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Probable Maximum Precipitation U.S. DEPARTMENT OF COMMERCE WEATHER BUREAU TECHNICAL PAPER NO. 42 Generalized Estimates of Probable Maximum Precipitation and Rainfall-Frequency Data for Puerto Rico and Virgin Islands for Areas to 400 Square Mlles, Durations to 24 Hours, and Return Periods from 1 to 100 Years U.S. DEPARTMENT OF COMMERCE LUTHER H. HoDGEs, Secretar:y WEATHER BUREAU F. W. REICHELDERFER, Chief TECHNICAL PAPER NO. 42 Generalized Estimates of Probable Maximum Precipitation and Rainfall-Frequency Data for Puerto Rico and Virgin Islands for Areas to 400 Square Mlles, Durations to 24 Hours, and Return Periods from 1 to 100 Years Prepared by Cooperative Studies Section Hydrologic Services Division U.S. Weather Bureau for Engineering Division LOI\t't COPX. Soil Conservation Service U.S. Department of Agriculture WASHINGTON, D.C. 1961 For sale by tbe Superintendent of Documents, U.S. Government Printina Office, W31!1hington 25, D.C. - Price 50 cents CONTENTS Page Introduction_____________________________________________________________________________ 1 Chapter 1. Tropical Storms of Puerto Rico and Virgin Islands__ __ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ 2 Introduction-Maximum observed rainfalls-Meteorological situations associated with maximum observed 24-hr. rainfalls-Tropical storms of Puerto Rico and Virgin Islands Chapter 2. The Hurricane ModeL__________________________________________________________ 9 Introduction-The convergence component of the model-Computation of convergence rainfall-The orographic component of the model-Computation of orographic rainfall-Combining convergence and orographic rainfall­ Tests of model Chapter 3. Probable Maximum Precipitation_________________________________________________ 21 Estimation-Depth-duration relations-Depth-area relations-Chronological distribution-Appraisal Chapter 4. Rainfall-Frequency Data_ _ __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ 34 Basic data-Frequency analysis-Tropical versus nontropicslstorm~<-Isopluvisl maps-Depth-ares relationships­ Seasonal variation References_______________________________________________________________________________ 89 Appendix A. Probable Maximum Precipitation for Local Cloudbursts___________________________ 90 Introduction-Cloudburst PMP-Depth-ares relations-Chronological distribution-Appraisal Appendix B. Glossary ______________________ ~---------------------------------------------- 93 LIST OF ILLUSTRATIONS 1-1 Adjusted maximum observed 24-hr. rainfalls (in.) for Puerto Rico __________________________________ ---- __ - 3 1-2 Adjusted maximum observed 24-hr. rainfalls (in.) for Virgin Islands _______________ - _____ --- ___ ---- __ ------ 4 1-3 World's maximum observed rainfalls _______________________________________________________ - ____ ---- __ - 6 2-1 Hurricane model surface wind field _________ . __________________________________ - _____ - _- ___ ------------ 10 2-2 Vertical distribution of convergence and divergence in hurricane modeL ________________________ -- ___ -----_- II 2-3 Vertical circulation in hurricane model (after Riehl) ________ ~ __________________________ - _____ ---- _------- 11 2-4 Variation of computed convergence rainfall intensity with distance from center of model hurricane ____________ _ 13 2-5 Track of hurricane Betsy across Puerto Rico, August 12, 1956 (after Col6n) ________________________________ _ 14 2-6 Variation of computed convergence rainfall intensity with distance along a line 8 mi. from-model hurricane cent.er and perpendicular to a radius (center line) _________________________________________________ ----------- 16 2-7 Variation of computed forward, or onslope, horizontal wind component along a line 8 mi. to right of model hurricane center and parallel to the direction of motion of the center _____________________________________________ _ 17 2-8 Profile of orographic rainfall intensity computed from the v1 profile of figure 2-7 for a slope of 1/4 at an elevation of 1 km., m.s.L _____________________________________________________ - _____ - _____ ----- _------------ 17 2-9 Combination of convergence and orographic rainfall intensity profiles for a slope of 1/4 at an elevation of 1 km., m.s.l. Resultant profile is for a line 8 mi. to right of model hurricane center and parallel to the direction of motion of the center-------------------------------------------------------------------------------------- 18 3-1 Selected tropical storm tracks showing various directions of approach to Puerto Rico and Virgin Islands- ------ -- 23 3-2 Pre~y estimate of probable maximum 24--hr. point precipitation based on application of hurricane model of chapt$"2 moving. from permissible directions at 5 m.p.h ______ - -- ___ ---- _------- ----------------------- 24 3-3 Mean (iii}:- of annual series of 24-hr. point precipitation ______________________ - __ -- __ ----------------------- 25 3-4 Adjusted standard deviation (sy) of annual series of 24-hr. point precipitation ______________________________ _ 25 3-5 Preliminary estimate of probable maximum 24-hr. point precipitation based on the equation XM =i + 15sN- ----- 26 3-6 Probable maximum 1-hr. point precipitation (in.) for Puerto Rico _________________ - _____ ------------------ 26 3-7 Probable maximum 6-hr. point precipitation (in.) for Puerto Rico ___ ~ ___________________ - _____ ------------ 27 3---8 Probable maximum 24-hr. point precipitation (in.) for Puerto Rico ______________________ ---- __ ------------ 27 3-9 Probable maximum 1-hr~ point precipitation (in.) for Virgin Islands __________________________________ ------ 28 IU Page 3-10 Probable maximum 6-hr. point precipitation (in.) for Virgin Islands ____ -- __ -- ___ -- ____ -____________________ 28 3-11 Probable maximum 24-hr. point precipitation (in.) for Virgin Islands_______________________________________ 29 3-12 Depth-duration diagrams for hurricane PMP (See par. 3.2.1 for example of use)_____________________________ 31 3-l 3 Depth-area curves for hurricane PMP (For use with figs. 3-6 to 3-11)-------_---- __ --- __ --- _ _ _ _ _ _ _ _ __ ___ _ _ 32 4-1 Duration-interpolation diagram_----------------------------------------------------.-------------____ 35 4-2 Return-period-interpolation diagram_--_----_----------------. -----------------------------------_ _ _ _ _ _ 35 4-3 Relation between K and return period for 20-, 50-, and 100-yr. records (after Gumbel)_----- __ ---------------_ 36 4-4 Grid showing points for which rainfall-frequency data were computed in construction of maps showing precipitation values for durations between 1 and 24 hr. and return periods between 2 and 100 yr________________________ 38 4-5 Depth-area curves for rainfall-frequency data (For use with figs. 4-7 to 4-104)______________________________ 38 4-6 Monthly distribution (in percent) of 24-li. rainfalls for various return periods _____________________ .;::________ 39 4-7 1-yr. 30-min. rainfall for Puerto Rico (in.)-----------------------------------------------------;,,._______ 40 4-8 2-yr. 30-min. rainfall for Puerto Rico (in.)---_--------------------------------------------- ___ ;:________ 40 4-9 5-yr. 30-min. rainfall for Puerto Rico (in.)-----------------------------------------------_---------_____ 41 4-10 10-yr. 30-min. rainfall for Puerto Rico (in.) ______ - __ --- ___ --_----_--------_--------------_______________ 41 4-11 25-yr. 30-min. rainfall for Puerto Rico (in.)------------------------------------------------------------- 42 4-12 50-yr. 30-min. rainfall for Puerto Rico (in.)------------------------------------------------------------- 42 4-13 100-;yT. 30-min. rainfall for Puerto Rico (in.)------------------------------------------------------------ 43 4-14 1-yr. 1-hr. rainfall for Puerto Rico (in.)---------------------------------------------------------------- 43 4-15 2-yr. 1-hr. rainfall for Puerto Rico (in.)---------------------------------------------------------------- 44 4-16 5-yr. 1-hr. rainfall for Puerto Rico (in.) ___ -- ___ -----------------------------------------------------___ 44 4-17 10-yr. 1-hr. rainfall for Puerto Rico (in.)_----------------------------------------------------- ____ ----- 45 4-18 25-yr. 1-hr. rainfall for Puerto Rico (in.)_ __ ------------.---------------------------_---- _______ -------_ 45 4-19 50-yr. 1-hr. rainfall for Puerto Rico (in.)--------------------------------------------------------------- 46 4-20 100-yr. 1-hr. rainfall for Puerto Rico (in.) ___ -_-------------------------------------- ___ -- ________ ----___ 46 4-21 1-yr. 2-hr. rainfall for Puerto Rico (in.)- __ ---------------------------------------------------- ____ ----_ 47 4-22 2-yr. 2-hr. rainfall for Puerto Rico (in.) ____ - __ --------------------------------_------_---- __ -__________ 47 4-23 5-yr. 2-hr. rainfall for Puerto Rico (in.) ____ --------------------------------------------------__________ 48 4-24 10-yr. 2-hr. rainfall for Puerto Rico (in.)_-------------------------------------------------------------- 48 4-25 25-yr. 2-hr. rainfall for Puerto Rico (in.)_-------------------------------------------------------------- 49 4-26 50-yr. 2-hr. rainfall for Puerto Rico (in) ___ - __ ------------------_---------_--- ___ -- ___________ --------- 49 4-27 100-yr. 2-hr. rainfall for Puerto Rico (in.)-------------------------------------------------------------- 50 4-28 1-yr. 3-hr. rainfall for Puerto Rico (in.) _____ ---- ______ - ____ -- __ -- _______________________________ -------- 50 4-29 2-yr. 3-hr. rainfall for Puerto Rico (in.) ____ -- ________
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