cqe tracmip paper2 draft2 - wxmaps.orgwxmaps.org/jianlu/cqe_tracmip_paper2_draft2.final.pdf · 81...

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Sub-cloudmoistentropycurvatureasapredictorforchangesintheseasonalcycleoftropical1

precipitation2

1BryceHarrop,1JianLu,1L.RubyLeung3

4

1AtmosphericSciencesandGlobalChangeDivision,PacificNorthwestNationalLaboratory,5

Richland,WA,USA6

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*Correspondingauthor:BryceHarrop,phone(509)375-2696;[email protected]

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Abstract10

ConvectiveQuasi-Equilibrium(CQE)maybeausefulframeworkforunderstandingthe11

precipitationminusevaporation(P-E)responsetoCO2-inducedwarming.Toexplorethis12

proposition,asuiteofaquaplanetsimulationswithaslaboceanfromTRACMIP(theTropical13

RainbeltswithanAnnualcycleandaContinentModelIntercomparisonProject)isanalyzed.A14

linearrelationshipbetweenP-Eandthecurvatureofsub-cloudmoistentropy,amarkerforthe15

spatialdistributionofsub-cloudmoistenergyandonsetofatropicaldirectoverturning16

circulationunderCQEconditions,isshowntoexistacrossmanyoftheTRACMIPsimulations.17

Furthermore,thislinearrelationshipisaskillfulpredictorofchangesinP-EinresponsetoCO2-18

inducedwarming.ThecurvaturemetricalsoshowsimprovementinpredictingP-Echanges19

comparedtothesimplermethodofrelatingP-Edirectlytothesub-cloudmoistentropyfieldor20

asimple‘wet-get-wetter’typenullhypothesis,especiallyonseasonalandshortertimescales.21

Usingfixedrelativehumidityinthecurvaturemetricandsub-cloudmoistentropydegrades22

2

theirabilitytopredictP-Echanges,implyingthatbothtemperatureandrelativehumidity23

changesintheboundarylayerareimportantforcharacterizingfutureprecipitationchanges.To24

understandwhythecurvaturemetricisaskillfulpredictorofhydrologicalchanges,amoist25

staticenergy(MSE)budgetanalysisisperformed,whichshowsthatMSEdivergenceonsub-26

dailytimescalesiswellparameterizedasadowngradientdiffusiveprocess.Additionally,this27

transientMSEdivergencehaveasimilarstructuretothecurvatureterm.Assumingthatthe28

transientMSEdivergenceisrelatedtoconvectiveactivity,thesefindingssuggestthatthe29

theoreticalunderpinningofthelinearrelationshipbetweenthecurvaturetermandP-Eresides30

incloudprocessesthatbothremovespatialgradientsofsub-cloudmoistentropyandgenerate31

precipitationatsub-seasonalandshortertimescales.32

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1.Introduction34

Precipitationisakeyfeatureandoneofthemosthuman-relevantcomponentsofthe35

climatesystem.Despiteitsimportance,climatemodelsstrugglewithaccuratelyreproducing36

precipitationinthecurrentclimateandpredictingfutureprecipitationchanges.Whiletheories37

suchasthe‘wet-get-wetter’hypothesispopularizedby(HeldandSoden2006;ChouandNeelin38

2004;ByrneandO’Gorman2015)orthe“upped-ante”mechanismproposedby(Neelinetal.39

2003)exist,acompleteunderstandingoftheregionalprecipitationresponsetoglobalwarming40

remainselusive.Thedeepconvectionresponsibleforalargefractionoftropicalsurface41

precipitationisalsoakeycomponentoftheatmosphericcirculation,playingacriticalrolein42

transportingenergyfromtheboundarylayertotheupperatmosphere.43

ConvectiveQuasi-Equilibrium(CQE)theory(originallyintroducedbyArakawaand44

Schubert,1974)suggeststhatconvectiveoverturningoftheatmosphereremovesconvective45

availablepotentialenergy(CAPE)atarateapproximatelyequaltotheratebywhichlarge-scale46

processesacttogenerateit(Emanueletal.1994).TheworkofPlumbandHou(1992)builton47

earlierworkbyLindzenandHou(1988)andHeldandHou(1980)usinganangularmomentum48

conservingframeworkfortheHadleycirculationtoestablishtheonsetcriterionforadirect49

overturningcirculation.Emanuel(1995)extendedthetheoryofPlumbandHou(1992)to50

accountforthemoistadiabaticprofiletypicalofatropicalatmosphereinquasi-equilibrium,51

resultinginapredictivetheoryforrelatingsub-clouddistributionsofmoistenergyorentropyto52

thelocationoronsetoftheITCZ(Emanuel1995;PrivéandPlumb2007a).53

Emanueletal.(1994)suggestedthatstrongercurvatureofthehorizontaldistributionof54

sub-cloudmoistentropyoughttoimplyastrongeroverturningcirculation(seetheirfigure755

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andtheirdiscussioninsection5boftheirmanuscript).Theirideawasthatanatmospherewith56

astrongermoistentropydifferenceinthehorizontalwilldriveastrongercirculation.Ifthe57

circulationisstrongenough,itmaysuppressdeepconvectionentirelyinthesubsidencezone,58

restrictingprecipitationtoanarrowregionoverthewarmersurfacetemperatures.The59

thresholdforthisoverturningcirculationbuildsontheworkofPlumbandHou(1992),andwas60

fullydevelopedforuseinamoistatmospherebyEmanuel(1995).Thecriticalitycriterionfor61

theonsetofadirectcirculationthatEmanuel(1995)derivedis:62

( ).

2 14 sinn

si

in 0s s t bT T sk j j

j

é ùæ öê úW +Ñ - Ñ <ç ÷ê úè øê úë û

º (1)63

Here,φislatitude,ΩistheEarth’srotationrate,aistheEarth’sradius,Tsissurface64

temperature,Ttistropopausetemperature,andsbisthesub-cloudmoistentropy.Equation(1)65

providesthecriterionrequiredforanoverturningcirculation,buttheideathatthestrengthto66

whichthethresholdisviolatedputforthbyEmanueletal.(1994)suggeststhatitsvaluemay67

provideadditionalinformationforthestrengthoftheoverturningcirculation.Indeed,recent68

workbySinghetal.(2017)showedthatthestrengthoftheHadleycirculationislinearlyrelated69

withthecriticalityconditionofEmanuel(1995)inanidealizedmodelingframework.Therefore,70

thereiscompellingevidencetothinkthatequation(1)canbetreatedasmorethanasimple71

thresholdcriterion.Werefertothecriticalitymetricasthecurvatureterm,orκ.Thedominant72

structureoftheseasonalityofκcomesfromthesub-cloudmoistentropyfield(determinedby73

alternatelyusingboththeannualmean(Ts-Tt)andsbfieldstocomputeκ;notshown).74

Thereforetheseasonalcycleofκismosteffectivelyinterpretedasarepresentationofthe75

curvature(thesecondspatialderivative)ofthesub-cloudmoistentropy.76

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Whiletheboundarylayerequivalentpotentialtemperaturehasbeenlinkedto77

interannualvariabilityinmonsoonprecipitation(HurleyandBoos2013),ShekharandBoos78

(2016)suggestthatCQEislessidealforlookingatmonsooncirculationsneardesertsowingto79

theimportanceofshallowcirculationsthatbreakthefirstbaroclinicstructureassumedina80

CQE-consistentHadleycell.BoosandEmanuel(2009),however,foundthatsub-cloudmoist81

entropyshowsspatialpatternchangesconsistentwiththerapidonsetofthemonsooninSouth82

Asia.OurgoalforthisworkistoexaminewhetherCQE,inparticularthecurvatureofsub-cloud83

moistentropy,canbeusedasaneffectivemarkeroftheseasonalcycleofprecipitationin84

presentdayandCO2-warmedclimates.Toestablishthepotentialofthistheory,webeginwith85

simpleaquaplanetsimulations.Thoughzonalasymmetriesareimportantforfeatureslikethe86

monsoon,muchcanbelearnedfromzonallysymmetricoraquaplanetexperimentstoexamine87

theHadleycirculation(FangandTung1996,1997;Satoh1994;HeldandHou1980;Lindzenand88

Hou1988;BordoniandSchneider2008;SchneiderandBordoni2008).89

Thismanuscriptfollowswithadescriptionofthedatausedinsection2,evidencefora90

linearrelationshipbetweenthecurvatureterm,κ,andP-Einmodelsinsection3,theuseof91

thatlinearrelationshipasapredictorofP-Echangesinsection4,andatheorytounderstand92

whysuchalinearrelationshipoughttoexistispresentedinsection5.Asummaryofour93

findingsispresentedinsection6.94

95

2.ModelData96

WemakeuseoftheTropicalRainbeltswithanAnnualcycleandaContinentModel97

IntercomparisonProject(TRACMIP)simulations(Voigtetal.2016).TheTRACMIPsuitehasfive98

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differentexperiments,butwefocusononlytwo:theAquaControlandAqua4xCO299

experiments.Bothexperimentsuseafixedoceanheatfluxandaslaboceanwith30mdepth.100

AsissuggestedintheTRACMIPname,theseasonalcycleisfullyrepresentedinthemodels.101

TheaquaplanetconfigurationsfollowtheexperimentaldesignoftheAqua-Planetexperiment102

(NealeandHoskins2000)withtheexceptionsoftheslaboceaninplaceofafixedseasurface103

temperaturepatternandthefullrepresentationoftheseasonalcycle. 104

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Table1liststhemodelsusedinthisstudy.Themodelsusedinthisstudyareasubsetof105

thetotalTRACMIPsuite;onlythosemodelsthathaveallofthevariablesneededtocalculate106

dailysub-cloudmoistentropyareusedhere.Eachmodelprovidestenyearsofdailyoutput,107

whichisusedfortheanalysesinthefollowingsections.108

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3.EvidencefortheκvsP-Erelationshipinmodels110

a.Computingκ111

Sub-cloudmoistentropyiscalculatedusingthesub-cloudtemperatureandmoisture112

fieldswiththefollowingrelationship:113

( )lnb p ebs c q= (2)114

Wherecpisthespecificheatatconstantpressurefordryairandθebistheequivalentpotential115

temperature(computedfollowingBolton1980)withintheboundarylayer.Wehavetwo116

methodsforcomputingthesub-cloudtemperatureandhumidityfieldsdependingonthe117

modeloutputdata.Forthosemodelsthatoutputthedataontheirnativegrids(CAM3,CAM4,118

andMPAS),thetemperatureandhumidityfieldsatthelowestmodellayerareused.Forthose119

modelsthatinterpolatetheiroutputtofixedpressurelevels,thetemperatureandhumidity120

fieldsareinterpolatedontoasurface20hPaabovethesurfacepressure.121

Becauseoftheuseofaquaplanets,allfieldsareaveragedzonally.Itisusefultonote122

thatEmanuel(1995)providestwosimilarequationsforcalculatingthecurvature:onemeant123

forzonallysymmetriccirculations(equation10ofEmanuel,1995)andonemeantfortwo124

dimensionalfields(equation25ofEmanuel,1995,equation(1)above),withthelatterignoring125

centrifugalterms.Wefindthattheuseofeitherequationhaslittleinfluenceonthe126

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conclusionsdrawninthisparticularstudy,suggestingitisthecurvatureofsb,notthe127

centrifugalcomponents,thatisimportantforunderstandingtheseasonalcycleoftheITCZ.128

Totheextentthatwecanignorethecentrifugalterms,wemakeuseofthesecond129

derivativeofsbto“fillthegap”neartheequator.Equation(1)isnotwell-definednearthe130

equatorowingtotheinversesinφterm.ThetheoryputforthbyEmanuel(1995)isnot131

designedtopredictP-Eattheequator.Infact,anygradientinsub-cloudmoistentropyacross132

theequatorshouldresultinadirectcirculationforming(LindzenandHou1988;Emanuel1995).133

However,forthepurposesofcreatingapredictivemodelforP-Eacrossallseasons,wedesirea134

meansofexpandingthecurvaturetermtobeabletooperatewhentheITCZcrossesthe135

equatorduringthetransitionseasons.Tothatend,weextendthecurvaturetermnearthe136

equatorassimply137

( )( )eq.

0s t bT T sk é ùº Ñ × - Ñ <ë û (3).138

Wekeepthe ( )s tT T- termtomaintainthesamedimensionsofκatalllatitudes.Weexamine139

whetherthis“fillingtheequator”termworksinsection4,explorewhetheritistheoretically140

justifiedinsection5.Thecombinedκfromequations(1)and(3)isusedtocalculatethe141

curvatureforallofthefiguresusedinthismanuscript.Forcomparisonpurposes,κisalso142

calculatedusingequation(1)withoutequation(3)forcompleteness.Whencomputingκ143

withoutmakinguseofequation(3),latitudebandsequatorwardof3°N/Sareremovedfrom144

thecalculations.145

146

b.AlinearrelationbetweenκandP-E147

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Figure1showstheseasonalcycleofthezonalmeancurvatureterm(κ;colors)andP-E148

(contours)foreachofthetwelvemodelsused.Despitehavingtenyearsofdata,thereisstilla149

noticeableamountofnoise.Todampenthenoiseandfocusonthelargescaleseasonalcycle,150

bothmodeledandpredictedP-Efieldsaresmoothedintimewitha15dayboxcarsmoother.151

Mostofthemodelsshowqualitativeagreementbetweenthetwofields,withtheCALTECH152

modelbeingthemajorexception.TheCALTECHmodel,however,hasvastlysimplifiedmoist153

physicswhichseparatesitfromtheothermodelsexaminedhere.Forexample,theCALTECH154

modeldoesnotincludecloudradiativeeffects,animportantcomponentofthesurface155

radiationbudget,whicharealsolikelytobeimportantforthecurvatureofsub-cloudmoist156

entropy.157

BasedontheworkofSinghetal.(2017),asimplelinearmodelisusedtorelateP-Etoκ.158

Figure2showsthe2Dhistogramofthesetwovariables,andthelinearrelationshipbetween159

thesevariablesisimmediatelyapparentformanyofthemodels(inthespacewhereκ<0).160

Thereare,however,somemodelswherethislinearrelationshipdoesnothold(ECHAM-6.3,161

MetUM-CTL,andMetUM-ENT).Thesethreemodelsalsohavetheworstagreement(outsideof162

theCALTECHmodel)inthespatialpatternofκandP-EinFigure1.Oneofthekeyfeaturesthat163

makesthelinearmodelforκandP-Eattractiveisthatthemodelcoefficientsaresimilar164

betweentheAquaControlandAqua4xCO2experiments(notshown).Thisconsistencyallows165

theuseoftheAquaControlexperiments’κ-P-EmodeltoalsobeusedfortheAqua4xCO2166

experiments.167

168

4.Usingκasapredictorofmoisturecyclechanges169

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a.CurvatureasapredictorinP-Eincurrentclimate170

Wefirstexaminehowwellthelinearmodelbasedonκcapturestheclimateofthe171

AquaControlexperiments.ThefirstyearofeachAquaControlexperimentisusedtofitP-Etoκ,172

andthenpredictP-Efortheremainingnineyears.Figure3showsthepredictedseasonalcycle173

ofP-Eusingtheκmodel.Therootmeansquareerror(RMSE)andpatterncorrelation174

coefficient(ρ)aregiveninthetitleofeachpanel.Thecontourintervalsforboththecolor-filled175

contoursandtheblackcontoursare4mm/dayineachpanelforFigure3.TheaverageRMSE176

foralltwelvesimulationsis3.6mm/day,whileρis0.72.Thefidelityoftheseasonalpatternof177

P-Easmeasuredbyρshowsgoodagreementforthepredictormodel.Thegeneralsuccessofκ178

toyieldrealisticprecipitationpatternsgivesusconfidencetoproceedwithourmaingoalof179

tryingtopredictthechangeinP-Einawarmerclimate.180

Ingeneral,theκ-basedlinearpredictivemodeldoesagoodjobofcapturingthe181

seasonalcycleofzonalmeanP-Einthe4xCO2experiment(notshown)withsixoftwelve182

modelshavinggreaterthan50%ofthevarianceexplained(ρ2)andallbuttheECHAM-6.3and183

CALTECHmodelshavinggreaterthan25%ofthevarianceexplained(notshown).Forthe184

twelvemodels,themeanRMSEis4.3mm/day(κ)andthemeanρis0.67(κ).Theerrorsare185

largercomparedtopredictingtheAquaControlP-E,asonemightexpect,butthepattern186

correlationisstillquitegood.187

Formostmodels,itmakeslittledifferencewhetherweuseequation(3)to“fill”inthe188

equatoriallatitudes(thoseequatorwardof3°)inourcalculationofκ.TheECHAMmodelsare189

anexception,inthattheyaresensitivetowhethertheequatoriallatitudesareincluded.In190

general,oursimpleassumptionofusingthesecondderivativeofthesub-cloudmoistentropy191

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to“fill”theequatorialregionisconsistentwiththecurvaturetermdefinedinequation(1).In192

otherwords,predictingP-Eintheequatorialregiondoesnotsignificantlyimproveordegrade193

theoverallpredictiveskill.194

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b.CQEasapredictorofΔ(P-E)196

ExamininghowwellthelinearmodelcapturesthechangeinP-EbetweenAquaControl197

andAqua4xCO2isofgreaterinterestthanreproducingthemeanclimatestate.Thesamelinear198

fitusedforpredictingP-EbasedonκintheAquaControlexperimentsworkswellinthe199

Aqua4xCO2experiments.Figure4showsthechangeinP-E,bothpredictedbythecurvature200

term(colors)andtheactualchange(contours–blackcontoursarepositive;red,negative).In201

Figure4,thecolorlevelsmatchthecontourlevels,andtheyvaryfrommodeltomodel.There202

isqualitativeagreementbetweentheactualΔ(P-E)andΔ(P-E)predictedusingκ.203

Toassesstheskilloftheκ-basedpredictormodel,anullhypothesisisformulatedtotest204

against.ThechosennulltestassumesthatthechangeinP-Eisthedifferenceinfixed205

percentagechangesintropicalmeanP-EbetweenAqua4xCO2andAquaControl.Itturnsout206

thatoverthetropics(20°S-20°N)inthesemodels,P-Eissmallinboththecontroland4xCO2207

experiments,andsothefractionalchangesinPandEareapproximatelyequivalent(not208

shown).Thus,thenullhypothesisis:209

( ) ( ) ( ) ( )4xCO2 ControlControl

, , 1 PP E t P E tP

j jæ öD

- = - × +ç ÷è ø

(4)210

Here,subscript‘4xCO2’referstotheAqua4xCO2experiments,subscript‘Control’referstothe211

AquaControlexperiments,ΔreferstoachangebetweentheAqua4xCO2andAquaControl212

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experiments,andanoverbardenotesthetropicalmean(averagedover20°S-20°N).Thisnull213

hypothesisissimilartothe“wet-get-wetter”conceptwherethelocationsthatcurrentlyfavor214

P-EseethegreatestincreaseinP-E.Becausethefractionalchangesinprecipitationand215

evaporationareapproximatelyequivalentwhenaveragedoverthetropics,thenullhasthe216

convenientconditionthatthetropicalmeanchangeinP-Eisapproximatelyequivalenttothe217

actualtropicalmeanchangeinP.218

Figure5showsρ(left)andRMSE(right)forthechangesinP-E.Thepredictormodel219

basedonκoutperformsthenullhypothesisforpredictingΔ(P-E)whenlookingatρforall220

modelsexceptCALTECH.Despiteoutperformingthenull,thecorrelationsarelowforthe221

ECHAM-6.3andCALTECHmodels.Thosearetheonlytwomodelsforwhichthepredictoris222

unabletocaptureatleast25%ofthevariance.ForRMSE,κisaskillfulpredictorofΔ(P-E)forall223

twelvemodels.Forκ-predictedΔ(P-E),theaverageRMSEis2.8mm/dayandtheaverageρis224

0.56.Forcomparison,themeanRMSEis6.9mm/dayandthemeanρis-0.03forthenull225

hypothesis.Clearly,thenullhypothesiscannotcapturetheseasonalpatternofΔ(P-E),even226

withoutthecomplicationoflandinaquaplanetsimulations.Therefore,weconcludethatκisa227

valuablepredictorofP-Echanges.228

229

c.Comparingwithsub-cloudmoistentropy230

Todeterminewhetherthisnewcurvaturemetricisquantitativelyuseful,wecompareit231

againstalinearrelationshipusingsbdirectly.(PrivéandPlumb2007a)showedthatthe232

monsoonprecipitationtendstosetupjustequatorwardofthemaximumsurfacemoiststatic233

energy,aregionwherethecurvatureislikelystrong.WhilealinearscalingbetweensbandP-E234

13

isasimplificationoftheideathatP-Eshouldincreasewithincreasingsb,thereisobservational235

evidenceforalinearrelationshipbetweenseasurfacetemperatureandprecipitation(abovea236

SSTthreshold)inthetropics(Cornejo-GarridoandStone1977;GrahamandBarnett1987;237

WaliserandGraham1993).ThoughwemaynotexpectarelationshipbetweensbandP-Eto238

exactlymatchthatbetweenSSTandP,thelinearsbrelationshipusedhereisattractivebecause239

ofitsconceptualsimplicityandthefactthatwealsousealinearmodeltorelateκandP-E.The240

relationshipbetweensbandP-Eistreatedaslinearaboveasbthresholdequaltothemeanof241

allsbvalueswhereP-Eislessthanzero.242

TheseasonalpatternofP-Epredictedbybothmodelsshowsqualitativeagreementwith243

theactualseasonalpatternofP-E.Themulti-modelmeanpatternsforboththeκ-predicted244

andsb-predictedP-EareshowninFigure6(notethatsb-predictedP-Eiscomputedthesame245

wayκ-predictedP-Ewasabove).ThefidelityoftheseasonalpatternofP-Easmeasuredbyρis246

similarforbothpredictormodels,buttheRMSEislowerfortheκmodel.UsingsbtopredictP-247

Ehasstrongsummermaxima,butmissestheprecipitationinthetransitionseasons.Usingκ,248

ontheotherhand,doesabetterjobofcapturingthetransitions,buttendstounderestimate249

precipitationduringthelocalsummers.250

WhilethesamelinearmodelcanbeusedwithκandP-E,forsb,thesamelinearfit251

cannotbeusedforbothAquaControlandAqua4xCO2experiments.Therelationshipbetween252

sbandP-Edependsstronglyonthemeantropicalsb.Toadjustforthis,thetropicalmean(20°S-253

20°N)sbchangebetweentheAqua4xCO2andAquaControlexperimentsisaddedtothelinear254

fitderivedfromtheAquaControlexperimentwhentryingtopredictP-EintheAqua4xCO2255

experiments.Explicitly,thisis:256

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( )( ) ( ) ( )b b bP E s s s P Ea b- = - D D-+ - (5)257

wherea andb arethelinearfitcoefficientsfromtheAquaControlexperiment,sbisthesub-258

cloudmoistentropyfortheAqua4xCO2experiment, bsD isthedifferenceintropicalmeansub-259

cloudmoistentropy(averagedfrom20°S-20°N),and ( )P ED - isthedifferenceintropical260

meanP-E(thistermisalsoincludedforthecurvaturerelationship).The ( )P ED - termis261

includedtoaccountforanyadditionalshiftsinthelinebetweentheAquaControland262

Aqua4xCO2experiments.However, ( )P ED - tendstobesmallineachofthemodelsowingto263

offsettingchangesinprecipitationandevaporation.WehavealsocomputedthesamesbvsP-E264

relationshipswheretropicalmeanprecipitationisremovedateachdaysuchthatanomaliesin265

sbarerelatedtoP-Einstead.ThedifferencesinalloftheP-Erelationshipswereinsignificantin266

termsofRMSEandρfromthepreviousmethod(forpredictingP-E,Δ(P-E),andtheITCZ267

position).268

SimilartotheP-Epredictions,theΔ(P-E)predictedbyκandsbalsoshowqualitative269

agreement(Figure6).Bothpredictormodelsdoagoodjobofrepresentingtheincreasein270

precipitationinthenorthernhemisphere,butstrugglewiththedecreaseinprecipitationtothe271

south.Thesbpredictormodel,inparticular,tendstohaveaverylargedecreaseinP-Ebetween272

10°S-20°S.Additionally,thesbmodelfailstocapturethedryingtrendatthesouthernfringeof273

theITCZduringthetransitiontoBorealsummer.DespiteconsiderablespreadintheP-E274

responseacrossthemodels(whichisunsurprisinggiventhattheyarepredictingtheirownSST275

responsetotheCO2quadrupling,Voigtetal.,2017)themodelsdoagreethatthenorthward276

shiftoftheITCZresultsprimarilyfromashiftintheprecipitationbandnorthwardduringAustral277

15

summer.Inotherwords,excursionsoftheITCZintotheSouthernHemisphereareweakenedin278

awarmerworld,whichbothκandsbmodelsalsoshow.TheρandRMSEvaluesforthe279

individualmodelsarepresentedinFigure5.Forκ-predictedΔ(P-E),theaverageofthe280

individualmodelRMSEsis2.8mm/dayandtheaverageρis0.56.Forsb-predictedΔ(P-E),the281

averageRMSEis3.1mm/dayandtheaverageρis0.56.Again,forcomparison,themeanRMSE282

is6.9mm/dayandthemeanρis-0.03forthenullhypothesis.Whileκtendstooutperformsb283

inmostmodels,thedifferencesarenotenormous.Sinceκdependsprimarilyonthe284

distributionofsb,thisisnotsurprising.Itisstillworthcomparingthetwo,though,sincethey285

implyfundamentallydifferentinterpretationsoftheITCZdynamicsandsbhasbeenmore286

commonlyusedfordiagnosingITCZposition(e.g.,PrivéandPlumb2007a;ShekharandBoos287

2016).288

289

d.ITCZposition290

ThepositionoftheITCZandhowitmaychangewithglobalwarmingisofgreatinterest.291

WeuseourtwopredictormetricstocomputetheshiftintheITCZfollowingequation1aof292

Adametal.(2016):293

( )( )( )( )20

20N

2N

S

0S

20

c dos

cos d

N

ITCZ N

P

P

f f ff

f f= òò

(6)294

N=10inequation(6).Tobeconsistentwiththepredictormetrics,weuseP-Einsteadof295

precipitation,butrestrictourcalculationtoregionswhereP-E>0.TheswitchbetweenPandP-296

EmakesverylittledifferencewhencomputingtheactualITCZposition(notshown).Thereexist297

alternativemeansofcomputingtheITCZpositionsuchastheprecipitationcentroid(thesame298

16

computationasequation(6),onlywithN=1)ortheprecipitationmedian(themedianlatitudeof299

theprecipitationdistributionbetween20°Sand20°N).WetesteddifferentvaluesofNin300

equation(6),rangingfrom1-10(notshown).WhilesmallervaluesofNtendtosmoothoutthe301

ITCZprofile,changingNdoesnotalterourconclusions.Inaddition,(Adametal.2016)founda302

closerelationshipbetweentheprecipitationcentroidandprecipitationmedianinobservational303

andreanalysisdatasets,suggestingthatconclusionsdrawnfromoneapplywelltotheother.304

Therefore,itisunlikelythatadifferentITCZpositionmetricwillyielddifferentconclusionsfrom305

theoneusedhere.306

TheshiftinannualmeanITCZpositionisshowninFigure7.Bothpredictormetricsdo307

anexcellentjobofreproducingtheannualmeanshiftintheITCZ.ThelowerrorinITCZshiftfor308

sb-predictedP-Ecomesfromabiascancellation.sb-predictedP-Ehasalargephaseerror(see309

Figure8).Thetransitionfromsummer-to-winter(orwinter-to-summer)comesearlywhenP-E310

ispredictedwithsb,butthisphaseerroristhesameforboththeAquaControlandAqua4xCO2311

experiments,andislostwhencomputingthedifferenceinannualmeanITCZposition.312

WhenlookingattheseasonalcycleofITCZposition,κ-predictedP-Eoutperformssb-313

predictedP-EinboththeAquaControl(averageRMSEforκ=3.2°,averageRMSEforsb=5.5°)314

andtheAqua4xCO2(averageRMSEforκ=4.4°,averageRMSEforsb=5.8°)experiments.315

Figure8showsthatthepolewardextentoftheITCZinsummerandwinterisrelativelywell-316

capturedbythesbmodel,soitisthephaseerrorthatcausesitsRMSEtobehigherthanthatof317

theκmodel.TheerrorsinITCZpositionusingκ-predictedP-Earelesscoherentacrossmodels.318

Forexample,κ-predictedITCZpositionintheCAM5Normodelshowsaphaseerrorwhile319

capturingthesummerandwinterextentoftheITCZwell,buttheMIROC5modelhastheexact320

17

opposite:thephaseiswellcaptured,butthesummerandwinterextentoftheITCZistoo321

equatorward.322

323

e.RelaxingchangesinκassumingfixedRH324

Upuntilthispoint,wehavebeenusingtheactualsub-cloudmoistentropy,sb,fromthe325

Aqua4xCO2experimentstopredicttheP-E,aswellascomputeκforthoseexperiments.326

Calculatingsbrequiresboththesub-cloudlayertemperatureandhumidity.Tounderstandhow327

muchoftheprecipitationchangescomefromtemperaturechangesandhowmuchfrom328

humiditychanges,wetestwhetherκandsbarestillusefulmetricsunderfixedrelativehumidity329

conditions.Assumingtheboundarylayertemperaturechangereflectsthatoftheunderlying330

SSTandthatrelativehumidityremainsfixed,wederiveapredictormodelthatreliessolelyon331

SSTchangestopredictΔ(P-E).Followingtheequationforsub-cloudmoistentropy,thechange332

isasfollows(droppingthesubscriptbforconvenience).333

1

ln( ); exp

d / d 0.07

vp e e

p

e vp p v

e

s

s

L qcT

T L qs c L qT T

s

q T K

c

c

q

q q q

q aq

a -

æ ö= » ç ÷ç ÷

è øD D æ öD = = + -ç ÷

è ø

º »

(7)334

Here,Lvisthelatentheatofvaporization,qisthespecifichumidity,TistheSSTasproxyforthe335

sub-cloudlayertemperature,αisthepercentchangeinsaturatedspecifichumidity(qs)per336

degreewarming.Wehaveanequationtogetthechangeinsbthatreliesonlyonthechangein337

SSTandtheclimateoftheAquaControlexperiments.Tocomputeκ,Δsbfromequation(7)is338

addedtotheAquaControlvalueofsbandthenequation(1)isusedasbefore.339

18

Figure9showsRMSEandρforΔPbetweenκ-orsb-predictedP-Eandmodelsimulated340

P-Eusingafixed-RHassumptionwithΔSST.Unsurprisingly,thepredictiveskillusingthe341

simplifiedformofΔsbinequation(7)islowerthanusingtheactualsbfromtheAqua4xCO2342

experiments.ThemeanRMSEandρforκ-predictedP-Eare3.7mm/dayand0.31,respectively.343

ThemeanRMSEandρforsb-predictedP-Eare3.2mm/dayand0.44,respectively.Themean344

RMSEandρforthenullarestill6.9mm/dayand-0.03,respectively,sincethenullis345

independentofourfixed-RHassumption.Theseresultssuggestchangesinbothtemperature346

andsub-cloudrelativehumidityareimportantforpredictingΔ(P-E),especiallyusingκ.347

ThequalitativepatternsofΔ(P-E)usingthefixedRHassumptionaresimilartothose348

usingtheactualκfromthe4xCO2experiments(notshown),suggestingthatκisstillauseful349

markerofpredictingchangesinthewatercycleevenundersuchsimplifications.Additionally,350

despitethereductioninskillfromassumingaconstantRH,allmodelsexcepttheCAM5Noror351

CALTECHmodelscontinuetobemoreskillfulthanthenullatpredictingΔ(P-E)witheithertheκ352

orsbmodel.Theresultsofthissectionsuggestthatknowingbothtemperatureandhumidity353

changesareimportantforunderstandingchangesintheITCZwithwarming.354

355

5.UnderstandingthelinearrelationshipbetweenκandP-E356

Weareinterestedinunderstandingwhythecurvatureterm,κ,islinearlyrelatedtoP-E357

insomanymodels.Todothisweexaminethemoiststaticenergybudgetofthetropicsinthe358

CAM3,CAM4,andMPASexperiments.Thesethreemodelsareusedbecausewehavetheir359

outputontheirnativemodelverticalcoordinates,allowingustoverticallyintegrateMSEfluxes.360

TheMSEbudgetis361

19

{ } { }

{}0

1 dsp

hh S

t

pg

¶+Ñ× =

¶

× º ×ò

v(8)362

Wherecurlybracketsdenoteacolumnintegral,psissurfacepressure,visthehorizontalwind363

vector,hismoiststaticenergy,andSisthenetsourcesandsinksofMSE.Thebudgetdoesnot364

closecompletelywhenusingdailydata,anditisassumedthattheresidualtermisdominated365

byMSEdivergence,specificallythetransienteddyMSEfluxdivergenceatsub-dailytimescales.366

{ } { } { }resolved residual

hh h S

t¶

+Ñ× +Ñ× =¶

v v (9)367

Figure10showsthetotaldivergenceofMSEforthethreemodels,aswellasthebreakdown368

intotheresolvedandresidualcomponents(firstthreecolumnsofFigure10).ContoursofP-E369

areincludedforreference.ThetotalMSEdivergenceisnotgenerallycorrelatedwithP-E,370

insteadtheformertendstolagbehindthelatterinphase.Theresidualcomponent,however,is371

wellcorrelatedwithP-E(ρ=0.46forCAM3,ρ=0.88forCAM4,andρ=0.92forMPAS).The372

correlationinFigure10(g-i)suggeststhattheresidualtermisrelatedtothesameprocesses373

thatareresponsiblefortheprecipitationspatio-temporaldistribution.374

Asimpleassumptionistotreattheresidualasadiffusivedivergenceofcolumn-375

integratedMSE,whichmaybeconsideredasimpleparameterizationofthetransienteddyMSE376

fluxdivergenceatsub-dailytimescales.Assumingconstantdiffusivity,thenewequationcan377

thusbewrittenasfollows.378

{ } { } { }2resolved e

hh K h S

t¶

+Ñ× - Ñ =¶

v (10)379

20

KeissolvedforbyfittingalinearmodeltotheresidualdivergencetermwiththeLaplacianof380

thecolumn-integratedMSE,yieldingKe=9.2x104m2/s,9.3x105m2/s,and2.8x105m2/sfor381

CAM3,CAM4,andMPAS,respectively.IntheTropics(20°S-20°N),thepatterncorrelation382

coefficientbetweentheresidualMSEdivergenceand-∇2{h}is0.62,0.73,and0.60,forCAM3,383

CAM4,andMPAS,respectively,meaningthatthissimplediffusiveapproximationexplains36-384

53%ofthevarianceoftheresidualterm,dependingonthemodel.385

GiventhatthetotalresidualmaybeapproximatedasthedivergenceofadiffusiveMSE386

flux,thenextquestionishowdoesthistermrelatetoP-E?Liketheresidual,thediffusiveterm,387

-Ke∇2{h},isalsocorrelatedwithP-E(ρ=0.66,ρ=0.65,andρ=0.63forCAM3,CAM4,andMPAS,388

respectively).Ifweignorethegeometrytermsfromequation(1),aswasdonefor“fillingthe389

equator”inequation(3),andweadditionallyassumethat(Ts-Tt)isconstant,wefindthatκand390

thediffusivetermconvergetothesameform:-Ke∇2{h}vs-(Ts-Tt)∇2sb.Weexpect{h}andsbto391

havesimilarspatialstructuressincetemperaturegradientsareconstrainedtotheboundary392

layerinthetropicsandmoisturegradientsarenecessarilyweakintheuppertroposphere393

owingtothelowspecifichumidityvaluesthere.Unsurprisingly,-Ke∇2{h}and-(Ts-Tt)∇2sbare394

correlated(ρ=0.62,ρ=0.62,andρ=0.54forCAM3,CAM4,andMPAS,respectively).Likeκ,-395

Ke∇2{h}workswellforpredictingP-E(Figure10panelsm-o)withalinearconversionfactorfrom396

MSEdivergencetomoisturedivergence(termedtheNormalizedGrossMoistStability,NGMS,397

seeRaymondetal.,2009,fordetails).NGMSiscomputedasalinearfitbetweentheresidual398

MSEdivergenceandP-E.399

TheaboveargumentssuggestthatthediffusivenatureoftheMSEdivergenceonsub-400

dailytimescalesisthereasonforthelinearrelationshipbetweenκandP-E.Additionally,we401

21

canverifytherelationshipthroughascalinganalysisusingthediffusiveresidualtermandthe402

linearslopecomputedfortheκvsP-Emodel(showninFigure2).Theslopeofthelinearmodel403

givesthechangeinP-Eforaunitchangeinκ,whichintermsofFigure2hasunitsofmmday-404

1/s-2.TogetthesamedimensionsforachangeinP-Eforunitchangein∇2{h},weneedto405

multiplyby–Keps/Γg,whereKeisthediffusivityconstantfrombefore,ΓistheunitlessNGMS406

conversionfactor,andtheps/gfactorconvertsthecolumn-integratedMSEintoamass-407

weightedaveragetoachievethesameunitsasκ.Thereforetheslopeoftheκ–(P-E)408

relationshipshouldberelatedto–Ke/Γ*ps/g*86400/Lv.Scaleanalysisshowsthistobe-409

105/10-1*105/101*105/106=-109mmday-1/s-2.Forcomparison,theslopesoftheκ–(P-E)410

relationshipforCAM3,CAM4,andMPASvarybetween-1.1x109and-1.6x109mmday-1/s-2.The411

exactvaluesoftheslopewillbesensitivetothefactorrelating{h}tosbandthegeometric412

termsinequation(1).413

TheseparationofMSEdivergenceintoresolvedandsub-dailytimescalecomponents414

revealsaninterestingrelationshipbetweenthetropicalcirculationandP-E.Convectionactson415

sub-dailytimescalestoremovegradientsinMSE/sb,whileatthesametime,convection416

producesalotofprecipitation.Physically,thisiswhyκisrelatedtoP-E,andwhythereisstrong417

agreementbetweenthesub-dailyMSEdivergence(thediffusiveresidualterm)andP-E.The418

totaldivergencepatternbalancesthetotalforcing,whichlagsbehindP-E(Figure10panelsa-c419

andj-l).Overtheseasonalcycle,thetotalMSEdivergencelagsP-Eandthislagisseen420

prominentlyintheresolveddivergencefieldinFigure10(panelsd-fandj-l).Thisphaselag421

betweenP-EandMSEdivergencesuggeststhatusingtheconceptofpolewardenergy422

transportedbythezonalmeanHadleycirculationtodiagnoseP-Echangesmaybemisleading423

22

onsub-seasonaltimescales.Italsosuggestsunderstandingthetropicalcirculationand424

hydrologicalcycleresidesinunderstandingcloudprocesses.425

Itisunfortunatethatthesub-dailyMSEdivergencemustbecomputedasaresidual426

here.Itisworthaskinghowmuchoftheresidualdivergenceisfromconvectionandhowmuch427

maybefrompossibleothersourcesoferror.Itisunclearhowregriddingerrorscouldbe428

parameterizedasadowngradientdiffusiveprocess,soitisunlikelythatthesearethedominant429

sourceoftheresidualterm.Thereisalsothepossibilityofshallowcirculations(eithernearthe430

surfaceoraloft)thatmaybeimportant.Futureworkwillquantifywhatpartsofthesystem431

giverisetotheresidualterm.Thethreemodelswithdifferentphysicsparameterizations432

(CAM3vs.CAM4)anddifferentdynamicalcores(CAM4vs.MPAS)wehavebeenabletoanalyze433

fortheirMSEbudgetsallshowalinearrelationshipbetweenκandP-E.Thereareafewmodels434

(e.g.ECHAM6.3,MetUM-CTL,MetUM-ENT)wheretherelationshipbetweenκandP-Eisweak435

andnon-linear.Forthesemodels,wehypothesizethatprocessesbeyondthosethatproduce436

rainarehelpingtoremovegradientsinsb.Futureworkisnecessarytoquantifytheimportance437

ofdeepconvectioninremovinggradientsinsbintherealworld.438

439

6.Conclusions440

WehavedemonstratedalinearrelationshipbetweentheintensityofP-Eandthe441

curvaturetermderivedbyEmanuel(1995)fortheonsetofadirectoverturningcirculation442

underCQE.Thislinearrelationshipisroughlyunchangedinawarmerclimate,makingthe443

curvatureterm,κ,anappealingpredictorofΔ(P-E).Wehaveshownthatκcanbeusedto444

predicttheseasonalpatternofthechangeinP-EinresponsetoCO2-inducedwarming.445

23

Additionally,thelinearκmodelismoreskillfulcomparedtoour‘wet-get-wetter’null446

hypothesis.LocalchangesinΔ(P-E)areoftenontheorderofafewmm/day,withsomemodels447

havingchangesontheorderoftensofmm/day,meaningthesechangesinP-Eareboth448

interestingandmeaningful.449

Asacomparison,asimplelinearmodelisalsoconstructedtorelateP-Etosub-cloud450

moistentropy,sb.Likeκ,sboutperformsthenullhypothesisforpredictingΔ(P-E).AfixedRH451

assumptiongenerallydegradestheperformanceofbothpredictors,suggestingthatboth452

temperatureandRHchangescontributeimportantlytochangesinP-E,thoughthepredictions453

arestillskillfulcomparedtothenull.WhilebothκandsbpredicttheshiftinITCZposition,454

whichoneperformsbettervarieswithtimescale.sbshowsgreaterskillacrossmodelsfor455

annualmean,whileκshowsgreaterskillseasonally.However,theimprovementinsbcompared456

toκfortheannualmeancomesfromoffsettingphasebiasesintheAquaControland457

Aqua4xCO2experiment.458

Futureworkisneededtoinvestigatewhetherκremainsausefulpredictorinthe459

presenceoflandorshallowcirculationsasnotedbyHurleyandBoos(2013)andShekharand460

Boos(2016).WhilePrivéandPlumb(2007b)showedthatzonalasymmetriesaddcomplexity,461

theyalsonotethatmonsoonprecipitationsetsupjustequatorwardofthesub-cloudmoist462

entropymaximum,potentiallywherethecurvatureisstrong,sothereisreasontosuspectthat463

κmaystillbeusefulinlessidealizedcases.Indeed,theworkpresentedheresuggestsκislikely464

abetterpredictorofthemonsoonsystemsthansbbecauseoftheimportantseasonalandsub-465

seasonaltimescalesassociatedwithmonsooncirculations.Similarly,ShawandVoigt(2015)466

24

showedthattheCQEtheorycanbeusedtopredictcirculationchangesbasedonchanging467

gradientsofsub-cloudmoistentropyacrossfullyAMIPstyleGCMexperiments.468

WehaveshownthatapproximatingthetransientMSEdivergenceasadowngradient469

diffusiveprocessisabletocapturetheseasonalcycleofP-E,andwehavesuggestedthis470

relationshipgivesrisetothelinearrelationbetweenκandP-EseenintheTRACMIPsuiteof471

models.Weargueherethatthisdiffusivetermresultsfromtheatmosphereattemptingto472

removegradientsinsb,andthatthisoccursmostefficientlywhereκisstronglynegative.Since473

deepconvectionislikelythedominantmechanismforremovinggradientsinsb,the474

coincidentalgenerationofPbydeepconvectionmayexplainwhythediffusivetermratherthan475

themeanMSEdivergencedeterminestheseasonalcycleofP-E.Moreworkinthefutureis476

neededtoconfirmourhypothesisthattheresidualcirculationisdominatedbysub-daily477

convectiveprocesses,andwhetherthesameeffectisseeninothermodels–includinghigh478

resolutionsimulationswhereconvectionisnotparameterized.ThedailyMSEdivergence479

cannotbereliablycomputedforthosemodelswhosedatahavebeeninterpolatedtofixed480

pressurelevels,whichismostoftheexperimentsusedhere.TheCAM3,CAM4,andMPAS481

modelsweretheonlytoprovidedataontheirnativeverticalgrids,andallthreeshowsimilar482

behaviorwithregardtohavingaresidualcirculationthatiscorrelatedtoP-E.483

Thediffusivenatureofthesub-dailytimescaleMSEdivergencesuggeststhatthe484

conceptofpolewardenergybeingtransportedbythezonalmeanHadleycirculation,as485

commonlyevokedtodiagnosethetropicalhydrologicalcycle,canbemisleadingatsub-486

seasonalandshortertimescales.ThattheresolvedMSEtransportlagsthephaseofP-Eis487

implicativeofthefactthatthezonalmeancirculationliketheHadleycellisaconsequenceof488

25

theclouddiabaticforcingandthecongruenthydrologicalcycle.Thisisalsoevidencedfromthe489

resolvedestimateoftheMSEfluxbythezonalmeancirculation,whichisfarofffromtheactual490

fluxforCAM4andMPAS,showingthatthedivergenceofMSEisnotwellrepresentedby491

coherentcirculationpatternsondailytoseasonaltimescales.Theessenceforunderstanding492

thetropicalcirculationandhydrologicalcycleresidesinunderstandingthecloudprocessesthat493

dominatethediabaticforcingforthelargescalecirculationinthetropics.494

495

Acknowledgments496

ThisstudyissupportedbytheU.S.DepartmentofEnergyOfficeofScienceBiologicaland497

EnvironmentalResearch(BER)aspartoftheRegionalandGlobalClimateModelingProgram.498

TheauthorswishtothankYiMingforusefuldiscussion.Weacknowledgetheuseof499

computationalresourcesoftheNationalEnergyResearchScientificComputingCenter,aDOE500

OfficeofScienceUserFacilitysupportedbytheOfficeofScienceoftheU.S.Departmentof501

EnergyunderContractNo.DE-AC02-05CH11231.ThePacificNorthwestNationalLaboratoryis502

operatedfortheDepartmentofEnergybyBattelleMemorialInstituteundercontractDE-AC05-503

76RL01830.504

505

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http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-11-00215.1.617

Stevens,B.,andCoauthors,2013:AtmosphericcomponentoftheMPI-Mearthsystemmodel:618

ECHAM6.J.Adv.Model.EarthSyst.,5,146–172,doi:10.1002/jame.20015.619

Voigt,A.,andCoauthors,2016:Thetropicalrainbeltswithanannualcycleandacontinent620

31

modelintercomparisonproject:TRACMIP.J.Adv.Model.EarthSyst.,8,1868–1891,621

doi:10.1002/2016MS000748.http://doi.wiley.com/10.1002/2016MS000748.622

——,andCoauthors,2017:Fastandslowshiftsofthezonal-meanintertropicalconvergence623

zoneinresponsetoanidealizedanthropogenicaerosol.J.Adv.Model.EarthSyst.,9,870–624

892,doi:10.1002/2016MS000902.http://doi.wiley.com/10.1002/2016MS000902.625

Voldoire,A.,andCoauthors,2013:TheCNRM-CM5.1globalclimatemodel:Descriptionand626

basicevaluation.Clim.Dyn.,40,2091–2121,doi:10.1007/s00382-011-1259-y.627

Waliser,D.E.,andN.E.Graham,1993:ConvectiveCloudSystemsandWarm-PoolSeaSurface628

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12893,doi:10.1029/93JD00872.630

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Williams,K.D.,andCoauthors,2015:TheMetOfficeGlobalCoupledmodel2.0(GC2)634

configuration.Geosci.ModelDev.,8,1509–1524,doi:10.5194/gmd-8-1509-2015.635

http://www.geosci-model-dev.net/8/1509/2015/.636

637

638

32

Table1:Listofmodelsused.639

ClimateModelLongName ShortName ReferenceCommunityAtmosphereModelversion3

CAM3 (Collinsetal.2006)

CommunityAtmosphereModelversion4

CAM4 (Nealeetal.2013)

CommunityAtmosphereModelversion5withCAM-Osloaerosols

CAM5Nor (Kirkevågetal.2013)

CentreNationaldeRecherchesMétéorologiques

CNRM-AM5 (Voldoireetal.2013)

MaxPlanckInstituteEarthSystemModelatmospherecomponent

ECHAM6.1 (Stevensetal.2013)

MaxPlanckInstituteEarthSystemModelatmospherecomponent

ECHAM6.3 (Stevensetal.2013)

InstitutPierre-SimonLaplaceatmospherecomponent

LMDZ5A (Hourdinetal.2013)

MetOfficeUnifiedModelcontrol

MetUM-CTL (Williamsetal.2015)

MetOfficeUnifiedModeldoubledentrainment/detrainment

MetUM-ENT (Williamsetal.2015)

ModelforInterdisciplinaryResearchonClimate

MIROC5 (Watanabeetal.2010)

ModelforPredictionAcrossScalesatmospherecomponent

MPAS (Skamarocketal.2012)

Idealizedgeneralcirculationmodel

CALTECH (O’GormanandSchneider2008;BordoniandSchneider2008)

640

641

33

Figures642

643

644

Figure1:Curvatureterm(κ,colors)versusP-E(contours)annualcycleaveragedovertenyears645

ofAquaControlsimulations.κhasunitsofs-2whileP-Ehasunitsofmm/dayandiscomputed646

usingequation(1)withequation(3)usedto“fill”intheequatorialregion.Thecontourinterval647

is4mm/day.648

649

34

650

Figure2:2Dhistogramofcurvatureterm,κ,[s-2]versusP-E[mm/day].Themagentalineisthe651

linearfitusingonlyvaluesofκwhereκ<0.652

653

35

654

Figure3:SeasonalP-ErateforfinalnineyearsofAquaControlusingκ-predictedP-E(black,655

color-filledcontours)comparedtoactualP-E(blackcontours).656

657

36

658

Figure4:SeasonalcycleofchangeinP-E[mm/day]foractualchange(contours)andpredicted659

change(colors).Thecontourincrementvariesfrommodeltomodel,butmatchesthecolor660

incrementsintheaccompanyingcolorbar.BlackcontoursareincreasesinP-E,whilered661

contoursdepictdecreasesinP-E.TheRMSE(abbreviatedassimply‘E’)andpatterncorrelation662

coefficient(ρ)aregiveninthetitleofeachpanel.663

664

37

665

Figure5:Patterncorrelationcoefficients(left)andRMSE(right)forannualcycleofzonalmean666

tropicalΔ(P-E)(20°S-20°N)betweentheactualandpredictedΔ(P-E).PredictedΔ(P-E)usesthe667

curvature(κ)model,sb,orthenullhypothesis.Forthecurvatureterm,“nofill”versus“fill”refer668

towhethervaluesofκarecomputedfortheequatoriallatitudesusingequation(3).RMSEhas669

unitsofmm/day.670

671

672

38

673

Figure6:Multi-modelmean(MMM)fortheκmodel(leftcolumn)andsbmodel(rightcolumn).674

ThepredictionofP-Eisinthetoprow(asinFigure3),andthepredictionofΔ(P-E)isinthe675

bottomrow(asinFigure4).676

677

39

678

Figure7:ShiftinannualaverageITCZlatitudeforactualversusκ(left)andactualversussb679

(right).TheletterscorrespondtoeachmodelintheordertheyarepresentedinTable1.680

681

40

682

Figure8:SeasonalITCZpositionfortheAqua4xCO2experimentsofTRACMIP.Blacklinesshow683

theactualITCZposition(measuredasthe(P-E)-weightedlatitudewithanexponentof10),blue684

linesrepresenttheκ-predictedITCZposition,andredlinesrepresentthesb-predictedITCZ685

position.GapsoccurwhenP-Eispredictedtobelessthanzeroacrossthetropics.Thethinlines686

representtheITCZpositionfortheAquaControlexperimentsofTRACMIP.Thethinblackline687

correspondstotheactualposition,thethinbluecorrespondstoκ-predictedITCZposition,and688

thethinredlinecorrespondstosb-predictedITCZposition.689

690

41

691

Figure9:SameasFigure5,onlysbfortheAqua4xCO2caseiscomputedusingthechangeinSST692

whileholdingRHfixed.693

694

42

695

Figure10:(a-c)TotalMSEdivergence(computedindirectlyasTOA-SFCfluxes–storage);(d-f)696

resolvedMSEdivergence;and(g-i)residualMSEdivergence.Colorsinpanelsa-iareallinW/m2.697

Contoursinpanelsa-iandm-oareP-Einmm/daywithacontourintervalof4mm/day.(j-l)The698

normalizedlatitudeoftheITCZ,maximumtotaldivergence,maximumresolveddivergence,and699

maximumresidualdivergence.(m-o)P-Epredictedusing∇2{h}(colors)vsactualP-E(contours)700

withvaluesofΓandKetakenfromtheresidualcirculationforeachcorrespondingmodel.The701

toprowpanelsareCAM3,themiddlerowpanelsareCAM4,andthebottomrowpanelsare702

MPAS.703

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