TheRoleofInnerCoreMoistureinTropicalCyclonePredictabilityandPracticalForecastSkill
KerryEmanuel1
LorenzCenter
MassachusettsInstituteofTechnology
Cambridge,Massachusetts
FuqingZhang
DepartmentofMeteorologyandAtmosphericScience,andCenterforAdvancedData
AssimilationandPredictabilityTechniques,ThePennsylvaniaStateUniversity,UniversityPark,
Pennsylvania
Revised
April,2017
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Corresponding author address and email: Rm 54-1814, MIT; 77 Massachusetts Avenue, Cambridge,
MA 02139. Phone: 617-253-2462. Email: [email protected] .
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Abstract
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Errorsintropicalcycloneintensityforecastsaredominatedbyinitialconditionerrorsouttoat
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leastafewdays.Initializationerrorsareusuallythoughtofintermsofpositionandintensity,
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buthereweshowthatgrowthofintensityerrorisatleastassensitivetothespecificationof
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innercoremoistureastothatofthewindfield.Wediscussimplicationsofthisfindingfor
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tropicalcycloneobservationalstrategiesandforoverallpredictabilityofstormintensity.
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1. Introduction
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Predictionoftropicalcycloneintensityremainsasignificantchallenge,withlittle
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improvementinforecastskilloverthepastfewdecades(DeMariaetal.,2014).Thislackof
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improvementhasbeenattributedtoavarietyoffactors,frominadequateobservationsofthe
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atmosphereandupperocean,tolackofabilitytoassimilateobservations,tomodelerrors,but
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inrecentyearstherehasbeenaconcertedefforttoimproveintensityforecasts(Galletal.,
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2013).
Inarecentlypublishedpaper(EmanuelandZhang,2016),theauthorsattemptedto
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quantifytheintrinsicpredictabilityoftropicalcycloneintensityandtodistinguishthevarious
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causesoflossofpredictability,usingaperfectmodelframeworktoisolatetheintrinsic
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predictability.Theyshowedthatforecastintensityerrorouttoafewdaysisdominatedby
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errorsintheinitialwindfield,afterwhicherrorsinforecastingthelarge-scaleenvironment
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begintodominatethroughtheireffectsonthetrackofandwindshearexperiencedbythe
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storms.Theyalsoprovidedevidencethatthereremainsasignificantgapbetweenoperational
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intensityforecastskillandskillthatistheoreticallyachievablegivenoptimisticestimatesof
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tropicalcycloneinitialconditionspecificationandoflarge-scaleenvironmentalpredictionskill.
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Inthatwork,thewatervaporcontentoftheinnercoreofthetropicalcyclonemodelwas
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heldfixedbetweenthecontrolandperturbationexperimentsandsowasnotconsideredasa
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sourceofforecasterror.Herewefocusontheimportanceofthecorrectinitializationofinner
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coremoisture.
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Hereweusetheterm“innercore”somewhatlooselytodenotethebroadregionofascent
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thatincludestheeyewallandweakerbutdeepconvectionjustoutsideit,butdoesnotinclude
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theeyeitself(ifthereisone)ortheregionofmoreisolatedspiralbandsfurtherawayfromthe
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center.Inidealizednumericalsimulationsthatbeginwithaweakcyclonicdisturbancenearthe
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surface,storm-scaleascentoccursinsidetheradiusatwhichtheradialmassfluxpeaks,andthis
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radiuscouldbeused,thoughnotwithoutsomeambiguity,toseparatetheinnercorefromthe
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outerregion,whiletheeyecouldbeidentifiedwithweakdescentinsidetheeyewall.
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Thereareabundantreasonstofocusoninnercoremoisture.Emanuel(1989)
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demonstrated,usingasimplebalancedaxisymmetrictropicalcyclonemodel,thattheinner
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core,definedasintheprecedingparagraph,hadtobenearlysaturatedbeforeintensification
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bysurfacefluxescouldbegin.Heshowedthatevensmalldegreesofsubsaturationresultedin
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convectivedowndrafts,drivenbyevaporationofrain,thatimportlowentropyairintothe
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subcloudlayerandtherebynegatethetendencyofsurfacefluxestoincreasesubcloudlayer
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entropy.
Moistureoutsidewhatweareherereferringtoastheinnercoreisalsoimportanttostorm
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intensity,especiallywhenenvironmentalshearispresent.Iftheshearisstrongenough,lower
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moiststaticenergyoutsidethecorecanbeadvectedintothecore,inaprocessthatisknownas
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“ventilation”(TangandEmanuel,2010).Butthishappensonanadvectivetimescale,sothat
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moistureanomaliesfarfromthestormcentertakesometimetoinfluencethecore,whereas
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initialerrorsininnercoremoisturehaveanalmostimmediateeffect.Whileweherefocuson
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innercoremoistureanomalies,wedonotclaimthatanomaliesoutsidethecoreare
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unimportant,particularlyatlongerleadtimes.
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Rappinetal.(2010)usedtheWeatherResearchandForecasting(WRF)modeltoperform
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three-dimensionalsimulationsoftropicalcyclogenesisathigh(convectionpermitting)
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horizontalresolution.Theyalsodemonstratedthatsurfaceintensificationofvorticesbegins
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onlyifandwhenamesoscalecolumninthestorm’scorebecomesnearlysaturated.Beforethat
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happens,orinfailedcasesofgenesis,convectivedowndraftsquenchanytendencyofenhanced
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surfaceenthalpyfluxestoincreaseboundarylayerentropy,eventhoughamesocyclonealoft
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mayintensifybyevaporationandmeltingoffallingprecipitation.
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Morefundamentally,PauluisandHeld(2002)showedthatinordinaryradiative-convective
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equilibrium,theoverallirreversibleentropyproductioninthesystemislimitedbytheradiative
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exportofentropytospace,andthatthegreatmajorityofthislimitedtotalentropyproduction
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isusedupinmixing(diffusion)acrossstronggradientsofwatervapor,leavingverylittlefor
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kineticenergydissipation.Totransitiontoastatehavinglargedissipationofkineticenergy,as
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withtropicalcyclones,theremustbeadrasticreductioninentropyproductionbymixingacross
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watervaporgradients.Thiscanonlyhappenifthemoistconvectiontakesplaceinnearly
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saturatedair,sothatthereislittlemixingofdryairintoclouds.
Evenwhenatropicalcyclonedoesdevelop,itremainssusceptibletomixingofdryairinto
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thecore,asfirstsuggestedbySimpsonandRiehl(1958).TangandEmanuel(2010)showed
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quantitativelyhowventilationofthetropicalcyclonecorereducesthestorm’sintensity,and
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thattoomuchventilationwilldestroyitaltogether.ThisisconsistentwithPauluisandHeld’s
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(2002)observationthatentropyproductioniseasilydominatedbymixingofdryandmoistair,
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subtractingfromthatwhichcouldbeusedforkineticenergydissipation.
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Itstandstoreason,therefore,thattherateofintensificationoftropicalcyclonesissensitive
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tothedegreeofsubsaturationoftheinnercore,wheretheeyewallconvectionoccurs.Inthe
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simpleCoupledHurricaneIntensityPredictionSystem(CHIPS;Emanueletal.,2004),used
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routinelytopredicttropicalcycloneintensityinnearrealtime2,theinnercoremoistureis
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initializedbymatchingtheinitialrateofintensitychangetotheobservedchangeofintensity
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overthehistoryofthestormtodate.Failuretoinitializetheinnercoremoistureproperlyyields
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largeforecasterrors,eveniftheinitialmaximumwindspeedisfreeoferror.
Ourpurposehereistoquantitativelyassesstheinfluenceofinitialinnercoremoisture
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errorsontropicalcyclonepredictionskill.Wetakethreeapproachestothis.First,weexaminea
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singlecasestudy:HurricaneJoaquinof2015.Usingafull-physicsWRFmodel(Skamarocketal.
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2008)andanensemble-baseddataassimilationsystem(Zhangetal.2009;WengandZhang
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2012,2016)weproduceseverallargeensemblesofforecaststhatdifferintheirinitializationof
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innercoremoistureeitherwithorwithoutinitialdifferenceinwindspeed,whilekeepingthe
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environmentalinitialconditionsandboundaryconditionsthesameforallensemblemembers.
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WerepeatthisexerciseusingthesimpleCHIPSmodel.Second,weextendtheworkofEmanuel
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andZhang(2016)toincludeinitialinnercoremoistureperturbations,comparingtheirgrowth
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tothegrowthoferrorfromothersourcesinaperfectmodelframework.Finally,weintroducea
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newtoyintensitymodel,consistingofapairofordinarydifferentialequations,designedto
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mimicthebehaviorofthefullCHIPSmodel,andusethistoassesserrorgrowthinasimple
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forecastsystem.
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http://wind.mit.edu/~emanuel/storm.html
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2. Sensitivitytoinnercoremoisture:Acasestudy
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Webeginwithasinglecaseasanexampleofthesensitivityofintensityforecaststoinitial
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innercoremoisture.ThecaseinpointisAtlanticHurricaneJoaquinof2015.Joaquindeveloped
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eastoftheBahamasonoraboutSeptember27thanddriftedslowlysouthwestward,turning
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backnortheastwardonOctober2nd.Itintensifiedveryrapidlybeginningatabout12GMTon
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September29th,adevelopmentthattheNationalHurricaneCenterforecastandmostobjective
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guidanceproductsfailedtoanticipate,asshowninFigure1.Moreremarkableisthelarge
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spreadinforecastintensities.At12GMTonOctober3rd,whenthestormreacheditspeak
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intensityof135kts,forecastintensitiesrangedfrom60to140kts.Thisisgoodexampleofthe
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largeuncertaintyandlowskillcurrentlyassociatedwithtropicalcycloneintensityforecasts.
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Tragically,inthiscase,failuretoanticipatetherapiddevelopmentandhighintensityachieved
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byJoaquinmayhavebeenamongthefactorsleadingtothelossoftheshipElFarowithall
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hands.
a. WRFmodelsimulations
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ConsistentwiththeoperationalpredictiondisplayedinFigure1,theensembleforecasts
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basedontheWeatherResearchandForecasting(WRF)modelversion3.5.1(Skamarocketal.
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2008)initiatedwiththeensembleKalmanfilter(EnKF)analysisperturbationsat12GMT29
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September2015fromthePennsylvaniaStateUniversity(PSU)experimentalreal-time
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convection-permittinghurricaneanalysisandforecastsystemproducedalargeensemble
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spread,consistentwiththelargeerrorsinJoaquin’sintensityforecasts,aswellasthelarge
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divergenceamongtheensembletrackforecasts(notshown).Thereal-timePSUWRF-EnKF
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system(WengandZhang2016)useda60-memberensemblewiththefinestgridspacingof3
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kmthatassimilatednon-radianceconventionalobservationsplusreconnaissanceairborne
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dropsondeandflight-levelobservationsforJoaquin.
Toseparatetheinfluenceoftheinner-coreversusenvironmentalconditionson
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Joaquin’sintensityforecastuncertainties,weperformedaWRF-basedensembleforecast
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experimentthatissimilartothereal-timePSUWRF-EnKFensembleexceptforusingonlythe
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real-timeensembleperturbationsintheinner-coreregion(withinaradiusof300km)while
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relocatingthecenterofeachmember’sinitialvortextothePSUWRF-EnKFanalysismean
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position.Theenvironmentalconditions(outsidearadiusof600kmfromthevortex)arethe
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sameinallmembersandareinterpolatedfromtheNCEPoperationalGlobalForecastSystem
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(GFS)analysis.Linearinterpolationisappliedtoeachmemberforradiibetween300and600
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km,assigningadecreasingweight(from1to0)tothereal-timeWRF-EnKFinitialensemble
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perturbationsandanincreasingweight(from0to1)totheGFSanalysis.Themeanand
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ensemblespread(intermsofstandardderivation)oftheazimuthallyaveragedtangentialwind
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andrelativehumidityareshowninFigure2.Thespreadinsurfaceazimuthalwindreaches
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peakvaluesofabout 10 ms -1 whiletherelativehumidityspreadreachesapeakamplitudeof
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around16%nearthestormcenterinthemiddletouppertroposphere.Butnotethatthe
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largesthumidityperturbationsareintheunsaturatedeyeregionandprobablydonothave
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mucheffectonsubsequentintensification.Wewilladdressthisissuepresently.
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ThisnewWRFensemblesimulationwithonlyinitialinner-coreperturbations
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reproducedtheintensityforecastuncertainties(Figure3)butasweusedthesameGFS
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environmentalconditionsforeachensemblemember,thereislittleforecastdivergenceinthe
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ensembletracks(notshown),implyingthatatleastforthisforecastinitializationtimeof
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Joaquin,thetrackforecastisprimarilyinfluencedbythelarge-scaleenvironment(tobe
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examinedinaseparatestudy),whiletheintensityforecastispredominantlydeterminedbythe
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initialinner-coredynamicandthermodynamicconditions.
Toisolatetheinfluenceofinner-coremoistureabovethehurricaneboundarylayer,we
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performtwootherensembleexperiments,identicaltothatillustratedinFigure3butone
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retainingonlymoistureperturbations(Figure2,right)andtheotherretainingonlymoisture
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perturbationsonlyabovetheboundarylayer(usingalineartransitionzonefromzero
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perturbationat900mbtofullperturbationat850mb)andoutsideoftheeye(fromzero
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perturbationsat25kmradiustofullperturbationsat50km).TheresultsareshowninFigures4-
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5.Thesetwoadditionalensembleexperimentsdemonstratethatwhileinitialinner-coreinitial
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vortexintensityperturbationsarestronglyinfluential,thereareconsiderableuncertaintiesin
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thehurricaneintensityforecastwithonlyinner-coremoistureperturbations(Figure4).
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Moreover,evenretainingtheinner-coremoistureperturbationsonlyabovetheboundarylayer
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andoutsidetheeyewillleadtoconsiderableintensityspread(Figure5).Anotherensemble
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experimentthesameasinFigure5exceptforretainingonlytheboundarylayermoisture
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perturbationsshowsasimilarlevelofinfluenceonhurricaneintensity(notshown).
Sensitivityoftropicalcycloneintensitytoinitialmoistureuncertaintieswasalsoinvestigated
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throughreal-datafull-physicsconvection-permittingensemblesimulationsinSippelandZhang
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(2008,2010),ZhangandSippel(2009)andMunselletal.(2013,2015),thoughnoneofthese
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previousstudiesexclusivelyfocusedonrealisticinner-coremoistureonlyperturbations.
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Meanwhile,recentlyidealizedfull-physicsWRFsimulations(ZhangandTao2013,Taoand
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Zhang2015)alsoshowedthattheintensityforecastcanbeintrinsicallylimited(especially
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duringthedevelopmentstage)evenifonlyperturbedwithminute,unobservableboundary
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layermoistureuncertaintiesformoderatelyshearedtropicalcyclones,thoughaconstant
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environmentalconditionwilleventuallygrowtheensemblememberstosimilarintensityafter
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rapidintensification.
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b. CHIPSsimulations
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CHIPS(Emanueletal.,2004)isasimple,axisymmetric,quasi-balancedtropicalcyclone
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modelphrasedinangularmomentumcoordinatesandcoupledtoasimple,one-dimensional
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upperoceanmodelthatallowsforthephysicsofstorm-inducedverticalmixing.CHIPShasbeen
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usedforabout15yearstomakereal-timeforecastsoftropicalcycloneintensityglobally.The
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forecaststhemselveshavebeenarchived,togetherwithkeyenvironmentalparametersalong
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theforecasttrack;theseincludepotentialintensityandverticalshearofthelarge-scale
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horizontalwind.Inrecentyears,wehaveruna7-memberensembledefinedbyperturbingthe
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initialintensityandinnercoremoisture,andpredictedenvironmentalwindshear.Thecontrol
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forecastforJoaquinmadeat12GMTon29September2015isshowninFigure1.
Afteraparticulareventhasoccurred,weroutinelyre-runtheCHIPSmodelusingthe
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observed(ratherthanforecast)trackandtheoperationallyanalyzedwindshearandpotential
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intensityalongthetrack.Thisallowsustominimizeerrorsourcesrelatedtoincorrectlyforecast
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trackandwindshearsoastofocusonmodelandinitializationerrors.
Herewecreateensemblesofsuchpost-stormsimulationsbyperturbingtheinitialintensity
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andinnercoremoisture.Eachensemblememberusesthesametrackandlarge-scale
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environmentalconditions.Theinitialvortexisspecifiedbyapeakgradientwindatthesurface,
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andtheradiusatwhichthisgradientwindreachesitspeakvalue.Thusperturbingtheinitial
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peakwindisstraightforward.
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Forreal-timeforecasts,CHIPSisrunfromtheinceptionofthestormuptothecurrenttime,
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andthedegreeofinnercoresaturationiscontinuouslyvariedsoastobestmatchthehistoryof
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thestorm’sintensity.Intheseforecasts,andinwhatfollows,“innercore”isdefinedtobe
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within1.3timestheradiusofmaximumwinds.TherateofintensificationofCHIPS-simulated
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stormsisquitesensitivetoinnercoremoisture,somatchingthesimulatedstorm’sintensityto
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thehistoryoftherealstorm’sintensityuptothecurrenttimehastheeffectofinitializingthe
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innercoremoisture.Thisishighlyadvantageousinviewofthepaucityofobservationsof
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troposphericwatervaporintheinnercoresoftropicalcyclones.Weshallreturntothispointin
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advocatingfortropicalcyclonedataassimilationthataccountsforatleasttherecenthistoryof
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thestorm.
Onceinitialized,theinnercoremoistureispredictedbyarateequationthataccountsfor
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verticaladvectionwithinthestormandaparameterizedinteractionwithenvironmentalwind
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shear.(SeeEmanueletal.,2004,foramorecompletediscussionofthis.)
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Forthepresentpurposes,weinitializetheinnercoremoisturethroughspecificationofa
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parameterwelabel d ,whichvariesfrom0to1.When d = 0 ,theinitialinnercoremoiststatic
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energyatmid-levelsinthetroposphereisidenticaltothatoftheunperturbedenvironment,
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while d = 1 correspondstosaturationoftheinnercore.Thus d isdefined
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dº
hic - he
, hic* - he
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where hic isthemoiststaticenergyoftheinnercore, hic* isitssaturationvalue,and he isthe
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environmentalmoiststaticenergy.
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Figure6ashowstheevolutionof21CHIPShindcastsinwhichtheinitialvalueofthe d 201
parameterisfixedat0.9whiletheinitialwindspeedisvariedovertherange -5 to +5 ms -1 in
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incrementsof 0.5 ms -1 .Thisrangeisconservativerelativetocontemporaryestimatesof
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uncertaintyintropicalcycloneintensity(LandseaandFranklin,2013).Clearly,theforecast
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intensityissensitivetotheinitialintensity,whichisconsistentwiththefull3-Dconvection-
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permittingWRFensembleexperimentsshowninFigure2forthesameevent.
AllofthehindcastsshowninFigure6bareinitializedattheobservedintensitybutwith
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initial d valuesrangingfrom 0.5 to 1 inincrementsof 0.05 .(Iftheenvironmentalrelative
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humiditywere50%,aninitial d valueof0.5wouldcorrespondtoaninnercorerelative
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humidityofabout75%.Inthiscase,varying d valuesrangingfrom 0.5 to 1 wouldcorrespond
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tovaryingtherelativehumidityoverarangeofabout25%.Thisisabitlargerthanthe
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ensemblevarianceweusedintheWRFsimulations(Figure2).Toourknowledgethereareno
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publishedstudiesoftheuncertaintyininitialestimatesofobservedtropicalcycloneinnercore
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humidity.)Theintensityevolutionisquitesensitivetoinnercoremoisturevariationsovera
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realisticrange.ThustheCHIPSmodelexhibitsroughlythesamesensitivitytoinitialinnercore
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moistureasexhibitedbythefullWRFmodelensembleexperimentsdiscussedintheprevious
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subsection(Figures4-5).
Thissensitivity,sofardemonstratedacrosstwomodels,isthemainresultofthepresent
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work.
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c. Tropicalcycloneintensitysimulator
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Partlytoencouragefurthertropicalcycloneintensitypredictabilitystudies,wedevelopeda
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highlysimplifiedtropicalcycloneintensityalgorithmthatcanbeveryrapidlycodedandsolved.
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WestartedwithatheoreticaldevelopmentequationdevelopedbyEmanuel(2012)forthe
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specialcaseinwhichatropicalcyclonehasacompletelysaturatedinnercoreanddevelops
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withoutinteractionwithshearorfeedbackfromtheoceanorfromisothermalexpansion
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effects:
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dV CD 2
@
(Vp - V 2 ) , dt
2h
(1)
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where V isthemaximumcircularwindspeednearthesurface, C D isthesurfacedrag
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coefficient, h isaboundarylayerdepth,and V p isthepotentialintensitymodifiedbya
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functionofthesurfaceexchangecoefficientsofenthalpyandmomentum.Wesoughttomodify
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(1)toaccountforunsaturatedinnercores,windshear,andinteractionwiththeunderlying
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ocean.Aftermuchexperimentation,wedevelopedthefollowingpairofordinarydifferential
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equations:
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and
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dV 1 CD
éëaV p2m3 - V 2 ùû , =
dt 2 h
(2)
dm 1 CD
=
é(1 - m )V - 2.2Sm ùû , dt 2 h ë
(3)
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where V isthemaximumcircularwindspeed, m isaninnercoremoisturevariablethatvaries
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between 0 and 1 , S isthemagnitudeofthe850–250hPaenvironmentalwindshear,and a 238
isanoceaninteractionparameter.(In(2)and(3),theunitsof V , V p , S , and h mustbe
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consistent.)TheoceanfeedbackparameterismodeledaftertheresultsofSchadeandEmanuel
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(1999):
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where
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a = 1 - 0.87e- z , (4)
z º 0.01G-0.4hmuTVpV -1. (5)
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Here G isthesub-mixedlayerthermalstratificationin K (100m) -1 , hm istheoceanmixedlayer
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depthinmeters,and uT isthestormtranslationspeedin ms -1 .
In(2)and(3)wehavenotexplicitlyaccountedforisothermalexpansioneffects,though
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theymaybeincorporatedinthedefinitionof V p .
Notethatintheabsenceofoceanfeedback (a = 1) andshear,thesteadysolutionof(2)
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and(3)is V = V p , m = 1 ,asexpected.Ifweregardtheproduct 2.2Sm astheventilationu 14
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introducedbyTangandEmanuel(2010),thenintheabsenceofoceanfeedback,thesteady
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solutionof(2)and(3)isgivenasthesolutionto
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V
*5
3
- V * + u * = 0, (6)
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wheretheasterisksindicatethatthequantityhasbeennormalizedbythepotentialintensity,
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V p .ThismaybecomparedtotheequilibriumequationdevelopedbyTangandEmanuel
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(2010),whichhastheform
V *3 - V * + u * = 0. 256
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Thedifferentexponentsin(6)and(7)arisefromdifferentassumptionsaboutthephysics
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andfromthedesireheretocloselymimicthefullCHIPSmodelbehavior.Solutionsto(6)and(7)
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,normalizedtohavethesamethresholdvalueofu * ,arecomparedinFigure7.Theyarequite
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similarinform.AsshownbyTangandEmanuel(2010),theupperbranchesofthesolutionare
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stableequilibria,whilethelowerbranchesareunstable.
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Inourcase(andperhapsinthatofTangandEmanuel,2010), u * dependson m, sothe
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solutionsto(6)arenottrulyintermsofexternalquantities.Expressedasafunctionofthe
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externalquantity S * (shearnormalizedbypotentialintensity),theequilibriumequationis
*1
- V * - S * = 0. (7)
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Solutionsof(8)areplottedinFigure8.Notethattheupperstableequilibriumintensity
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decaysalmostlinearlywithincreasingshear,untiltheshearapproachesitscriticalvalue,when
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theintensitydropsoffmoresharply.Alsonotethatthecriticalintensityneededfor
V
3
15
(8)
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amplification(thelowerbranchofthecurve)isverysmalluntiltheshearapproachesitscritical
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value.Abovethecriticalshear,givenbytheright-mostpointinFigure8,noequilibriumsolution
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existsandallsolutionsdecayovertime.
Weapplythesystemgivenby(2)and(3)totheforecastofJoaquininitializedasbeforeat
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12GMTon29September2015.Asbefore,wedrivethesimplemodelwiththeanalyzed
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potentialintensity,environmentalwindshear,andupperoceanpropertiesalongthetrack.We
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use CD = 1.2 ´ 10-3 and h = 1400 m, andintegratethesystemwithasimpleleap-frogtime
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schemewithanAsselinfiltervalueof0.1andatimestepof240s.A6-dayforecastwiththis
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schemerunsinabout0.002sonanordinarylaptopcomputer.
Asbefore,werunoneensembleinwhichperturbationsrangingfrom -5 ms -1 to 5 ms -1 in
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incrementsof 0.5 ms -1 areaddedtotheobservedinitialwindspeed.Forthesesimulations,we
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initialized m withavalueof 0.3. Inasecondensemble,wefixtheinitialintensityatits
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observedvaluewhilevaryingtheinitialvalueof m from 0.1 to 0.6 inincrementsof 0.05. The
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resultsofthesetwosetsofsimulationsareshowninFigure9togetherwiththeevolutionsof
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theobservedpotentialintensityandenvironmentalwindshearalongtheobservedtrack,the
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best-trackintensity,andasinglesimulationofthefullCHIPSmodel(oneofthesimulations
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displayedinFigure6).
ComparingtheseresultswiththoseofthefullCHIPSmodelinFigure6,itisclearthatthe
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simplemodelintensityerrorsdonotamplifyasquickly(ordecayfaster),perhapsbecausethe
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nonlinearityofthesimplemodelisweakerthanofthefullCHIPS.Buteveninthissimplemodel,
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errorsresultingfromthemoistureinitializationamplifyquicklyoverthefirstdayorsoand
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persistformanydays.Butoncethestormceasesintensifying,theerrorscollapsesmoothlyto
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zeroasthestormequilibratestoenvironmentalconditions.Thiserrordecayisalsoevidentin
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thefullCHIPSsimulations(Figure6)buthappensmoreslowly.
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Wehopethatoursimplesystem,consistingofequations(2)-(5),willinspirefurtherstudies
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ofintrinsictropicalcycloneintensitypredictability,andwebelieveitmayserveasanalternative
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topurelystatisticalintensityalgorithmsforuseintropicalcycloneriskmodels.
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3. Comparativeeffectsofinitialinnercoremoistureonintensityerrors
Toexploremorecomprehensivelytheerrorgrowthowingtomoistureinitialization
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errors,weapplytheframeworkdevelopedbyEmanuelandZhang(2016).Theyusedthe
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tropicalcycloneriskmodelofEmanueletal.(2008)tosimulate3100tropicalcyclonesinthe
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NorthAtlantic,downscaledfromNCAR/NCEPreanalyses.Thestormswereinitializedwith
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intensitiesvaryingrandomlybetween10and110ktsandrunforwarduntiltheirsurfacewinds
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droppedbelowathreshold.Thestormswerethenre-initializedwithperturbationsappliedto
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theirinitialintensitiesand/ortotheirtracksandenvironmentalwindshears.Comparisonof
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theseperturbedsimulationstothecontrolgaveestimatesofintensityerrorgrowthovertime.
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(SeeEmanuelandZhang,2016,fordetaileddescriptionsoftheexperiments.)
AlltheeventssimulatedinthatworkwereinitializedwiththeCHIPSmoistureparameter
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d setto1,sosensitivitytomoistureinitializationwasnotexamined.Hereweaddonenewset
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ofsimulationsidenticaltothecontrolsetbutwith d = 0.8, soeacheventbeginswithadrier
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innercore.(Foranenvironmentalrelativehumidityof50%,thiscorrespondstoaninnercore
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relativehumidityofabout90%.)Theroot-mean-squaredifferencebetweenthissetof
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simulationsandthecontrolisshownbythecyancurveinFigure10andcomparedtotheother
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errorsourcesdocumentedbyEmanuelandZhang(2016).(Figure10isidenticaltotheirFigure4
314
exceptfortheadditionofthecyancurveshowingerrorgrowthduetoinitialinnercore
315
moistureperturbations.)
ConsistentwithouranalysesoftheJoaquinsimulations,errorgrowthowingtoinitialinner
316
317
coremoistureerrorsisveryfastandreachesalimitveryquickly.Fortheperturbationtothe
318
CHIPS d parameterusedhere,thislimitingerrorissomewhatlargerthanthatresultingfrom
319
theinitialintensityperturbationsusedbyEmanuelandZhang(2016).Theinitialinnercore
320
humidityperturbationisequivalentto20%ofthedifferencebetweentheactualandsaturation
321
specifichumiditiesonthemiddletroposphere,yetthisissufficienttocauserapiddivergenceof
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thesolutionfromthecontrol.
ThisresultgeneralizesourfindingsfromthesinglecasestudyofHurricaneJoaquin:Failure
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toproperlyinitializeinnercorewatervaporinthefreetropospherecanbealargesourceof
325
tropicalcycloneintensityerror.
326
327
4. Summary
328
Usingthefull-physicsconvection-permittingtropicalcyclonedataassimilationandforecast
329
systemdevelopedbyZhangetal.(2009)andrefinedbyWengandZhang(2016),weshowed
330
thattheevolutionofforecastintensityissensitivetoinitialinnercoretroposphericmoistureas
331
wellastotheinitialwindfield.ThissensitivityisalsoapparentinthesimplerCHIPSmodel
18
332
(Emanueletal.,2004)aswellasaverysimpleintensitysimulatorpresentedhereforthefirst
333
time.Forreasonableestimatesofitsmagnitude,initialinnercoremoistureerrormaywell
334
dominateforecastintensityerrorouttoseveraldays’leadtime.Beyondthat,errorsinfree
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troposphericmoistureoutsidethecore,thoughnotexaminedhere,alsoplayaroleasthey
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affectthemagnitudeofventilationofthecoreiflarge-scaleshearispresent.
Sensitivitytoinitialinnercoremoisturehasbeendemonstratedinseveralprevious
337
338
modelingstudiesandisconsistentwiththefindingbyPauluisandHeld(2002)thatirreversible
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entropyproductionintropicalconvectingsystemsisdominatedbyirreversiblemixingacross
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strongmoisturegradients.Thisdominancepersistsunlessoruntiltheconvectionpenetratesair
341
thatisalreadysaturatedorverynearlyso,thusreducingentropyproductionbymixingacross
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watervaporgradients.Onlythencanentropyproductionbydissipationofthekineticenergyof
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windbecomeanimportantentropysource.
Thesensitivityoftropicalcycloneintensificationtoinnercoremoisturehasobvious
344
345
implicationsforinitializingtropicalcycloneintensityforecasts.Unfortunately,watervaporis
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amongtheleastwellobservedquantitiesintropicalcyclonecores,andthepresenceofdeep
347
convectionandstrongflowssuggeststhatwatervaporpresentsasignificantsamplingproblem.
348
Ontheotherhand,thisverysensitivitytomoisturepresentsasignificantopportunityfor
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dataassimilation,sincethetimehistoryofintensity,beingstronglyinfluencedbyinnercore
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moisture,containsimportantinformationaboutthelatter.Ourcrudeinitializationofthe
351
operationalCHIPSmodeltakesadvantageofthisfactbyadjustingtheinitialcoremoistureto
352
matchtherecentlyobservedintensificationrate.Thissuggeststhatassimilationinthetime
19
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domain,suchas4D-VarorcyclingEnKFwithflow-dependentbackgrounderrorcovariance,may
354
becriticaltothequalityoftropicalcycloneforecastinitialization,provideditimplicitlyor
355
explicitlyrecognizesthecorrelationbetweenintensificationratesandinnercorehumidity.
Ourresultssuggestthatexcellentinitializationoftheinstantaneouswindandassociated
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thermalfieldscannotbythemselvesyieldaccurateintensityforecastsabsentahighquality
358
initializationoftroposphericwatervapor,atleastinthestorm’sinnercore.Unlikewith
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temperatureandwind,thereisnoinstantaneousbalanceconditionthatconstrainswatervapor
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unlesstheairiscompletelysaturated.Thusimprovementintropicalcycloneintensityforecasts
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willdependinpartonbetterobservationsofinnercorewatervaporand/ordataassimilation
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schemesthatareabletolinkinnercoremoisturetoobservedratesofintensification.
363
Acknowledgements:ThefirstauthorgratefullyacknowledgessupportfromONRthroughgrant
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N000141410062.ThesecondauthorispartiallysupportedbyONRgrantN000140910526and
365
NOAAundertheHurricaneForecastImprovementProgram(HFIP).TheauthorsthankYonghui
366
WengandRobertNystromfortheirhelpontheWRFexperiments.Computingwasconducted
367
attheTexasAdvancedComputingCenter.
368
20
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Figures
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Figure1:EvolutionovertimeofthemaximumsurfacewindspeedinHurricaneJoaquinas
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observed(thickblue)andpredictedon12GMTonSeptember29thaccordingtotheNational
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HurricaneCenter(OFCL,black),andfourobjectiveintensityguidanceproducts:theCoupled
424
HurricaneIntensityPredictionSystem(CHIPS,lightblue),theStatisticalHurricanePrediction
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(DSHP,green),theGeophysicalFluidDynamicsmodel(GFDL,yellow),andtheHurricane
426
Weather,ResearchandForecastingmodel(HWRF,red).
24
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Figure2:Ensemblemean(solidblackcontours)andstandarddeviations(coloredshading)of
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azimuthallyaveragedtangentialwind(left;inms-1)andrelativehumidity(right;inpercent)for
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theWRFmodelsimulations.
25
180
Best Track
Ensemble Members
160
140
V max (knots)
120
100
80
60
40
20
29
30
01
02
September - October
03
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Figure 3: The intensity forecast of the WRF ensemble using only the PSU WRF-EnKF real-time
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ensembleanalysisperturbationsintheinner-coreregion.Thethickredlineshowstheensemble
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memberconsideredtobetheclosestmatchtobest-trackobservations.
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26
180
Best Track
Ensemble Members
160
140
Vmax (knots)
120
100
80
60
40
20
29
30
01
02
03
September - October
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Figure4:AsinFigure3exceptforretainingonlytheinner-coremoistureperturbations.Theinitial
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wind speed corresponds to PSU WRF-EnKF real-time analysis mean shown in the left panel of
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Figure2.
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27
439
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Figure5:AsinFigure4exceptforusingonlyinitialinner-coremoistureperturbationsabovethe
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boundarylayer(withalineartransitionzonefromzeroperturbationat900mbtofullperturbation
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at850mb)outsideoftheeye(fromzeroperturbationsat25kmradiustoperturbationsat50km).
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TheinitialwindspeedcorrespondstoPSUWRF-EnKFreal-timeanalysismeanshownintheleft
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panelofFigure2.
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Figure6:EvolutionofCHIPShindcasts(red)ofJoaquin,initializedat12GMTon29September
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2015,comparedtobest-trackintensity(blue).Ina),eachhindcastisinitializedwith d = 0.9 and
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withtheinitialwindspeedvaryingby ±5 ms -1 fromtheinitialbesttrackvalue.Inb)each
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hindcastisinitializedwiththeobservedwindspeedbutwith d valuesrangingfrom 0.5 to 1 .
29
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Figure7:Equilibriumsolutionsfornormalizedmaximumwindasafunctionofnormalized
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ventilation,forTangandEmanuel(2010;red)andof(6)(blue).Theupperbranchesarestable
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equilibria,whilethelowerbranchesareunstable.
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453
Figure8:Solutionof(8)fortheequilibriummaximumwindspeedasafunctionofthe
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normalizedenvironmentalwindshear,S*.Asbefore,theupperbranchisstablewhilethelower
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branchisunstable.Theright-mostpointofthecurverepresentsacriticalshearabovewhichno
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equilibriumsolutionexistsandallsolutionsdecaywithtime.
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Figure9:Evolutionsofensemblesofthesimplemodel(red)initializedat12GMTonSeptember
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29th2015,comparedtothebest-trackintensity(black)andasinglehindcastusingthefullCHIPS
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model(blue).Potentialintensity(dashedblue)andenvironmentalshear(green)arealsoshown.
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Theleftpanelshowsandensembleformedbyvaryingtheinitialintensityby ±5 ms -1 withthe
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initialvalueof m fixedat 0.3, whiletheensembleintherightisinitializedwiththeobserved
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intensitybutvariestheinitialvalueof m from 0.1 to 0.6 .
32
463
Figure10:SameasFigure4fromEmanuelandZhang(2016),exceptfortheadditionofroot-
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mean-squareintensityerrorowingsolelytoinitialinnercoremoistureperturbations(cyan
465
curve).Othercurvesareerrorsresultingfrominitialintensityerroronly(deepblue),errorsin
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forecastenvironmentalshear(red),initialintensityandforecastsheartogether(yellow),
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forecasttrackerrors(magenta)andinitialintensityandforecasttrackerrortogether(green).
33