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Quantifying the shapes of U.S. landfalling tropical cyclone rain shields
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Permanent Link: http://ufdc.ufl.edu/IR00001369/00001
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Title: Quantifying the shapes of U.S. landfalling tropical cyclone rain shields
Series Title: The Professional Geographer, 59:2, 158-172
Physical Description: Journal Article
Creator: Matyas, Corene
Publisher: The Professional Geographer
Publication Date: 2007
 Notes
Abstract: Tropical cyclones (TCs) produce complex rainfall patterns that are difficult to predict due to atmospheric and land surface forcings. This study utilizes geographic information systems to spatially analyze radar returns and calculate several metrics that quantify the shapes of TC rain shields. Three stepwise discriminant analyses are performed to determine which of the shape metrics distinguish among TCs categorized by: intensity, distance traveled inland, and orientation of terrain encountered. Results confirm that TC rain shields often assume noncircular shapes. Utilizing shape indices to model rain shields could help produce TC rainfall forecasts that are more spatially accurate.
Acquisition: Collected for University of Florida's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Corene Matyas.
Publication Status: Published
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Source Institution: University of Florida Institutional Repository
Holding Location: University of Florida
Rights Management: All rights reserved by the submitter.
System ID: IR00001369:00001

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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