points where 6-hr local-storm PMP controls. East of 105th meridian PMP taken from eastern states study (Schreiner and Riedel 1978). 139 The range of ratios shown in figure 5.7, 0.28 to 0.71 in the Pacific drain- age of California, 0.17 to 0.59 in the Northwest, 0.18 to 0.56 in the South- west, shows apparent consistency between the Northwestern and Southwestern Regions. East of the 105th meridian, the ratios range between 0.12 and 0.23. The trend in ratios that appears in going from the west coast to east of 105°W is what one might expect. There is a tendency for the ratios to de- crease eastward from the Pacific coast and then increase again on windward slopes. This tendency is consistent with the results for similar ratios in HMR Nos. 36 and 43. The ratios shown on figure 5.7 should not be used for basin PMP estimates. Variation in terrain features between 1° grid points could give a consider- ably different basin average PMP; i.e., because of topographic variations, the ratios are not necessarily representative of the area surrounding the grid point. 5.7 An Alternate Approach to PMP An additional study was made of the variation in ratios of 100-yr rainfall to PMP estimates for the region most similar to the Southwest States that also had detailed estimates of both the precipitation criteria. This region is the Columbia River drainage east of the Cascade Divide. A conclusion of the study was that the 100-yr to PMP ratio should vary with the raininess of the location, and that a 90% envelope of a grid of ratios for the Northwest varies from 0,25 for a location with a MAP of 10 inches (254 mm) (dry region) to a ratio of 0.50 for a location with a MAP of 70 inches (1,780 mm) (wet region) . The curvilinear relation between 100-yr/PMP ratios and MAP (not shown) from the Columbia River drainage east of the Cascade Divide was used to estimate PMP for the Southwestern States over a 1° latitude-longitude gridl. Figure 5.8 gives the ratios of PMP by this alternate approach (100-yr /PMP vs. MAP) to the general-storm PMP of this study. It is important to point out that PMP estimates obtained by the ratio of 100-yr to PMP is not a recommended method for determining PMP. In any case, such a method includes transposi- tion of an index relation without modification. Considerations such as the strength of the inflow wind and moisture potential would have an effect on the ratio of PMP to a lesser storm, such as the 100-yr precipitation, and the relation of the ratio to MAP. The ratios can, however, be used as a check on the general level of the PMP estimates assuming we know the general level of PMP to the north, we have confidence in the 100-yr precipitation estimates, and accept the trans- position of the index relation. Figure 5.8 indicates that the PMP estimates based on the transposed 100-yr/PMP relation vary from a low of 67% of the estimates in this study to a high of 223%. However, more than 60% of the values are within 25% of this report's PMP values. We believe this varia- tion is acceptable, taking into account use of a transposed relation and unknowns in the generalized charts of mean annual precipitation and frequen- cy values as well as in PMP. Charts used were for MAP and NAP referenced in section 3.1.3, and those for Nevada (Hardman 1965) and southern California (Rantz 1969). .140 Figure 5.8. — Ratios of PMP determined from an alternate approaah (see section 5.7) to that of this study for 10 mi% (26 km?) 24 hr. 115° 110° .e8_I.Q5_l08 1.29 1.0 '•54 1.62 l,<7 '• 20 .94 1.24 1.36 1.22 l!L5_l.lB_. 85 _.«£>:« 40°— V-<8 i. '•01 1.21 |.29 V. 15 1.14 1.07 .95 1.27 M7 .98 .83 .7B_40° I I I ^ 1.34 l.,7 1.46 ,.24 1 ( .22 1.31 1.29 1.10 1.24 112 .88 .8 \ \ U4 ''" '- 27 '■** 1-33 1.36 1.37 1.22 1.15 ^.23 1.01 N I I < '•»M.10 1.20 1.27 .!l5_,.^_L27_,.Q7_1.2 J _,'.U_l.l^No ) 23 '-33 1.11 l.^J.26 UQ , 27 )23 ]J3 | 07 )os 25^~^/\.23 1.4 1 , u ,\ ! .*? 1.15 1.35 l.,9 1.84 1.39 1U '•' 6 '.01, ,.24 i.,3 ,.,o .95 .95 l'.02. 35° 115° DISTANCE SCALE v!6 1.19 1.19 1.05 \0ov& Pei/i/s d*t e) i Nevada Area mi 2 (km 2 ) Latitude -4/ * 20 ' , Longitude //5Vfl of basin center Month Oct. *- Duration (hrs) 6 12 18 24 48 72 A. Convergence PMP 1. Drainage average value form ^ one of figures 2.5 to 2.16 9.2 in. (pafT 2. Reduction for barrier- elevation [fig. 2.18] 50% 3. Barrier-elevation reduced PMP [step 1 X step 2] ^(^ in. ^jjarff 4. Durational variation [figs. 2.25 to 2.27 „ ... „ and table 2.7]. £2 82 95 [00 J/9 122 X 5. Convergence PMP for indicated durations [steps 3X4] ?.fl 3.<5 4.3 46 £5 5.9 in. 2 2 6. Incremental 10 mi (26 km ) PMP [successive subtraction in step 5] 2.8 1-0 0-5 Q.3 09 0.4 in. (gflfl 7. Areal reduction [select from figs. 2.28 and 2.29] 63 85 93 98 100 100 % 8. Areally reduced PMP [step 6 X step 7] /.8 0.8 0.5 fl.3 0.9 (9.4 in. (pfi 9. Drainage average PMP [accumulated values of step 8] IQ_ 2& 3J_ 34 ^3 47 in . (jpatf B. Orographic PMP 1. Drainage average orographic index from figure 3.11a to d. 3.3 in. ^P*0 2. Areal reduction [figure 3.20] 82 % 3. Adjustment for month [one of figs. 3.12 to 3.17] IQQ % 4. Areally and seasonally adjusted PMP [steps 1X2X3] 2.7 in. <>f0 5. Durational variation [table 29 5G> 79 100 160 169 % 3.6] 6 - SSL™ £ x r 5 ? lven dm " QAJAZL2143S±^.^ C. Total PMP 1. Add steps A9 and B6 £6 47 52 ^7 &6 98 in. £prf5 2. PMP for other durations from smooth curve fitted to plot of computed data. 3. Comparison with local -storm PMP (see sec. 6.3). 152 Table 6.3A. — Local-storm PMP computation, Colorado River, Great Basin and California drainages. For drainage average depth PMP. Go to table 6.3B if areal variation is required. 2 2 Drainage Area mi (km ) Latitude Longitude Minimum Elevation ft (m) Steps correspond to those in sec. 6.3A. 2 2 1. Average 1-hr 1-mi (2.6-km ) PMP for in. (mm) drainage [fig. 4.5], 2. a. Reduction for elevation. [No adjustment for elevations up to 5,000 feet (1,524 m) : 5% decrease per 1,000 feet (305 m) above 5,000 feet (1,524 m) ] . % b. Multiply step 1 by step 2a. in. (mm) 3. Average 6/1-hr ratio for drainage [fig. 4.7]. Duration (hr) 1/4 1/2 3/4 1 2 3 4 5 6 4. Durational variation for 6/1-hr ratio of step 3 [table 4.4]. % 1-mi 2 (2.6-km 2 ) PMP for indicated durations [step 2b X step 4] . in. (mm) Areal reduction [fig. 4.9]. % 7. Areal reduced PMP [steps 5X6]. in. (mm) 8. Incremental PMP [successive subtraction in step 7]. in. (mm) } 15-min. increments 9. Time sequence of incre- mental PMP according to: Hourly increments [table 4.7]. in. (mm) Four largest 15-min. increments [table 4.8]. in. (mm) 153 Table 6.3B — Local-storm PMP computation, Colorado River and Great Basin, and California drainages. (Giving areal distribution of PMP) . Steps correspond to those in sec. 6.3B. 1. Place idealized isohyetal pattern [fig. 4.10] over drainage adjusted to 1:500,000 scale to obtain most critical placement. 2. Note the isohyets within drainage. 2 2 3. Average 1-hr 1-mi (2.6-km ) PMP for drainage [fig. 4.5]. in. (mm) 4. a. Reduction for elevation. [No adjustment for elevations up to 5,000 feet (1,524 m) , 5% decrease per 1,000 feet (305 m) above 5,000 feet (1,524 m) ] . % b. Multiply step 3 by step 4a. in. (mm) 5. Average 6/1-hr ratio for drainage [fig. 4.7]. "° Obtain isohetal labels for 15-min incremental and the highest PMP from table 4.5 corresponding 6/1-hr ratio of step 5. Isohyet PMP Increment ABCDEFGHIJ Highest 1-hr Highest 15-min. 2nd " 3rd " in % 4th " Obtain isohyetal labels in % of 1-hr PMP for 2nd to 6th highest hourly incremental PMP values from table 4.6 using 6/1-hr ratio of step 5. 2nd Highest 1-hr PMP 3rd 4th " in % 5th " 6th " 8. Multiply steps 6 and 7 by step 4b to get incremental isohyetal labels of PMPo Highest 15-min. 2nd " . 3rd " 4th " Highest 1-hr in in. (mm) 2nd " ._„_'. 3rd " "" 4th " 5th " 6th " 9o Arrange values of step 8 in time sequence [tables 4.7 and 4.8]. 154 Table 6.4A. — Example of computation of local-storm PMP. Average val ues for the drainage . Drainage Sycamore Ck. (above Verde River) r Arizona Area 360 mi Qsatr) Latitude 34 ° 53' Longitude 112* 08' Minimum Elevation 3&5Q ft £jatf Steps correspond to those in sec. 6.3A. 9 9 1. Average 1-hr 1-mi (2.6-km ) PMP for J 0.1 in. £jaiff) drainage [fig. 4.5], 2. a. Reduction for elevation. [No adjustment for elevations up to 5,000 feet (1,524 m) : 5% decrease per 1,000 feet (305 m) above 5,000 feet (1,524 m) ] . JQQ % b. Multiply step 1 by step 2a. JQ, / in. £pBfO 3. Average 6/1-hr ratio for drainage [fig. 4.7]. /. 2. Duration (hr) 1/4 1/2 3/4 1 2 3 4 5 6 4. Durational variation for 6/1-hr ratio of step 3 [table 4.4]. 74_ 89. 95_ 100 JJ0 J/5 JJ3 J/9 120 % 5. 1-mi 2 (2.6-km 2 ) PMP for indicated durations [step 2b X step 4]. 15 _9V _26 10J_ IU_ IJJo U9 120 12J_ in. £*m1 6. Areal reduction [fig. 4.9]. J6_ 20_ 23 26 30 34 37 385 40 % 7 o Areal reduced PMP [steps 5X6]. JZ J8_ 22 26 33 39 44 4^43 m. (^ 8. Incremental PMP [successive subtraction in step 7] 26 02 0606 0202 in. (jprttf /2 0.6 0.4 Q.4 } 15-min increments 9. Time sequence of incre- mental PMP according to: Hourly increments [table 4.7]. 02 0.6 2.6 OJ 0.5 02 m. prf Four largest 15-min. increments [table 4.8], LA 06 04 04 in. (jprtO 155 Table 6.4B. — Example computation of local-storm PMP. Areal distribution over the drainage . Steps correspond to those in sec c 6.3Be lo Place idealized isohyetal pattern [fig. 4.10] over drainage adjusted to 1:500,000 scale to obtain most critical placement. 2. Note the isohyets within drainage D 2 2 3o Average 1-hr 1-mi (2.6-km ) PMP for drainage [fig„ 4.5]. IQ. I in. (jparT 4. a. Reduction for elevation c [No adjustment for elevations up to 5,000 feet (1,524 m) , 5% decrease per 1,000 feet (305 m) above 5,000 feet (1,524 m) ] . IQQ % b. Multiply step 3 by step 4a c IQ.j in. (rustf 5. Average 6/1-hr ratio for drainage [fig. 4.7], / 2 6 Obtain isohyetal labels for 15-min PMP from table 4.5 corresponding 6/1-hr ratio of step 5 and labels for highest 1 hr c Isohyet PMP Increment ABC D E F G H I J Highest 1-hr 100 82 56 44 ?2 23 l(o IS 12 // Highest 15-min. 14 5(o 32 2/ 14 3 7 G 5 4 2nd /5 15 15 It 9 6 4 3 .3- 3 3rd Q> Q> G> 6 5 5 3 2 2 2 4th 5 6 5 5 4 4 2 2 2 2 in % 7. Obtain isohyetal labels in % of 1-hr PMP for 2nd to 6th highest hourly incremental PMP values from table 4.6 using 6/1-hr ratio of step 5. in % Multiply steps 6 and 7 by step 4b to get incremental isohyetal labels of PMP„ Highest 15-min. 2nd 2nd Highest 1-hr // II II // IQ 8 7 5 5 S 3rd it 4 4 4 4 4 4 4 4 4 4 4th ii ? 1 3 3 3 3 3 3 3 3 5 th it 2 2 2 2 2 2 2 2 2 2 6 th it I 1 / / / 1 / / / / 3rd 4 th 7.5 5.7 3.2 2.1 1.4 1.5 1.5 1.6 /•2 o.? 0.G O.G 0. 6 0.(o 0.5 0.5 0.5 0.5 0.5 04 10. 1 03 5.9 4.4 32 If /./ I.I l-l 1,0 0.4 0.4 0.4 0A 0.4 0.3 03 C 3 03 0.3 0.2 0-2 0.2 0.2 0.2 0.1 o.i 0,1 O.I 0J Highest 1-hr jQj_ &3_ 5,9 4± Z2. 23 J£_ _A3_ JUL JLL in in - ( ^ 2nd 3rd 4th 5th 6th O.Q 0.7 0.G 0.5 0.4 O.Co 0.4 03 03 0.3 0* 03 0.2 0.2 0.2 0.4 02 0.2 02 o.z 23 1A A3 1.2 II O.B 07 0.5 0.5 6-5 0.4 0.4 0.4 0.4 0-4 03 03 03 03 03 0.2 0.2 0.2 0.2 0.2 O.I 0.1 0.1 04 01 9. Arrange values of step 8 in time sequence [tables 4.7 and 4.8]. 156 ACKNOWLEDGEMENTS From the time this study was first begun, many members of the Hydro- meteorological Branch have been involved. Some have since left the Branch, but should be remembered here. Robert Weaver did much of the groundwork and outlined the direction the study should take, and Albert Shipe aided computations with his programming ability. Many days of painstaking tasks were undertaken by former technicians Miriam McCarty, Ray Evans and Wallace Brewer. Currently, Ro:;anne Johnson, and particularly Marion Choate, our lead technician have carried out these tasks. Appreciation is also given to John F. Miller, Chief of the Water Manage- ment Information Division (WMID) and to Dr. Vance A. Myers, Chief of the Special Studies Branch, WMID, for their helpful guidance and critical re- views of our efforts. 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