Evolution of freshwater plumes and salinity fronts in the northern Bay

FullArticleforEvolutionoffreshwaterplumesandsalinityfrontsinthenorthernBayofBengal

LingjuanWu,1,2,3FanWang,1DongliangYuan,1andMaochangCui1Received21September2005;revised20March2007;accepted8May2007;published31August2007.

[1]Theevolutionoffreshwaterplumesandtheassociatedsalinityfrontsinthe

northernBayofBengal(henceforththebay)isstudiedusingrotatedempirical

orthogonalfunction(REOF)analysisandextendedassociatepatternanalysis(EAPA).Theresultsshowthatseasurfacesalinitydistributionisfeaturedbyeastern-bayandwestern-bayplumesinthenorthernbayduringdifferentseasons.Thewestern-bayplumebeginsinearlyJuly,peaksinlateAugust,andthenturnsintoabay-shapedplumewiththetwoplumesineithersideofthebay,whichpeaksinlateOctober.Thesouthwardextensionofthewestern-bayplumecanbeexplainedbythesouthwestwardgeostrophicflowassociatedwiththecyclonicgyreinthenorthernbay,whichcountersthenortheastwardEkmandriftdrivenbywindstress.Theoffshoreexpansionofthewestern-bayplumeisinducedbytheoffshoreEkmandriftwhichalsoproducesasalinityfrontneartheeastcoastofIndia.Thebay-shapedplumeappearswhenthecyclonicgyreshiftswestwardandaweakanticyclonicgyreoccupiesthenortheasternbay.Astheseasonadvances,thewesternpartofthebay-shapedplumedecayswhiletheeasternpartpersistsuntilthefollowingJune,whichisbelievedtobeassociatedwiththeanticyclonicgyreinthenorthernbay.Theevolutionoftheplumesexcepttheeasternpartofthebay-shapedplumeinfallcanbepartlyexplainedbytheseasonalvariationofmasstransportassociatedwiththeSverdrupbalance.Thefactthatthewestern-bay(eastern-bay)plumeappearswhensurfacefreshwaterfluxinthe

northeasternbayincreases(decreases)dramaticallysuggeststhattheplumesarenotproduceddirectlybysurfacefreshwaterflux.Riverdischargeseemstobethe

freshwatersourcefortheplumesandhaslittletodowiththeevolutionoftheplumes.

Citation:Wu,L.,F.Wang,D.Yuan,andM.Cui(2007),EvolutionoffreshwaterplumesandsalinityfrontsinthenorthernBayofBengal,J.Geophys.Res.,112,C08017,doi:10.1029/2005JC003308.

1.Introduction

[2]TheBayofBengal(hereafterreferredtoasthebay)isthefreshestregionintheIndianOceanbecauseofdirectmonsoonalrainfallandlargeriverrunofffromtheborderingcountries.MajorriverssuchasBrahmaputra,Ganges,Irrawaddy,Godavari,MahanadiandKrishna(Figure1)dischargeabout1.5Â1012m3/yroffreshwaterintothebay[Martinetal.,1982],andtherateofrainfallrangesbetween1–3m/yrinthewholebay[BaumgartnerandReichel,1975].HanandMcCreary[2001]showsthatwhenbothriverinflowsandsurfacefreshwaterflux(precipitationminusevaporation)areincludedina4.5layermodel,thesalinitysimulationintheupperIndianOceanaresignificantlyimprovedincomparisonwiththatforcedonlybysurfacefreshwaterflux,especiallyinthenorthernbayandalongthe

InstituteofOceanology,ChineseAcademyofSciences,Qingdao,China.

2NorthChinaSeaBranchofStateOceanicAdministration,Qingdao,China.

3GraduateSchooloftheChineseAcademyofSciences,Beijing,China.Copyright2007bytheAmericanGeophysicalUnion.0148-0227/07/2005JC003308$09.00

1eastcoastofIndia.RaoandSivakumar[2003]showedthatthepeakdischargefrommajorriversandadvectionbyoceancurrentareimportanttothepronounceddilutioninthecoastalnorthwesternbayareaduringtheheightofsummermonsoon.[3]Existingstudieshavemostlyfocusedonthefreshwa-terdistributioninthewesternpartofthebayinsummer.Afreshwaterplumenorthofabout17°NwasobservedalongtheeastcoastofIndiaduringJuly–August1989.TheplumewaspushedoffshorebyupwellingfavorableEkmantrans-port,whichalsoproducedasalinityfrontneartheeastcoastofIndia[Shetyeetal.,1991].ThesouthwardfreshwaterextensionwasexplainedusingthesteadystateSverdruptheory,whichlinksthemeridionaltransportintheopenbasintowindfieldbyShetye[1993].Theplumebetween85°Eand87°EwasthoughttobecausedbyEastIndiaCoastalCurrent(EICC),carryingfreshwaterfromriverBrahmaputraandGangessouthward[Sarmaetal.,1999].FourdifferentdrivingmechanismshavebeenproposedtoaccountforEICCvariability:interiorEkmanpumping,localalongshorewinds,remotealongshorewindsadjacenttothenorthernandeasternboundariesofthebayandremoteforcingfromtheequator.Shetyeetal.[1993]proposedthatEkmanpumpingintheinteriorbayisthe

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Figure1.Bottomtopographyofthebay(m)andmajorrivers.TheparallelogramregionenclosedinthicklineisusedinFigure5.

primaryforcingmechanismofthenortheastwardEICCfromFebruarytoMay.McCrearyetal.[1993]suggestedthatforcingbybothlocalandremotealongshorewindsinfluencestheEICC.Shankaretal.[1996]showedthattheinteriorEkmanpumpingpartlycontributedtotheseasonalEICCcycleandthesuperpositionofforcingbylocalalongshorewindsandoffshoreEkmanpumpingyieldedamodelEICCinagreementwiththeshipdriftsfromJunetoDecember,buttheonsetofnorthwardflowinspringoccurredlaterthaninobservations.McCrearyetal.[1996]extendedtheShankaretal.[1996]studybyusingalinearnumericalmodeltoinvestigatetherelativecontri-butionsofthefourprocessesthatforcetheEICC.ModelresultsofPotemraetal.[1991],Yuetal.[1991]andMcCrearyetal.[1996]indicatedtheimportanceofremoteforcingfromtheequator.However,mostnumericalmodelsusuallyusedhighlysimplifiedbasingeometrywhereastheeasternboundaryofthetropicalIndianOceaniscomposedofachainofislands.Thecirculationinthenorthernbayisverycomplicatedandtheinfluenceofoceancirculationonthefreshwaterdistributioninthenorthernbay,especiallyinnortheasternbay,hasnotbeenstudiedyet.Inthepresentpaper,basedondatafromanoceangeneralcirculationmodel(OGCM)fortheEarthSimulator(OFES),theevo-lutionanditspossiblemechanismofthefreshwaterplumesinthenorthernbaywillbediscussed.

Model(MOM3)developedatGeophysicalFluidDynam-icsLaboratoryofNationalOceanicandAtmosphericAdministration(GFDL/NOAA),areusedtostudytheevo-lutionofthefreshwaterplumesoverthebay(5°N–25°N,75°E–100°E).Thiseddy-resolvingsimulationhasbeenintegratedfrom1950to1999forcedwithmonthlymeanmomentum,heatandsalinityfluxesofNCEP/NCARreanal-ysis.AdditionalrestoringtothemonthlymeanSSSofWorldOceanAtlas1998[Boyeretal.,1998]atarelaxationtimescaleof6daysisused.TheKPPboundarylayermixingschemeisemployedfortheverticalmixing.DetailsofOFESisgivenbyMasumotoetal.[2004].

[5]ThedatasetofHamburgOceanAtmospherePara-metersandFluxesfromSatellitedata(HOAPS)withhorizontalgridspacingof0.5°,whichhasbeenderivedfromthepassivemicrowaveandinfraredsatellitedataoftheSpecialSensorMicrowave/Imager(SSM/I)andtheAdvancedVeryHighResolutionRadiometer(AVHRR)[Schulzetal.,1998;Grassletal.,2000],isemployedtoobtainfreshwaterfluxacrosstheseasurface.Thedailyanomaliesarerelativetoa4-yearmeanfrom1996to1999andaresmoothedwitha7-dayrunningmeanfilter.MonthlyclimatologyofriverdischargefromGlobalRunoffDataCentre(GRDC)isusedtodiscusstheinfluenceofriverdischargeontheevolutionofthefreshwaterplumes.MonthlymeansurfacewindstressfromEuropeanCentreforMedium-RangeWeatherForecasts(ECMWF)Re-Analysis40-year(ERA-40)isusedtocalculatesurfaceEkmandriftandbarotropicmasstransportassociatedwiththeSverdrupbalance.

[6]Rotatedempiricalorthogonalfunction(REOF)anal-ysisisbasedonvarimaxrotationwhichisknowntoyield

2.DataandMethods

[4]Dailyseasurfacesalinity(SSS)andseasurfaceheight(SSH)datafrom1January1996to31December1999fromOFES,whichisbasedontheModularOcean

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Figure2.AnnualcycleoftheSSSfromOFESforthebay(psu).

stablespatialpatternsingeneral[Richman,1986;Chengetal.,1995].TwoindependentREOFspatialmodescanbeextractedeveniftheyhavesimilarpatternsbecauseREOFmodesdonotretaincompleteorthogonalityinspace.Associatepattern(orregressiondistribution)isdefinedasanoptimalfieldpatternrelatedtothegiventimeseriesbytheleastsquaresmethod,whichhasbeenwidelyusedinclimatestudies[Zoritaetal.,1992;vonStorchetal.,1993].Associatepatternanalysismaynotbeefficientinextractinginformationwithlongtimelagbecausetheanalysiscannottellhowmuchtheassociatepatterniscorrelatedtothegiventimeseries.Toovercomethisshortcoming,extendedassociatepatternanalysis

(EAPA)hasbeenproposedbyCuietal.[2004a](seedetailsinAppendixA),whichhasbeenusedtostudythemechanismoftheElNin˜ophenomenon[CuiandWu,2005]andthesurfacehydrographyandcirculationvaria-tionsoftheChinaseas[Cuietal.,2004b;WuandCui,2005].

3.SeasonalVariationsofSSS,SSH,SurfaceFreshwaterFlux,EkmanDrift,andGeostrophicFlows

[7]Figures2–4showtheannualcycleofSSS,SSHandfreshwaterflux,respectively.ItisevidentinFigure2that

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Figure3.SameasFigure2,exceptforSSH(cm).Valueslessthan50areshaded.

thelow-salinityareainnorthernbayiscomposedoftwofreshwaterplumesduringdifferentseasons.Theplumesinthenortheasternandnorthwesternbayarecalledtheeastern-bayplumeandwestern-bayplume,respectively.InJuly,freshwaterspreadsrapidlyalongthewesternboundaryofthebayandthewestern-bayplumenorthof12°Nforms,whichpersistssteadilyuntilSeptemberwhilespreadsoff-shore.AnearshoresalinityfrontalongtheeastcoastofIndiaappearsduringthisperiod.DuringOctober–December,abay-shapedplumeincludingboththeeastern-bayandwestern-bayplumesformsinthenorthernbay.IntheJanuary

ofthenextyear,thewesternpartofthebay-shapedplumedisappearswhiletheeasternpart(i.e.,theeastern-bayplume)persistsuntilJune.

[8]Figure3showsthesimulatedmonthlymeanSSHfields,whichexhibitacyclonicgyreoverthenorthernbayfromJunethroughSeptember.Thegyreshiftssouthwest-wardinfall,movessouthwardinwinterandisreplacedbyananticyclonicgyreinspring.Thesimulatedcirculationpatternsaresimilarwiththosederivedfromtheship-driftcurrents,shipboardsurveys[Shetyeetal.,1991,1993,

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Figure4.SameasFigure2,exceptforsurfacefreshwaterfluxfromHOAPS(m/month).

1996],andTOPEX/POSEIDONaltimeter[Basuetal.,2000;EigenheerandQuadfasel,2000].

[9]DuringMay–July,surfacefreshwaterfluxincreasesdramaticallyinthenorthernbay,especiallyinthenorth-easternbay.AfterJuly,surfacefreshwaterfluxinthenorthernbaydecreasesandbecomesnegativeinwinter,whichpersistsuntilMay.

[10]MonthlymeansurfaceEkmandriftandgeostrophicflowaveragedoverthediamondregion(Figure1)areplottedinFigure5.Thepositivevalueindicatesnorthwardflowalongthecoastandoffshoreflowacrosstheshelf.ItisevidentinFigure5that,fromJanuarythroughoutMay,bothEkmandriftandgeostrophicflowarenorthward,whichmightcontributetothedisappearanceofthewesternpartofthebay-shapedplume.Duringthesummermonsoon,thesouthwardextensionofthewestern-bayplumeisconsistentwiththealongshoregeostrophicflowwhilethealongshoreEkmandriftistothenorth,oppositetothedirectionoffreshwaterextension.Ontheotherhand,offshoreEkmandrift,whichisstrongerthantheonshoregeostrophicflow,explainsthesignificantoffshoreexpansionofthewestern-bayplume.Theassociatedupwellingmightexplainthe

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Figure5.Surfacemonthlymeanoffshore(thicksolidline)andalongshore(thickdashedline)Ekmandrift(cm/s)averagedovertheparallelogramregion.Offshore(thinsolidline)andalongshore(thindashedline)geostrophicflows(cm/s)averagedoverthesameregion.Positivevaluesindicatenorthwardflowalongthecoastandoffshoreflowacrosstheshelf.

formationofthenearshoresalinityfront.Asthesummermonsoonrelaxes,theoffshoreandalongshoreEkmandriftweakenswhilethealongshoregeostrophicflowstrengthensrapidly,givingrisetothenarrowwestern-bayplumealongtheeastcoastofIndia.Withtheonsetofthewintermonsoon,bothEkmandriftandgeostrophicflowareonshoreandsouthward,whichisconsistentwiththepeakofsouthwardEICCinNovember.

4.REOFModesandExtendedAssociatedPatterns

[11]Figures6aand6bshowthefirstandsecondREOFspatialmodesofSSSanomalyinthebay,whichaccountfor61.6%and18.7%ofthetotalvariance,respectively.Thefirstmoderepresentsanareaoflowsalinity,followingtheshapeofthenorthernbayingeneral(calledthebay-shapedmodeinthefollowingtext).Thebay-shapemodeincludestheeastern-bayandwestern-bayplumes,anditstimeseriesindicatethattheamplitudeofthismodepeaksinlateOctober.Thesecondmodeindicatesthatthewestern-bayplumeandthesalinityfrontalongtheeastcoastofIndia(calledthewestern-baymodeinthefollowingtext).TheamplitudeofthismodepeaksinlateAugust.

[12]EAPAisusedtostudytheevolutionofboththewestern-bayandbay-shapedmodes.Theformerleadsthelatterbyaboutfortydays.SSS,SSHandsurfacefreshwaterfluxassociatepatternswithtimeleadsfromeighteentozeropentadsinreferencetothewestern-baymodearecalculatedandplottedonFigure7.Asshownintheappendix,takenwestern-baymodeasX,SSS,SSHandsurfacefreshwaterfluxfieldasY,thecorrelationcoefficientsbetweenthewestern-baymodeandtheassociatemodearemorethan0.5,andthevariancesexplainedbytheassociatepatternsareabout10%exceptthosewithtimeleadsexceeding9pentads(Figure8a).

[13]Fromeighteentothirteenpentadsbeforethepeaksofthewestern-baymode(i.e.,frommid-JunetoearlyJuly),SSSanomaliesspreadgraduallyalongtheeastcoastofIndia(Figures7aand7b,left).AfterearlyJuly(Figures7cand7d,left),western-bayplumereaches12°NandexpandsofftheeastcoastofIndia.Meanwhile,thenearshoresalinityfrontispresent,whichisconsistentwiththeSSSanomalyfields.ThissalinitypatternrepresentsthefreshwaterplumefromriverBrahmaputra,Ganges,KrishnaandGodavari,whichpeaksinlateAugust(Figure7e,left).

[14]Throughoutmid-JunetolateAugust,acyclonicgyredominatesthenorthernbaywithasouthwestwardcurrentalongthewesternboundaryandanorthwestwardcurrentalongtheeasternboundary(Figure7,middlecolumn).Thecyclonicgyremovesnortheastwardandbecomesstronger,whichenhancesthesouthwardfreshwaterextension.

[15]Surfacefreshwaterfluxincreasesdramaticallyinthenortheasternbayfrommid-JuneandpeaksinearlyJuly(Figures7aand7b,right).Surfacefreshwaterfluxinthenortheasternbayincreasesmorethanthatinthenorthwest-ernbay,suggestingthatthewestern-bayplumeisnotproducedbythesurfacefreshwaterflux.

[16]Similarly,SSS,SSHandsurfacefreshwaterfluxassociatepatternswithtimelagsfromminusfourtoninepentadsinreferencetothebay-shapemodeareplottedonFigure9.Theassociatepatternwithnine-pentadleadfromthebay-shapemodeisnotshownbecauseitissimilartothatwiththepeakofthewestern-baymode.Thecorrelationcoefficientsbetweenthebay-shapemodeandtheassociatemodearemorethan0.6withthevariancesexplainedbytheassociatepatternsmorethan30%(Figure8b).

[17]AfterlateAugust,lowsalinitystartstodistributealongboththewesternandeasterncoastsofthebay,especiallyintheestuariesofriverBrahmaputraandGanges;lowsalinityintheAndamanSeaindicatesthesouthwestwardexpansionoffreshwaterfromriverIrrawaddy(Figure9a,left).Consequently,theSSSpatternturnsintothebay-shapemode,whichreachesitsmaximumamplitudeinlateOctober(Figure9b,left).Thismodedecaysinmid-December(Figures9cand9d,left).

[18]DuringSeptember–December,thecyclonicgyreinthenorthernbayshiftssouthwardandwestward;aweakanticyclonicgyreoccupiesthenortheasternbay(Figure9,middlecolumn).Thecirculationpatternisconducivetothebay-shapeSSSmodeincludingboththeeasternandwesternplumesinthenorthernbay.Surfacefreshwaterfluxinthenortheasternbaydecreasessignificantlyfrommid-August(Figures7d,7e,9a,and9b)andnegativefreshwaterflux

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Figure6.(a)Firstand(b)secondREOFspatialmodesofSSSanomalyforthebayandtimeseriesofthe(c)first(redline)andsecond(blueline)REOFmodes.

dominatesthenorthernbayafterOctober(Figures9cand9d),suggestingthattheeasternpartofthebay-shapemodeisnotproducedbythesurfacefreshwaterflux.

cyclonicgyreshiftswestwardandaweakanticyclonicgyreoccupiesthenortheasternbay.Asseasonadvances,thewesternpartofthebay-shapedplumedecayswhiletheeasternpartpersistsuntiltheJuneofthefollowingyear,whichisbelievedtobeassociatedwiththeanticyclonicgyreinthenorthernbay.

[21]Thereforeouranalysesindicatethattheoceancircu-lationinthenorthernbayplaysanimportantroleintheevolutionofthefreshwaterplumes.Tounderstandtheirforcingmechanism,thesteadystateSverdrupcirculationiscalculatedonthebasisof

b@Y=@x¼curlt;

ð1Þ

5.DiscussionandConclusions

[19]TheresultsoftheREOFanalysisandEAPAshowthatthelow-salinityareainthenorthernbayischaracter-izedbytheeastern-bayandwestern-bayplumesduringdifferentseasons.Thewestern-bayplumebeginsinearlyJuly,peaksinlateAugust,andturnsintoabay-shapedplumewiththetwoplumesineithersideofthebay.Thebay-shapedplumepeaksinlateOctoberandthentrans-formsintotheeastern-bayplumeintheJanuaryofthefollowingyear.

[20]Thesouthwardextensionofthewestern-bayplumeislikelyproducedbythesouthwestwardgeostrophicflowassociatedwiththecyclonicgyreinthenorthernbay,whichcountersthenortheastwardEkmandriftdrivendirectlybythewindstress.Theoffshoreexpansionofthewestern-bayplume,ontheotherhand,isinducedbytheoffshoreEkmandriftwhichalsoproducesanearshoresalinityfront.Thebay-shapedplumeappearswhenthe

whereb=@f/@yrepresentsthevariationofCoriolisparameterfwithlatitude,curltindicatesthewindstresscurl,Ystandsfortheverticallyintegratedtransportstreamfunction.

[22]ItisevidentinFigure10thatfromJanuarythroughApril,ananticyclonicpatternofSverdruptransportoccu-piesthewholebay,withasoutheastwardflowalongtheeasternboundaryofthebayandnortheastwardflowalong

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Figure7.SSS(psu,left),SSH(cm,middle),andsurfacefreshwaterflux(mm/d,right)associatedpatternswithtimeleadsfromeighteentozeropentadsinreferencetothewestern-baymode.

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Figure8.(a)Correlationcoefficientsbetweenthewestern-baymodeandtheassociatedmode(solidline),andvariancesexplainedbyassociatepatternsfortimeleadsfromeighteentozeropentadsinreferencetothewestern-baymode(dashedline).(b)SameasFigure8aexceptfortimelagsfromminusninetoninepentadsinreferencetothebay-shapemode.

thewesterncoastofthebay.Thepatternsuggeststhatthedecayofthewesternpartofthebay-shapedplumeandthepersistenceoftheeasternpartarerelatedwiththeanticy-clonicpatternofSverdruptransport.DuringJune–Septem-ber,acyclonicpatternnorthof16°NisenclosedbyasouthwestwardcurrentalongtheeastcoastofIndia,correspondingtotheformationandpersistenceofthewestern-bayplumeinsummer.FromSeptembertoDecem-ber,thecyclonicpatternmoveswestwardandsouthward.Thesouthwestwardcoastalflowshiftssouthward.Thepatternisconsistentwiththenarrowwesternpartofthebay-shapedplumeobservedinfall.However,theSverdrupflowalongtheeasternbayistothenorth,whichisoppositetotheexpansionoftheeasternpartofthebay-shapedplumeinfall.ThereforetheseasonalvariationofSverdrupcirculationcontributestotheevolutionoftheplumesexcepttheeasternpartofthebay-shapedplumeinfall.[23]However,thewestern-bayplumeappearsafterJunewhenthefreshwaterfluxincreasesdramaticallyinthenortheasternbay.Theeasternpartofthebay-shapedplumeinfallispresentwhenthefreshwaterfluxdecreasessignificantlyinthenortheasternbay.Theeastern-bayplumeexistsfromJanuarytoJunewhennegativefreshwaterfluxdominatesinthenorthernbay.Thepatternsimplythattheplumesarenotdirectlyproducedbysurfacefreshwaterflux.

[24]Theseasonalcycleofthefreshwaterdischargefrommajorriverssurroundingthenortherncoastsofthebayexperiencestwophases(Figure11).OneisthefloodphasefromJunetoOctober,duringwhich,theremarkablede-creaseinSSSisassociatedwiththepeakdischargefrommajorriverssurroundingthenorthwesternbay.However,SSSpatterninthenorthernbaychangesfromtheeastern-bayplumepattern,tothewestern-bayplumepattern,thentothebay-shapedplumepatternduringthisperiod.Theotheristhedryphase,duringwhich,thelowSSSisassociatedwithrelativelylessriverdischarge.However,SSSpatterninthenorthernbaychangesfromthebay-shapedplumepatterntotheeastern-bayplumepattern.Thereforeriverdischargeseemstobethefreshwatersourcefortheplumes

anditscontributiontotheevolutionoftheplumesislookingforwardtofurtherstudy.

AppendixA:ThreeKeyPointsofEAPA

[25]GiventimeseriesXandvariablefieldY,

X¼fxðjÞjj¼1;......;ng

Y¼fyði;jÞji¼1;......;m;j¼1;......;ng;

withzeromean(hXi=hYi=0).AspacevectorA

A¼faðiÞji¼1;......;mg

canbecalculatedbytheleastsquaresmethodtosuitthecondition

X

j

½yði;jÞÀaðiÞÁxðjÞ󰀍2¼minði¼1;......;mÞ:

ðA1Þ

ItmeansthattheinformationgivenbytimeseriesXcanbeexplainedbyitsregressionvaluea(i)atanyspacepointiofvariablefieldY.ThereforespacevectorAcanusedforthestudyontheformationmechanismoftimeseriesX.AiscalledastheassociatepatternofXinfieldY.

A1.CorrelationBetweenGivenandAssociateTimeSeries

[26]IffieldYisprojectedonthedirectionofA,anewtimeseriesX0,whichisusuallywellcorrelatedwiththeoriginaltimeseriesX,canbeobtainedanddefinedastheassociatetimeseriesofX.ThetimeseriesX0canbeusedforthesimulationandforecastofXandtheircorrelationcoefficientr(X,X0)representstheprecisionofthesimula-tionandforecast.

A2.ExplainedVariancebyAssociatePattern

[27]ThematrixproductY0ofthecolumnvectorX0TandunifiedrowvectorofAisdefinedastheassociatefieldseparatedfromthefieldYbythetimeseriesX.Atanyspace

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Figure9.SameasFigure7,exceptfortimelagsfromminusfourtoninepentadsinreferencetothebay-shapemode.

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Figure10.AnnualcycleoftheSverdruptransportstreamfunctionY(106m3/s)inthebay.Negativevaluesareshaded.

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pointc)orweakly(atpointb)correlated.Theseextremumpoints(notedasjk,k=1,...,23),whicharelikethefirecenterradiatingstrongrays,greatlycontributetothelinearregressionvalue(about95%)incontrastwithweaklyshiningpoints.

[29]Thecondition(A1)indicatesforanyspaceiandtimej

yði;jÞ¼aðiÞÁxðjÞ:

[30]Asmentionedabove,fortheextremumpointsjk,

yði;jkÞ¼aðiÞÁxðjkÞ;

sothat

Figure11.Monthlymeanriverdischarges(1010m3/mo)ofBrahmaputra(solidline),Ganges(solidlinewithboxes),Irrawaddy(solidlinewithcrosses),Godavari(solidlinewithtriangles)andKrishna(dashedline).

hhyði;jkÞiik¼aðiÞÁhhxðjkÞiik;

where

X

hhxðjkÞiik¼

k

sgnðxðjkÞÞÁxðjkÞ

23

pointiinthefieldsYandY,thestandarddeviationsY(i)andsY0(i)canbeeasilycalculated.ThevarianceexplainedbyassociatepatternAcanbewrittenas

sY0ðiÞ

varðiÞ¼ÁrðX;X0ÞÁ100%;

sYðiÞ

hhyði;jkÞiik¼

ðA2Þ

0X

k

sgnðxðjkÞÞÁyði;jkÞ

23

whichrepresentshowmuchthevarianceofthefieldYcontainedinthefieldY0.

A3.StatisticalMeaningofAssociatePattern

[28]Only3spaces(a:2.5°N,97.5°W;b:22.5°N,157.5°W;c:42.5°N,177.5°W)areconsidered.TakenNino3indexasXandmonthlySSTanomaly(1950.01À2000.12)asY,theresult(FigureA1)showsthatthe14ElNin˜oand9LaNin˜aextremaareveryimportantforthelinearregression,wheneverXandYarepositively(atpointa),negatively(at

couldbedefinedas‘‘absolutemean’’fory(i,jk)andx(jk),respectively.

[31]ThereforeassociatepatternAsuitsthesimilarcondition

XÂ

i

Ã2

hhyði;jkÞiikÀaðiÞÁhhxðjkÞiik¼min

ItmeansthatassociatepatternAisactuallythe‘‘absolute’’meanoffieldYwitharatiowhenXreachesitsElNin˜oorLaNin˜aextrema.Thereforeitisskillfullyequivalenttothecompositeanalysisofstatisticalclimatology.Thismethodis

FigureA1.LinearregressionsbetweenNino3indexandSSTat3points(dotforallofpointsandtrianglesforthe14ElNin˜oand9LaNin˜aextrema;solidlineistheregressionlineforallpoints,anddashedlineisfortheextremumpoints).

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anaturalextensionofassociatepatternanalysisandshouldbecalledextendedassociatepatternanalysis(EAPA).[32]Acknowledgments.ThisworkissupportedbyNationalBasicResearchProgramofChina(2006CB403601and2006CB403603)andNationalScienceFoundationproject(40576016).Theauthorsgreatlyappreciatethreeanonymousreviewers’suggestiveadviceandtheOFESdatasupportoftheEarthSimulatorCenter.

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M.Cui,F.Wang,L.Wu,andD.Yuan,InstituteofOceanology,ChineseAcademyofSciences,7NanhaiRoad,Qingdao,Shangdong266071,China.(fwang@ms.qdio.ac.cn;wulingjuan@ms.qdio.ac.cn;d_yuan@yahoo.com)

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