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1
Sub-cloudmoistentropycurvatureasapredictorforchangesintheseasonalcycleoftropical1
precipitation2
1BryceHarrop,1JianLu,1L.RubyLeung3
4
1AtmosphericSciencesandGlobalChangeDivision,PacificNorthwestNationalLaboratory,5
Richland,WA,USA6
7
*Correspondingauthor:BryceHarrop,phone(509)375-2696;[email protected]
9
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
33
3
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
4
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
5
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
6
differentexperiments,butwefocusononlytwo:theAquaControlandAqua4xCO299
experiments.Bothexperimentsuseafixedoceanheatfluxandaslaboceanwith30mdepth.100
AsissuggestedintheTRACMIPname,theseasonalcycleisfullyrepresentedinthemodels.101
TheaquaplanetconfigurationsfollowtheexperimentaldesignoftheAqua-Planetexperiment102
(NealeandHoskins2000)withtheexceptionsoftheslaboceaninplaceofafixedseasurface103
temperaturepatternandthefullrepresentationoftheseasonalcycle. 104
7
Table1liststhemodelsusedinthisstudy.Themodelsusedinthisstudyareasubsetof105
thetotalTRACMIPsuite;onlythosemodelsthathaveallofthevariablesneededtocalculate106
dailysub-cloudmoistentropyareusedhere.Eachmodelprovidestenyearsofdailyoutput,107
whichisusedfortheanalysesinthefollowingsections.108
109
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
8
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
9
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
10
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
11
to“fill”theequatorialregionisconsistentwiththecurvaturetermdefinedinequation(1).In192
otherwords,predictingP-Eintheequatorialregiondoesnotsignificantlyimproveordegrade193
theoverallpredictiveskill.194
195
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
12
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
14
( )( ) ( ) ( )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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638
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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