Responses of terrestrial aridity to global warming Qia - PDF document

Responsesofterrestrialariditytoglobalwarming QiangFu 1,2 andSongFeng 3 1 CollegeofAtmosphericSciences,LanzhouUniversity,Lanzhou,China, 2 DepartmentofAtmosphericSciences,Universityof Washington,Seattle,Washington,USA, 3 DepartmentofGeosciences,UniversityofArkansas,Fayetteville,Arkansas,USA Abstract Thedrynessofterrestrialclimatecanbemeasuredbytheratioofannualprecipitation( P )to potentialevapotranspiration(PET),wherethelatterrepresentstheevaporativedemandoftheatmosphere, whichdependsonthesurfaceairtemperature,relativehumidity,windspeed,andavailableenergy.Thisstudy examineshowtheterrestrialmeanaridityrespondstoglobalwarmingintermsof P/ PETusingtheCoupled ModelIntercomparisonProjectphase5transientCO 2 increaseto2×CO 2 simulations.Weshowthatthe (percentage)increase(rate)in P averagedoverlandis~1.7%/°Coceanmeansurfaceairtemperatureincrease, whiletheincreaseinPETis5.3%/°C,leadingtoadecreasein P /PET(i.e.,adrierterrestrialclimate)by~3.4%/°C. Notingasimilarrateofpercentageincreasein P overlandtothatinevaporation( E )overocean,weproposea frameworkforexaminingthechangein P/ PET,inwhichwecomparethechangeinPEToverlandand E overocean,bothexpressedusingthePenman – Monteithformula.Weshowthatadrierterrestrialclimateis causedby(i)enhancedlandwarmingrelativetotheocean,(ii)adecreaseinrelativehumidityoverlandbutan increaseoverocean,(iii)partofincreaseinnetdownwardsurfaceradiationgoingintothedeepocean,and (iv)differentresponsesofPEToverlandand E overoceanforgivenchangesinatmosphericconditions (largelyassociatedwithchangesintemperatures).Therelativecontributionstothechangeinterrestrialmean aridityfromthesefourfactorsareabout35%,35%,15%,and15%,respectively.Theslightslowdownofthe surfacewindoverbothlandandoceanhaslittleimpactontheterrestrialmeanaridity. 1.Introduction Thedrynessofterrestrialclimatecanbemeasuredintermsofanaridityindexthatisde
nedbytheratio ofannualprecipitation( P )toannualpotentialevapotranspiration(PET)[ MiddletonandThomas ,1992].The PETistheevaporativedemandoftheatmosphere,indicatingthemaximumamountofevaporationone wouldget,inagivenclimate,fromawell-wateredsoilvegetationsurface[ Arya ,2001].Thetrueevaporation ( E )overlandthatusuallyre  ectstheamountofwatersupply(e.g.,precipitation)willbelessthanthePET unlessthesoilissaturatedwithwater.The P/ PETratioisthusaquantitativeindicatorofthedegreeof waterde
ciencyatagivenlocation,whichmaybenearzeroindesertbutcanexceedunityinwetclimate. UndertheUnitedNationsConventiontoCombatDeserti
cation[ UnitedNationsConventiontoCombat Deserti
cation ,1994]classi
cation,drylandsarecharacterizedby P/ PET 0.65andarefurtherdivided intohyperarid( P/ PET 0.05),arid(0.05 P/ PET 0.2),semiarid(0.2 P/ PET 0.5),anddrysubhumid (0.5 P/ PET 0.65)regions[ Mortimore ,2009; Hulme ,1996; MiddletonandThomas ,1992].Knowledgeof howanthropogenicclimatechangewillaffecttheterrestrialaridityisessentialforwaterresourceandland usemanagements,especiallyoverdrylandregions[e.g., Mortimore ,2009; Reynoldsetal .,2007; Fu ,2008; Fu andMa ,2008; OverpeckandUdall ,2010]. Byanalyzingclimatemodelsimulationsfortheperiod1948 – 2100, FengandFu [2013]showthatthe P/ PET decreasesinmosttropicalandmidlatitudelandregionsastheEarthwarms.Thisdryingwouldleadto theworld ’ sdrylandstobecome5.8×10 6 km 2 (or10%)largerthanthecurrentclimatologybytheendof thiscenturyunderahighgreenhousegasemissionscenario(RepresentativeConcentrationPathway 8.5(RCP8.5)).ThemajorexpansionofaridregionswouldoccuroversouthwesternNorthAmerica,the northernfringeofAfrica,southernAfrica,andAustralia,whilemajorexpansionsofsemiaridregionswould occuralongthenorthcoastoftheMediterranean,southernAfrica,andpartsofNorthandSouthAmerica [ FengandFu ,2013].Anincreaseinaridityandexpansionofdrylandsinresponsetoglobalwarmingwill increasethefractionoftheworld ’ spopulationaffectedbywaterscarcityandlanddegradation.The21st centurydryingisalsoshownby Cooketal .[2014]. FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 1 PUBLICATION S JournalofGeophysicalResearch:Atmospheres RESEARCHARTICLE 10.1002/2014JD021608 KeyPoints:  Theresponseofterrestrialaridityto globalwarmingintermsofP/PET  AdecreaseinP/PET(i.e.,adrier terrestrialclimate)by~3.4%/°C  ExaminetheP/PETchangeby comparingchangesinPEToverland andEoverocean Correspondenceto: Q.Fu, qfuatm@gmail.com Citation: Fu,Q.,andS.Feng(2014),Responses ofterrestrialariditytoglobalwarming, J.Geophys.Res.Atmos. , 119 ,doi:10.1002/ 2014JD021608. Received4FEB2014 Accepted10JUN2014 Acceptedarticleonline13JUN2014 ClimatemodelsrobustlypredictanincreaseinglobalmeanprecipitationinresponsetoaCO 2 increase [ Mitchelletal .,1987; AllenandIngram ,2002; HeldandSoden ,2006; LambertandWebb ,2008; StephensandEllis , 2008; PendergrassandHartmann ,2014].Theprojectedincreaserateis~1.4%°C
1 ,withrespecttoglobal meansurfacetemperatureincreaseduetoatransientCO 2 doubling,andhasbeenattributedtoan atmosphericenergybudgetconstraint[e.g., AllenandIngram ,2002; PendergrassandHartmann ,2014].Here wequantifythechangeofterrestrialmean P/ PETduetoatransientCO 2 increaseanddiscusstheunderlying physicalprocessesresponsibleforit. Globalmeanannualprecipitationandevaporationmustremainequalsincetheatmosphereisasmall reservoirforwater.Assumingasimilarincreaseinterrestrialmeanprecipitationtothatoverocean, Sherwood andFu [2014]arguethatthePETwillincreasemuchfasterthan P inresponsetoglobalwarming,leadingto drierconditionsoverlandinthefuture.Thisisbecauselandsurfaceswarmabout50%morerapidlythan oceans[e.g., Manabeetal .,1992; Joshietal .,2008],andrelativehumidityonaveragedecreasesoverland butincreasesoverocean[ Simmonsetal .,2010; IntergovernmentalPanelonClimateChange ( IPCC ),2013]. ScheffandFrierson [2014]examinedthechangesinPET
eldscalculatedfromtheoutputsoftheglobal climatemodelsparticipatinginthephase5oftheCoupledModelIntercomparisonProject(CMIP5)[ Taylor etal .,2012]between2081 – 2099fromtheRCP8.5scenarioand1981 – 2099fromthehistoricalruns.They showedthatthe%changeinlocalannualmeanPETisalmostalwayspositive,onaverageinthelowdouble digitsintermsofmagnitude,usuallyincreasingwithlatitude.Theincreaseisdominatedbythedirect, positiveeffectsofwarmingatconstantrelativehumidity.However,therateofpercentagechangeofterrestrial mean P/ PETwithrespecttotemperatureincreaseduetoatransientCO 2 increaseanditspartitioningtochanges inrelevantmeteorologicalvariableshasnotbeenquanti
edanddocumentedbefore. Thispaperexaminesthechangeof P/ PETinthe1%increaseinCO 2 untilthedoubledscenariofromthe CMIP5globalclimatemodels(GCMs).Section2describesthemethodsanddatausedinthisstudy.The changesin P and E overbothlandandoceanandPETand P/ PEToverlandarepresentedinsection3. Thecausesofthechangein P/ PETareexaminedinsection4,followedbythesummaryandconclusions insection5. 2.MethodsandData 2.1.ThePETAlgorithm WecalculatedthePETusingthePenman – Monteithalgorithm[ Maidment ,1993; Allenetal .,1998]that includestheeffectsofavailableenergy( R n
G ,where R n isthenetdownwardradiationand G istheheat  ux intotheground),surfaceairtemperature( T a ),relativehumidity(RH),andwindspeed( u ).ThePenman – MonteithalgorithmwasrecommendedbytheFoodandAgricultureOrganizationasthestandardmethod forcomputingthePET[ Allenetal .,1998].Thisalgorithmcanbewrittenintheform[ Allenetal .,1998; Scheff andFrierson ,2014] PET ¼ R n
G ðÞ
T a ðÞþ
a c p e  T a ðÞ 1
RH ðÞ C H u jj
T a ðÞþ  1 þ r s C H u jj ðÞ = L v ; (1) where e *isthesaturatedwatervaporpressure,
= de*/dT ,
a isthesurfaceairdensity, c p isthespeci
c heatofair, C H isthebulktransfercoef
cient, r s isthebulkstomatalresistanceunderwell-wateredconditions, L v isthelatentheatofvaporizationforwater,  =( c p p s )/( 0 . 622L v ),where p s isthesurfacepressure,and u isthe windat2mabovethesurface. Equation(1)isderivedfromthestandardbulkformulaeforthesensibleheat(SH)andlatentheat(LH)  uxes alongwiththesurfaceenergybudgetequationintheforms SH ¼
a c p C H T s
T a ðÞ u jj ; (2) LH ¼
a L v C H q  T s ðÞ
q  T a ðÞ RH ðÞ u jj = 1 þ r s C H u jj ðÞ ; (3) R n
G ¼ SH þ LH ; (4) where T s isthetemperatureatthesurfaceinterface,LH=PET* L v ,and q *isthesaturatedwatervapormixing ratio(i.e.,0.622 e */ p s ).Inequation(3),thewatervaporatthesurfaceinterfaceisassumedtobesaturated. Equation(3)indicatesthatPETisdeterminedbythevaporpressurede
cit,i.e., e * ( T s )
e * ( T a )RH,andthe surfacewind. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 2 ThePenman – Monteithalgorithmisphysicallybasedandissuperiortoempiricallybasedformulations thatusuallyonlyconsidertheeffectoftemperature[ Donohueetal .,2010; Dai ,2011; Shef
eldetal .,2012]. InthecalculationsofPETinthispaper,weuseda r s of70s/manda C H of4.8×10
3 [ Allenetal .,1998]. Scheff andFrierson [2014]usedequation(1)withsimilar r s and C H values. Theactualevaporation( E )overoceancanbeconsideredasthepotentialevaporationoverwater.Since equations(2) – (4)arevalidoverwaterbysetting r s =0,weusedequation(1)tocalculatetheactual evaporation( E )overoceanwith r s =0.Additionally,weuseda C H of1.5×10
3 overocean[ RichterandXie , 2008;I.Richter,personalcommunication,2014].Wewillcomparethe E anditschangeoveroceanas obtainedfromthePenman – Monteithalgorithmwiththeircounterpartsobtaineddirectlyfromthemodels. Aswewilldiscusslater,thisisaveryusefulapproachthatpermitsustoplacePEToverlandand E over oceaninthesameframeworkasabasisforinterpretingthechangesofterrestrialmeanaridityinresponseto globalwarming. InthecalculationofPEToverland( E overocean)usingequation(1),weusedtheactualLH+SHto replace R n
G [ ScheffandFrierson ,2014].AlhoughtheactualLHandSHoverlandforthegiven R n
G are differentfromthosederivedfromequations(2) – (4),whereasaturatedwatervaporisassumedatthe surface,theirsummationsarethesamefollowingequation(4).Finally,thechangeinthesurfacestability (i.e., T a
T s )overoceancanbederivedinthePenman – Monteithframework,whichwillalsobecompared withthatobtaineddirectlyfromtheCMIP5models. 2.2.CMIP5Data Weusedtheoutputfromthe25globalclimatemodels( Table1)thatparticipate dintheCMIP5transient CO 2 1%/yrincrease(1pctCO 2 )experiments[ Tayloretal .,2012].The1pcCO 2 experimentisdesignedto diagnosetransientcli materesponseto1%yr
1 CO 2 increase,whichisinitializedfromthemulticentury preindustrialquasi-equilibriumcontrolsimulat ions.Themodelswereintegratedfor140years,but onlythe
rst70yearsofthedatawereanalyzedinourstudy.Formodelswithmultiple-ensemble simulations,the
rstensemblerunwasused.Thechangewa stakenasthedifferencebetweenthe averagesfortheyears61 – 70and1 – 10ofthesimulations,wheretheyear70correspondstothetimeof Table1. AListofCMIP5GCMsUsedinThisStudy ModelNameOrigin ACCESS1.0CommonwealthScienti
candIndustrialResearch,Australia ACCESS1.3CommonwealthScienti
candIndustrialResearch,Australia CanESM2CanadianCentreforClimate,Canada CCSM4NationalCenterforAtmosphericResearch,USA CESM1-BGCNationalCenterforAtmosphericResearch,USA CMCC-CMCentroEuro-MediterraneoperiCambiamenti,Italy CNRM-CM5CentreNationaldeRecherchesMeteorologiques,France CNRM-CM5-2CentreNationaldeRecherchesMeteorologiques,France CSIRO-Mk3.6CommonwealthScienti
candIndustrialResearch,Australia GFDL-CM3GeophysicalFluidDynamicsLaboratory,USA GFDL-ESM2GGeophysicalFluidDynamicsLaboratory,USA GFDL-ESM2MGeophysicalFluidDynamicsLaboratory,USA GISS-E2-HNASAGoddardInstituteforSpaceStudies,USA GISS-E2-RNASAGoddardInstituteforSpaceStudies,USA HadGEM2-ESMetOf
ceHadleyCentre,UK INM-CM4InstituteforNumericalMathematics,Russia IPSL-CM5A-LRInstitutPierre-SimonLaplace,France IPSL-CM5A-MRInstitutPierre-SimonLaplace,France IPSL-CM5B-LRInstitutPierre-SimonLaplace,France MIROC5AtmosphereandOceanResearchInstitute,Japan MIROC-ESMJapanAgencyforMarine-EarthScienceandTechnology,Japan MPI-ESM-LRMaxPlanckInstituteforMeteorology,Germany MPI-ESM-MRMaxPlanckInstituteforMeteorology,Germany MPI-ESM-PMaxPlanckInstituteforMeteorology,Germany MRI-CGCM3MeteorologicalResearchInstitute,Japan JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 3 CO 2 doubling.Notethatonlythe changeintheCO 2 isconsideredinthe 1pcCO2experiment,whiletheRCP scenarioexperimentconsideredthe changesinlanduse,aerosols,CO 2 ,as wellasothergreenhousegases. Inthisstudy,wede
nethelandasthe terrestrialregionsbetween60°Sand 90°N,whichcovers26.5%oftheglobe. Wewillpresentresultsaveragedover land,ocean,andovertheglobe.The oceancovers70.8%oftheglobe,and theremaining2.7%oftheglobe isAntarctica. Theensemblemeanofthe25models usedinthisstudyshouldbeinterpreted asourbestestimateofclimateresponse totheCO 2 increase.Incontrast,the individualensemblememberssimulate randominternalvariationsofthe climatesystem,andtheycontainbiases inherentinindividu almodels.Herewe use1standarddeviationofthe25 modelsasameasureofuncertainties associatedwithnaturalvariationsand modelerrors. Table2showstheannualmeanvaluesof the
rst10yearsfor P , E ,PET, T a ,RH, u , R n
G , R n , R n , s ,and R n , L ,averagedover land,ocean,andtheglobefromthe ensemblemeanofthe25CMIP5models. Thenumbersintheparentheses indicatethe1standarddeviationofthe 25modelresults.Asexpected,theglobal Table2. AnnualMeanValuesintheFirst10YearsoftheTransientCO 2 IncreaseSimulations(1pctCO 2 )AveragedOver Land,Ocean,andGlobeFromtheEnsembleAverageof25CMIP5GCMs(TheNumbersintheParenthesesIndicate1 StandardDeviationofthe25ModelResults) a LandOceanGlobeGlobe(obs) P (mm)870(90)1194(55)1083(55)1124(128) E (mm)604(60)1300(62)1083(55)1124(128) PET(mm)1112(66)notapplicable(NA)NANA T a (°C)12.2(1.0)15.7(0.6)13.5(0.6)13.8 RH(%)66.8(3.3)81.0(3.7)77.3(3.0)77.7 u (m/s)3.1(0.5)7.1(0.5)6.0(0.5)3.8 R n
G (W/m 2 )85.4(5.3)118.1(4.5)106.0(4.0)112(12) R n (W/m 2 )86.2(5.4)119.0(3.9)106.8(3.6)112.6(12) R n , s (W/m 2 )159.0(7.3)174.9(4.3)167.1(3.5)165(7) R n , L (W/m 2 )
72.7(6.6)
55.9(3.7)
60.3(3.8)
52.4(10) a Thequantitiesincludeprecipitation( P ),evaporation( E ),potentialevapotranspiration(PET),near-surfaceairtempera- ture( T a ),relativehumidity(RH),surfacewindspeed( u ),availableenergy( R n
G ),netdownwardradiation( R n ),net downwardsolarradiation( R n , s ),andnetdownwardlong-waveradiation( R n , L ).Observedglobalmeanquantitiesare alsoshownforthecomparison: Ta ,RH,and u arefromNationalCentersforEnvironmentalPredictionreanalysisduring 1961 – 1990,andothersarefrom Stephensetal .[2012],withtheobservationaluncertaintiesintheparentheses. Figure1. Temporalvariationsofannualmean(a)precipitation( P ), (b)potentialevapotranspiration(PET),and(c)aridityindex( P /PET) averagedoverland(Thearidityindexshownhereistheannualmean P averagedoverlanddividedbyannualmeanPETaveragedoverland). Theblacklinesaretheensembleaverageofthe25CMIP51pctCO 2 simulations,andthegreyshadingdenotes1standarddeviationofthe 25models.Theunitsareinpercentageanomaliesrelativetotheaver- agedvaluesofthe
rst10years. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 4 meanprecipitationandevaporation arethesameandareequivalent toalatentheat  ux(i.e., L v P )of 84.8Wm
2 .Notethattheglobalmean precipitation(latentheat  ux), R n
G , sensibleheat  ux(i.e., R n
G
LH), andnetdownwardradiation,aswellas itsshort-waveandlong-wave components,agreewellwiththe observationswithinobservational uncertainties(Table2).Thesimulated T a andRHvaluesagreewellwith thosefromthereanalysis,while thesimulatedglobalmeansurface windspeedislargerthanthatfrom thereanalysis. Thepercentagechangesinvarious surfacevariables(e.g.,mean precipitationoverland)fromeach modelarescaledbythechangein surfaceairtemperatureaveraged overocean,whichde
nestherateof percentagechange.Weusetheocean meansurfaceairtemperature increaseratherthantheglobalmean temperatureincreaseforscaling becausethechangeinlandsurfaceair temperatureislargelydeterminedby thatoverocean[e.g., Manabeetal ., 1992; Joshietal .,2008].Theuseofthe oceanmeansurfaceairtemperature changeforscalingalsohelpsfacilitate theinterpretationofthe P /PET changesintermsoftheevaporation overocean. 3.Changesof P , E ,PET,and P /PET 3.1.TemporalVariationsin P ,PET,and P /PETandSpatialPatternsoftheChanges Figure1showsthetimeseriesofannualmean P ,PET,and P /PET,averagedoverland,inunitsofpercentage anomalieswithrespecttoaveragedvaluesofthe
rst10years.Weseeincreasesin P andPETbuta decreasein P /PETduetoanincreaseinCO 2 concentrationintheatmosphere.Anincreasein P cannotkeep pacewiththeincreasingPET,causingadecreasein P /PET(Figure1). Figure2showstheglobaldistributionsofthepercentagechangesin P ,
PET,and P /PETbetweenthe years61 – 70and1 – 10.Notethatthesummationofpercentagechangesin P and
PETisapproximatelyequal tothepercentagechangein P /PET(seeequation(5)).ThespatialpatternsshowninFigure2areverysimilarto thoseofthechangesin P ,PET,and P /PETattheendofthe21stcenturyrelativetocurrentclimate,from theCMIP5scenarioRCP8.5simulations[see FengandFu ,2013,Figures7and8].Oneimportantdifferenceis thattheareaofprecipitationdecreaseneartheMediterraneanSea,associatedwiththeCO 2 increase only(Figure2a),issigni
cantlylarger(extendingmoreeastandsouth)ascomparedwiththatduetochanges innotonlyCO 2 butalsoaerosols,landsurface,ozone,andothergreenhousegasesinRCP8.5.Thisleadstoa largerdryingareaovernorthernAfricaandAsia(Figure2c). Figure2. Globaldistributionsofpercentagechanges(%)in(a) P ,(b)
PET, and(c) P /PETtakenasthedifferencebetweentheaveragesfortheyears 61 – 70and1 – 10oftheCMIP51pctCO 2 simulations( P /PETiscalculatedas theaveraged P dividedbyaveragedPET).Gridpointsarestippledwhen morethan80%ofthe25modelsagreeonthesign. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 5 3.2.RatesofChangein P , E ,PET, and P /PET Beforepresentingtheratesofchange in P , E ,PET,and P /PET,Figure3 showstheocean T a changes (Figure3a)andtheratioof T a changes overlandandocean(Figure3b)from theindividualmodels.Theensemble meanocean T a increasesby1.39°C, withastandarddeviationof0.28°C, whilethemeanlandtooceanratiois 1.59,withastandarddeviationof0.13. Theglobalmean T a increaseper°C ocean T a increaseis1.16witha standarddeviationof0.03(notshown). Figure4showsthepercentagechange ratesinannualmeanprecipitation (left)andevaporation(right)averaged overland,ocean,andtheglobe. Themultimodelensemblemean precipitationchangeratesoverland andoceanareboth~1.65%/°C, supportingthestatementof Sherwood andFu [2014]thatthemean precipitationoverlandandocean changessimilarly.Notethatthe intermodeldifferencesaresigni
cantlylargerforland P changes,whichre  ectsalargerinterannual variabilityin P overland(notshown).Alternatively,theglobalmean P changescaledbytheocean T a change(i.e.,1.66%/°C)canberescaledastheglobalmean P changedividedbytheglobalmean T a change:1.66%/°C/1.16=1.43%/°C,whichisconsistentwithpreviousstudies[e.g., PendergrassandHartmann , 2014].Asfor P ,land E changesshowlargerintermodeldifferencesthanocean E .Themultimodelmeanvalue forland E changesissmallerthanthatforocean E .Figure4showsthattherateofpercentagechangeof ocean E isverysimilartothoseofboth landandocean P ,indicatingthatthe averaged P changesoverbothlandand oceanarelargelyconstrainedbythe evaporationoverocean. Figure5showstheratesofpercentage changeinannualmeanPET(middle)and P /PET(right)overland.Thechangeratein P isalsoshowninFigure5(left)foradirect comparison.Themultimodelensemble meanrateis5.3%/°CforPET,whichismuch largerthantherateofincreaseof precipitation.Allmodelsprojectadrier futureclimateoverland[ FengandFu , 2013; Cooketal .,2014].Themultimodel meanchangerateinthearidityindexis
3.4%/°C.Figure5indicatesthatalthough landonaveragewillgetmoreprecipitation inawarmingclimate,itwillnotget enoughtokeeppacewiththegrowing evaporativedemand,leadingtoadrier Figure3. (a)Thechangeofsurfaceairtemperature( T a )averagedover ocean,takenasthedifferencebetweentheaveragesfortheyears61 – 70and 1 – 10oftheCMIP51pctCO 2 simulations,versusindividualmodels.(b)The changeofsurfaceairtemperature( T a )averagedoverlandscaledbyocean meansurfaceairtemperaturechange.Themultimodelensemblemeanvalue alongwithitsstandarddeviationandrangeisshownineachpanel. Figure4. Percentage(%)changesin(left)annualmean P and(right) evaporation( E )averagedoverland,ocean,andglobe,scaledby oceanmeansurfaceairtemperatureincreases(°C)fromtheCMIP5 1pctCO 2 simulations.Theresultsareplottedwithboxandwhisker diagramsrepresentingpercentilesofchangescomputedfromthe 25models.Thecentralline(blackdot)withineachboxrepresentsthe median(mean)valueofthemodelensemble.Thetopandbottomof eachboxshowsthe75thand25thpercentiles,andthetopand bottomofeachwhiskerdisplaythe95thand5thpercentilevaluesin theensemble,respectively. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 6 terrestrialclimate[ SherwoodandFu ,2014]. Below,wewillexaminetheeffectsofchangesin varioussurfacemeteorologicalvariablesincluding surfaceairtemperature,relativehumidity,wind speed,andavailableenergyonthe P /PETchanges. 4.Attributionsof P /PETChanges OverLand Thepercentagechangein P /PETcanbewritten inthefollowingform[ FengandFu ,2013]:
P PET
 = P PET


P P

PET PET : (5) Approximatingthepercentagechangein P over landwith E overocean,equation(5)becomes
P PET
 = P PET


E E
 Ocean

PET PET : (6) Sincetheactualevaporationoveroceanisthesameasthepotentialevaporationthere,whichcanalso bederivedusingthePenman – Monteithalgorithm,wecanexaminethechangein P /PETintheframeworkof thePETbycomparingitschangesoverlandandocean(seeequation(6)).Table3showsthatthe E andits changeoveroceanfromthePenman – Monteithalgorithmareconsistentwiththoseobtaineddirectlyfrom theGCMs. SherwoodandFu [2014]arguethatthedifferencesbetween
PET PET and
E E  Ocean arelargelycausedbythe enhancedwarmingoverlandrelativetooceanaswellastherelativehumiditychangesoverlandandocean withoppositesign.Herewequantifytheseeffectsaswellastheeffectsofchangesinwindspeedand availableenergyatthesurface.Beforedoingso,we
rstpresentthechangesinrelevantsurface meteorologicalvariablesoverlandandthoseoverocean. 4.1.Changesin T a ,RH, u ,and R n
G OverLandandOcean Theratesofchangein T a ,RH, u ,and R n
G overlandandoceanareshowninFigure6.Therateofchange insurfaceairtemperatureoveroceanisonefollowingthede
nition. TheGCMssuggestthat T a overlandincreases~60%fasterthan T a overoceanwithsmallmodel-to-model differences(Figure6,left).Thisphenomenoniswelldocumentedanddiscussedinliteratures[e.g., Manabe etal .,1992; Joshietal .,2008; ByrneandO ’ Gorman ,2013].AlargerwarmingwouldleadtoalargerPET increase[ FengandFu ,2013; ScheffandFrierson ,2014].Therefore,thereisalargerincreaseinPEToverland thantheincreasein E overoceanduetothedirecttemperatureeffects. TheRHoverlanddecreasesinalmostalltheGCMswithameanvalueof
0.76%/°C,whileitincreasesinall theGCMsoveroceanwithameanvalueof0.27%/°C(Figure6,middleleft).Previousstudiesalsoshowa decreaseinRHoverlandandanincreaseoveroceanfrombothmodelsimulationsandobservations [ RowellandJones ,2006; RichterandXie ,2008; Simmonsetal .,2010; O ’ GormanandMuller ,2010].SincePET Figure5. Percentage(%)changesinthe(left)annualmean P , (middle)PET,and(right) P /PETaveragedoverland,scaledby oceanmeansurfaceairtemperatureincreases(°C)fromthe CMIP51pctCO 2 simulations.Theresultsareplottedwithbox andwhiskerdiagramsasde
nedinFigure4. Table3. ComparisonofAnnualMeanEvaporation( E )andItsPercentageChangeRateandSurfaceStability( T a
T s ) ChangeRateOverOceanEstimatedUsingthePenman – MonteithAlgorithmandThoseDirectlyFromtheGCMs a E (mm)PercentageChangeRatein E (%/°C)ChangeRatein T a
T s (°C/°C) Penman – Monteith1267(90)1.92(0.39)0.07(0.03) DirectlyfromtheGCMs1300(62)1.71(0.40)0.06(0.02) a Theensemblemeanvaluesalongwith1standarddeviation(thenumbersintheparentheses)ofthe25modelresults areshown. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 7 increaseswithdecreasingRH(seeequation(1)),thechangesinRHoverland(ocean)wouldresultinan increase(adecrease)ofPET( E )overland(ocean),leadingtoalargerdifferencebetweenlandPETandocean E .NotethatthemultimodelmeanvalueoftheglobalmeanRHchangesisnear0(notshown). Themeanratesofchangeofsurfacewindspeedsoverlandandoceanareboth
0.004m/s/°C(Figure7, middleright).Therefore,theyshouldhavelittleeffectonthechangesofPEToverlandand E overocean. ThechangesofPEToverlandand E overoceanarethenlargelycausedbythechangesinthevapor pressurede
citthatarethusabout5.3%/°Coverlandand1.7%/°Coverocean.Itisinterestingtonoticethat thereisasigni
cantdecreaseinobservedsurfacewindspeedsglobally[ McVicaretal .,2012].Forexample, about40%decreaseinsurfacewindwasreportedinthelast4decadesoverIndia[ Padmakumarietal ., 2013].Aerosolscouldcausethedecreaseofsurfacewind[ Yangetal .,2013].Understandingofobserved changesinsurfacewindanditsimpactonthePET( E )arebeyondthescopeofthepresentstudybutwillbe addressedinourfutureresearcheffort. PETisproportionaltotheavailableenergy( R n
G ).Theratesofchangeof R n
G overlandandoceanare showninFigure6(right).Themultimodelmeanvalueis1.47W/m 2 /°Coverlandand0.78W/m 2 /°Cover ocean.Therefore,thechangein R n
G mayalsocontributetoalargerincreaseinPEToverlandthan E over ocean.BycomparingthenetdownwardradiationchangesinFigure7(left)withthe R n
G changesin Figure6(right),wenotethatthereisanear-zero G changeoverlandbutarateofchangeof~1.0W/m 2 /°C overocean.Despitetheslightlysmaller R n increaseoverlandthanoverocean(Figure7,left),thereisalarger increasein R n
G overland,becausepartoftheincreasednetdownwardradiationattheoceansurfaceis transportedtodeepocean[ Hansen etal .,2005; Johnsonetal .,2011; Loeb etal .,2012; Stephensetal .,2012]. Itisalsointerestingtonotethatthereis anincreasein R n , s overlandbuta decreaseoverocean,althoughbothare statisticallyinsigni
cant(Figure7, middle).Thereisasigni
cantincrease in R n , L overbothlandandocean,and theincreaseoverlandissmaller (Figure7,right).Theatmospheric warmingduetoCO 2 leadstomoreH 2 O intheatmosphere.Theincreaseofboth CO 2 andH 2 Ocauseslargerdownward surfaceinfraredradiation.Asmaller R n , L butalarger R n , s overlandthanthose overoceanindicateadecreaseincloud fractionoverlandrelativetothat overocean. Figure6. Changesin(left) T a ,(middleleft)relativehumidity(RH),(middleright)windspeed( u ),and(right)availableenergy ( R n
G )averagedoverlandandocean,scaledbyoceanmeansurfaceairtemperatureincreases,fromtheCMIP51pctCO 2 simulations.Theresultsareplottedwithboxandwhiskerdiagramsasde
nedinFigure4. Figure7. Changesin(left)netdownwardradiation( R n ),(middle)netdown- wardshort-waveradiation( R n , s ),and(right)netdownwardlong-wave radiation( R n , L )averagedoverlandandocean,scaledbyoceanmeansur- faceairtemperatureincreases,fromtheCMIP51pctCO 2 simulations.The resultsareplottedwithboxandwhiskerdiagramsasde
nedinFigure4. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 8 Theevaporationchangeoveroceancorrespondstoachangeof1.73Wm
2 /°Cintermsoflatentheat  ux. Notingthechangeof0.78Wm
2 /°Cin R n
G orSH+LH,wehaveachangeof
0.95Wm
2 /°CinSHover ocean.Usingequation(2),weobtainarateofchangeof0.07°C/°Cfor T a
T s ,whichisconsistentwiththat obtaineddirectlyfromtheGCMs(Table3). RichterandXie [2008]showthatoceansurfaceevaporation increasesby2%/°Cofsurfacewarming,ratherthanthe7%/°Cratesimulatedforatmosphericmoisture, becauseoftheincreaseinsurfacerelativehumidityandsurfacestabilityandthedecreaseinsurfacewind speed.IntheframeworkofthePenman – Monteithalgorithm,thechangein T a
T s alongwith E ,scaledby the T a change,ispredictedbythechangesinavailableenergy,surfacewind,andrelativehumidity. 4.2.EffectsofChangesin T a ,RH, u ,and R n
G Upon P /PET Usingequation(1)tocalculatetheevaporationoverocean,weobtainarateofpercentagechangeof ~1.9%/°Cintheannualmeanevaporationoverocean(Table3),similartothatobtaineddirectlyfrommodels. Hereweemployequation(1)toquantifytheindividualcontributionsofchangesintemperatures,relative humidity,windspeed,andavailableenergytothetotalpercentagechangesinPEToverland, E overocean, andultimately P /PEToverland.Forexample,inordertoisolatetheeffectofthetemperaturechangeon PEToverland,wecalculatethePETusing T inthelast10yearsbutRH, u ,andSH+LHfromthe
rst10years andcompareitwithPETusingtheinputsfromthe
rst10years.SeeAppendixAforthedetailsonthe methodofderivingtheindividualcontributions. Thesecond(third)columnofTable4showsthatthechangeinPET( E )overland(ocean)isdominatedbythe changeintemperatures,whilethechangesinRHandavailableenergyalsomakeappreciablecontributions [ ScheffandFrierson ,2014].(Thenumbersintheparentheseswillbediscussedlater.)Theincreasein temperaturesresultsinalargerPEToverlandandalarger E overocean(seesecondrowinTable4),butthe formerismorethantwiceaslargeasthelatter.Thisisbecauseoftheenhancedwarming(60%)overland relativetothatoveroceanandalsopartlybecausethe E overoceanislesssensitivetotemperaturewhen r s =0.0[ ScheffandFrierson ,2014]. Thedecrease(increase)inRHoverland(ocean)resultsinanincrease(decrease)inPET( E )(seethethirdrowin Table4)andhencealargerdifferencebetweenPETand E .Theincreaseinavailableenergyoverbothlandand oceanincreasesPEToverlandand E overocean(seethe
fthrowinTable4).However,theincreasein availableenergyoverocean,andthus E ,issmallerbecausepartofdownwardradiationistransported downwardintothedeepocean(section4.1).Surfacewindspeedchangeslittleandthusmakeslittle contributiontothechangeofterrestrialmeanaridity(seethefourthrowinTable4). Thenetcontributionsfromindividualsurfacemeteorologicalvariables(i.e., T a ,RH, u ,and R n
G )tothe changesin P /PETarethedifferencesbetweenthethirdandsecondcolumnsfollowingequation(6),which areshowninthefourthcolumninTable4.Intermsofthetotalchangeratein P /PET,theycorrespond torelativecontributionsof53%,37%,1%,and8%,respectively(seethe
fthcolumninTable4).Note thatthesecontributionsarenotonlydeterminedbythecontrastingchangesoverlandandoceanin surfacemeteorologicalvariablesbutalsoareaffectedbythecoef
cientsandbackgroundatmospheric Table4. EffectsofSurfaceAirTemperature( T a ),RelativeHumidity(RH),WindSpeed( u ),andAvailableEnergy ( R n
G )onthePercentageChangeRatesinPotentialEvapotranspiration(PET)OverLand,Evaporation( E )Over Ocean,and P /PETOverLand,EstimatedUsingthePenman – MonteithAlgorithmBasedon25CMIP51pctCO 2 Increaseto2×CO 2 Simulations a PET(%/°C) E (%/°C) P/ PET(%/°C) RelativeContributiontothe Total P/ PETChange(%) T a 3.481.68(2.19,
0.51)
1.80(
1.29,
0.51)53(38,15) RH0.95
0.31(
0.34,0.03)
1.26(
1.29,0.03)37(38,
1) u
0.03
0.06(
0.03,
0.03)
0.03(0.0,
0.03)1(0,1) R n
G 0.880.62(0.47,0.15)
0.26(
0.41,0.15)8(12,
4) Total5.281.92(2.29,
0.37)
3.36(
2.99,
0.37)100(89,11) a Thepercentagechangein P /PETisapproximatedbyequation(6).The
rstnumberinparenthesesgivesthechange basedonthePenman – Monteithalgorithmusingthelandcoef
cientsandbackgroundatmosphericconditions,while thesecondoneistheeffectofdifferencesincoef
cientsandbackgroundconditionsbetweenlandandocean.See thetextandAppendixAforthedetailsonthemethods. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 9 conditionsusedinthePenman – Monteithequation,whichaffectthesensitivityofPET( E )tothechanges inthesevariables. The
rstnumberintheparenthesisofthethirdcolumninTable4isthesecondcolumnscaledby
x O /
x L , where
x O and
x L arethechangesinthecorrespondingsurfacevariablesfromthemultimodelensemble meansoveroceanandland,respectively.Wehave
x O /
x L =0.628,
0.355,1.0,and0.531forchangesin T a , RH, u ,andSH+LH,respectively.Forexample,wehave3.48×0.628=2.19.Theythuscanbeconsideredas the E changesoveroceanfromthePenman – Monteithalgorithmusingthelandcoef
cients( r s and C H ) andthebackgroundatmosphericconditions.Thesecondnumberintheparenthesesisthedifference betweenthenumberoutsidetheparenthesesandthe
rstnumberinsidethem.Itshowstheeffectofusing thecoef
cientsandbackgroundatmosphericconditionsoveroceanversusthoseoverlandforgiven changesinatmosphericconditions.Thenumbersintheparenthesesinthefourthand
fthcolumnsarethe correspondingvaluesforthechangesin P /PETandtherelativecontributions,respectively.Thesenumbers thusshowtheeffectsofcontrastingchangesinsurfacemeteorologicalvariablesoverlandandocean, versusthoseduetotheuseofthedifferent(landversusocean)coef
cientsandbackgroundatmospheric conditionsinestimatingtheeffectsofgivenatmosphericchanges.Therefore,thecausesofthedrier terrestrialclimatearefurtherquanti
edhereintermsof(i)enhancedlandwarmingrelativetoocean,(ii)a decreaseinRHoverlandbutanincreaseoverocean,(iii)partofincreaseinnetdownwardradiationgoing intothedeepocean,and(iv)differentresponsesofPEToverlandand E overoceanforgivenchangesin atmosphericconditions.Therelativecontributionstothechangeinterrestrialmeanaridityfromthesefour factorsare38%,38%,12%,and11%,respectively(Table4). Table4(andTables5and6later)con
rmsthatthePETover landismoresensitivetothesurfaceairtemperaturethan the E overocean.Thisisbecausethedenominatorin equation(1)becomesmoresensitivetotemperaturewhen r s =0.0overocean,cancelinglargerpartofthetemperature sensitivityofthenumerator.Italsoindicatesthatthe E overoceanismoresensitivetotheavailableenergychange. Thisisbecausetheenergyterminequation(1)makesupa largerproportionofthenumeratorduetoasmaller C H over ocean.ThePEToverlandand E overoceanhowever respondsimilarlytoagivenchangeinRH(Table4).Overall, theeffectofdifferingresponsesofPEToverlandversus E overoceanforgivenchangesinatmosphericconditionsis largelyassociatedwithchangesintemperatures. Table5isthesameasTable4exceptthatthe
rstnumberin theparenthesesgivesthechangebasedonthePenman – Monteithalgorithmusingtheoceancoef
cientsand backgroundatmosphericconditions,whilethesecond oneistheeffectofthedifferencesincoef
cientsand backgroundconditionsbetweenlandandoceanforgiven atmosphericconditionchangesoverland.Therelative contributions(thenumbersintheparenthesesofthe
fth Table5. SameasTable4ExceptThattheFirstNumberintheParenthesesGivestheChangeBasedonthePenman – MonteithAlgorithmUsingtheOceanCoef
cientsandBackgroundAtmosphericConditions,WhiletheSecondOneis theEffectofDifferencesinCoef
cientsandBackgroundConditionsBetweenOceanandLand PET(%/°C) E (%/°C) P/ PET(%/°C) RelativeContributiontothe Total P/ PETChange(%) T a 3.48(2.67,0.81)1.68
1.80(
0.99,
0.81)53(30,23) RH0.95(0.87,0.08)
0.31
1.26(
1.18,
0.08)37(35,2) u
0.03(
0.06,0.03)
0.06
0.03(0.0,
0.03)1(0,1) R n
G 0.88(1.17,
0.29)0.62
0.26(
0.55,0.29)8(16,
8) Total 5.28(4.65,0.63)1.92
3.36(
2.73,
0.63)100(81,18) Table6. RelativeContributionsofSurfaceair Temperature( T a ),RelativeHumidity(RH),Wind Speed( u ),andAvailableEnergy( R n
G )onthe PercentageChangeRatesin P /PET a RelativeContributiontothe Total P/ PETChange(%) T a 53(34±4,19±4) RH37(36±2,0±2) u 1(0±0,1±0) R n
G 8(14±2,
6±2) Total100(85±4,15±4) a The
rstnumberinthparenthesesgivesthe relativecontributionsofcontrastingchangesof T a ,RH, u ,and R n
G basedonthePenman – Monteithalgorithmusingthesamecoef
cients andbackgroundatmosphericconditionsover landandocean.Thesecondnumberinthe parenthesesisthecorrespondingcontributions duetodifferingresponsesofPEToverlandand E overoceantogivenchangesinatmospheric conditions.Theuncertaintiesareassociatedwith referencecoef
cientsandbackgroundconditions thatareusedeitheroveroceanorland. JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 10 column)usingtheoceancoef
cientsandatmosphericbackgroundconditions(Table5)areslightly differentfromthoseusingthelandconditions(Table4).Bytakingtheaverageofthe
fthcolumnsfrom Tables4and5,weobtaintheTable6.Itshowsthattherelativecontributionstothechangeinterrestrial meanaridityareabout35%,35%,15%,and15%,respectively,duetocontrastingchangesoverlandversus oceanin T a ,RH,SH+LH,anddifferingresponsesofPEToverlandand E overoceantogivenchangesin atmosphericconditions. Inthisstudy,weuseda C H of4.8×10
3 anda r s of70s/m,correspondingtoagrass-likesurface[ Allenetal ., 1998],asuniversalconstantsoverland. ScheffandFrierson [2014]examinedtheeffectofsetting r s =0,as usedby Burkeetal .[2006]and Dai [2013],aswellasinthecaseofpanevaporation.Itisfoundthatthechange inPETdueto T a becomes24%smaller.SincesucheffectonthePETchangesassociatedwithother meteorologicalvariablesisnegligible,thepercentagechangerateinPETisabout4.6%/°Cfrom 5.3%/°C×(0.53×0.76+0.37+0.01+0.08)(seeTable4),andthepercentagechangeratein P /PETbecomes about
2.9%/°C,when r s =0. ScheffandFrierson [2014]alsoexamineda “ rough, ” forest-likesurface,and theyfoundaslightlystrongerPETresponseto T a thanthe “ smooth ” grasssurface.Therefore,theresults presentedinthisstudyarerobustandarenotverysensitivetothewidelydifferentchoicesofvegetation parametersusedinthePenman – Monteithalgorithm. Theobservedpanevaporationhasnotincreasedasexpectedoverthepastfewdecades[ Wangetal .,2012]. Thisisbecausesigni
cantglobal “ stilling ” ofnear-surfacewindsandslightdecreasesindownwardsurface solarradiationcompensatefororevenexceedthechangesduetotemperatureandrelativehumidity [ McVicaretal .,2012].Butneitherthestillingofwindsnorthereducedsurfaceinsolationappearstobe connectedtoglobaltemperaturerise,andthesuggestedcausesareinsteadassociatedwithlanduse, aerosols,and/orinternalvariability[ Bichetetal .,2012; Wever ,2012; Yangetal .,2013; McVicaretal .,2012]. Recently, ZhangandCai [2013]showedthatprojectedcropwaterde
citsattheendofthe21stcentury arelikelytodeclineslightlydespitetherisingtemperature.TheyusedanempiricalequationforPETasa functionofthetemperatureanddiurnaltemperaturerange(DTR),developedby HargreavesandSamani [1985],wheretheeffectofsolarradiationisparameterizedintermsofDTR.Inawarmingclimatecausedby theincreaseofgreenhousegases,theDTRwilldecrease[ IPCC ,2013],whilethe R n , s willincrease(seeFigure7, middle).ThebottomlineisthatthedecreaseinPETcausedbythedecreaseinDTRfromtheempirical equationhasnophysicalbasisforthelong-termclimatechange.Inaddition,theempiricalequationdoesnot considertheeffectofchangesinRHand R n , l ,bothcontributingtotheincreaseinPET.Itisimportantto noticeherethatanempiricalrelationshipmaynotbeappropriatebeingappliedtothelong-termclimate changeatall,althoughitmay
tthecurrentclimatereasonablywell. 5.SummaryandConclusions Thedrynessofterrestrialclimatecanbeexpressedintermsoftheratioofannualprecipitation( P )to potentialevapotranspiration(PET).ThePETistheevaporativedemandoftheatmosphere,indicatingthe maximumamountofevaporationonewouldget,inagivenclimate,fromawell-wateredsurface.PETisa functionofsurfaceairtemperature,relativehumidity,windspeed,andavailableenergy.Thisstudyexamines howtheterrestrialmeanaridityrespondstoglobalwarmingintermsof P /PETusingtheCMIP5transientCO 2 1%/yrincreaseto2×CO 2 simulations.WecalculatedthePETusingthePenman – Monteithalgorithm,whichis basedonthebulkformulaeforthesensibleheatandlatentheat  uxesandthesurfaceenergybudget equation.ItisfoundthatthePenman – Monteithalgorithmcanalsobeusedtocalculatetheevaporation ( E )overoceanwiththeRHand r s valuesoverocean. Weshowthattherateofpercentageincreasein P averagedoverlandis~1.65%/°Criseinoceanmeansurface airtemperature,whiletheincreaseinPETis5.3%/°C,leadingtoadecreasein P /PET(i.e.,adrierterrestrial climate)by~3.4%/°C.Notingsimilarpercentageincreaseratesfor P overlandandevaporationover ocean,weproposeaframeworkforexaminingthepercentagechangeratesin P /PETbycomparingthe changeinPEToverlandwith E overocean,bothestimatedusingthePenman – Monteithformula.We documentthechangesin T a ,RH, u ,and R n
G overbothlandandoceanandquantifytheireffectsonthe changein P /PET.Itisfoundthatthecontributionsfrom T a ,RH, u ,and R n
G changestothechangesin P /PET are53%,37%,1%,and8%,respectively.Thesecontributionsarenotonlydeterminedbythecontrasting changesoverlandandoceanintherelevantsurfacemeteorologicalvariablesbutalsoareaffectedbythe JournalofGeophysicalResearch:Atmospheres 10.1002/2014JD021608 FUANDFENG ©2014.AmericanGeophysicalUnion.AllRightsReserved. 11 coef
cientsandbackgroundconditionsused,whichdeterminethesensitivityofPET( E )tothechanges insurfacevariables. Wefurtherseparatetheeffectsofthecontrastingchangesoverlandversusoceaninthesurface meteorologicalvariablesandthoseduetodifferingresponsesofPEToverlandand E overoceanforgiven atmosphericchanges.Adrierterrestrialclimatecanthenbeinterpretedby(i)enhancedlandwarming relativetoocean,(ii)adecreaseinRHoverlandbutanincreaseoverocean,(iii)partofincreaseinnet downwardradiationgoingintothedeepocean,and(iv)differingresponsesofPEToverlandand E over oceantogivenchangesinatmosphericconditions(largelyassociatedwithchangesintemperatures). Therelativecontributionstothechangeinterrestrialmeanaridityfromthesefourfactorsareabout35%, 35%,15%,and15%,respectively. AppendixA:ChangeinPETandContributionsFromChangesin T a ,RH, u ,and R n
G Herewede
ne E = R n
G andusethesubscripts “ 0 ” and “ 1 ” torepresentthemeanvaluesfortheyears1 – 10 and61 – 70ofthesimulations,respectively.Wealsodenotethechangeofavariable x as  x = x 1
x 0 .The changeinPETusingequation(1)canthenbewrittenintheform  PET ¼ E 1
T a 1 ðÞ þ
a c p e  T a 1 ðÞ 1
RH 1 ðÞ C H u 1 jj
T a 1 ðÞþ  1 þ r s C H u 1 jj ðÞ = L v
E 0
T a 0 ðÞþ
a c p e  T a 0 ðÞ 1
RH 0 ðÞ C H u 0 jj
T a 0 ðÞþ  1 þ r s C H u 0 jj ðÞ = L v ¼ E 0
T a 1 ðÞþ
a c p e  T a 1 ðÞ 1
RH 0 ðÞ C H u 1 jj
T a 1 ðÞþ  1 þ r s C H u 1 jj ðÞ = L v
E 0
T a 0 ðÞþ
a c p e  T a 0 ðÞ 1
RH 0 ðÞ C H u 0 jj
T a 0 ðÞþ  1 þ r s C H u 0 jj ðÞ = L v þ  E
T a 1 ðÞ
T a 1 ðÞþ  1 þ r s C H u 1 jj ðÞ = L v þ
a c p e  T a 1 ðÞ
 RH ðÞ C H u 1 jj
T a 1 ðÞþ  1 þ r s C H u 1 jj ðÞ = L v Fromtheaboveequationandnotingthatthechangeinwindspeedissmall,wecanisolatetheeffectof temperaturechangebycomputingthePETusing T inthelast10yearsbutRH, u ,and E fromthe
rst10years minusthePETusingtheinputsfromthe
rst10years.TheeffectsofthechangesinRHor E howeverare estimatedbyusingPETwiththeinputsfromthelast10yearsminusthatcalculatedusingRHor E inthe
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