Rainfall Frequency/Magnitude Atlas

for the 

South­Central United States 

by

Gregory E. Faiers

Department of Geography

University of Pittsburgh at Johnstown

Johnstown, PA 15902

Barry D. Keim

Department of Geography

University of New Hampshire

Durham, NH 03824

Robert A. Muller, Director

Southern Regional Climate Center 

Department of Geography and Anthropology

Louisiana State University

Baton Rouge, LA 70803

SRCC Technical Report 97­1

Geoscience Publications

Department of Geography and Anthropology 

Louisiana State University

Baton Rouge, LA 

CONTENTS

Introduction

Justification             

Geographic Patterns and Relationships to TP40                                                      

Rainfall Frequency/Magnitude Maps                                                                                 

Appendix                                                                                                                             

Bibliography                                                                                                                       

Frequency­magnitude   relationships   of   heavyrainfall events are commonly utilized in designprojects   by   providing   useful   guidelines   toengineers,   planners,   and   hydrologists   aboutfuture expectable storm events.  Despite its age,the   most   widely   used   publication   employingthese   relationships   is  Technical  Paper  No.  40(hereafter   referred   to   as   TP40)   by   DavidHershfield   (1961).     TP40   examined   extremerainfall events in the United States and provided“expectable”   precipitation   amounts   forrecurrence   intervals   from   1   to   100   years   fordurations from 30 minutes to 24 hours.   Otherpapers   addressing   this   topic   include   WeatherBureau  Technical   Papers   No.   2  (1947)   onmaximum recorded rainfall   from 5 minutes   to24 hours at  first­order stations;  No. 24  (1954)rainfall return periods for 5 minutes to 4 hours;No. 29 (1958) which presents rainfall intensity­duration­frequency distributions;  No. 49  (1964)on 2 to 10 day rainfalls for return periods from 2to  100  years;   and  Hydro­35  (Frederick   et   al.,1977) which examines 5 to 60 minute rainfallfor the central and eastern United States.

The   rainfall   frequency   and   magnitudepatterns   illustrated   in   TP40   need   to   bereexamined:

* because there are 35 additional years ofprecipitation data since its publication in 1961

*   because   of   recent   concerns   aboutglobal climate change

* because of the short periods of recordin   TP40   with   less   than   half   of   the   stationshaving more than 15 years of record; and 

*   because   of   the   very   generalizedanalysis for the 48 conterminous states.

There can also be great spatial variabilityin frequency­magnitude relationships over shortdistances,   especially   in   mountainous   areas(Haiden et al., 1992; Zurndorfer, 1990).

Another   serious   limitation   is   that   since

the publication of TP40, it has become widelyaccepted   that   there   is   no   single   statisticaldistribution   which   provides   the   best   fit   forextreme precipitation data in all climate regionsof the country (Sevruk and Geiger, 1981; Huff1990).    Alternative  statistical  approaches  havealso   been   suggested   in   recent   publications(Hosking,  199;  Huff   and  Angel,  1992;  Wilks,1992; Zwiers and Ross, 1992).   Concerns werefurther increased by the findings of Sorrell andHamilton   (1989)  who  found   that   the  24­hour,100­year value from TP40 was exceeded over 3times more often than expected in Michigan andby   Angel   and   Huff   (1991)   who   found   thatIllinois   and   Wisconsin   had   almost   twice   asmany 100­year, 24­hour events as anticipated byTP40.

In   the   South   Central   United   States,extreme precipitation events, and the floods theygenerate have occurred frequently in the 1980sand 1990s.  Recent examples include:

* June 26­July 1, 1989 – rainfall up to 20inches from Tropical Storm Allison resulted inflooding across Much of Louisiana and portionsof eastern Texas and western Mississippi;

* November 7, 1989 – heavy rains of upto   19   inches   fell   in   the   New   Orleans   area(NOAA, 1989);

* May 18, 1990 – 13 inches of rain wereobserved   in   just   nine   hours   at   Hot   Springs,Arkansas;

*   October   5,   1991   –   a   75   minuteaccumulation of 6 inches, along with a 12­houraccumulation   of   10   inches,   was   reported   atTuskahoma, Oklahoma;

* October 15­19, 1994 – storm totals ofnear 30 inches occurred north of Houston and 8­inch   storm   totals   or   more   were   widespreadacross   southeastern  Texas   (Muller   and  Faiers,1995);

* May 8­9, 1995 – rainfall in excess of25   inches   fell   in   parts   of   Hancock   County,

INTRODUCTION

Mississippi, with 10 to 20 inches over much ofmetropolitan   New   Orleans   accompanied   bysignificant   flooding   over   much   of   low­lyingNew Orleans and Slidell,  Louisiana (Muller etal., 1995),

The question of an increasing frequencyof events in recent decades has also been notedin   professional   publications   and   reports.Belville  and  Stewart   (1983)   found an  unusualnumber of rain events in excess of 10 inches inLouisiana in 1982 and 1983.  Widespread recordflooding   associated   with   persistent   frontalrainfall was reported during March and April of1990 in eastern Texas and Oklahoma by Jensen(1990).     It   was   also   found   that   recentmagnitudes   of   New   Orleans   storms   weresignificantly   larger   than   storms   over   thepreceding 100 years  and heavy rainfall  eventsappear to be increasing in frequency (Keim andMuller, 1992; 1993).   Muller and Faiers (1984)had found earlier that most record peak stageson rivers in the East­Central climate division of Louisiana   had   occurred   since   1973   with   anincreasing trend throughout the 1970s and early1980s.   Hirschboeck and Coxe (1991) detected

increases   in   urban   flash   flooding   in   theLouisiana cities of Monroe and Alexandria.  Finally, Keim (1997) found an increasing trendin heavy rainfalls at several locations along anaxis extending from northeastern Texas throughthe Appalachians.  

Collectively,   these   studies   indicate   thatexcessive   rainfall   and   flooding   events   werebecoming more common in the U.S.  South  inthe recent past, especially in the 1980s and early1990s.     Impacts   of   these   extreme   eventsincluded   disruption   of   transportation   systems,river­basin   flooding,   inundation  of   farm  landsand homes, loss of life, thus creating an obviousneed for evaluations of the temporal and spatialcharacteristics   of   extreme   rainfalls   across   thisregion (Fig. 1).

Fig. 1. the six­state region of the Southern Regional Climate Center

Several of the Regional Climate Centers (RCCs)have   undertaken   re­evaluations   of   extremerainfall   frequency­magnitude   relationshipswithin their respective regions (Changnon et al.,1992;   Huff   and   Angel.   1992;   Knappenbergerand Michaels, 1993; Wilks and Cember, 1993).A   pilot   study   was   also   undertaken   by   theSouthern RegionalClimate   Center   (SRCC)   to   evaluate   extremerainfall   frequency­magnitude   relationshipsacross   the   state   of   Louisiana   (Faiers   et   al.,1994a).     In   this   study,   methods   used   weresimilar to those employed in TP40, but longerperiods   of   record,   including   data   through   the1980s and part of the 1990s, were used to derivethe  quantile   estimates;   quantiles   are   estimatesrepreseting return periods and associated stormmagnitudes.  Patterns from the updated maps forLouisiana were compared to those in TP40 (Fig.2).     Overall   storm   magnitudes   did   not   varygreatly between the two studies, but the SRCCproduct depicted a more complex spatial patternwith   shifts   in   the   regions   of   extreme   rainfallmaxima   from   southeastern   to   southwesternLouisiana.

The   findings   from   this   pilot   study,   aswell   as   results   from   other   regional   studies,verified the need for a regional format across thesix­state   region  of   the  SRCC,  and   for  greaterspatial   resolution   of   the   “expected”   extremerainfalls   than depicted  in  TP40.    Furthermore,frequency­magnitude   relationships   of   extremerainfall  have had a high user demand, rankingamong the most commonly requested data setsat   the  SRCC.    As   a   result,   deriving   accuratefrequency­magnitude   estimates   of   extremeprecipitation across the six southern states of theFig.   2.   Twenty­four­hour   2­year   rainfalls   inLouisiana according to the Technical Paper No. 40and   our   updated   version   using   similar   methods.Source: Faiers et al., 1994a.                                                                   

JUSTIFICATION

SRCC   (Fig.   2)   became   part   of   the   researchagenda   at   the   SRCC.     This   research   yieldedmore   regionally   representative   estimates   thanTP40, and it should support improved drainageand   containment   designs.     This   documentsummarizes   the   new   estimates   of   therelationships for durations of 3, 6, 12, 

and 24 hours for 2­, 5­, 10­, 25­, 50­, and 100­year   return   periods   with   regional­scale   maps.Text sections describe the geographical patternsand   the   primary   differences   to   TP40.     Thedevelopment of  the data  sets  and methods areincluded as an appendix.

Three­Hour Storms

Figures   3.1   to   3.6   represent   the   rainfallmagnitudes   for   3­hour   storms   at   each   of   theselected   recurrence   intervals.   Much   of   thegeographical pattern that emerges here becomeseven   more   apparent   at   the   longer   recurrenceintervals   and   extended   durations.   The   generalpattern of quantile estimates depicts a regionalmaxima along   the  Gulf  Coast   extending   fromsoutheastern Texas into southwestern Louisiana.Another   area   with   relatively   large   stormmagnitudes   occurs   over   the   coastal   areas   ofsoutheastern Louisiana and coastal Mississippi.At   the   longer   recurrence   intervals,   thesoutheastern   Texas   to   southwestern   Louisianacoastal   maxima   becomes   larger   than   theestimates for southeastern Louisiana and coastalMississippi.  Storm magnitudes decrease to  thenorth   and   west   of   these   two   maximum   areasalong   the   coast,  with   another   local  maximumdeveloping  over   the  Ouachita­Ozark  mountainregions of Arkansas and eastern Oklahoma wereorographic   precipitation   increases   stormmagnitudes.   Another   region   of   greater   stormmagnitudes   generated   by   orographicprecipitation   occurs   along   the   BalconesEscarpment   and   Hill   Country   west   andsouthwest of Austin and San Antonio extendingsouthwestward  towards   the Rio Grande River.This   is  an  area  plagued by  an  unusually  highnumber   of   catastrophic   flood   events(Hirschboeck, 1987a). 

In   eastern   Tennessee,   there   is   again   astrong   orographic   increase   of   averageprecipitation   and   magnitudes   of   individualstorm events across the western margins of the

Great  Smoky  Mountains   and   the  Appalachiansystem of mountains and valleys as a whole. Asdetailed by Haiden et al. (1992) local variationsin extreme rainfall magnitudes can vary greatlyover short distances, but they cannot be depictedin   this   regional   study   because   of   thegeographical scale of the maps and also becauseof   insufficient   station   densities   in   themountainous terrain, with high mountain crestsadjacent to deep valleys. 

The  upper   tributaries   of   the  TennesseeRiver system have eroded "rain­shadow" valleyswhere average precipitation and the magnitudesof extreme events tend to be significantly lowerthan adjacent uplands.   The very broad HolstonRiver  Valley northeast  of  Knoxville   is  a  rain­shadow region  large enough to be representedon the maps. Storm magnitudes there are muchlower and similar to those found in the semi­aridand   arid   regions   of   western   Texas   andOklahoma.   Another   smaller   region   withrelatively lower magnitudes  is   located west  ofLake Pontchartrain   is  southern Louisiana.  Theanomalous   region   was   also   identified   in   aregional   study   conducted   by   the   NationalWeather  Service  Office  of  Hydrology   (Vogel,1992). At this time, a definitive explanation forthis anomaly has not been found; however someatmospheric   mesoscale   interaction   with   LakePontchartrain during extreme rainfall  events   iscertainly a possibility. 

When comparing the 3­hour storm mapsto those in TP40, the 2­year recurrence intervalis   strikingly   similar   in   magnitude   and   spatialpattern,   but   the   likeness   decreases   withsuccessively longer recurrence intervals. This isnot   surprising   because   TP40   was   able   toaccurately estimate shorter recurrence intervalseven with its short  station records, but at longer

GEOGRAPHICAL PATTERNS AND RELATIONSHIPS TO TP40

Figures 3.1 through 6.6 referred to in this section are

 all located in the atlas section starting on page 11

recurrence   intervals,   these   records   wereinadequate.  With   the   longer  periods  of   recordused in this analysis, we are more comfortablewith   the   longer   recurrence   interval   estimatesthan those displayed in TP40. In both versionsof the 3­hour 2­year storm, the 3.5­inch isohyetextends   roughly   from   coastal   Mississippiwestward along the coast.  The SRCC version,however,   continues   this   interrupted   isohyetwestward to Gavleston, while TP40 terminatesthis isohyet south of Lake Charles, LA. The 3­inch and 2.5 inch isohyets in the SRCC map aredisplaced farther to the north than in TP40, andTP40   does   not   depict   the   orographicenhancements   of   the   Ouachitas   and   Ozarks,which   are   not   captured   at   any   recurrenceinterval   nor   for   any   duration   in   TP40.   Thisnorthward displacement suggests higher rainfalltotals   in  the SRCC maps.  The two documentstend  to  be  more  similar   to   the  west  and  east,with   the   following  exceptions  depicted   in   theSRCC   maps:   (1)   the   recognition     of   theBalcones Escarpment and Hill Country in Texasas   a   zone  of   increased   storm magnitudes,   (2)more of a southeast­northwest orientation of theisohyets in extreme western Texas, which mirrorthe  orientation  of   the  Davis  Mountains,   (3)   agreater emphasis placed on the rain shadow ineastern Tennessee, and (4) the lower magnitudeanomaly depicted west of Lake Pontchartrain inLouisiana. 

These differences appear in maps of alldurations   and   recurrence   intervals,   with   thedifferences   accentuated   at   longer   recurrenceintervals.     Finally,   with   the   3­hour   100­yearstorms,   it   becomes   apparent   that   the   coastalareas of the region have the greatest increases inmagnitude over those found in TP40, while thedifferences   to   the west  and north are more  ininterpretations   of   orographic   and   rain­shadowpatterns. There is also a shift in the location ofstorm maxima, with the SRCC product showingthe greatest  magnitudes   from  the  upper  TexasCoast into southwestern Louisiana, while TP40

always has the regional maxima in the extremeMississippi River Delta area of Louisiana. It isalso interesting to note that the magnitudes of 3­hour 100­year storms range as high as 11 inchesalong the southeastern Texas and southwesternLouisiana   coasts.   Quantile   estimates   drop   toabout 5 inches along the northern borders of theregion,  and down to  less  than 3 inches acrossmuch   of   extreme   western   Texas   around   andsoutheast of El Paso, and also in the rainshadowof   the   Holston   River   valley   in   northeasternTennessee in the vicinity of Bristol. 

Six­Hour Storms

At   the   shorter   recurrence   intervals,   6­hourstorms (Figs.  4.1   to  4.6)  are   relatively similarbetween   this   document   and   TP40,   andgeographical patterns and deviations are similarto the relationships found for the 3­hour storms.Again, as the recurrence intervals increase, thedifferences   increase with  the  same changes  aspreviously  discussed.  For   example,   for   the  6­hour   100­year   storm,   the   greatest   magnitudedepicted   is   10   inches   in   extreme  southeasternLouisiana in the TP40 version, while the SRCCmap (Fig. 4.6) depicts  the greatest  magnitudes(12   inches)   along   an   axis   from   west   ofGalveston into coastal southwestern Louisiana.Along the north and west fringes of  the studyregion,   both   reports   still   depict   similarmagnitudes. The lowest estimates are less than 3inches   from   El   Paso   southeastward   down   theRio  Grande.     In   the   rainshadow valley  of   theHolston   River   in   northeastern,   Tennessee,   theestimates are less than 4 inches. 

Twelve­Hour Storms

As storm durations increase to 12 hours (Figs.5.1   to   5.6)   and   magnitudes   increase,   thepreviously established relationships between the

documents   are   sustained   and   the   absoluteincreases   in  magnitudes  along   the  Gulf  Coastbecome more apparent.   For example,    on the12­hour 100­ year SRCC isohyet map (Fig. 5.6),the Lake Charles area of southwestern Louisianahas   a   magnitude   of   approximately   14   inches,while   TP40   depicts   a   value   of   just   under   11inches.   Also,   in   the   upland   areas   of   westernArkansas,   there   are   locations   with   100­yearreturn estimates of more than 11 inches, about 3inches greater than in TP40. There are still smallareas in the vicinity of El Paso with less than 3inches,  and   less   than  4   inches   in   the  HolstonRiver valley in northeastern Tennessee. 

Twenty­Four­Hour Storms

Finally, for the 24­hour durations (Figs. 6.1 to6.6), there are similar differences between TP40and this document, with the differences tendingto be greater for the longer return periods.  Themaximum   differences   in   storm   estimates   arefound   in   the   coastal   Texas­southwesternLouisiana   areas   and   in   the   Ouachita­OzarkMountains   where   the   100­year   stormmagnitudes are again about 3 inches greater inthe   SRCC   product   (Fig   6.6).   The   greatestmagnitudes   for   100­year   events   are   about   16inches   between   Galveston   and   Lake   Charles,more than 14 inches over extreme southeasternLouisiana, and more than 12 inches across mostof the Ouachita Mountains in western Arkansasand   eastern   Oklahoma.   Minimum   stormmagnitudes of less than 4 inches are restricted tothe   Rio   Grande   Valley   southeast   of   El   Pasotoward   the  Big   Bend   country,   and   again   lessthan  5   inches   in   the   rainshadow   areas   of   theHolston River valley in northeastern Tennessee. Quantile   estimates   are   almost   the   same   as   inTP40 for the west, north and east fringes of theregion. 

Summary and Conclusions

*   The   magnitudes   of   extreme   events   vary   insystematic   patterns   geographically   for   alldurations   and   return   periods,   with   maximumintensities along the Gulf Coast in the vicinity ofthe   Texas   and   Louisiana   border,   decreasinggradually to the northeast and north, and muchmore rapidly towards the northwest,  west,  andsouthwest. 

* This generalized regional pattern is interruptedwith   steep   increases   where   mountain   barriersand broad uplands induce additional orographicprecipitation, and equally steep decreases across"rainshadow" valleys. 

* Three­hour two­year storms range from about3.5   inches   along   the   southeastern   Texas   andsouthern Louisiana coasts down to less than 1.5inches in extreme western Texas and Oklahoma,with the magnitudes of 100­year storms rangingfrom 11 inches along the coasts of southeasternTexas and southwestern Louisiana down to lessthan 3 inches in extreme western Texas and inrainshadow valleys of northeastern Tennessee. 

* Twenty­four­hour two­year storms range from6   inches   along   the   southeastern   Texas   andsouthern Louisiana coasts down to less than 2inches   in   extreme   western   Texas,   with   themagnitudes of 100­year storms ranging from 16inches   along   the   southeastern   Texas   tosouthwestern Louisiana coasts, down to about 4inches along the Rio Grande valley southeast ofEl Paso. 

* When magnitudes in this report are comparedto TP40, differences are small and insignificantover   the   western   half   of   Texas   and   all   ofOklahoma. 

*   Magnitudes   in   this   report   are   greater   thanTP40 across most of Louisiana, Mississippi, andTennessee,  with  the greater  increases of about10 percent for the longer return periods from 25to 100 years. 

* Magnitudes in this report are also greater forupland areas with orographic precipitation suchas   the  Ouachitas  and  Ozarks  of  Arkansas  andOklahoma,   and   lower   in   large   rainshadowvalleys in northeastern Tennessee. 

Rainfall Frequency/Magnitude 

Maps

Fig. 3.1 3­hour 2­year rainfall pattern.

Fig. 3.2. 3­hour 5­year rainfall pattern. 

Fig. 3.3  3­hour 10­year rainfall pattern. 

Fig. 3.4. 3­hour 25­year rainfall pattern

Fig. 3.5. 3­hour 50­year rainfall pattern. 

Fig. 3.6. 3­hour 100­year rainfall pattern. 

Fig. 4.2.  6­hour 5­year rainfall pattern. 

Fig. 4.1. 6­hour 2­year rainfall pattern

Fig. 4.3. 6­hour 10­year rainfall pattern 

Fig. 4.4  6­hour 25­year rainfall pattern 

Fig. 6­hour 50­year rainfall pattern. 

Fig. 4.6. 6­hour 100­year rainfall pattern. 

Fig. 5.2. 12­hour 5­year rainfall pattern 

Fig. 5.1. 12­hour 2­year rainfall pattern. 

Fig. 5.3. 12­hour 10­year rainfall pattern. 

Fig 5.4. 12­hour 25­year rainfall pattern. 

Fig. 5.5. 12­hour 50­year rainfall pattern. 

Fig. 5.6. 12­hour 100­year rainfall pattern. 

Fig 6.1.  24­hour 2­year rainfall pattern. 

Fig. 6.2. 24­hour 5­year rainfall pattern. 

Fig. 6.3. 24­hour 10­year rainfall pattern.

Fig. 6.4. 24­hour 25­year rainfall pattern. 

Fig. 6.5. 24­hour 50­year rainfall pattern. 

Fig. 6.6.  24­hour 100­year rainfall pattern. 

APPENDIX

Data Series

Only cooperative and first­order station data ofNational Weather Service (NWS) are utilized inthis study. The data were organized into partialduration series (PDS).   PDS were selected overannual   series   (AS)  data  because  they generatemore   accurate   exceedence   probabilities   inextreme   rainfall   analyses   (Hershfield   1961;Dunne   and   Leopold   1978).   The   primarydifference between  these   two series   is   that  anAS includes only the largest precipitation eventfrom every year, while PDS contain the largestevents at  a given site regardless of when theyoccur   during   the   period   of   record.   Thedifference  is   important  because  some calendaryears   have   several   extreme   events   which   areincluded in the PDS, but would be excluded inan AS. Typically AS data are adjusted to PDSusing coefficients (Hershfield, 1961), but use ofPDS  in   this   study made  these   transformationsunnecessary. 

Climatic variability from year to year isrecognized,   but   there   is   no   recognition   ofclimatic trends or changes through the years ofrecord.     The   period   of   record   for   most   sitesranges from 1949 through 1991, but records atsome sites began around 1930, and a few siteshave data which date back into the late 1800s.Only   in   cases  where   regional   anomalies  werestudied in detail were records with less than 40years utilized in this research, with some recordsbeing updated through 1994 when needed. 

Homogeneity of Data

Initially, PDS were extracted for the 3­hour and24­hour series at 27 first­order sites across theregion (Fig. 7). These sites were selected basedupon quality of data (especially with respect tominimizing   missing   observations)   and   aminimum length of record criterion of 35 years.

Each PDS for each location was then tested forhomogeneity in an attempt to avoid assumptionviolations   inherent   to   extreme   probabilitystatistics. In this case, an inhomogeneous PDSwould   contain   significantly   different   stormmagnitudes   based   upon   varying   stormcharacteristics,   resulting   in   a   "mixeddistribution." A distribution is considered mixedwhen   the   overall   'parent"   population   may,   inactuality,   be   composed   of   two   or   moresubpopulations,   each   with   its   own   distinctdistribution"   (Hirschboeck   1987b,   200).   If   aseries   of   extreme   rainfall   contains   distinctlydifferent   distributions,   statistically­derivedexceedence probabilities were found to contain astrong   negative   bias   (Ekanayake   and   Cruise,1994). 

Previous   research   by   Hershfield   andWilson (1960) investigated mixed distributionsin extreme rainfall series in the eastern UnitedStates.  This work was conducted to determinemethods implemented in TP40. They found nosignificant   differences   between   "tropical"   and"non­tropical"   extreme   rainfall   distributions.However, they classified tropical events as onlythose associated  with  "named"   tropical   stormsor   hurricanes,   while   all   other   events   wereclassified   as   non­tropical.     This   method   ofclassification   has   serious   limitations   becausethere are storms of tropical origin near the GulfCoast   that   produce   heavy   rainfall   but   neverreach tropical storm or hurricane status and wereerroneously  included  in   the non­tropical  class.Furthermore,   in   the   non­tropical   classificationthere   are   at   least   two   physically­basedmechanisms (frontal and air mass) that produceheavy rainfall in the eastern United States whichshould   be   partitioned   in   the   search   forphysically­based   mixed   distributions.   Othershave also investigated mixed distributions in avariety   of   extreme   event   studies   (Diehl   and

APPENDIX: DATA AND METHODS 

Potter,   1987;   Singh,   1987;   Cruise   and   Arora,1990). 

To   test   for   mixed   distributions,   eachstorm   in   each   series  was   classified   as   frontal(FR),   tropical   disturbance   (TD),   combinedfrontal and tropical disturbances (FTD), and airmass   (AM).   Similar   classifications   have   beenutilized   and   described   in   detail   in   previousstudies   of   heavy   rainfall   (Matsumoto,   1989;Faiers et al. 1994b;Keim and Faiers, 1996). Thecombined   FTD   category   was   created   becausethese   synoptic   weather   systems   sometimesinteract to produce great atmospheric instabilityand   enhanced   heavy   rainfall.   An   analysis   ofthese heavy­rainfall producing classes allow forthe   determination   of   whether   extreme   rainfallevents   of   different   origins   can   be   pooledtogether   as   members   of   the   same   probabilitydistribution   across   the   South   Central   UnitedStates. 

To determine statistically whether thereare differences between the magnitudes of   thestorms by synoptic weather types, the Kruskal­

Wallis   one   way   non­parametric   analysis   ofvariance test (Barber 1988), an extension of theMann­Whitney   test,   was   used.   In   situationswhen data are censored at a fixed point (as is thecase   with   these   data),   Bradley   (1968)recommends use of the Mann­Whitney test andthat the truncated data be accounted for using atechnique   developed   by   Halperin   (1960).However,   this  modification  is  only accurate  ifno more than 75% of the population is censored.Clearly,   in   the   analysis   of   extreme   rainfallevents,   well   over   75%   of   rain   events   arecensored   from   the   samples,   making   therecommended   adjustment   inappropriate.   Thisadjustment  was  found appropriate   for  analysisof flood data, but has never been applied to theanalysis of extreme rainfall because of the largepercentage   of   censored   rainfall   events.Therefore,   the   unadjusted   Kruskal­Wallis   testwas used and potential errors in the results wererecognized. 

Table   1   shows   the   Kruskal­Wallis   testfor statistics and probabilities for 3­hour and 24­hour   storm distributions  at   the  27  NWS  sites

Fig. 7.  Twenty­seven first­order stations of the National Weather Service.

across   the region.  Only 26 sites  are  shown ineach table because, in both cases, there was onestation which had all of its series produced byone weather   type.  None of   the  24­hour   seriesindicated   mixed   distributions.   However,   foursites,   Chattanooga,   Galveston,   New   Orleans,and   San   Angelo,   have   significantly   differentdistributions at the .05 level in the 3­hour series.These differences result from the fact that thereare more air mass storms in the shorter durationevents, and these storms tend to be clustered onthe   lower  end of   the  distributions.  Given  thatonly four of the 27 sites indicate the presence ofmixed distributions,  the region­wide data weretreated as though they were homogeneous, andpooling   together   storms   produced   by   thesevarious   mechanisms   does   not   produce   thenegative bias an noted by Ekanayake and Cruise(1994). 

Deriving Quantile Estimates

Since no mixed distribution  problems exist   inthe PDS for the region, valid quantile estimatescan be derived. To derive the quantiles severalprobability   distributions   and   other   techniqueswere  investigated   to  determine  the  best  singlemethod   for   region­wide   implementation.Random sampling using PDS across the regionproduced highly varied results. To demonstratethese differences, a pilot study of the arid Trans­Pecos climate division (Fig. 8) was undertaken.This was conducted to evaluate the performanceof   four   commonly   used   probabilitydistributions, in addition to the Huff­Angel log­log regression method wich was used to createthe  Rainfall   Frequency   Atlas   of   the   Midwest(Huff and Angel, 1992) and a related semi­logregression method developed at the SRCC. Thefour additional probability distributions used tofit   the   PDS   include   the   Generalized   ExtremeValue   (GEV),   Three   Parameter   Log   Normal(3PLOGN), Log Pearson Type III (LOGP III),and Wakeby. Daily rainfall records at 24 

Table 1. Kruskal-Wallis Probabilities of "Mixed"Rainfall Distributions.

LOCATION 3-HOUR K-WSTATISTICAND P.

24-HOUR K-WSTATISTIC AND

P.

AMARILLO 1.85 .17 ---- ----

AUSTIN 5.27 .15 3.06 .22

BATON ROUGE 2.77 .43 6.92 .07

BRISTOL 3.84 .28 6.34 .10

BROWNSVILLE 2.28 .52 3.03 .39

CHATTANOOGA 8.62 .03 2.41 .12

CORPUS CHRISTI 3.81 .28 6.54 .09

EL PASO 2.10 .55 3.19 .36

FORT SMITH 1.30 .52 3.86 .28

GALVESTON 9.97 .01 6.53 .09

JACKSON 1.09 .78 5.53 .14

KNOXVILLE 1.09 .58 0.21 .65

LAKE CHARLES 1.08 .78 5.08 .17

LUBBOCK 1.63 .44 5.42 .14

MEMPHIS 5.12 .16 1.28 .53

MERIDIAN 3.55 .31 2.10 .35

MIDLAND 5.49 .14 0.67 .88

NASHVILLE 1.17 .56 0.32 .85

NEW ORLEANS 7.62 .05 1.29 .52

OKLAHOMA CITY 0.43 .81 0.50 .78

PORT ARTHUR 1.32 .73 5.88 .12

SAN ANGELO 6.37 .04 3.66 .16

SAN ANTONIO 0.41 .81 0.56 .90

SHREVEPORT ---- ---- 2.49 .48

TULSA 0.77 .68 2.04 .36

WACO 1.23 .75 3.73 .29

WICHITA FALLS 2.92 .23 3.35 .19

cooperative stations of the NWS in the Trans­Pecos climate division (Fig. 8) provided the datanecessary to derive the extreme rainfallfrequency­magnitude relationships. These selected   sites  have   record   lengths  between 30and 74 years, while most are approximately 45years in length, beginning in the late 1940s andcontinuing   through  1991.  PDS were  extractedfrom these daily records. 

Each of the six methods were fit to thePDS   data   using   the   Weibull   plotting  positionformula:  

P= R/n + 1where P = probability,  R = rank of  the storm

(where   the   largest   storm   =   1),   and   n=   thenumber of storms in the series (which is basedon record length). To determine which methodprovided   the   best   fit   to   the   Weibull   plottingpositions,   the   quantile   estimates   from   eachmethod   for   the   1­,2­,5­,10­,   25­,   and   50­yearstorms were tested against the plotting positions,the quantile estimates from each method for the1­,2­,5­, 10­,25­, and 50­year storms were testedagainst   the   plotting   positions   using   linearregression   and   determining   the   mean   squareerror.   The   fitting   procedure   only   analyzedrecurrence   intervals   up   to   the   length   of   therecord   under   examination   since   recurrenceintervals beyond the length of record cannot bederived   using   the   Weibull   plotting   positionformula.     For   example,     the   longest   recordincluded in  this  analysis  is only 74 years, andreturn periods up to 75 years (due to the +1 inthe   numerator   of   the   Weibull   formula)   wereincluded   in   the   analysis   for   that   site   becausethere   are   no   plots   beyond   75   years.   This

technique for determining "best fit" is 

commonly   used   in   evaluating   frequency­magnitude relationships (Bobee and Robitaille,1976;  Naghavi   et   al.,   1991;   Huff   and   Angel,1992).

In   addition   to   the   probabilitydistributions,   the   Huff­Angel   estimates   werederived by determining the base common logsfor each of the PDS storm magnitudes and theWeibull   estimated   quantiles   and   performinglinear   regression  between   these  values.   In   theSRCC   method,   the   only   recurrence   intervalswere   logged   and   linear   regression   was   usedagain to  determine the relationships and allowfor the estimation of storm quantiles. The SRCCmethod is therefore very closely related to theHuff­Angel method. 

In   the   pilot   study   of   the   Trans­Pecosclimate division,  daily cooperative station datawere   used   because   of   the   use   of   dailycooperative station data in the final analysis ofthe   entire   region.     Storm   estimates   based   onobservational daily records (observations madeonce   every   24   hours,   with   the   hour   ofobservation   varying   from   station   to   station)were   increased   by   13   %   to   make   themequivalent   to   24­hour   moving­window   storms(rather   than   storms   based   on   discreteobservational days). Shortcomings of the hourlydata records make their utilization less desirablefor   extreme   rainfall   studies   (Faiers   et   al.,1994a),   thereby   making   the   1.13   adjustmentnecessary.     This   coefficient   is   becomingstandard   since   it  was   found   to  be  appropriateacross the United States (Hershfield, 1961),  inthe   Midwest   (Huff   and   Angel,   1992),     inLouisiana   (Faiers   et   al.,   1994a)   and   SRCCresearch  indicates   that   it   fits  across   the SouthCentral United States.

In most instances, the mean square errorfor the four probability distributions were small

Fig. 8. NWS cooperative stations in the Trans­Pecos climate division of NWS. 

ranging   from   .0009   inches   (3PLOGN   at   ElPaso) to .3545 inches (GEV at Sanderson). Nosingle  distribution  performed  well   at  all   sites,with every distribution being the worst fit at onesite   or  more.    Wakeby   and  LOGP   III   fit   theobserved data across the region most adequately(Table 2). Wakeby was the best fit at 10 siteswhile LOGP III fit best  at six sites.  However,the LOGP III distribution was the second best fitat many sites (14) causing it to have almost thesame cumulative rank as Wakeby for  all   sitescollectively.  The 3PLOGN distribution was thebest fit at four sites but did not perform well atmany  others,  while   finishing   last   at   six   sites.The   GEV   fit   best   at   four   sites   but   thisdistribution reacted very strongly to outliers atsome   sites   causing   the   50­year   and   100­yearestimates   to   be   far   too   large   in   our   bestestimation.  No geographic pattern was evidentin   regard   to   where   particular   distributions   fitbest. 

Given   that   no   single   probabilitydistribution clearly fit the extreme rainfall datafrom   this   region,   the   alternative   methoddeveloped   by   Huff   and   Angel   (1992)   wasinvestigated. The Huff­Angel method was foundto adequately estimate the 1­, 2­, 5­, and 10­yearstorms   in   the   Trans   Pecos,   but   at   sites   withextreme outliers this method produced 50­ and100­year   quantile   estimates   which   appearexcessively  large.  For example,   locations  suchas Crane and Red Bluff Dam in the northeasternpart of the Trans­Pecos have 24­hour 100­yearHuff­Angel   estimates   in   excess   of   10   inches(Figs. 9 and 10). In TP40, for example, the 10­inch, 100­year storm isohyet is located east ofAustin and San Antonio. 

Using the semi­log method developed atthe SRCC, the excessively large estimates of theHuff­Angel   method   at   the   longer   recurrenceintervals  are reduced in  this  arid environment.For example, in Figures 9 and 10 the 100­yearevents  at  Crane and Red Bluff  Dam by Huff­Angel are slightly greater than 10 inches, but the

SRCC method  lowers   the  100­year   recurrenceinterval magnitude to slightly less than 8 inchesat  both   sites.  Similar  excessively   large   resultsfor   the  50­   and   100­year   estimates   were   alsofound using   the Huff­Angel  method  is  coastalLouisiana.   The SRCC method again decreasedthese extremes to more climatically appropriatevalues.    For   these   reasons,   the  SRCC methodwas selected to  produce the quantile  estimatesacross   the   South­Central   United   States,   usingdaily data from 654 NWS cooperative stationsacross the region (Figure 11).

Table 2.  Ranks of  Probability Distributions  for Trans PecosStations, Texas.    

LOCATION GEV 3PLOGN LOGP III WAKEBYAlpine 3 4 2 1Balmorhea 4 3 2 1Boquillas 4 2 3 1Candelaria 2 1 4 3Chisos Basin 4 2 1 3Cornudas SS 3 1 2 4Crane 4 3 2 1El Paso 2 1 3 4Fort Davis 4 3 2 1Fort Stockton 4 3 2 1Grandfalls 1 4 3 2Imperial 4 3 1 2Kent 3 1 4 2La Tuna 4 3 1 2Marathon 1 4 2 3Mount Locke 4 3 2 1Pecos 3 4 2 1Presidio 1 4 2 3Red Bluff Dam 4 3 2 1Sanderson 4 3 2 1Sheffield 3 4 1 2Valentine 4 3 1 2Van Horn 1 3 2 4Wink 4 3 1 2SUM 75 68 49 48

GEV= Generalized Extreme Value3PLOGN = 3 Parameter Log NormalLOGP III = Log Pearson Type IIIWAKEBY

Three­, Six­, and Twelve­Hour 

It would be ideal to extract and analyze 3­, 6­,and   12­hour   storms   derived   from   continuoushourly  observations.  However,   because  of   thelimited   number   of   hourly   data   sets,   andfrequently   missing   data   during   very   heavyrainstorms, relationships between short­durationand adjusted daily durations were derived.  Thisderivation of short  duration storms from dailystorms   has   proven   expeditious   in   previousstudies   (Hershfield,   1961;   Huff   and   Angel,1992). To derive the shorter duration storms, thefrequency­magnitude relationships of 3­,6­, and12­hour storms to 24­hour storms at the NWSfirst­order   station   sites   in   Figure   7   werecalculated, and ratios of the 3­,6­, and 12­hourstorms relative to the 24­hour storm magnitudesfor each recurrence interval were determined foreach location. 

While  some regional variation in ratioswas   found,   average   region­wide   ratios   weredetermined and applied for each duration (Table3). The most significant geographic anomaly tothese ratios was detected across western Texaswhere short duration storms (especially 3­hour)are  often  close   to   the  24­hour   values.  Hence,these   region­wide   average   ratios   willunderestimate   the   shorter   duration   quantileestimates in this region. This because of the propensity for short, intensebursts of heavy rainfall, but with relatively fewlonger­duration   rainstorms   associated   withmidlatitude   cyclones   and   fronts.   As   a   result,there   is   an   atypically   large   number   of   short­duration storms included in the longer durationPDS. The ratios of the 3­to 24­hour storms tendto   decrease   eastward   across   Texas   with   thelowest   3­hour   ratios   for   the   region   found   insoutheastern   Texas.     There,   the   three   hourstorms were found to be just under 50% of thecorresponding   24­hour   storm   magnitudes.Elsewhere,   no   consistent   regional   patternsemerged. 

Table 3.  Average Ratio of 3­6­12­Hour/24­Hour Rainfall.

DURATION 

(IN HOURS)

RATIO 

(3­6­12­HOUR/24­HOUR)12 .886 .743 .62

Storms Shorter Than Three Hours

One primary difference between this new atlasand TP40 is that storms of durations shorter than3­hours  were  not  examined.  Precipitation  datafor   durations   less   than   one   hour   are   severelylimited in availability and mapping such data atthis scale was impractical. Without region­wideavailability   of   minute­by­minute   precipitationdata, relationships between discrete hourly dataand   60­minute   moving­window   data   wereunattainable for the region.  

Fig.   9.   Quantile   estimates   of   storm   rainfall   forCrane,   Texas,   by   the   Huff­Angel   and   SRCCmethods.

Fig. 10. Quantile estimates of 24­hour storms at Red Bluff Dam, Texas. 

Fig. 11. NWS cooperative stations in the region utilized in this study. 

This   is   similar   to   the   problem   whereobservational­day   data   were   converted   to   24­hour moving window equivalents by using the1.13   coefficient.     Therefore,  Hydro­35(Frederick  et   al.,   1977)   still  provides   the  bestestimates   for   storm   events   of   very   shortduration. 

Seasonality 

Another   problem   that   may   be   encounteredthrough   use   of   this   document   involves   theseasonality of storm activity across the region.Hershfield   (1961)   briefly   examined   this   issueand   detected   distinct   seasonality   for   selectedregions.   Angel and Huff (1995) also examinedthe seasonal variability of storms in the Midwestand discovered that quantile estimates can varyconsiderably   between   seasons.     Furthermore,Keim   and   Faiers   (1996)   found   significantdifferences in PDS heavy rainfall  distributionsby season in Louisiana.  Figure 12 shows that atthese   four   sites   in   Louisiana,   winter   tends   tohave the lowest quantile estimates while springtypically   has   the   largest.     These   findings,however, are only valid for Louisiana, but theydemonstrate   the   need   for   awareness   thatprobabilities of heavy rainfall differ by season.Keim (1996) also demonstrated that the seasonalfrequency   of   heavy   rainfalls   over   a   3­inchthreshold varied across the United States Southand   that   each   season   was   the   peak   seasonsomewhere   in   the   region.     Peak   stormfrequencies   during   spring   and   autumn   arecharacteristic   across   much   of   Texas,   winter­spring peaks dominate Louisiana and Arkansas,while   summer   is   the   peak   season   in   extremeeastern Tennessee.  Cartographic   Procedure   and   MapInterpretation

Maps   for   3­,   6­,   12­,   and   24­hour   rainstormswith recurrence intervals of 2­, 5­, 10­, 25­, 50­,and   100­years   are   displayed   in   Figures   3­6respectively.   These maps were prepared usingquantile   estimates   derived   from   the   methodsdescribed   in   sections   of   this   appendix.Manually­drawn   isohyets   were   used   to   depictthe spatial pattern of heavy rainfall while usingmeteorological and climatological knowledge ofthe region to include or exclude some individualstation   anomalies   that   were   clearly   out   ofcharacter   with   surrounding   environments.     Inmost cases, it was assumed that these anomalies,though few, were generated by extreme outliersin   the   PDS  which  obscured   the   derivation  ofregionally representative quantile estimates.

Isolines were drawn at 0.5­inch intervalsfor recurrence intervals between 2­ and 10­yeardesign storms and 1­inch intervals were used forthe   25­,   50­,   and   100­year   design   stormmagnitudes.   While automated procedures wereconsidered, such methods often fail to recognizeorographic and coastal patterns and generally donot   improve   the   quality   of   the   resulting   mapwhen compared to manually­drawn precipitationmaps (Mulugeta, 1996).   Interpolation of thesemaps   will   be   required   in   most   cases.     Forexample, a design storm for a specific locationwill   often   fall   between   two   isohyets.     In   thisinstance, the user must assume that change fromone isohyet to the next occurs consistently andmust   estimate   the   quantile   value   from   theregional isohyet pattern.  In Figure 3.1, if a userwanted   the   3­hour   2­year   design   storm   forMemphis, Tennessee (in the extreme southwestcorner  of   the   state),   interpolation  between   the2.5­ and the 3­inch isohyet would be required.Since  Memphis   is  displaced approximately  30percent from the 2.5­inch isohyet relative to the3­inch   line,   one   can  conclude   that   the  designstorm at Memphis is 2.65 inches.

Summary

• PDS of observational­day (daily) storms havebeen   extracted   for  27  NWS first­order   andcooperative stations in the region;

• For each site, Weibull plotting positions havebeen assigned to each storm in the PDS;

• Semi­log regression relationships have beendetermined   between   logged   recurrenceintervals and storm magnitudes;

• Quantile   estimates   have   been   increased   by13%   to   make   daily   storm   magnitudesequivalent to 24­hour moving­window stormmagnitudes;

Fig. 12. Quantile estimates by seasons at 4 first­order stations of the NWS in Louisiana. Source: Keimand Faiers 1996. (Printed with permission from the American Water Resources Association.)

• Three­, six­ and twelve­hour storm• magnitudes   have   been   calculated   from

average regional ratios at first­order stationsto   adjusted   daily   magnitudes   for   eachrecurrence interval;

The authors wish to thank the following peoplefor their contributions towards the developmentand production of this document:

• John   M.   Grymes   III   and   Chi   Nguyen   fordeveloping computer programs for extractionof extreme hourly and daily rainfall data;

• Youngeun Choi and Liyun Ye for data entryand quality control;

• Dr. Robert V. Rohli and Dr. James R. Angelfor contributing to the derivation of the 

• Regional   maps   have   been   developed   fromindividual station plots of the 3­, 6­, 12­, and24­hour storms for recurrence intervals of 2,5, 10, 25, 50, and 100 years.

• methods  used   for  determination  of  quantileestimates;

• Dr.   James   Cruise   and   Dr.   Katherine   K.Hirschboeck   for   their   insights   about   datahomogeneity and synoptic climatic aspects ofthe events;

• Peter Hanlon for plotting data on draft maps;• Special   thanks   to  Mary  Lee  Eggart   for   the

maps,   diagrams,   and   layout,   and   to   EstherShaffer for the production of this document.

ACKNOWLEDGEMENTS

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