This item is only available as the following downloads:

MatyasPG2007 ( PDF )

PAGE 1

QuantifyingtheShapesofU.S.LandfallingTropicalCyclone RainShields*CoreneMatyasUniversityofFloridaTropicalcyclones(TCs)producecomplexrainfallpatternsthataredifculttopredictduetoatmosphericand landsurfaceforcings.Thisstudyutilizesgeographicinformationsystemstospatiallyanalyzeradarreturnsand calculateseveralmetricsthatquantifytheshapesofTCrainshields.Threestepwisediscriminantanalysesare performedtodeterminewhichoftheshapemetricsdistinguishamongTCscategorizedby:intensity,distance traveledinland,andorientationofterrainencountered.ResultsconrmthatTCrainshieldsoftenassume noncircularshapes.UtilizingshapeindicestomodelrainshieldscouldhelpproduceTCrainfallforecaststhat aremorespatiallyaccurate.KeyWords:GIS,radar,rainfall,shapeanalysis,tropicalcyclones.Tropicalcyclones(TCs)aredangerous stormscapableofproducingstrongwinds, stormsurges,tornadoes,andoodingrainfall. Priorto1970,thestormsurgecausedthemajorityofTC-relateddeaths(Rappaport2000). Fortunately,improvementsintrackandintensityforecastmodels(Aberson1998)nowallow timefortheevacuationofsurge-proneareas, whichhasreducedthenumberofsurge-related deaths.MorerecentlyRappaportfoundthat during19701999,heavyrainfallanditsassociatedoodingaccountedfor59percentofdeaths causedbyTCs.ThefactthatTCscanproduce excessiverainfallmanykilometersinlandfrom thecoastincreasestheportionofthepopulation thatisvulnerabletothishazard.Forexample, oodingcausedbyTropicalDepressionCharley (1998)resultedintwentydeathsnearDelRio, Texas,locatedmorethan350kmfromthepoint oflandfall(Pasch,Avila,andGuiney2001).As recentlyas2000,theAmericanMeteorological Societyacknowledgedthatskillfulprediction ofrainfallfromlandfallingtropicalcyclonesremainselusive''(AMS2000,1344).Toreducethe lossoflifeandpropertydamagecausedbythis freshwaterooding,modelsmustbedeveloped thataccuratelyforecasttheamountandspatial extentofrainfallproducedbylandfallingTCs. Thedevelopmentofarainfallclimatology andpersistencemodel(R-CLIPER;Marks, Kappler,andDeMaria2002)facilitatedthevalidationofrainfallforecastsforTCs(Marchok, Rogers,andTuleya2007).Todevelopthismodel,researchersdividedeachTCintosections usingfty10-kmwideannularringsandthen calculatedtheaveragerainfallratewithineach ring.Therainfalldistributiongeneratedbythe R-CLIPERmodelissymmetrically-shaped withmaximumrainratesapproximately50km fromthestormcenter.Duetoadistance-decay assumption,theR-CLIPERmodelpredictsa steadydecreaseinrainfallratesastheTCtracks inland.However,researchershavenotedthat manyTCsproducerainfallthatisheavilyconcentratedtoonesideofthestormtrack(Gilbert andLaSeur1957;Elsberry2002;Corbosiero andMolinari2003).Also,topographicalfeaturesortheinteractionwithmiddlelatitude weathersystemscanacttobothincreaserainfall andcausetheshapeoftherainshieldtobecome asymmetrical(Bender,Tuleya,andKurihara 1985;Linetal.2002;AtallahandBosart2003). AsuccessfulTCrainfallforecastmustincorporatetheseasymmetricalshapes. ImprovingthespatialaccuracyofTCrainfall forecastsrequirestheabilitytomodelhowthe*PartialfundingforthisresearchwasprovidedbyafellowshipfromtheSocietyofWomenGeographers.Assistanceinsecuringtheradardataby RebeccaYothersandthePennsylvaniaStateUniversityDepartmentofMeteorologywasgreatlyappreciated,aswasthegeoreferencingscript providedbyScottShipley,andthesupportgivenbyAndySherwood.ThanksarealsoextendedtoTimFikforhisassistanceinrevisinganearlydraftof thisarticle,andtofouranonymousreviewers.Finally,Ithankmyadvisor,AndrewCarleton,andcommitteemembersBrentYarnal,JenniEvans,and DonnaPeuquetfortheirtimeandinsightsintothiswork.TheProfessionalGeographer,59(2)2007,pages158172rCopyright2007byAssociationofAmericanGeographers. Initialsubmission,April2006;revisedsubmission,August2006;nalacceptance,October2006. PublishedbyBlackwellPublishing,350MainStreet,Malden,MA02148,and9600GarsingtonRoad,OxfordOX42DQ,U.K.

PAGE 2

atmosphereandlandsurfaceinuencetheshape oftherainshield.ATCthattracksinland,rather thanmovingparalleltothecoastlineormoving backovertheocean,becomesremovedfromits sourceofmoisture.Thereductioninmoisture altersthestormstructure(Tuleya1994)and leadstoadecreaseinrainfall.IfmoistaircontinuestoentertheTC,asdescribedbyBluestein andHazen(1989)forHurricaneAlicia(1983), rainfallmayoccurononesideofthestormonly, yieldinganelongatedrainshieldshape.Also, TCsmakinglandfallintheUnitedStatestend tohaveanorthwardcomponenttotheirmotion, whichallowsapproachingmiddlelatitude featurestoalterrainshieldsintononcircular shapes(AtallahandBosart2003). Thetaskofquantifyingchangesinshapes lendsitselftogeographers,whoexplorevarious typesofspatialdatawithtoolssuchasgeographicinformationsystems(GIS)andshape analysis(MacEachren1985;Wentz2000).The researchobjectivesofthisarticlearetwofold:(1) utilizeGISandshapeanalysistoquantify changesintheshapesoftherainshieldsof landfallingTCs;and(2)determinethespecific shapeindicesthatquantifyalterationsofthe rainshieldcausedbylandsurfaceandatmosphericforcingmechanisms.Thisarticle investigatesthreesuchmechanisms:stormintensity,thedistanceinlandoverwhichthestorm moves,andtheorientationofelevatedtopographyencounteredbythestorm.Iftheshape indicescalculatedinthisstudycansuccessfully modelthewayinwhichaTC'srainshield changes,theirinclusioninarainfallforecast modelcouldimprovepredictionsofwhere ood-producingrainfallislikelytooccur. Asspatialanalysisrequireshigh-resolution data,thefollowingsectiondiscusseshowbase reectivityradarreturnsareutilizedinthis study.Theprimaryobjectiveofthisresearchis todenetheshapesoftherainshieldsasindicatedbytheradardata.Twotechniquesthat facilitatethistask:(a)overlayingeachhourly radarcompositewithacirculargrid;and(b) performingshapeanalysisarethendescribedin thenextsection,SpatialAnalysis.WhendevelopingtheR-CLIPERmodel,Marks,Kappler, andDeMaria(2002)employedacirculargridto sectioneachTC.Inthecurrentstudy,acircular griddivideseachTCintosections,andthe percentageofareawithineachsectionthatis coveredbyradarreturnsiscalculated.Forthe secondtechnique,threemeasuresofshapefrequentlyemployedbygeographers(Stoddart 1965;Frolov1975;DeMers2000)arecalculatedtoquantifychangesintheshapeoftherain shield:thearea-to-perimeterratio(APR),the major-to-minoraxisratio(MMR),andtheEulernumber(EN).Theseindicesarecalculated todeterminethecompactness,elongation,and fragmentationoftherainshield.Anadditional shapemetric,therainshieldarc-length,quantiesthedegreetowhichtherainshieldencirclesthestormcenter. TheStatisticalAnalysissectiondescribeshow discriminantanalyses(DAs)areemployedto accomplishthesecondobjectiveofthisresearch,whichistoidentifythegridsectionsor shapeindices,orboth,thatbestquantifyhow thespatialextentofTCrainshieldsareaffected bytheatmosphereandthelandsurface.Three separateDAsareperformedtodeterminewhich ofthegridsectionsand/orshapeindicesbest differentiatebetween(1)TCsofhurricane(tropicalstorm)intensity;(2)TCswhosecirculation centersareinlandandlocatednearto(farfrom) thecoastline;and(3)TCsencounteringelevated topographythatisorientedindifferentdirections.Thenaltwosectionsofthisarticlediscuss theresultsoftheDAsandaddressthepotential fortheshapeindicescalculatedinthisstudytobe incorporatedintoaTCrainfallforecastmodel.DataandMethodsTheWeatherSurveillanceRadar88Doppler (WSR-88D)levelIIradardatautilizedinthis researchwereobtainedfromthePennsylvania StateUniversityDepartmentofMeteorology (PSUDM).Thesebasereectivityradarreturns areobtainedinbinsofvaryingresolutionoutto 235kmfromthereceiverforeachdegreeofthe 360 1 scan(KlazuraandImy1993).Theradar dataaregeoreferencedutilizingNex2SHP.exe, aVisualBasicscript(Shipley,Graffman,and Ingram2000),andimportedintoArcViewGIS (ESRI2002).TwelveTCsfrom19972003are analyzed(thesearelistedinTable1inorderof maximumsustainedwinds).Changesintheformattingofradardata(KrugerandKrajewski 1997)donotallowtheNex2SHP.exescriptto decodedatapriorto1997.Alterationstothe compressionalgorithmsusedbyPSUDMto storeradardatadonotallowNex2SHP.exeto recognizedatafromyears2001and2002.TheQuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields159

PAGE 3

authorobtaineddatafromNOAAPORTdata broadcastsystemforClaudette(2003)andIsabel(2003)astheseTCsmadelandfall,thus bypassingthedatacompressionprocess.Data lesfromTCsEarl(1998),Frances(1998),and Floyd(1999)werecorruptedandcouldnotbe analyzed. Radarreturnsfromthescannearestthetopof eachhourforeachstationarecompositedinto onelayercontainingdatafromallstations.The interpolationofthesedatabyinversedistance weightingcreatesthepolygonsthatdenethe spatialboundariesoftherainshield.Toobtaina completelyclosedpolygon,theentirerain shieldmustbewithinreceivingrangeofthe radarstation(s).Thiscriteriondetermineswhen analysiscommencesorceasesforeachTC.Partialpolygonsarenotanalyzed.Atotalof486 hourlyobservationsareanalyzedinthismanner fromtwelveU.S.landfallingTCs(Figure1). Selectionofthereectivitythresholdfrom whichthesepolygonsarecreatedisimportantas itaffectstheresultingshapes.TCresearchers haveemployedboth20dBZ(Jorgensen1984; Toracintaetal.2002)and25dBZ(Barnesetal. 1983;Powell1990)reectivityvaluestodene theboundariesofTCrainshieldsandindividual rainbands.Reectivityvalueslessthan20dBZ mayresultfrominsectswarmsorocksofbirds (KlazuraandImy1993)andarenotsuitable forthecurrentstudy.Polygonscreatedfrom boththe20dBZand25dBZcontourswere comparedbyMatyas(2005).Theseanalyses revealedthatshapemeasurescalculatedfrom the20dBZcontoursproducedstatisticallysignificantresultsthatsupersededthoseproduced bythe25dBZpolygons,asthelatterwere highlyfragmentedandsmallinsize.Forbrevity,thisarticleonlydiscussesshapemetrics calculatedfromthepolygonsboundby20dBZ contours. TheNationalHurricaneCenter(NHC)providesadditionaldataforeachTC,includingthe coordinatesofthecirculationcenter,maximum sustainedwindspeed,andminimumcentral pressure.Theseobservationsareavailablein six-hourlyincrements.Asthisstudyanalyzes theradarimagesinhourlyincrements,itisnecessarytointerpolatetheNHC-provideddata (Vickery,Skerlj,andTwisdale2000).Within thisarticle,observationtimesarereferencedto thehouroflandfall(e.g., t 0forthelandfall hour, t 6forsixhourspostlandfall,etc.)Also, asthreeTCsmademultipleU.S.landfalls,the followinglocationsserveasthereferencedlandfallpoints:FortMorgan,Alabama,forHurricaneDanny(1997);Biloxi,Mississippi,for HurricaneGeorges(1998);andCapeSable, Florida,forHurricaneIrene(1999).SpatialAnalysisToascertainwhetherthetechniqueusedtodeveloptheR-CLIPERmodelprovidesadequate informationfromwhichtomodeltheshapeofa TCrainshield,asetofannularringsdivided intoquadrantsisplacedovereachrainshield (Matyas2006).WithintheGIS,thecirculation centerofthestormisbufferedbyeightrings spaced50kmapart.Theheadingofthestorm determineswhereeachquadrantislocated. Thiscirculargrid(Figure2)clipstheoriginal polygonsintonewshapes,whoseareasare summedtodeterminetheamountofspace Table1 CharacteristicsofanalyzedtropicalcyclonesattimeoflandfallTropical cyclone(year) Minimum centralpressure (mb) Maximum sustainedwinds (m/s) Forwardmotion (degrees/m/s) Average gale-forcewind radius(km) Bret(1999)95151.4285/3.2194 Bonnie(1998)96448.920/2.7196 Isabel(2003)95746.3325/8.8405 Georges(1998)96446.3345/3.2225 Claudette(2003)97941.2285/6.5194 Danny(1997)98436.025/1.1– Irene(1999)98736.030/6.1220 Dennis(1999)98430.9305/4.3185 Gordon(2000)99128.320/6.9135 Charley(1998)100020.6295/4.6194 Hermine(1998)100018.0360/1.058 Helene(2000)100618.045/5.891160Volume59,Number2,May2007

PAGE 4

withineachregionthatiscoveredbythe20dBZ reectivitythreshold.Aseachannularringenclosesadifferentamountofspace,thepercentageofspaceoccupiedbypolygonsbetweeneach pairofringsiscalculated.Hereafter,theregion insideofring1isreferredtoasR1,theregion betweenringsoneandtwoisR2,andsoforth (Figure2).Summingtheareasofallpolygonsin theimagedeterminesthetotalarealextentof therainshield.Thetotalareaofthepolygons Figure1 Hourlylocationsof stormcirculationcenterforeach tropicalcycloneinthisstudy. Figure2 Buffered50kmannular ringsandquadrantsusedtoclip therainshieldpolygons.Storm motionistowardthenorth-northeast.QuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields161

PAGE 5

insideeachquadrantisalsocalculated.Additionally,asresearchershavenotedthetendency forTCstoproduceprecipitationthatisasymmetricaltothestormtrack(Elsberry2002; ChanandLiang2003),theareasofallpolygons ontheleftsideofthestormtrackaresummed andsubtractedfromthoseontherightsideof thetrack.Whenthevalueofthisright-minusleftasymmetry(RLSYM)variableisnegative (positive),moreoftherainshieldexistsonthe left(right)sideofthestorm. Previousresearchershavedeterminedthe spatialdistributionofprecipitationabouta TC'scenterusinggridsofvaryingdimensions (RaoandMacarthur1994;Rodgers,Chang,and Pierce1994;CervenyandNewman2000). However,thedevelopmentofamodelthatpredictschangesinTCshapepropertiesshould alsoquantifytherainshieldasawhole.Toaccomplishthistask,threegeographicalmeasures ofshapeareexamined(Matyas2007):area-toperimeterratio(APR),major-to-minoraxis ratio(MMR),andEulernumber(EN).The APR,whichiscalculatedforthelargestpolygon ineachimage,providesasimplemeasureof stormcompactness: APR A p = P 0 : 282 ; 1 where A istheareainsideeachpolygon,and P is theperimeterofeachpolygon(Figure3).The MMRdescribeswhethertherainshieldiscircularorelongated(Figure4).Thismeasureis calculatedrelativetothegeographicalcentroid ofallpolygonscomprisingtherainshield.Radiallinesareextendedoutfromthecentroidto theedgesofthepolygons.Thelongestline,determinedbysummingthelengthofeachline withthatextending180 1 awayfromit,servesas themajoraxisoftherainshield( Lmaj).Theradialslocated90 1 toeachsidearesummedto calculatetheminoraxislength( Lmin).The minoraxislengthisdividedbythemajoraxis lengthtoproducetheMMR. MMR Lmin= Lmaj: 2 BoththeAPRandMMRvaluesrangefromzero tooneandcomparetherainshield'sshapeto thatofacircle,whichhasanAPRandMMR valueofone.TheENaccountsforboththe numberofpolygonspresent(fragmentation) Figure3 Examplesofthearea-to-perimeterratio(APR)compactnessmeasure.(A)isacompactrainshield shapefromDanny(1997)whereareaismaximized(APR 0.54).(B)isalinearshapefromHelene(2000) whereperimeterismaximized(APR 0.14).162Volume59,Number2,May2007

PAGE 6

andholeswithinthepolygons(perforation): EN H F 1 ; 3 where H isthenumberofholesand F isthe numberoffragmentsintheexaminedregion (Figure5).AnegativeENvalueindicatesa fragmentedshape. OneadditionalmeasureofshapethatconsiderstheentireTCrainshieldisdeveloped specificallyforthisstudy.Thisshapemetric quantiesthedegreetowhichtherainshield encirclesthecirculationcenterofthestorm,and ishereafterreferredtoastherainshieldarclength(RSAL).TCscontainingplentifulmoistureandfastwindscanadvectmoisturearound theentire360 1 arc.Reectivityvaluesgreater than20dBZmayonlyexistaroundhalfofthe arc(180 1 )ifTCshaveslowerwinds,areadvectingdryairintotheircirculation(Gilbertand LaSeur1957),orexperiencestrongdirectional windshear(CorbosieroandMolinari2002).To calculatetheRSALmetric,radiallinesareextendedoutwardin5 1 incrementsfromthecoordinatesoftheTCcirculationcenter.The degreesoftheradiallinesthatencounterthe leadingandtrailingedgesoftherainshieldare subtractedtoprovidetheRSAL(Figure6).StatisticalAnalysisThreeforwardstepwiselineardiscriminant analyses(DAs)areperformedtodetermine whichofthepredictorvariables(Table2)best relatechangesinTCrainshieldsduetostorm intensity(DA1),distanceinland(DA2),andthe orientationofelevatedterrain(DA3).DAis similartolinearregressionanalysis;themain differenceisthatDApredictsmembershipin twoormoremutuallyexclusivegroupsfroma setofpredictorvariables(Saundersetal.2000). Thetwenty-twopredictorvariables(Table2) consistofthearealcoverageofrainderivedfrom thecirculargridsandthegeographicalshape indicesforallTCsinsix-hourlyincrementsbeginningwiththehouroflandfall.Theinclusion ofhourlyobservationsinthestatisticalanalysis isproblematicduetotemporalautocorrelation. Theuseofsix-hourlydataisjustiedinthis studybecauseaTC'scirculationchangesrapidlyoncelandfallcommencesascomparedto thatwhileoveropenwater.Therefore,theuse ofsix-hourlyobservationsreducestemporal autocorrelationinthedata. Throughalinearcombinationofthepredictorvariables,theDAderivesafunctionthat Figure4 Examplesof(A)elongated(MMR 0.19;Charley1998)and(B)round(MMR 0.89;Georges 1998)rainshieldshapes.MMR major-to-minoraxisratio.QuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields163

PAGE 7

maximizestheseparationofthegroups.Given thatmanyenvironmentalforcingmechanisms cansimultaneouslyaffectaTC'srainfallproduction(e.g.,interactionwithmiddlelatitude weathersystemswhilemovingovermountainousterrain),itisappropriatetoplacetheobservationsinthisstudyintogroupsratherthan attempttopredicttheprecisevalueofthedependentvariable.Thelargenumberofpredictorsintheseanalyses(Table2)dictatestheuseof stepwiseDA.Thepredictorthatisincludedin themodelateachstepistheonethatdecreases theWilks'sLambdastatisticbythegreatest amount(TabachnickandFidell2001).This statisticvariesbetweenzeroandoneandisa measureofthedifferencebetweengroupsofthe centroidofmeansontheindependentvariables. Valuesnearzeroindicatethatthegroupmeans differ.Eachstepintheanalysisaddsavariable tothemodelthatmostincreasesthedistance betweenthegroupcentroids. TwotechniquesvalidatetheclassicationaccuracyofthemodelproducedbyeachDA.First, theperformanceofajackknifedata-resampling procedureensuresthattheanalysisresultsare notbiasedtowardanyoneTC(DeMariaand Kaplan1994).Thisprocedureremovesone sampleatatimeandrecalculatesthemodel Figure6 Calculationoftherainshieldarc-length (285 1 )forDennis(1999)atsixhourspost-landfall. Figure5 ExamplesofEulernumbercalculationsfor(A)Gordon(2000;EN 15)and(B)Dennis(1999;EN 2).164Volume59,Number2,May2007

PAGE 8

statisticsuntilallsampleshavebeencrossvalidated.Second,arandomselectionofobservationsfromeachgroupisenteredintothe analysiswithoutpriorgroupclassication.The DAthenconstructsamodelfromtheobservationsthatareclassiedandusesthatmodelto predictgroupmembershipforallobservations thathadnotbeenclassiedoriginally.Ahigh percentageofobservationsthatarecorrectly classiedusingboththejackknifeprocedure andthedatathataremanuallywithheldindicate modelsuccess. TheintensityofaTChasimportantinuencesonitscloudformation,leadingDvorak (1975)toforecaststormintensitybyclassifying theshapesofcloudsobservedonsatelliteimagery.Itisreasonabletoassumethatintensity willalsoaffecttheshapeoftherainshieldas viewedonradarimagery.Fastertangential windscancarrymoisturecompletelyaround theinnercoreofahurricane,whereasslower windsintropicalstormsmaynotallowmoisture toencirclethestorm'scenter.Therefore,faster windsshouldbeassociatedwithamorecircular rainshieldshape.ThisstudystratiesTCsinto twogroupsforDA1(Table3):thosehaving windsaboveandbelowhurricane-force(33m/s). Toeliminateproblemsassociatedwithborderline''observations,caseswithwindspeedsof 3135m/sarenotincludedintheanalysis.Observationsincludedinthetwogroupsarefrom thehouroflandfallandsixhoursafterlandfall. After t 6,moststormscontainedweaktropical stormortropicaldepression-forcewinds.The resultsofadditionalDAsincorporatingdata through t 24(notshown)indicatethatintensityisnotadominantcontroloftherainfall distributionafter t 6. AsaTCmigratesinland,thecirculationcenterisremovedfromthewarmoceanwatersthat providetheenergyrequiredtomaintainthe circulation(Hubert1955;TuleyaandKurihara 1978;R.W.Jones1987);asaresulttheshape andtheextentoftherainshieldchange.Some TCs,however,remainnearthecoastlineafter landfall,ormigrateacrossthecoastlineafter spendingseveralhoursoverland.Beinglocated nearwarmoceanwatersallowsforthecontinual advectionofmoistureintoaTC'scirculation, andthismayallowforcoastalTCstobemore symmetricalinshapeortohavealargerrain shieldthaninlandTCs.ForDA2,observations from t 6to t 36areplacedintotwogroups: thosewithin100kmofthecoastline,andthose locatedmorethan200kmfromthecoastline (Table3).ThisdistanceisdeterminedbymeasuringthedistancebetweenthecirculationcenteroftheTCandthenearestpointonthe coastline,notthecoordinatesoflandfall.The 100-and200-kmdistancesarechosentodelineatethecategoriesbecausetheyrepresentnaturalbreaksinthedata. Researchershavedocumentedhoworographicupliftcanenhanceprecipitationonthe rightsideofaTCrelativetostormmotion (Bender,Tuleya,andKurihara1985;Wood 2001;Linetal.2002).AsaTCapproacheselevatedterrainataperpendicularangle,itsrain Table2 PredictorvariablesenteredintoalldiscriminantanalysesVariabletypeListing CirculargridAreaofrainshieldinRR, RF,LF,LRquadrants Percentageofregion occupiedbyrainshieldin R1,R2,etc. Totalarealextentofrain shield Rightminusleftasymmetry (RLSYM) ShapeindicesMajor-to-minoraxisratio, area-to-perimeterratio; Eulernumber Distanceandbearingof shieldcentroidfrom stormcenter Orientationofmajoraxis (ORI) Rainshieldarc-length(RSAL) Note:RR rightrear,RF rightfront,LF leftfront,LR leftrear;R1 radius1,R2 radius2. Table3 Groupmembershipforeachdiscriminantanalysis(DA)GroupGroupingcriteria IntensityDA1DistanceinlandDA2TopographyDA3 1Windspeed 4 35m/s(12cases) o 100kmofcoastline(23cases)EdwardsPlateauinTexas(east-west orientation)(14cases) 2Windspeed o 31m/s(10cases) 4 200kmfromcoastline(17cases)AppalachianMountains(northeastsouthwestorientation)(15cases)QuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields165

PAGE 9

shieldshouldbecomeasymmetrical,withincreased(decreased)arealcoverageontheright (left)sideofthestorm.Theshield'smajoraxis shouldalsobecomeorientedinadirectionparalleltotheaxisoftheelevatedterrain.Inthis study,severalTCsencounteredelevatedterrain intworegionsoftheUnitedStates:theAppalachianMountains(northeast-southwestorientation)inNorthCarolina,Virginia,WestVirginia, Maryland,Pennsylvania,andNewYork,andthe EdwardsPlateau(east-westorientation)incentralTexas(Figure7).ForDA3,observations takenfrom t 12to t 24forsevenTCsare groupedaccordingtothesetworegions(Table3).ResultsandDiscussionThemodelsdevelopedbyallthreeDAsutilize oneortwopredictorstocorrectlyclassify95 percentormoreofthecross-validatedand manually-withheldobservations.Thepredictorsforallthreemodelsconsistofshapeindices thatconsidertherainshieldasawhole,rather thanthevariablesderivedfromthecircular grid.Thegraphicsdevelopedtoillustratethe representativeshapesofeachgroupaccording tothemodelpredictorsofallthreeDAs (Table4)illustratethatacircleisnota representativeshapeforallTCrainshields. ThesendingsdemonstratethatfutureTC rainfallforecastmodelsneedtoconsidernoncircularrainshieldshapesandindicatethat shapemetricscanbeutilizedtomodelthese asymmetricalrainshieldshapes.Havingsucha highsuccessratealsovalidatesthetechniqueof usingaGIStospatiallyanalyzeradarreectivity returns.ThedetailsofeachDAarediscussed below. Table4 Resultsofeachdiscriminantanalysis(DA)Intensity(DA1)Distanceinland(DA2)Topography(DA3) Predictor(s)RSALMMRORIRLSYM Group1. Mean349 1 0.67278 1 57 SD39 1 0.1026 1 34 Group2. Mean171 1 0.3141 1 25 SD45 1 0.0920 1 58 Wilks'sLambda (significance) 0.169(0.000)0.267(0.000)0.193(0.000) Percentageof correctcases 95.5%95%100% Note:RSAL rainshieldarc-length;MMR major-to-minoraxisratio;ORI orientationofmajoraxis;RLSYM rightminusleft asymmetry;SD standarddeviation.166Volume59,Number2,May2007

PAGE 10

IntensityandanEnclosedCirculationCenter TheintensityDAmodelonlyrequiresonepredictor,theRSAL,todistinguishbetweenhurricaneandtropicalstormrainshields.Themean valuesofRSALforeachgroupindicatethat hurricanerainshieldsnearlyenclosetheircirculationcenters(Table4).Thisisinstarkcontrasttotropicalstormrainshields,wherethe averageRSALisonly171 1 .ThelowerRSAL valuefortropicalstormsislikelyduenotonlyto slowertangentialwindscausedbyaweakening pressuregradientforce,butalsotothestrong directionalwindshearthatthestormsinthis studyexperiencedduringlandfall(Franklinet al.2001;Lawrenceetal.2001;Pasch,Avila,and Guiney2001).Whendirectionalwindshear actsonTCs,verticalcirculationbecomesasymmetricasupward(sinking)motionsareinduced downshear(upshear)(Blacketal.2002).Sinking motioninhibitsconvection.Theweakeningof tangentialwindsalsoprohibitsmoisturefrom completelycirculatingaroundthestorm.Asa result,precipitationisdisplaceddownshearleft Figure7 Elevationmapdepictingtheobservationsutilizedin DA3for(A)theEdwardsPlateau incentralTexasand(B)theAppalachianMountains.Circlesdenotestormcenterpositions. DA discriminantanalysis.QuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields167

PAGE 11

ofthecirculationcenter(Rogersetal.2003).As manyTCsexperiencestrongdirectionalwind shearpriortoand/orafterlandfall,itisimportanttomodelthechangesinTCrainfallpatternscausedbythisforcingmechanismandto determinetowhatextenttheRSALiscapableof quantifyingthesechanges.Futureworkwillfocusonthedevelopmentofashapemetricspecifictowindsheargeneratedrainshield asymmetries. OnlyoneobservationismisclassiedbyDA1. HurricaneIsabelbegantotransitionintoan extratropicalstorm(Gautametal.2005)at t 6,whichcauseditsrainshieldtoassumean asymmetricalshape.Duringthistransition,the stormchangedfromasymmetricalwarm-cored toanasymmetricalcold-coredsystem(Hartand Evans2001).Anareaofincreasedrainfalloccurrednearthesteepthermalgradientbetween thetropicalandcontinentalairmassestypically locatednorthofthestorm'scenter(Klein,Harr, andElsberry2000;S.C.Jonesetal.2003).For Isabel,thisprocesscaused94percentofitsrain shieldtobedisplacedaheadofthecirculation centereventhoughitsmaximumsustainedwind speedwasstill36m/s.Asaresult,itsRSAL decreasedto225 1 from360 1 sixhoursearlier. AlthoughtropicalstormsDennis(1999)and Gordon(2000)alsoexperiencedanextratropicaltransition,thisstudycurrentlydoesnot possessenoughobservationsfromTCsthatexperiencedthistransitiontoinvestigatetherelatedrainshieldshapechangesthrough statisticalanalysis.However,thistransitionisa criticalfactorthatneedstobeincorporatedinto futureTCrainfallforecastmodels,andcombinationsofshapeindicessuchasRLSYMand RSALmaybeabletomodelthesestorms. DistancefromtheCoastlineandElongated TropicalCyclones ResultsfromDA2indicatethatTCslocated within100kmofthecoastlinehaveamorecircularshapethanthoselocatedmorethan200 kminland,whicharemoreelongated.Ninetyvepercentoftheobservationsarecorrectly classiedusingonepredictor(MMR).AnexaminationofthemeanMMRforeachgroup revealsthatTCslocatedclosertothecoastline aretwiceascircular,onaverage,asthosefurther inland(Table4).Thisresulthasimportant implicationsforthedevelopmentofarainfall forecastmodelbecauseitillustratesthatitis importanttomodeltheshapeoftheentirerain shieldasawholebyutilizingshapemeasures suchastheMMR,asanalyzingindividualsegmentsoftheshieldwouldnothaveproduced thisresult. TheDA2modelsdevelopedwiththejackknifetechniqueandtherandomly-withheldobservationsmisclassifyonecasefromeachgroup. Claudettewas365kminlandat t 18,yetitis classiedasacoastalstormbecauseitsMMR value(52)wasthehighestoftheinlandgroup. The t 6observationforCharleyismistakenly categorizedasinlandbyDA2whenitislocated 83kmfromthecoastlinebecauseithasanMMR valueof37.Charleyretainsaveryelongated shapethroughoutlandfall(Figure4)because thestrongdirectionalwindshearitexperiences doesnotallowmoisturetocompletelyencircle thecirculationcenterofaTC.Duringthe thirty-eighthoursafterlandfallinwhichshape indicesarecalculatedforCharley,thepolygons locatedontherightsideofthestormtrack comprise88percentormoreoftheentirerain shield,illustratingthatanelongatedshapeisnot necessarilycenteredoverthestormtrack,asthe R-CLIPERmodelcurrentlypredicts.Bothof thesefactsdemonstratethecomplexitythata successfulTCrainfallforecastmodelmust possessasitmustaccountformultipleforcingmechanisms,suchasaninlandlocation, strongdirectionalwindshear,andmovement overelevatedterrain(DA3)thatcanoccur simultaneously. Topography’sEffectonTropicalCyclone Orientation TCsencounteringtheeast-to-west(northeastto-southwest)orientedEdwardsPlateauincentralTexas(AppalachianMountains)haverain shieldsthatarealsoorientedeast-to-west(northeast-to-southwest),asconrmedbyDA3 (Table4).Addingasecondpredictor,RLSYM, reducestheWilks'sLambdastatisticto0.193, thelowestattainedinthisstudy(Table4).Itis notsurprising,therefore,thatallobservations withheldusingthejackknifetechniqueandobservationsthatwererandomlywithheldarecorrectlyclassiedbytheDA3model.Again,this ndingdemonstratesthatitisnecessarytouse shapemeasuresthatconsiderthecharacteristics oftheentirerainshieldwhenrelatingchangesin therainshieldtoatmosphericandlandsurface forcingmechanisms.Italsoillustratesthata168Volume59,Number2,May2007

PAGE 12

modelmustincorporatemeasuresofasymmetry,ratherthanassumeacircularshape,to moreaccuratelyforecasttherainfallpatternsof landfallingTCs. Atrstglance,thefactthattheTCstracking neartheAppalachianMountainshavemoreof theirrainshieldontheleftsideoftheircirculationcenterseemstocontradictpreviousresearch,whichindicatesthataTCencountering mountainousterrainexperiencesincreasedprecipitationonitsrightsideduetoorographic uplift(Bender,Tuleya,andKurihara1985). However,thisscenarioonlyholdstrueifthe stormmovesinadirectionperpendiculartothe axisoftheelevatedterrain.GordonandHelene trackedparalleltotheAppalachianMountains (Figure1),causingmoistureadvectedfromthe AtlanticOceantobeupliftedbythetopography ontheleftsideofthestormtrack.Additionally, otherforcingmechanismsmayinuencethe storm.TCsthatmigrateintohigherlatitudes areinuencedbymiddlelatitudeweathersystems.Aspreviouslymentioned,Dennis,Gordon,andIsabelbecomeextratropicalcyclones whileovertheUnitedStates.Duringthistransition,themaximumprecipitationamounts shifttotheleftfrontquadrantofthestorm (RitchieandElsberry2001;AtallahandBosart 2003),causingpredictorRLSYMtohavea negativevalue.Again,thisndingillustrates thatmultipleprecipitation-alteringprocesses affectTCsandthattheseinteractionsbetween theatmosphere/landsurfaceandTCswarrant furtherinvestigationbeforeanaccuraterainfall forecastmodelcanbedeveloped.ConclusionsandFutureResearchThisstudyemploysaGIStoexaminehow stormintensity,distanceinland,andtopographycanaffecttheshapesofTCrainshields. Changesintheseshapesarequantiedbydividingthestormintosegments,amethodemployedbypreviousTCresearchers,andby calculatingseveralindicesofshapethatconsider therainshieldasawhole,amethodemployed bygeographers.ThreeseparateDAsthen determinewhichofthesevariablescanbestdistinguishbetweenTCsofhurricaneortropical stormintensity,TCslocatedwithin100ofor over200kmfromthecoastline,andTCstrackingneartheAppalachianMountainsorencounteringelevatedterraininTexas.Asshape indices,ratherthanregionsofthestormdenedbytheannularrings,werethekeypredictorsintheDAs,thisstudydemonstratesthatitis importanttoconsiderhowtheshapeoftheentirerainshieldischanging,ratherthanjustanalyzingindividualsegments.Thisstudyalso showsthatthegeographicalmeasuresofshape calculatedinthisstudyarecapableofquantifyingthesechangesinshape. ThethreeDAmodelsdescribedinthisarticle producestatisticallysignificantresultsbyutilizingshapemetricsthatquantifyaspectsofthe entirerainshieldtopredictgroupmembership. Thespecificrelationshipsbetweentheatmosphere/landsurfaceandthechangesinshapeare asfollows: Ashurricaneshavefasterwindsthatadvect moisturecompletelyaroundtheircirculationcenters,theyhaveahighRSAL (349 1 ).Tropicalstormshaveslowerwinds andmaybeaffectedbystrongdirectional windshearthatlimitsthearc-lengthof theirrainshieldtoanaverageof171 1 TCsremainingwithin100kmofthe coastlineexhibitamorecircularshape (averageMMR0.67)thandothoselocated morethan200kminland(averageMMR 0.31)asquantiedbytheMMR. WhenTCsencounterelevatedterrain,the orientationoftheirrainshieldsparallels thatoftheaxisoftheelevatedterrain (averageORIof278 1 fortheeast-west EdwardsPlateau,averageof41 1 forthe northeast-southwestAppalachianMountains).TCstrackingneartheAppalachian Mountainsarealsoinuencedbymiddle latitudeweathersystemsthatshifttherain shieldtotheleftsideofthestormtrack (negativeRLSYM). ThesendingsalsodemonstratethatTCrain shieldsoftenassumeasymmetricalshapes.The shapemeasurescalculatedinthisstudyare capableofquantifyingtheseshapesandcould beemployedtoimprovefutureTCrainfall forecasts. Tostrengthenthendingsofthisstudy,futureresearchwillinvestigatechangesintherain shieldshapesofadditionalTCs.Recenttechnologicaldevelopments(AnsariandDelGreco 2005)willallowtheexaminationofstormsbeginningwiththe1995seasonuptopresentday,QuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields169

PAGE 13

foratotalofmorethanftyU.S.landfalling TCs.ThisincreasedsamplesizewillallowTCs tobestratiedaccordingtothevariousforcing mechanismsthataffectthem,includingseveral forcingmechanismsmentionedbutnotexaminedinthisstudy(e.g.,extratropicaltransition, windshear).Theshapemeasuresdescribedin thisarticle,alongwithothermetricsnotdiscussedhere,willbecalculatedandusedtomodelchangesintherainshield.Theultimategoal ofthisresearchistodevelopaTCrainfallmodel capableofcombiningdatafromaclimatologyof rainshieldshapechangesspecifictoeachphysicalforcingmechanismwithdatapertainingtoa currentstorm'shistorycollectedviapre-landfall satelliteimagerytopredicttheshapeofitsrain shieldatlandfallandthroughoutthepost-landfallperiod.Theforecastedshapecouldthenbe inputintohydrologicalmodelsthatalreadyoperatewithinaGIS(Vieux2001)toimprove predictionsofwherefreshwateroodingwill occur.Theevacuationofood-proneareas priortoastorm'slandfallcouldreducethe numberofliveslostandpropertydamage causedbyoodingrainfallproducedbylandfallingTCs. ’LiteratureCitedAberson,S.D.1998.Five-daytropicalcyclonetrack forecastsintheNorthAtlanticbasin. Weatherand Forecasting 13(4):100515. AMS.2000.Policystatement:Hurricaneresearchand forecasting. BulletinoftheAmericanMeteorological Society 81(6):134146. Ansari,S.,andS.DelGreco.2005.GIStoolsfor visualizationandanalysisofNEXRADradar (WSR-88D)archiveddataattheNationalClimaticDataCenter.Paperreadatthe21stInternational ConferenceonInteractiveInformationProcessing Systems(IIPS)forMeteorology,Oceanography, andHydrology,12January2005,SanDiego,CA. Atallah,E.H.,andL.R.Bosart.2003.Theextratropicaltransitionandprecipitationdistributionof HurricaneFloyd(1999). MonthlyWeatherReview 131(6):106381. Barnes,G.M.,E.Zipser,D.Jorgensen,andF.D. Marks.1983.Mesoscaleandconvectivestructureof ahurricanerainband. JournaloftheAtmosphericSciences 40:212537. Bender,M.A.,R.E.Tuleya,andY.Kurihara.1985.A numericalstudyoftheeffectofamountainrangeon alandfallingtropicalcyclone. MonthlyWeatherReview 113(4):56782. Black,M.L.,J.F.Gamache,F.D.Marks,C.E.Samsury,andH.E.Willoughby.2002.EasternPacific HurricanesJimenaof1991andOliviaof1994:The effectofverticalshearonstructureandintensity. MonthlyWeatherReview 130(9):22912312. Bluestein,H.B.,andD.S.Hazen.1989.Dopplerradaranalysisofatropicalcycloneoverland:HurricaneAlicia(1983)inOklahoma. MonthlyWeather Review 117(11):25942611. Cerveny,R.S.,andL.E.Newman.2000.Climatologicalrelationshipsbetweentropicalcyclones andrainfall. MonthlyWeatherReview 128(9): 332936. Chan,J.C.L.,andX.D.Liang.2003.Convective asymmetriesassociatedwithtropicalcyclonelandfall.PartI:f-planesimulations. Journalofthe AtmosphericSciences 60(13):156076. Corbosiero,K.L.,andJ.Molinari.2002.Theeffects ofverticalwindshearonthedistributionofconvectionintropicalcyclones. MonthlyWeatherReview 130(8):211023. .2003.Therelationshipbetweenstormmotion,verticalwindshear,andconvectiveasymmetriesintropicalcyclones. JournaloftheAtmospheric Sciences 60(2):36676. DeMaria,M.,andJ.Kaplan.1994.Astatisticalhurricaneintensitypredictionscheme(SHIPS)forthe Atlanticbasin. WeatherandForecasting 9(2):20920. DeMers,M.N.2000. Fundamentalsofgeographicinformationsystems ,2nded.NewYork:Wiley. Dvorak,V.F.1975.Tropicalcycloneintensityanalysis andforecastingfromsatelliteimagery. Monthly WeatherReview 103:42030. Elsberry,R.L.2002.Predictinghurricanelandfall precipitation:Optimisticandpessimisticviews fromthesymposiumonprecipitationextremes. BulletinoftheAmericanMeteorologicalSociety 83(9): 133339. ESRI.2002.ArcViewGIS3.3.EnvironmentalSystemsResearchInstitute,Redlands,CA. Franklin,J.L.,L.A.Avila,J.L.Beven,M.B.Lawrence,R.J.Pasch,andS.R.Stewart.2001.Atlantic hurricaneseasonof2000. MonthlyWeatherReview 129(12):303756. Frolov,Y.1975.Measuringofshapeofgeographical phenomena:Ahistoryoftheissue. SovietGeography: ReviewandTranslation 16:67687. Gautam,R.,G.Cervone,R.P.Singh,andM.Kafatos. 2005.Characteristicsofmeteorologicalparameters associatedwithHurricaneIsabel. GeophysicalResearchLetters 32(4):Art.no.L04801. Gilbert,S.C.,andN.E.LaSeur.1957.Astudy oftherainfallpatternsandsomerelatedfeatures inadissipatinghurricane. JournalofMeteorology 14: 1827. Hart,R.E.,andJ.L.Evans.2001.Aclimatologyofthe extratropicaltransitionofAtlantictropicalcyclones. JournalofClimate14(4):54664.170Volume59,Number2,May2007

PAGE 14

Hubert,L.E.1955.Frictionalllingofhurricanes. BulletinoftheAmericanMeteorologicalSociety 36:44045. Jones,R.W.1987.Asimulationofhurricanelandfall withanumerical-modelfeaturinglatentheatingby theresolvablescales. MonthlyWeatherReview 115 (10):227997. Jones,S.C.,P.A.Harr,J.Abraham,L.F.Bosart,P.J. Bowyer,J.L.Evans,D.E.Hanley,B.N.Hanstrum, R.E.Hart,F.Lalaurette,M.R.Sinclair,R.K. Smith,andC.Thorncroft.2003.Theextratropical transitionoftropicalcyclones:Forecastchallenges, currentunderstanding,andfuturedirections. WeatherandForecasting 18(6):105292. Jorgensen,D.P.1984.Mesoscaleandconvective-scale characteristicsofmaturehurricanes.PartI:General observationsbyresearchaircraft. JournaloftheAtmosphericSciences 41(8):126885. Klazura,G.E.,andD.A.Imy.1993.Adescriptionof theinitialsetofanalysisproductsavailablefromthe NEXRADWSR-88Dsystem. BulletinoftheAmericanMeteorologicalSociety 74(7):1293311. Klein,P.M.,P.A.Harr,andR.L.Elsberry.2000. ExtratropicaltransitionofwesternNorthPacific tropicalcyclones:Anoverviewandconceptual modelofthetransformationstage. Weatherand Forecasting 15(4):37395. Kruger,A.,andW.F.Krajewski.1997.Efcientstorageofweatherradardata. Software-Practice&Experience 27(6):62335. Lawrence,M.B.,L.A.Avila,J.L.Beven,J.L.Franklin,J.L.Guiney,andR.J.Pasch.2001.Atlantic hurricaneseasonof1999. MonthlyWeatherReview 129(12):305784. Lin,Y.L.,D.B.Ensley,S.Chiao,andC.Y.Huang. 2002.Orographicinuencesonrainfallandtrack deectionassociatedwiththepassageofatropical cyclone. MonthlyWeatherReview 130(12):292950. MacEachren,A.M.1985.Compactnessofgeographic shape:Comparisonandevaluationofmeasures. GeograskaAnnaler 67B:5367. Marchok,T.,R.Rogers,andR.Tuleya.2007.Validationschemesfortropicalcyclonequantitativeprecipitationforecasts:Evaluationofoperational modelsforU.S.landfallingcases. Weatherand Forecasting 22. Marks,F.D.,G.Kappler,andM.DeMaria.2002. Developmentofatropicalcyclonerainfallclimatologyandpersistence(R-CLIPER)model.Paper readatthe25thConferenceonHurricanesand TropicalMeteorology,AmericanMeteorological Society,29April3May,SanDiego,CA. Matyas,C.J.2005.Usinggeographicinformation systemsforthespatialanalysisofbasereectivity radardataandapplicationstothestudyoftropical cycloneprecipitationpatterns.Paperreadatthe 15thConferenceonAppliedClimatology,AmericanMeteorologicalSociety,2023June,Savannah, GA. .2006.Usingannularringsandquadrantsto clippolygonsrepresentingtropicalcycloneprecipitationinageographicinformationsystem. Paperreadatthe22ndInternationalConference onInteractiveInformationProcessingSystemsfor Meteorology,Oceanography,andHydrology,29 January3February,Atlanta,GA. .2007.Shapemeasuresofrainshieldsasindicatorsofchangingenvironmentalconditionsina landfallingtropicalstorm.Workingpaper,DepartmentofGeography,UniversityofFlorida. Pasch,R.J.,L.A.Avila,andJ.L.Guiney.2001. Atlantichurricaneseasonof1998. MonthlyWeather Review 129(12):3085123. Powell,M.D.1990.Boundary-layerstructureand dynamicsinouterhurricanerainbands.1.Mesoscalerainfallandkinematicstructure. MonthlyWeatherReview 118(4):891917. Rao,G.V.,andP.D.Macarthur.1994.TheSSM/I estimatedrainfallamountsoftropicalcyclones andtheirpotentialinpredictingthecyclone intensitychanges. MonthlyWeatherReview 122(7): 156874. Rappaport,E.N.2000.LossoflifeintheUnited StatesassociatedwithrecentAtlantictropicalcyclones. BulletinoftheAmericanMeteorologicalSociety 81(9):206573. Ritchie,E.A.,andR.L.Elsberry.2001.Simulationsofthetransformationstageoftheextratropicaltransitionoftropicalcyclones. MonthlyWeatherReview 129(6):146280. Rodgers,E.B.,S.W.Chang,andH.F.Pierce.1994.A satelliteobservationalandnumericalstudyofprecipitationcharacteristicsinwesternNorthAtlantic tropicalcyclones. JournalofAppliedMeteorology 33 (2):12939. Rogers,R.F.,S.S.Chen,J.Tenerelli,andH.E. Willoughby.2003.Anumericalstudyoftheimpact ofverticalshearonthedistributionofrainfallin HurricaneBonnie(1998). MonthlyWeatherReview 131:157799. Saunders,M.A.,R.E.Chandler,C.J.Merchant,and F.P.Roberts.2000.AtlantichurricanesandNW Pacifictyphoons:ENSOspatialimpactsonoccurrenceandlandfall. GeophysicalResearchLetters 27(8): 114750. Shipley,S.T.,I.A.Graffman,andJ.K.Ingram.2000. GISapplicationsinclimateandmeteorology.Paper readattheESRIInternationalUser'sConference, 2630June,SanDiego,CA. Stoddart,D.R.1965.Theshapeofatolls. Marine Geology 3:36883. Tabachnick,K.E.,andL.S.Fidell.2001.Discriminantfunctionanalysis.In Usingmultivariatestatistics ,ed.R.Pascal,456516.Boston:Allyn&Bacon. Toracinta,E.R.,D.J.Cecil,E.J.Zipser,andS.W. Nesbitt.2002.Radar,passivemicrowave,and lightningcharacteristicsofprecipitatingsystemsQuantifyingtheShapesofU.S.LandfallingTropicalCycloneRainShields171

PAGE 15

inthetropics. MonthlyWeatherReview 130(4): 80224. Tuleya,R.E.1994.Tropicalstormdevelopmentand decay:Sensitivitytosurfaceboundary-conditions. MonthlyWeatherReview 122(2):291304. Tuleya,R.E.,andY.Kurihara.1978.Anumerical simulationofthelandfalloftropicalcyclones. JournaloftheAtmosphericSciences 35(2):24257. Vickery,P.J.,P.F.Skerlj,andL.A.Twisdale.2000. SimulationofhurricaneriskintheUSusingempiricaltrackmodel. JournalofStructuralEngineering-ASCE 126(10):122237. Vieux,B.E.2001. Distributedhydrologicmodelingusing GIS .38vols.Vol.38. WaterScienceandTechnology Library ,ed.V.P.Singh.Boston:KluwerAcademic. Wentz,E.2000.Ashapedefinitionforgeographic applicationsbasedonedge,elongation,andperforation. GeographicAnalysis 32(2):95112. Wood,E.C.2001.Theanalysisandpredictionof tropicalcyclonerainfall.MSthesis,Departmentof Meteorology,PennsylvaniaStateUniversity. CORENEMATYASisanAssistantProfessorinthe DepartmentofGeographyattheUniversityofFlorida,Gainesville,FL32611.E-mail:matyas@u.edu. Herresearchinterestsincludesevereweather,rainfall patterns,andsynopticclimatology.172Volume59,Number2,May2007