ean A RNAUD C ZAJA DepartmentofPhysicsImperialCollegeLondonUnitedKingdom J OHN M ARSHALL DepartmentofEarthAtmosphereandPlanetarySciencesMassachusettsI nstituteofTechnologyCambridgeMassachusetts ID: 142053
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ThePartitioningofPolewardHeatTransportbetweentheAtmosphereandOc ean A RNAUD C ZAJA DepartmentofPhysics,ImperialCollege,London,UnitedKingdom J OHN M ARSHALL DepartmentofEarth,AtmosphereandPlanetarySciences,MassachusettsI nstituteofTechnology,Cambridge,Massachusetts (Manuscriptreceived28February2005,infinalform28September2005) ABSTRACT Observationsofthepolewardheattransportoftheearth( H )suggestthattheatmosphereistheprimary transportingagentpolewardof30°,thatoceanic( H O )andatmospheric( H A )contributionsarecomparable inthetropicalbelt,andthatoceantransportdominatesinthedeepTropic s. Tostudythepartitionweexpresstheratio H A / H O as H A H O A O C A A C O O , where (withsubscripts A and O denotingatmosphereandocean,respectively)isthemeridionalmass transportwithin layers(moistpotentialtemperaturefortheatmosphere,potentialtempe ratureforthe ocean),and C ( C beingthespecificheat)isthechangeinenergyacrossthecirculationdef inedby . Itisarguedherethattheobservedpartitioningofheattransportbetween theatmosphereandoceanis arobustfeatureoftheearthsclimateandreflectstwolimits:(i)domina nceofatmosphericmasstransport inmid-to-highlatitudes( A O with C A A C O O andhence H A / H O 1)and(ii)dominanceof oceanicenergycontrastintheTropics( C O O C A A with A O andhence H A / H O 1). Motivatedbysimpledynamicalarguments,theseideasareillustratedthr oughdiagnosisofatmospheric reanalyses,longsimulationsofanoceanmodel,andacoupledatmosphere oceanmodelofintermediate complexity. 1.Introduction Figure1ashowsanestimateoftheatmospheric( H A , black)andoceanic( H O ,gray)heattransportfromdata publishedbyTrenberthandCaron(2001),basedon NationalCentersforEnvironmentalPrediction (NCEP)andEuropeanCentreforMedium-Range WeatherForecasts(ECMWF)atmosphericreanalyses (continuousanddashedcurves,respectively).Bothat- mosphericproductssuggestthat(Fig.1b),polewardof about30°,theatmosphericcontributiontothetotal polewardheattransportamountstoroughly90%ofthe total.Asoneapproacheslowerlatitudes,however,both contributeinroughlyequalamounts,althoughaprecise estimateismadedifficultbythefactthatboth H O and H A becomesmallintheTropics(notethelargespread betweenthedashedandcontinuouscurvesinFig.1b equatorwardof10°). Anobviousquestioniswhetherthereisasimple physicalexplanationforthepartitioningsuggestedin Fig.1b.Animportantsteptowardthisgoalwasrecently madebyHeld(2001),whorepresentedtheoceanicand atmosphericheattransportastheproductofanover- turningmasstransportstreamfunction andanenergy contrast C , H A , O A , O C A , O A , O 1 wherethesubscripts A , O denoteatmosphericandoce- anicvalues,and C and are,respectively,theheat capacityanddifferenceinanappropriatelydefinedpo- tentialtemperatureacrosstheupperandlower branchesoftheoverturningcirculation(asweshallsee therelevantquantityismoiststaticenergyfortheat- Correspondingauthoraddress: Dr.ArnaudCzaja,Dept.of Physics,ImperialCollege,PrinceConsortRoad,London,SW7 2AZ,UnitedKingdom. E-mail:a.czaja@imperial.ac.uk 1498 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 ©2006AmericanMeteorologicalSociety JAS3695 mosphereandpotentialtemperaturereferencedtothe surfacefortheocean).Suchadecompositioniscom- monlycarriedoutinoceanography(e.g.,Talley2003). UsingEq.(1),theratioofatmospherictooceanicheat transportbecomes H A H O A O C A A C O O . 2 IntheTropics,wheretransferbyquasi-two- dimensionalatmosphericeddiesislargelyabsent,Held (2001)arguedthatoceanicandatmosphericmasstrans- portsareclosetooneanotherandsetbytheEkman meridionalmasstransport.Hewentontoproposethat therelativemagnitudeof C inEq.(1)mustbere- sponsibleforthepartitioning.Torationalizethis,Held suggestedthat C isessentiallyameasureoftheoce- anicandatmosphericstratificationintheTropics.Oce- anicstratificationishighinthedeepTropicswhere upwellingofcoldfluidtothewarmsurfaceontheequa- torformsapronouncedthermocline.Intheatmo- sphere,bycontrast,tropicaldeepconvectionactsto returnthefluidtomarginalstabilitytomoistprocesses inwhich A ,themoiststaticenergy,hasweakvertical gradients.ThestateofaffairsisschematizedinFig.2. Hence,asHeld(2001)emphasized,dominanceof oceanheattransportoveratmosphericisexpectedin thedeepTropics. Itisnotstraightforwardtocarrythisargumentto mid-to-highlatitudeswhereitiswellestablishedthat atmospherictransienteddiescannotbeignoredwhen estimatingmeridionalmasstransports.Thuswemight expect A and O todecouplemovingawayfromthe Tropics,andtheroleofstratificationinsettingthepar- titioningbecomesmuchlessclear. Inthispaper,weattempttoestimateoceanicand atmosphericheattransportsglobally,motivatedbythe decompositionEq.(1).Todoso,wewillestimatethe meridionalmasstransportswithinpotentialtempera- turelayers definedbymoiststaticenergyintheat- mosphereandpotentialtemperatureintheocean whichwillallowustoestimate and C directlyfrom data.Ourmainconclusionisthatthepartitioningseen inFig.1bcanbesimplyunderstoodastwolimitsofEq. (2):amasstransport limit inmid-to-highlatitudes where A O andtheatmosphericcontributionto H H O H A dominates;anenergycontrast C limit intheTropicswhere C A A C O O andwhere theoceaniccontributionto H overwhelmsthatofthe atmosphere. Thepaperissetoutasfollows.Sections2and3 F IG .2.Schematicofthedistributionofatmosphericmoistpo- tentialtemperature( A ,i.e.,moiststaticenergy)andoceanicpo- tentialtemperature( O )asafunctionoflatitudeandheight (blackcontours).Theequatorisindicatedasaverticaldashed line. F IG .1.(a)Estimatesofoceanic( H O ,gray)andatmospheric ( H A ,black)heattransportinPW(1PW 10 15 W).(b)Relative contributionofocean(gray)andatmosphere(black)tothetotal energytransport H H O H A using(a).Continuouscurves correspondtoNCEP-basedestimates,whiledashedcurvescorre- spondtoECMWF-basedestimates.Theratiosin(b)werenot plottedinthedeepTropics(2 ° S 2 ° N)where H A H O vanishes. M AY 2006 CZAJAANDMARSHALL 1499 presentanestimateof A and O from,respectively, theNCEP NationalCentersforAtmosphericResearch (NCAR)reanalysesandalongsimulationofanocean circulationmodel.Applicationoftheseestimatestothe partitioningproblemwillbepresentedinsection4.In section5weproposesimplescalingstounderstandthe masstransportandenergycontrastlimitshighlighted above.Motivatedbythesesimplearguments,insection 6weanalyzeacoupledclimatemodelofintermediate complexityruninanaquaplanetgeometry.Apartition- ingverysimilartothemodernobservationalrecordis found,suggestingthatitislikelytobearobustfeature oftheearth sclimate.Wesummarizeandconcludein section7. 2.Atmosphericmasstransport a.Meridionalmasstransportwithinmoiststatic energylayers Weusedailyestimatesoftemperature T ,geopoten- tial ,andspecifichumidity q fromtheNCEP NCAR reanalysis(Kalnayetal.1996)ona2.5 ° 2.5 ° gridand 17pressurelevels.Thecentraldiagnosticvariableisa quantity A proportionaltothemoiststaticenergy, 1 definedbytherelation C A A C A T L q , 3 where L isthelatentheatofvaporizationand C A isthe specificheatcapacityofdryair.Figure3showsthe zonal-meandistributionof A (dashedcontours),which canbecomparedtothedrypotentialtemperature (continuouscontours).Themoststrikingfeatureisthe homogeneityof A intheTropics,whichisconsistent withthetropicalatmosphericlapseratebeingcloseto thatofamoistadiabat(XuandEmanuel1989).An- otherinterestingtropicalfeatureisthepresenceofa lowtomidlevelminimumof A ,associatedwiththe subsidenceofdryairfromaloft.Inmidlatitudes,one observesthat A contoursslopemoresteeplythan contoursduetothewatervaporloadingterminEq.(3). NotethattheshadinginFig.3indicatesthezonalmean distributionofErtel spotentialvorticity(PV) the 3-PVUcontour(thedashedwhiteline)willbeused belowtodefinethepositionofthetropopause[1po- tentialvorticityunit(PVU) 10 6 Km 2 s 1 kg 1 ]. Onagivenday,themeridionalmasstransportwithin anaircolumnispartitionedintoasetof A layerswith aresolution A 5K(finer A gridswerealsocon- sideredbuttheresultswerefoundtobeinsensitiveto thischoice).Foreach A layerthetotalmeridional transportacrossagivenlatitudewasthencomputedby summingthecontributionsovereachlongitude.Note thattoenforcemassconservation,thelong-termmean northwardmasstransportpertemperatureclass(ex- pressedinkgs 1 K 1 andhereafterdenotedby M ), summedoveralltemperatureclasses,wassettozero foreachlatitude.From M ,ateachlatitude wecom- puteamasstransportstreamfunction A (inkgs 1 ) usingthedefinition: A , A A min A M , A d A , 4 whereweimposedthat A vanishesforalllatitudesat achosenlowtemperature min A .Withthesignconven- tionadopted,apositive A indicatesclockwisecircula- tioninthe( , A )plane.Anappendixsetsoutmore detailsofthemasstransportcalculations. Figure4showsourestimateof A fortheperiodof 1May2003to30September2003(Fig.4a;Southern Hemispherewinter)andfortheperiod1November 2002to31March2003(Fig.4b;NorthernHemisphere winter).IntheSouthernHemisphere,oneobservesa singleequator-to-polecirculationinbothseasons,with polewardmasstransportathigh A andequatorward masstransportatlow A .Thewintertimecellisthe mostintense,reachingamaximumofmorethan200Sv atalatitudeof 40 ° .Notethatwehaveredefineda Sverdrup(thetraditionaloceanographer sunitofvolume transport)torepresentamasstransport(i.e.,1Sv 10 9 1 Notethat A asdefinedinEq.(3)isrelatedto,butnotthe sameas,moistpotentialtemperature.Itisameasureofenthalpy ratherthanentropy. F IG .3.Zonalmeandistributionof A (dashedcontours)and (continuouscontours)fortheperiodfrom1May2003to30Sep 2003(contourintervalis10K).Thezonalmeandistributionof Ertel sPV,inPVU(1PVU 10 6 Km 2 s 1 kg 1 )isshaded.The tropopause(definedasthe3-PVUcontour)isindicatedbythe thickdashedwhiteline. 1500 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 kgs 1 ). 2 IntheNorthernHemispheresummer(Fig.4a) weagainobserveasingleequator-to-polecellwitha maximumofabout100Svnear30 ° oflatitude.Inwin- ter,however,thereisindicationoftwoseparatecenters ofactioninFig.4bnear20 ° and50 ° oflatitude,each withanamplitudeofabout140Sv.Wenotethatme- ridionalmasstransportsof100 200Svaresignificantly largerthanthetypical20Svobservedintheocean. Belowwesuggestthatthisisindeedthemajorreason whytheatmosphericcontributionto H dominatesover thatoftheoceaninmid-to-highlatitudes. InFig.4,wealsoplot(graylowercurve)thezonally averagedmeansurface A .Itisreadilyseenthatmost oftheequatorwardmasstransportoccursinlayerswith temperaturescolderthanthemean(zonallyaveraged) surface A .Inmidlatitudesthisisbecause[seeHeldand Schneider(1999)]theequatorwardmasstransportis achievedbycoldairoutbreaks,thatis,transientfea- turesofthegeneralcirculation.IntheTropicshowever, thereisadifferentreason:apictureverysimilartoFig. 4canbeobtained(inthe20 ° S 20 ° Nlatitudeband)if seasonalmean,ratherthandailyfieldsofmeridional velocityandmoistpotentialtemperatureareused(not shown).Equatorwardmasstransportatalower A than thatofthe(zonallyaveraged) A atthegroundoccurs becauseofzonalasymmetriesinthesurface A ,the equatorwardflowbeingfoundmostlyatlowlevelsover thecoldtonguesoftheAtlanticandPacificoceans(not shown). TheuppergraycurveinFig.4isthevalueof A on thetropopause.Itisseenthatthelattergivesagood estimateoftheupperboundaryofthecellsforallsea- sonsandbothhemispheres. b.Discussionofatmosphericmasstransport Astrikingresultintheaboveanalysisisthatthe Hadleyandmidlatitudeeddy-drivencellstendtobe joinedintoasinglecell(Figs.4a,b).Thisisapro- nouncedfeatureofourdiagnostics,evenmoresothan inpreviousestimatesofmeridionalmasstransport streamfunctionwithindrypotentialtemperaturelay- ers theso-calledresidualcirculation(e.g.,Karolyet al.1997;HeldandSchneider1999). Tounderstandtheoriginofthisdifference,wedis- playinFig.5theanalogofFig.4butforacalculation inwhichwehaveset L 0in(3),therebyonlycon- sideringthecontributionofdrystaticenergytotheheat transport.Onethenobservesamuchmorepronounced twocellstructureineachwinterhemisphere,withthe tropical(Hadley)celldominating.Thedifferencesbe- tweenFigs.4and5canonlyarisebecauseofmoisture effects.Theysimplyreflectthatmoistureanddrystatic energyarebothtransportedpolewardinmid-to-high latitudes,andsoaddtooneanothertocreatethevig- orousoverturningcellinmidlatitudesseeninFig.4, whiletheyopposeeachotherintheTropics,therebyre- ducingthepronouncedHadleycellcomponentinFig.4. Asecondimportantaspectwewishtodiscussis whetherthemidlatitudecirculationinFigs.4a,bcan 2 Thischoiceismadeforreadycomparisontooceanicmass transports.Thedensityofseawaterisalwayscloseto10 3 kgm 3 , sothataSverdrupof10 6 m 3 s 1 representsamasstransportof10 9 kgs 1 .Accordingly,amasstransportof,say,20 10 9 kgs 1 isthe sameasavolumetransportof20 10 6 m 3 s 1 intheocean,i.e., volume(Sv) and massSverdrups areequivalenttoonean- other. F IG .4.Atmosphericmeridionalmasstransportstreamfunction withinmoiststaticenergylayers(contouredevery25Svwhere1 Sv 10 9 kgs 1 ;positivewhenclockwise,seearrows;zerocontour omitted;extremaindicatedontheplot)for(a)Southernand(b) NorthernHemispherewinterof2003.The x axisdenoteslatitude andthe y axis A (K).Theupper(lower)graycurveisthezonally average A atthetropopause(ground). M AY 2006 CZAJAANDMARSHALL 1501 indeedbeinterpretedasanoverturningcellintheme- ridional-heightplane.Toaddressthisissue,wecheck againstobservationsthat A iswellapproximatedby TEM A ,thestreamfunctionadvectingthezonalmean A inatransformedEulerianmean(TEM)formulation (Andrewsetal.1987).Thisiswrittenas A A TEM A Eul A Stokes , 5 where Eul A istheEulerianmeanmassstreamfunction and Stokes A isthequasi-Stokesmassstreamfunction (e.g.,Hoskins1983)definedas A Stokes L x g A A p . 6 InEq.(6), L x isthelengthofalatitudecircle, g is gravity, p pressure,and A isthemeridionaleddyflux ofmoistpotentialtemperature(primesdenotedepar- turesfromzonalandtimemean,denotedbyanover- bar). Figure6compares A fromthedirectcalculation (Fig.6a,reproducedfromFig.4a)andanestimateof eachtermintherhsofEq.(5)fortheSouthernHemi- spherewinterof2003.BoththeEulerian(Fig.6c)and thequasi-Stokes(Fig.6b)streamfunctionswerecom- putedinthelatitude pressureplane,thenmappedonto thelatitude A planeusingzonalmean,wintertimeav- eraged A profiles. 3 Itisseenthatinmidlatitudes,the quasi-Stokescontributionaloneisaverygooddescrip- tionoftheintensityandmeridional/ A scalesof A (as before,graycurvesindicatethe A ofthetropopause andtheground).Inmidlatitudes,theEuleriancontri- 3 Notethat,fortheSouthernHemispherecaseconsideredin Fig.6,onlytransienteddieswereincludedinthecomputationof A in(6).Thecontributionofsteadyeddieswasfoundtobe negligibleexceptclosetotheAntarcticcontinent,wherethecon- tributionwasnoisy(notshown). F IG .6.Variousestimatesofthemassstreamfunctionwithin A layers(a)direct,asinFig.4a,(b)usingEq.(6),and(c)the Eulerianmean.Contourintervalis20Sv.Graycurvesasin Fig.4a. F IG .5.SameasFig.4butforthemeridionalmassstreamfunc- tionwithindrystaticenergylayers.The y axisnowdenotesan equivalentpotentialtemperaturecomputedas C A T . 1502 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 bution theFerrelcell isathermallyindirectcell, 4 of muchsmallerintensity.AstheTropicsisapproached, however,theEuleriancontribution thewintertime Hadleycell dominatesthetotalmasstransportand providesagoodapproximationto A . ThattheapproximationEq.(5)holdsgivessupport totheinterpretationof A asatrueoverturningcellin themeridional heightplane. 5 Thisinterpretationcan alsobeunderstoodmorephysicallybynotingthat Stokes A inEq.(5)isanapproximationtotheStokesdrift associatedwithbaroclinicwaves(e.g.,Wallace1978). 3.Oceanicmasstransportwithin layers Theoceanicanalogtomoiststaticenergyissimply theinternalenergy, C O O ,where C O isthespecificheat capacityofseawaterand O isthepotentialtempera- turereferencedtothesurface[seeWarren(1999)fora detaileddiscussionofhow C O O approximatestheoce- anictotalenergy,i.e.,theBernoullifunction,asde- fined,e.g.,byGill(1982)].Wethereforepresentan estimateofthemeridionalmasstransportwithinpoten- tialtemperature( O )layersfromalongsimulationof theMassachusettsInstituteofTechnology(MIT)gen- eralcirculationmodel(GCM;Marshalletal.1997).The modelisastateoftheartGCMforcedbyseasonally varyingsurfacewindsandbuoyancyforcing.Itwasrun onthecubedspheregrid(Adcroftetal.2004)atcoarse resolution(15verticallevelsandC32 2.8 ° 2.8 ° in thehorizontal).Moreinformationaboutthesimulation canbefoundintheappendix. Fromthelast50yrofathousand-yearintegration,we haveestimatedatimemeanmeridionalvelocity( )and potentialtemperaturefield,aswellasatimemeanbo- lusvelocity( *)introducedbytheGentandMcWill- iamsscheme(GentandMcWilliams1990).Thelatteris meanttorepresenttheStokesdriftassociatedwith barocliniceddies(section2b),which,unlikeintheat- mosphericcalculationsabove,arenotexplicitlyre- solvedinthiscoarseoceanmodelsimulation.Ateach gridpoint,thewatercolumnispartitionedintoasetof O layers(witharesolutionof O 1K)andthe meridionalmasstransport( *)withineachlayeris computed.Notethatthisprocedureneglectstime- dependenteffectsthat,inthissimulation,arelimitedto theseasonalcycle(nointerannualvariabilityinthesur- faceforcing).Theerrortherebyintroducedinthean- nualmeanwasestimatedbycomparingtheoceanheat transportcomputedfromtimemean *and O with thatobtainedfromthetimemeanoftheproduct( *) O .Itwasfoundtobenegligible.Furtherdetailsof thenumericalprocedurearediscussedintheappendix. Figure7showsthemassstreamfunctionwithin O layersfortheglobalocean,calculatedfromEq.(4)in thesamewayasintheatmosphere.Oneobserves prominentcellsatwarmtemperatures( O 15 ° 30 ° C),flankedbycold( O 10 ° C)deepcellsathigher latitudes.Theintensityofthewarmandcoldcellsis comparable( 30Sv).Thepolewardflowinbothcold andwarmcellstypicallyoccursatatemperaturethatis largerthanthezonallyaveragesurfacetemperature (shownbythethickmediangraycurveinFig.7;the warmestandcoldestsurfacetemperaturearealsoindi- catedastheupperandlowergraycurves).Thisisthe oceanicanalogtotheobservationthatintheatmo- sphere,equatorwardflowoccursatatemperature lowerthanthesurfaceowingtotheeffectoftransient eddies(seesection2).Intheocean,itisaconsequence ofthethree-dimensionalcharacterofthesteadycircu- lationdepictedinFig.7,withadvectioninwarmwest- ernboundarycurrentsandtheirinteriorextensionbe- ingakeyaspect.Aswewillseebelow, O differsfrom basintobasin.Overall,thefeaturesinFig.7aresig- nificantlymorecomplicatedthanitstwo-dimensional atmosphericcounterpartinwhichthereisasingleover- turningcellineachhemisphere,seeFig.4. Analysisofthemeanthicknessofthe O layersre- 4 Bythermallydirect(indirect)wemeanameridionalcircula- tionwithascentwherethefluidiswarm(cold)anddescentwhere itiscold(warm). 5 Thegoodagreementbetween A and TEM A isnotunexpected forthose A layerswhichdonotintersecttheground(seeMcIn- toshandMcDougall1996). F IG .7.Annualmeanmassstreamfunctionintheoceanwithin O layers(contouredevery5Sv,continuouswhenclockwise;zero contouromitted).The x axisislatitudeandthe y axispotential temperature 0 ( ° C).Themiddlegraycurveisthezonallyaverage surface O whiletheupperandlowergraycurvesindicatethe maximumandminimumsurface O asafunctionoflatitude. M AY 2006 CZAJAANDMARSHALL 1503 veals(notshown)thatthewarmcellsoccupyavolume offluidwithhighstratification(thinlayers)andcanbe identifiedwiththemasscirculationwithintheventi- latedthermoclinesoftheSouthernandNorthern Hemispheres.Thisisfurtherconfirmedbythefactthat theirpolewardextensionisratherwellpredictedbythe positionofthemidlatitudezerowindstresscurllines (notshown). Thecoldcellsareassociatedwiththick O layers (weakstratification)andcorrespondtothecirculation ofNorthAtlanticDeepWaterandAntarcticBottom Water.NotethatthetraditionalEulerianmassstream- functiondisplaysmoremodest( 10 15Sv)coldcell masstransports. Furtherinformationabout O isprovidedinFig.8, wherethecalculationwasrepeatedseparatelyforthe Indo-Pacific(Fig.8a)andAtlantic(Fig.8b)basins.A simplepartitioningistherebyobtained,inwhichthe twowarm(symmetric)cellsoriginateinthemainfrom theIndo-Pacificbasinandthe(asymmetric)Northern coldcellfromtheAtlanticbasin. 4.Thepartitioningofheattransport Wenowcombineoceanicandatmosphericmass streamfunctionswithintheirrespectivepotentialtem- peraturelayers.Insodoing(Fig.9),wehavemapped the y axisofFigs.4and7ontoanenergyaxis,whichis C A A fortheatmosphereand C O O fortheocean. ThefirststrikingfeatureofFig.9isthat,asantici- patedinsection2,theintensityoftheoceaniccellis muchweakerthanitsatmosphericcounterpart(both areannualaverages,seecaptionofFig.9).Evenat20 ° , where O reachesitsmaximum,theatmosphericmass transportisroughly4timesthatoftheocean.Itisonly withinthedeepTropicsthatthetwotransportsare comparable.ThisisfurtherdemonstratedinFig.10 (continuousblackcurve),whichshowstheratioofthe maximumof O andthatof A ,computedfromFig.9 ateachlatitude.Notethatsinceboth O and A be- comesmallclosetotheequator,themassratioshown inFig.10israthernoisyatlowlatitudes. ThesecondimportantfeatureseeninFig.9isthat thethicknessofthecellsinenergyspaceiscomparable. Toestimatethismoreprecisely,wehaveusedFig.9 andcomputedthechangein C O O and C A A (hereafter denotedas C O O and C A A ,respectively)acrossa referencecontourofmasstransport.Thelatterwas chosentobe10%oftheoverallmaximumof O (0.1 32Sv 3Svintheocean)and A (0.1 143Sv 14 Svintheatmosphere).Theratio C O O / C A A isplot- tedinFig.10(gray).AsoneapproachestheTropics, where A issmall,theratiodiverges.Conversely,on movingtohighlatitudeswhereoceanicpotentialtem- peraturevariationsaresmall(weakstratification),the ratioapproacheszero.Inmidlatitudes, C O O / C A A F IG .8.SameasFig.7butforthe(a)Indo-Pacificand(b) Atlanticbasins. F IG .9.Annualmeanatmospheric(black)andoceanic(gray) massstreamfunctionwithinconstantenergylayers.Thecontour intervalis10Sv,dashedwhencirculatinganticlockwise.The y axis isanenergycoordinate( C )inunitsof10 4 Jkg 1 .Theoceanic cellsarethesameasshowninFig.7(annualmean)whilethe atmosphericcellsareanannual-meanestimateobtainedbyaver- agingFigs.4a,b. 1504 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 isoftheorderofunity,thedifferencesinheatcapacity ( C O / C A 4)beingcompensatedforbyalargertem- peraturedifferenceacrosstheatmosphericcell( A 40Kcomparedto O 10K). Theproductofthecontinuousblack( ratio)and gray( C ratio)curvesallowsanestimateofthere- spectivecontributionofmasstransportandenergycon- trasttothepartitioningofheattransport.Itisshownas theblackdot dashedlineinFig.10,andfallsbetween theblackandgraycurves.Indeed,theenergycontrast tendstofavortheoceanasthemajorcontributortothe totalheattransportuptolatitudesof40 ° 50 ° .How- ever,themasstransportstronglyfavorstheatmosphere asthedominantcontributortothetotalheattransport atalmostalllatitudes.Thenetresultofthesetwocom- petingeffects(dot dashedcurve)isconsistentwiththe partitioningshowninFig.1b,withtheatmosphere dominatingthetotalheattransportforlatitudespole- wardofabout20 ° . Finally,webrieflycommentontheinterpretationof the C termasameasureofstratification.Ascanbe seenfromFig.4,inboththeTropicsandmidlatitudes, C A A ,thetypicalchangeinmoiststaticenergyacross A ,issignificantlydifferent(twiceaslarge)fromthe tropopausetoground A difference.Similarlyinthe ocean,itisreadilyseenfromFig.7that C O O forthe warmcellsissignificantlydifferent(byabout20% 30%)thana(zonallyaveraged)surfacetothermocline bottomtemperaturedifference.Onemustbecareful, then,whenestimatingtheenergycontrastacrossthe oceanicandatmosphericcirculationsappropriatefor computationofmeridionalenergytransport. 5.Scalings Ourdiagnosticssuggestthattheobservedratio H A / H O , whichislarger(smaller)thanunitypoleward(equator- ward)ofroughly30 ° ,canbeunderstoodasaconse- quenceoftwosimplelimitsofEq.(2): (i)dominanceofatmosphericmasstransportinmid- to-highlatitudes( A O with C A A C O O andhence H A / H O 1) (ii)dominanceofoceanicenergycontrastintheTrop- ics( C O O C A A with A O andhence H A / H O 1) Thesecondlimit alsoinvokedbyHeld(2001) isthe easiesttorationalizesinceitsimplyinvokessmallen- ergycontrastswithinthetropicalatmosphere(and roughlyequivalentmasstransports,seeintroduction). Thisisaconsequenceofdeepconvectionreturningthe atmospheretoamoistadiabaticlapserateanddynami- caladjustmentssmoothingoutsignificanthorizontal potentialtemperaturegradientswithin 15 ° ofthe equator.Ontheotherhand,thepredominanceofat- mosphericoveroceanicmeridionalmasstransportin midlatitudes[limit(i)]isperhapssomewhatcounterin- tuitiveinviewofthemuchlargerdensityofwatercom- paredtoair.Wenowattempttounderstand A O usingdynamicalscalings. Ourstartingpointistoviewthemasscirculations A and O asoverturningcellsinthemeridional height plane.ThissimplificationisjustifiedbyFig.6forthe atmosphere,inwhichthequasi-Stokesadvectionpro- videsagooddescriptionof A inmidlatitudes(see section2b).Itisprobablylesssointheoceanbecause ofamorefundamentalthree-dimensionalcirculation thatcontributesto O (seesection3).Neverthelesswe willlimitourselvestothissimplepicture.Forsuchan overturningcirculation,asimpleestimateofthemass transportisgivenby(appropriatetobothoceanand atmosphere) zVL z P g VL , 7 where isthedensity, V isatypicalmeridionalvelocity, z istheverticalscaleoftheoverturning,and L isthe zonallengthscaleoverwhichthecirculationextends, andthehydrostaticrelationhasbeenused.Allterms areestimatedforeitherthepolewardortheequator- wardbranchofthecirculation.Sincetheoceanhasa muchgreaterdensitythantheatmosphere,the z P / g terminEq.(7)willalwaysbelargerforanoceaniccell. Ontheotherhand,meridionalvelocitiestendtobe muchlargerintheatmospherethanintheocean.Since zonallengths L areofsimilarmagnitudeinbothocean F IG .10.Theratio C O O / C A A (gray),max( O )/max( A ) (continuousblack),andtheirproduct(dot dashed),computed fromFig.9.Aratioofunityisindicatedbythehorizontaldashed line. M AY 2006 CZAJAANDMARSHALL 1505 andatmosphere,theremustbeastrongcompensation ofmassandvelocityeffects.Thissuggeststhatasimple scalingbasedon(7)willbeproblematicalsinceitmust accountfortwolarge,compensatingterms. Toovercomethisproblem,wefocusdirectlyonthe masstransportstreamfunctions A and O andwithin aquasigeostrophicframeworkproposeasimultaneous treatmentoftheirdynamics.Fortheocean,wewill considerboththecaseofachannelgeometry(with meridionaloverturningcellbutnogyres)andthatofa basingeometrywithmeridionalboundaries(bothgyres andoverturningcell). Letusconsider,then,thezonallyaveragedzonalmo- mentumbalancefortheoceanortheatmosphere,mod- eledasBoussinesqfluidsinaCartesiangeometry(ne- glectingadvectionofmeanmomentumbythemean flow), f ref p x u y 1 ref z . 8 Here, x , y, and z denotelongitude,latitude,andheight, respectively, f istheCoriolisparameter, p thepressure, u and denotethezonalandmeridionalvelocities, ref isareferencedensity,and representtheturbulent stressduetosmall-scaleprocesses.Asin(6),primes denotedeparturesfromthezonalandtimemean(in- dicatedbyanoverbar).Theparameter issettounity forthecaseoftheoceanwithbasingeometry,acknowl- edgingthepresenceofeast westpressuregradients acrosslatitudecircles,andanticipatingtheresultspre- sentedinsection6,itissettozerointhecaseofan oceanchannelgeometryandintheatmosphericcase. 6 FollowingthestandardtransformedEulerianmean procedure(e.g.,Andrewsetal.1987;Marshalland Radko2003),werewrite(8)as f res f 1 ref res z ref p x u y 1 ref z eddy z , 9 where res , res aretheresidualmeanmeridionalveloc- ityandmassstreamfunction,respectively( res 0is clockwiseinthelatitude heightplane,i.e.,representing athermallydirectcirculationintheNorthernHemi- sphere),and eddy istheassociatededdystressgivenby eddy ref f d dz , 10 where d / dz isareferencepotentialtemperaturegra- dient.Notetheconnectionof(10)withtheStokes streamfunctiondefinedin(6). IntheatmosphereweintegrateEq.(9)with 0in theverticalfromtheseasurface(where res 0and s ,thezonalsurfacewindstress,positiveformid- latitudewesterlies)tothelevelwheretheresidualmean streamfunctionisamaximumand 0(Fig.11).A furthersimplificationarisesbecauseoverthisbottom layertheReynoldsstresstermin(9)canbesafelyne- glected.Denotingby res ,A theinteriormaximumof res (wheretheeddystressis A ),weobtain res, A A s f . 11 Sincetypically A s seefurtherdiscussionbelow , thisequationshowsthatbarocliniceddiestendtodrive athermallydirectcirculation( A , res ,A 0inthe NorthernHemisphere)opposedbyathermallyindirect Ekman(orFerrell)cellassociatedwithsurfacewind stress. Intheoceanweintegrateverticallyovertheupper layerofthemeridionalcirculation,fromthedepth D where res reachesitsmaximum(denotedby res , O ; see Fig.11)andtheturbulentstress vanishesatthesea surfacewhereagain res 0and s .Eventhough currents,andhenceReynoldsmomentumfluxes,are thelargestinthislayer;evenhere,Reynoldsstresses 6 Thisneglectsformdragatthelowestoceanicandatmospheric levels. F IG .11.Schematicoftheresidualcirculation res intheatmo- sphereandtheoceaninanaquaplanetgeometrysuchasthe SouthernOcean.Atthesurface, res vanishesinbothoceanand atmosphere,whilealongthehorizontaldashedlineitreachesa maximumvalueintheinterioroftherespectivefluids.Thismaxi- mumisdenotedby res ,A (atmosphere)and res ,O (ocean).Equa- tion(9)isintegratedovertheoceanicandatmosphericlayers boundedbythesurfaceandthedashedline. 1506 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 canbeneglectedcomparedtotheeddystress eddy , owingtothesmallRossbynumberintheocean.Inte- grationof(9)thusyields res, O O s f f D 0 x pdz , 12 whichincludesacontributionfromzonalpressuregra- dient dp / x ,whichwehaverewrittenas x p ,inthecase ofabasingeometry( 1).Inthelattercase,wemust relate x p toothervariables.Thisisdone,following Marshall(1997),byconsideringtheverticallyaveraged (fromsurfacetobottomdepth H )zonalmomentum balanceoftheocean.FromEq.(8)with 1,neglect- ingbottomturbulentstressesandagainReynoldsmo- mentumstresses,wehave f H 0 dz 0 1 ref H 0 x pdz s ref , 13 whichyields H 0 x pdz s . 14 Asimpleclosureisnowchoseninwhichweassume thatthezonalpressuregradientintegratedovertheup- perlayeroftheresidualflowisproportionaltothe depth-averagedzonalpressuregradient,thus, D 0 x pdz a H 0 x pdz a s , 15 where a isa(nondimensional)constantofproportion- alityandwehaveused(14).MakinguseofEq.(15)in (12),wefinallyobtain res, O O 1 a s f . 16 Justasinitsatmosphericcounterpart[Eq.(11)],Eq. (16)indicatesthateddystressestendtodriveather- mallydirectcirculation.Unliketheatmosphere,how- ever,thepresenceofmeridionalboundaries( 0) introducesapressuregradientterm,whichpartlycom- pensatesthezonalwindstressforcing.Equations(11) and(16)suggestascalingoftheratioofatmosphericto oceanicmasstransportstreamfunction,thus, A O res, A res, O A s O 1 a s . 17 Inthecaseofpurelyaxisymmetricdynamics(noeddies, A O 0,and 0),theratioofatmosphericto oceanicmasstransportis A / O 1.Thesenseof circulationandmasstransportoftheatmosphericand oceaniccellsisthesame(theEkmanmasstransport),as inHeld s(2001)discussionofthecoupledtropicalcir- culation.Inmidlatitudes,however,theeddystresses cannotbeneglected,andtheratio A / O dependson theirstrengthrelativetothesurfacewindstress. InspectionofFig.6suggeststhat,intheatmosphere inmidlatitudes,theStokesstreamfunction(seesection 2b)ismuchlarger(byatleastafactorof2)thanthe Eulerian(Ferrell)circulation( A s )andEq.(17) reducesto A O A O 1 a s . 18 IntheSouthernOcean,characterizedbyachannel geometry( 0),diagnosticandtheoreticalstudies suggestthatthesenseoftheresidualcirculationisset bythewind(theso-calledDeaconcell, O s / f with anequatorwardupperlevelflow),althoughitsmagni- tudecanbesignificantlyreducedbythepresenceofthe eddystressterm O (KarstenandMarshall2002;Mar- shallandRadko2003;Olbersetal.2004).Inabasin geometry( 1),suchasoccursintheNorthAtlantic Ocean,theupperflowispolewardinmidlatitudes,that is,oppositetothedirectEkmanflowdrivenbythe surfacewesterlies.Eddystressesand,evenmorelikely, zonalpressuregradientsacrossthebasinmustthus dominateEq.(16).Indeed,about15Svofwateris believedtoflowpolewardatupperlevelsintheNorth Atlantic(GanachaudandWunsch2000)whileoverthe samebasintheEkmancontributionisabout5Svequa- torwardinmidlatitudes. 7 Neglecting O in(16),thisre- quires a 4.Suchavaluereflectsthelargebaroclinic structureofthepressurefield,yieldinglargerupper levelpressuregradientsthandepth-averagedones,see Eq.(15). Insummary,themasstransportintheatmospherein midlatitudesisdrivenbybarocliniceddiesandisasso- ciatedwithathermallydirectcirculation.Thesurface westerliesproduceanEkmantransportopposingthe eddy-drivenmassflux.Thissituationissomewhat analogoustotheoceaninachannelgeometrywhere cancellationexistsbetweeneddy-andwind-drivenme- ridionalmasstransports,withtheimportantdifference thatsurfacewesterliesaredrivenbyatmosphericeddies whereasoceaniceddiesareaconsequenceofthesur- facewindthroughitsroleingeneratingpotentialen- ergy(Gilletal.1974).Thesedifferentcausalrelation- shipsprobablyexplainwhyintheatmospheretheeddy- drivenmassfluxdominatesoverEkman,whilethe 7 Thisisassuming s 0.1Nm 2 , f 10 4 s 1 ,andazonal lengthscaleof5000km . M AY 2006 CZAJAANDMARSHALL 1507 reversesituationoccursintheSouthernOcean.The presenceofmeridionalboundariesmaydramatically changethestateofaffairs,asitallowsthelarge-scale geostrophicflowtoaddconstructivelytotheeddy drivenflowandcontributetoanetthermallydirect overturningcirculation,asobservedintheNorthAt- lantic. Overall,theabovediscussionsuggeststhat,inmid- latitudes,thesignof A / O isprobablydependent uponthegeometry(negativeinachannelwheresur- faceflowscanbeinthesamedirectioninboththe atmosphereandocean,seeFig.11;positiveinabasin, withoppositedirectionofsurfaceflows,seeFig.9),but thatitsamplitudeisprimarilycontrolledbytheratioof atmosphericeddystresstosurfacewindstress,assum- ingthat O (1 a ) s s .Wethusobtainthe followingscalingfortheratioofmasstransportas A O A s . 19 Thisratioappearsasthekeyparameterofourstudy. Sincesurfacewindstressbalancestheverticallyinte- gratededdyfluxesofzonalmomentum, A / s canbe thoughtofasameasureoftheimportanceofeddyheat fluxes[seeEq.(10)]versusmomentumfluxes,thatis,of therelativestrengthoftheverticalandhorizontalcom- ponentsoftheEliassen Palmflux(e.g.,Edmonetal. 1980).Itisuncleartouswhetherornotthereisany- thingfundamentalaboutaratio A / s 1,associated withmostofthewaveactivitypropagatingupwardand beingdissipatedinplace(verticalEliassen Palmflux limit). 6.Partitioninginacoupledclimatemodel Thescalingsproposedintheprevioussectionare ratherbasicinthesensethattheydonotrelyona detailedrepresentationofgeometryandorography, etc.Onethusexpectsthattheheattransportpartition- ingseenintheobservationsshouldalsobefoundinthe presenceofverydifferentcontinentalconfigurations. Wenowbrieflyexplorethispossibilitybyanalyzingthe partitioningofheattransportinalongsimulationofa coupledmodelofintermediatecomplexityruninthe absenceofcontinents(aquaplanetgeometry)butwith anactivedynamicalocean. Thecoupledmodelconsistsofafive-layerprimitive equationatmospherewithsimplifiedphysicalrepresen- tations(Molteni2003),coupledtotheMITocean modelasdescribedinMarshalletal.(2004).Theatmo- sphereandoceanarerunonthesamecubedsphere grid(seeAdcroftetal.2004)atahorizontalresolution ofC32( 2.8 ° 2.8 ° ).Theoceanbottomisflatwitha constantdepthof5200m.Alinearbottomdragisap- pliedtothelowestoceaniclayerstocontrolthemodel barotropicmode.Thecoupledsystemalsoincludesa simplethermodynamicseaicemodelbasedonWinton (2000).Theresultspresentedbelowarebasedonthe last500yrofa1500-yrintegration. Figure12displaysthecontributionoftheatmosphere (black)andtheocean(gray)tothetotalheattransport ( H A / H and H O / H ,respectively)intheaquaplanet coupledmodelinaformatsimilartoFig.1b.Oneob- serves(continuouscurves)thatagainasimpleparti- tioningisfound,withtheatmospheredominatingpole- wardof20 ° andtheoceandominatingequatorwardof 20 ° .Forreference,wehavealsoindicatedthecorre- spondingcurvesfromobservations(seecaptionofFig. 12)asbrokenblackandgraycurves.Thesimilarity betweenthetwosetsofcurvesisstriking.Evenina worldverydifferentfromourown,thepartitioningof heattransportbetweentheatmosphereandoceanre- mains,tofirstorder,thesame. Furtherdiagnosticsindicatethatthissimilaritycan againbeexplainedfromthetwolimitsinvokedinsec- tion5.Theoceanicenergycontrastsarelargeinthe Tropicswhereequatorialupwellingcreatesasharp, strongthermocline,whereasmoiststaticenergycon- trastsareextremelyweakinthemodeltropicalatmo- sphere,evenmoresothanintherealworldowingto theabsenceofzonalSSTgradientsassociatedwiththe coldtongueandtheabsenceofland seacontrastsin theaquaplanetgeometry.Theatmosphericmasstrans- portpeaksatabout30 ° withavalue 200Svwhilethe F IG .12.AsinFig.1bbutforthecoupledmodelinanaqua- planetgeometry(continuouscurves).Asareference,observed ratiosarealsoindicated(brokencurves).Thelatterwerecom- putedfromtheobservationspresentedinFig.1a,averagingthe NCEPandECMWFoceanicandatmosphericheattransports. 1508 JOURNALOFTHEATMOSPHERICSCIENCESV OLUME 63 oceanicmasstransportpeaksat20 ° withavalueof 60 Sv,leadingtheatmospheretobethemaincarrierof energypolewardof20 ° . 7.Summaryandconclusions Adiagnosticstudyofthepartitioningofthetotal polewardheattransportbetweentheoceanandatmo- spherewaspresentedinacoordinatesystemcompris- inglatitudeandenergy.Inthiscoordinatesystem,the polewardheattransportbyboththeoceanortheat- mospherescalesas H C ,where representsthe meridionalmasstransportwithin layers(moiststatic energyormoistpotentialtemperaturefortheatmo- sphere,potentialtemperaturefortheocean)and C scalestheenergydifferenceacrossthecirculationde- finedby . Boththeoceanic( O )andatmospheric( A )meridi- onalmasstransportsareremarkable.Intheatmo- sphere,asingleequator-to-polecellappearsineach hemisphere,afeaturehighlightedinpreviousstudiesof theresidualcirculation,butwhichisevenmorepro- nouncedherewheremoist,ratherthandry,potential temperatureisused.Theoceanicstreamfunctionshows adistincthemisphericasymmetryinbothwarmwind- drivencellsandcoldbuoyancy-drivencells. Twosimplelimitsemergefromourdiagnostics.In mid-to-highlatitudes,theintensityoftheatmospheric meridionalmasstransportdominatesthatoftheocean ( A 100Svcomparedto O 30Sv).Withsucha dominantmasstransport,heretheatmosphereisthe maincontributortothetotalpolewardheattransport ( H A / H O A / O 1).IntheTropicshowever, A / O 1,energycontrastsetsthepartitioningandthe oceanbecomesthemajorcontributortothetotalpole- wardheattransport( H A / H O C A A / C O O 1). Wehavearguedthatthesetwolimitsreflectfunda- mental,robustdynamicsoftheocean atmospheresys- tem.Thedominanceoftheatmosphericmeridional masstransportinmidlatitudesisaconsequenceofthe efficiencyofbarocliniceddiesindrivingathermally directcirculation.Thestrengthofthelatterismore thantwicethatofthe(indirect)Eulerianmeancircula- tion(theFerrelcell),whichroughlyscalestheocean meridionalmasstransport.Thetendencyoftheatmo- spheretobeclosetoneutralitywithrespecttomoist processeswithin15 ° orsooftheequatorischieflyre- sponsibleforthesecondlimit. Asaconsequenceofthesebasicideas,wehavefur- therarguedthattheobservedpartitioningisarobust featureoftheearth sclimate,unlikelytochangesig- nificantlyinadifferentconfigurationofcontinents,as hashappenedongeologicaltimescales.Somesupport forthisclaimwasobtainedfromalongsimulationofan intermediatecomplexityclimatemodelruninanaqua- planetgeometry(nocontinentsatall!). CombinedwiththestudyofStone(1978),whoar- guedthatthetotal(ocean atmosphere)heattrans- portisessentiallysetbytheplanetaryalbedo,thesolar constantandtheradiusoftheEarth,ourresultssuggest thattheoceanicandatmosphericheattransportmight themselveschangerathermodestlyinverydifferentcli- matestates.Inotherwords,climatevariabilitymaybe associatedwithonlysmalldeparturesfromfixedback- ground H A , H O curves.Thishypothesisdoesnotrule outthepossibility,knownasBjerknes compensation idea(Bjerknes1964),thatchangesin H A and H O op- poseeachotheronlongtimescales.Ourstudysuggests thatsuchcompensatedchangesmaymodifytheparti- tioningbyonlyasmallamount,withtheatmosphere continuingtodominatethetotalheattransportpole- wardof20 ° andtheoceaninthedeepTropics.These ideaswillundoubtedlysoonbecometestableasoceanic andatmosphericreanalysesproductsimprove,anda vasthierarchyofcoupledocean atmospheremodels,in variousgeometries,becomeavailableforanalysis. Acknowledgments. Thisworkwassupportedbya grantfromNOAA sOfficeofGlobalProgramsaspart ofAtlanticCLIVAR.Jean-MichelCampinwasoftre- mendoushelpinanalyzingtheresultoftheocean GCM.Wewouldalsoliketothankthethreereviewers fortheirhelpfulcomments. APPENDIX SpecificDetailsoftheMassTransportCalculation within Classes a.Atmosphere DailyoutputsfromtheNCEP NCARreanalysis (Kalnayetal.1996)wereusedtocomputemoistpo- tentialtemperature A andmeridionalvelocity ateach nominalpressurelevel.First,onagivenday, A and wereinterpolatedontoafiner,regular( P 10mb) pressuregrid,inordertoprovideabetterresolutionin temperatureclass.Layerswithpressuregreaterthan thesurfacepressureforthatday(thelatteralsobeing takenfromtheNCEP NCARreanalysis)wereex- cludedfromthecalculationsincetheyphysicallywould liebelowtheground.Themeridionalmasstransport withinthefinergridcolumn( P / g foragivenpressure layer,where g isgravity)wassubsequentlyrepartioned asafunctionofmoistpotentialtemperatureclass,with M AY 2006 CZAJAANDMARSHALL 1509 aresolutionof A 5K.Finerandcoarserresolutions weretestedfortheSouthernHemispherewinterperiod of2003andfoundtoproduceverysimilarresults.We thususedthisresolutionforallcalculationspresented here,includingmeridionalmasstransportwithindry potentialtemperaturelayers. b.Ocean Weuseyearlyoutputsfromathousand-year-longin- tegrationoftheMIToceanGCM(Marshalletal.1997) runonthecubespherein z -levelcoordinates(Adcroft etal.2004)witharealisticgeometry.Themodelwas forcedbyaseasonallyvaryingclimatologyofsurface windstressandnetsurfaceheatfluxandevaporation minusprecipitation(thesimulationisthesameasthat discussedinMarshalletal.2004).Themodelhasno surfacemixedlayerbutasimpleconvectiveadjustment scheme.Surfacetemperatureandsalinityarerestored toobservedclimatologywithatimescaleof2months and2yr,respectively.Thereisnoseaicemodel,butthe temperatureismaintainedabovefreezing.Avertical diffusivityof K 3.10 5 m 2 s 1 wasusedfortempera- tureandsalinity.TheGentandMcWilliams(1990) schemeisusedtogetherwithanisopycnaldiffusion (Reditensorformalism)coefficientsetto K 800 m 2 s 1 . Theproceduretoobtainthemeridionalmasstrans- portwithinasetof O (potentialtemperature)layersis almostidenticaltothatusedfortheatmosphere(re- placingthefinerpressuregridbyafinergeometric heightgridwith z 10m).Onlyonechangewas made:sincetheoceanmodelpredictsatransportwithin eachlayer, waskeptthesamewheninterpolatingonto thefinerzgrid(yieldingastaircaselikeprofile,asinthe rawmodeloutputs).Thisprocedureexactlypreserves the(verticallyintegrated)meridionalmasstransportat eachgridpoint,butonlyapproximatelyconservesthe (verticallyintegrated) O transportateachgridpoint. Theerrorinthelatterwasfoundtoneverexceed1%, however. 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