NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSWITHINTHEEARTH - PDF document

NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSWITHINTHEEARTH’SCLIMATESYSTEMJOSÉA.RIAL,ROGERA.PIELKESR.,MARTINBENISTONMARTINCLAUSSEN,JOSEPCANADELL,PETERCOX,HERMANNHELDNATHALIEDENOBLET-DUCOUDRÉ,RONALDPRINN ClimaticChange11–38,2004.©2004KluwerAcademicPublishers.PrintedintheNetherlands. JOSÉA.RIALETAL.thethermohalinecirculationoftheNorthAtlanticocean,suggesttheexistenceofthresholds,multipleequilibria,andotherfeaturesthatmayresultinepisodesofrapidchange(StockerandSchmittner,1997).AsdescribedinKabatetal.(2003),theEarth’sclimatesystemincludesthenaturalspheres(e.g.,atmosphere,biosphere,hydrosphereandgeosphere),theanthrosphere(e.g.,economy,society,culture),andtheircomplexinteractions(Schellnhuber,1998).Theseinteractionsarethemainsourceofnonlinearbehavior,andthusoneofthemainsourcesofuncertaintyinourattemptstopredicttheeffectsofglobalenvironmentalchange.Insharpcontrasttofamiliarlinearphysicalprocesses,nonlinearbehaviorintheclimateresultsinhighlydiverse,usuallysurprisingandoftencounterintuitiveob-servations,soitisimportant,beforeembarkingonthediscussionofdata,thatweagreeonafewbasiccharacteristicsofnonlinearclimate.1.1.LINEARANDNONLINEARSYSTEMSEvenanelementarydescriptionofEarth’sclimatesystemmustdealwiththefactthatitiscomposedoftheabovesubsystemsallinterconnectedandopen,allowinguxesofmass,energyandmomentumfromandtoeachother(seeFigure1).SincetheEarthitselfisaclosedsystem,theseuxeseventuallycyclethrough,sothatoutputsre-enterthesystemtobecomeinputs,creatingfeedbacksandfeedbackchains.Eventually,eachsubsystemaffectstheresponseofeveryothersubsystemandoftheclimateasawhole.Itisthiscrosstalkamongthedifferentpartsoftheclimatethatengendersthedisproportionaterelationsbetweeninputandoutputtypicalofanonlinearsystem.Thephrase‘thewholeismorethanthesumofitsparts’underscoresthefailureoftheprincipleofsuperpositioninanonlinearsystemsuchastheclimate.Insharpcontrast,wheresuperpositionisvalidthewholeisexactlyequaltothesumofitsparts.Thesystemislinearandthereisnocrosstalk;eachpartbehavesasifitwereactingalone.Howdowetellwhenthereisnonlinearityintheclimateweobserve?Thereareatleastthreeimportantobservablecharacteristicsthatseparatelinearfromnonlinearsystems,allofwhichareexempliedinthedatatobediscussed.(1)Whilelinearsystemstypicallyshowsmooth,regularmotioninspaceandtimethatcanbedescribedintermsofwell-behaved,continuousfunctions,nonlin-earsystemsoftenundergosharptransitions,eveninthepresenceofsteadyforcing.Thesetransitionsusuallyresultfromcrossingunstableequilibriumthresholds(e.g.,abruptclimatechange,asdescribedbyAlleyetal.,2003).(2)Theresponseofalinearsystemtosmallchangesinitsparametersortochangesinexternalforcingisusuallysmoothandproportionatetothestimulation.Incontrast,nonlinearsystemsaresuchthataverysmallchangeinsomeparameterscancausegreatqualitativedifferencesintheresultingbehavior(chaos)assug-gestedforinstancebyuiddynamicmodelsofatmosphericconvection(Lorenz, NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure1.StructureofCLIMBER-2,anEarthSystemModelofIntermediateComplexity(EMIC;Claussenetal.,2002).Themodelconsistsoffourmoduleswhichdescribethedynamicsoftheclimatecomponentsatmosphere,ocean,terrestrialvegetation,andinlandice.Thesecomponentsinteractviauxesofenergy,momentum(e.g.,windstressontheocean),water(e.g.,precipitation,snow,andevaporation),andcarbon.Also,theland-surfacestructureisallowedtochangeinthecaseofchangesinvegetationcoverortheemergenceandmeltingofinlandicemasses,forexample.Theinteractionbetweenclimatecomponentsisdescribedinaso-calledSoilVegetationAtmosphereTransferScheme(SVAT).CLIMBER-2isdrivenbyinsolation(whichcanvaryowingtochangesintheEarthorbitorinthesolarenergyux),bythegeothermalheatux(whichisverysmall,butimportantinthelongrunforinlandicedynamics),andbychangesimposedontheclimatesystembyhumanactivities(suchaslanduseoremissionofgreenhousegases(GHG)andaerosols).(3)Aftertransientsdissipate,anoscillatorylinearsystem’sfrequencyalwaysequalsthatoftheforcing,whilethespectralresponseofanonlinearsystemtooscillatoryexternalforcingusuallyexhibitsfrequenciesnotpresentintheforcing(suchascombinationtones),phaseandfrequencycoupling,synchronizationandotherindicationsofnonlinearityoftendetectedinpastclimatedata(e.g.,Pisiasetal.,1990).1.2.CHAOSANDCOMPLEXITYThus,nonlinearitygivesrisetounexpectedstructuresandeventsintheformofabrupttransitionsacrossthresholds,unexpectedoscillations,andchaos(KaplanandGlass,1995).Actually,theclimatesystemisnotonlychaotic,itisalso‘complex’(Rind,1999),inthesensethatitiscomposedofmanypartswhose JOSÉA.RIALETAL.interactionscan,throughaprocessstillnotcompletelyunderstood(Cowanetal.,1999),provokespontaneousself-organizationandtheemergenceofcoherent,col-lectivephenomenathatcanbedescribedonlyathigherlevelsthanthoseoftheindividualparts(GoldenfeldandKadanoff,1999).Therefore,itisusefultoestab-lishforclarity’ssakethatchaosandcomplexityaredifferentaspectsofnonlinearresponse.Chaosreferstosimplesystemsthatexhibitcomplicatedbehavior,suchastheintricatetimeseriesproducedbyadrippingfaucet,theunpredictableoscil-lationsofadoublependulum,ortherandombehaviorofpopulationsinmodelsoflogisticgrowth(May,1976).Conversely,complexityreferstocomplicatedsystemsthatexhibitsimple,so-calledemergentbehavior.Forinstance,inthehighlycom-plextectonic-geologicsubsystem,theemergentbehaviorisanearthquake,intheworldeconomy,astockmarketcrash,andinthebiosphere,amassiveextinction.Intheclimatesystem,abruptclimatechangeisalikelyexampleofunpredictableemergentbehavior.Infact,observationsindicatethattheclimatesystemis,andhasbeenformillionsofyears,riddledwithepisodesofabruptchange,rangingformlarge,suddenglobalwarmingepisodes(e.g.,theendofthelasticeage),todrasticandrapidregionalchangesinthehydroclimaticcycle,precipitationandaridity(e.g.,theexpansionoftheSahara).Becauseoftheirobviousimportanceinunderstandingfutureclimatetrends,theseandotherexamplesofabruptclimatechangearediscussedinthispaper.Withintheclimatesystemchaoticbehaviorexhibitssensitivedependencetoinitialconditions,connementandtypicalaperiodicity.Thisistosaythattinydif-ferencesininitialstatescanexponentiallyblowuptobigdifferencesinlaterstates,butthevaluesoftherelevantvariablesremainconnedwithinxedboundaries,neverexactlyrepeating.Intheclimatesystem,andasweshallsoondiscuss,plau-sibleexamplesofchaosareENSO(ElNiño,SouthernOscillation)andNAO(NorthAtlanticOscillation).Infact,simpledeterministicmodelsthatexhibitchaoticbehaviorqualitativelyreproducetheirregularoscillationsofENSOforstrongcou-plingbetweenoceanandatmosphere(e.g.,Tzipermanetal.,1994).ENSOmayinfactbechaoticinthesensethattheequatorialPacicclimatemayipinachaoticway(randomly)fromonetoanotherofitsthreepreferredquasi-stablestates(normal,LaNiña,ElNiño).1.3.FEEDBACKSANDTHRESHOLDSAlthoughchaoticdynamicsandemergentpropertiesmaybesurmisedfromdatainterpretationandfromthecomparisonofdatatomodels,feedbacksaretheonlyclimateprocesseswhosepresenceandeffectscanoftenbequantiedand,insomecasesunderstoodwithalmostcertainty.Inthispaperweillustratehowthepresenceofseveraltypesofamplifying(positive)andcontrolling(negative)feedbacks,somephysical(icesheet-albedointeraction),somebiogeophysical(albedo-vegetationin-teraction),andsomebiogeochemical(anthropogenicgases-atmosphereinteraction)canbededucedfromobservations.Feedbacksarethemostlikelyprocessesbehind NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSmostofthenonlinearitiesintheclimate.Therelativelystableglobaltemperatureandbenignclimatetheearthhasenjoyedforbillionsofyearsistestimonytotheactionofregulatingnegativefeedbackswhichbalanceandneutralizeamplifying(explosive)positivefeedbackscontinuously(e.g.,WatsonandLovelock,1984).ItisquitelikelythatsuchacontinuouslyactiveregulatingfeedbackmechanismfailedtodevelopinVenus,leadingtothepresenthellishenvironmentofitssurface.WecanthenimaginethatnaturehasarrangedthingsinsuchwaythatonEarth,andontheaverage,thenetclimate-drivingfeedbackisnegative,slightlystrongerthanthenetpositivefeedback,atleastforsmallvaluesofsome(externalorinternal)forcing.Itiswhentheforcinggrowstoapointinwhichthepositivefeedbacktakesoverthatitsexplosiveamplicationproducesthenonlineareffectsthatweseeinthedata.Thus,acriticalthresholdmayinfactbethepointatwhichthetwocom-petingfeedbackeffectsarejustbalanced.Sincetherearecountlessfeedbacksandthresholds,rapidamplicationofpotentiallyexplodingvariablesbecomeshighlyprobable,andsharp,abruptclimatechangeshouldthenbethenorm,asappearstobesuggestedbythepastrecordsofclimatechange.Wemustemphasizehoweverthatthereisasyetnobasicunderstandingofabruptclimatechange(Clarketal.,1.4.PAPERORGANIZATIONThegoalofthispaperistodiscusskeyissuesandquestionsrelatedtononlinearityintheEarth’sclimatesystemanditsimplicationsinglobalclimatechangeresearch.First,wediscussexamplesofnonlinearclimateresponsefromobservationsofabruptclimatechangedetectedinbothpre-historicandrecenttimeseries(Exam-ples2.1–2.5).Nextwediscussmodelsofcoupledoceanandatmospheremediatedbychaoticdynamics(Examples3.1–3.2).Finallywelookatnonlinearitiesinthecarboncycleandtheeffectsofbiogeochemicalfeedbacksinmodelsofpresentandfutureclimatechange(Examples4.1–4.4).Aftertheexamples,weaddressscaleandmethodologicalissuesasrelatedtosomeofthechallengesinpredictingtheconsequencesofhumanactionsontheEarth’sclimatesystem.Forexample,giventhenearlycertainoccurrenceofsuddentransitionsbetweenclimatestates,is‘prediction’perseachievable?Wesuggestanalternative–andhighlyrobust–approachusingintegratedassessmentswithintheframeworkofvulnerabilitystudies,thedetailsofwhichwethendiscussandjustify.Toconcludeweprovideaseriesofrecommendationsforresearchpriorities,includingelucidatingpotentialsourcesofnonlinearity,identifyingkeyfeedbacksandlinkagesintheEarth’sclimatesystem,andestablishingEarthSystemsScienceprogramsinordertoprovidethenextgenerationofscientistsamorecompleteviewonthiscrucialtopic. JOSÉA.RIALETAL.2.Nonlinearity,AbruptClimateChangeandFeedbacksinPastandPresentClimateTimeSeries2.1.THENONLINEARPACEMAKEROFTHEICEAGESNaturehasbeenperformingclimateexperimentsformillionsofyears,andmanyoftheresultsarerecordedindeep-seasedimentsandicecores(e.g.,Cronin,1999).Itisthereforeimportantthatwebeginourdiscussiondescribingpaleoclimatedatatoprovideahistoricalperspective.Asweshallsee,thepaleoclimaterecordssuggestastronglynonlinear,complexclimatesystem.TheiceagesofthePleistoceneareremarkablequasi-periodiceventsofpastglobalclimatechange.Attheirpeakglobalmeantemperaturewasover4Clowerthantoday,andenormousicesheetsseveralkilometersthickcoveredmostofnorth-ernNorthAmericaandEurasia.However,therecordsoftheiceagesarefarfromunderstood,mostlybecausetheresponseoftheclimatetothepresumedforcing(secularchangesinEarth’sorbitaleccentricity,spinaxis,andprecession)appearstobestronglynonlinear.Forinstance,itiswellknownthatwhilethemaindrivingfrequencyoftheiceagesisabout100ky(1ky=1,000years)thetimingbetweenconsecutiveglacialperiodshasbeensteadilyincreasingfrom80kyto120kyoverthelast500ky(Raymo,1997;Petitetal.,1999).Thisfeature,plusthenearabsenceofalargeresponseatthestrongesteccentricityforcingperiod(413ky)andthepresenceofsignicantvarianceatfrequenciesnotpresentintheorbitalforcing,arestrongevidenceofnonlinearityintheclimate’sresponsetoorbitalforcing(e.g.,Nobesetal.,1991;Ghil,1994).Toexplainthesenonlinearfeatures,Rial(1999)introducedtheideathattheclimatesystemtransformstheastronomicallyamplitude-modulatedinsolationintofrequencymodulateductuationsofglobalicemass.Thisisfrequencymodulationentirelyanalogoustotheelectronicprocessbywhichthefrequencyofacarriersignalischangedinproportiontotheamplitudeofarelativelylowerfrequencysignal,asinFMradioandtelevisionbroadcasting.Manywell-knownpropertiesofFMsignalsareinfactfullyconsistentwithfea-turesofthepaleoclimatedatathathavepuzzledresearchersforyears,suchastheabovementionedvaryingdurationoftheiceagecycle,thepresenceofcombinationtonesoforbitalfrequencies,andperhapsthemosttelling,theapparentabsenceofspectralpowerat413ky(Imbrieetal.,1993).Frequencymodulationisaphase-andfrequency-lockingprocessthattransfersenergyfromonefrequencybandintoanother,andcreatesnewfrequencies(calledsidebands)ascombinationtonesofthecarrierandthemodulatingfrequencies,andthusagoodexampleofnonlinearcrosstalkamongthefrequenciesthatmakeuptheresponse. NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS2.2.THEMIDPLEISTOCENECLIMATESWITCHAround950kyago,aprominentswitchinthefrequencyresponseofthecli-matesystemtoorbitalforcingoccurred.Thisphenomenon,usuallycalledthemid-Pleistocenetransition(MPT),resultedinachangefromthe41kypredomi-nantglaciationperiodtoanew100kyperiod,withoutacorrespondingchangeintheforcingorbitalfrequencies,asshowninFigure2a.Thoughanumberofexplanationshavebeenproposed,theMPTcontinuestobeoneofthemostpuz-zlingexamplesofthenonlinearcharacterofclimateresponse.Figure2aclearlyshowsthattheoscillatoryresponseoftheclimateswitchesfrequencyandampli-tudeatabout950kyagowhiletheforcingisessentiallythesamethroughout.MudelseeandSchulz(1997)estimatetheicemasstohaveincreasedbyaboutkg,equivalenttoanicesheetareaexpansionof3andthicknessofupto3km.Suchalargeincreaseiniceextent(andicetopog-raphy)musthavecreatedanewatmosphericcirculationpatternandnewfeedbackstomaintainthenew,unprecedentedclimaticconditions(longerglaciationsandgreater,thickericecaps).AprobablecluetotheoriginoftheMPTisthefactthataroundonemillionyearsagothemeanlong-termtrendoftheinsolationdroppedslightlytoanewmean(BergerandLoutre,1991).Thecorrespondingdecreaseinmeanglobaltemperature,ampliedbyfeedbacks,couldhaveshiftedtheclimatesystem’ssensitivitytoforcingatlowerfrequency.Thetransformationofameantemperaturestep-likedropintoaswitchtoamuchlowerresonantfrequencyisaclearexampleofnonlinearresponse,consistentwiththepreviouslymentionedtransformationofamplitudemodulationintofrequencymodulation.2.3.ABRUPTWARMINGEPISODESINTHEPALEOCLIMATERECORDPaleoclimaterecordsovermanytimescalesexhibitepisodesofrapid,abruptcli-matechange,whichmaybedenedassuddenclimatetransitionsoccurringatratesfasterthantheirknownorsuspectedcause(Rahmstorf,2001).Abruptcli-matechangeisbelievedtobetheresultofinstabilities,thresholdcrossingsandothertypesofnonlinearbehavioroftheglobalclimatesystem(Clarketal.,1999;Alleyetal.,1999;Rahmstorf,2000),butneitherthephysicalmechanismsinvolvednorthenatureofthenonlinearitiesthemselvesarewellunderstood.Figure2bshowsselectedexamplesofabruptclimatechangeintheformofrapidwarm-ingepisodesfollowedbymuchslowercoolingepisodes.Eachwarming/coolingsequenceusuallyrepeatsatnearlyequaltimeintervals,givingthetimeseriesacharacteristicquasi-periodicsaw-toothappearancethat,remarkably,appearsatmultipletimescales(asshownintheenlargement)anddisplaysanunclearrelationtoastronomicalforcing.Throughoutmostofthepaleoclimateproxydatafromsedimentsandicecores,thereisafrequentrepetitionofthissametheme;abruptandfastwarming(some-timeslastingonlyafewdecades)followedbymuchslowercooling.Thisisapatternthat,havinghappenedofteninthepast,willlikelyhappeninthefuture, JOSÉA.RIALETAL. Figure2a.Examplesofnonlinearitiesinthepaleoclimate.Themid-Pleistocenetransition(MPT).Theglobalicevolumeproxyshowsasuddenchangeinpredominantfrequencyaround950kyago.Thetoppanelshowsthedata(Site806),thenexttwopanelsshow(toptrace)theresultoflteringthedatawithanarrowband-passltercenteredat100kyandbelowitthecorrespondingastronomicalforcing(insolation)lteredinthesamemanner.Thelowertwopanelsshowasimilarcomparisonbutforaltercenteredat41ky.Thelongerperiodrecordsreecttheselectivenonlinearityofthesystem,astheresponseto100kyforcingisnegligiblefortimesearlierthan1Ma,andafterthatitbecomesstrong,withoutacorrespondingchangeintheforcing.Nosimilarrelationisseenintheshortperiods.(ModiedfromClarketal.,1999;MudelseeandSchulz,1997).whichmakescompellingevidencefortheurgentneedtoimproveourunderstand-ingofthephysicalprocessesinvolved.Byitself,Figure2balreadyprovokesanumberofobviousandstimulatingquestions,suchas,whyarewarmingepisodesgenerallysomuchfasterthancoolingones(saw-tooth)?Howcanrapidclimatechangebetriggeredbyslowchangeinorbitalparameters?Doesself-similarityofresponsemeansimilarityofprocessesregardlessoftimescale?Whatnonlinearprocessesareatwork?Couldthepresentrateofanthropogenicwarmingtriggeroneofthoseabrupt,hugewarmingeventsofthelasticeage?TheDansgaard–Oeschger(D/O)oscillationsofthelastglacialshowninFig-ures2band3aareamongtheclearestexamplesofabruptwarmingepisodes NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure2b.Samplesofclimatechangeacrossdifferenttimescalesandproxyrecords(stableisotopicratios)forglobaltemperatureandicevolume,includingSST(seasurfacetemperature)deep-seasediment(Site667)andicecores(Vostok,GRIP).Notethetypicalsaw-toothshapewhich,createdbythefastwarming/slowcoolingsequences,appearstobeindependentoftimescale,displayinganintriguingself-similarity.Mainwarmingperiodsareindicatedbyverticallightgraystripes.Also,notetheclosesimilaritybetweenthetemperatureoscillationsinGreenlandandinthesub-tropics(Bermuda)(datatakenfromRaymo,1997;GRIPProjectMembers,1993;Petitetal.,1999;SachsandLehman,1999).(regionaltemperatureinGreenlandincreasedsuddenlybyupto10Cinjustafewdecadesandonmultipleoccasions).Theclimatewasindeedhighlyvariableduringglacialtimesandswitchedabruptlyandfrequentlybetweencoldandwarmmodes.GanopolskiandRahmstorf(2001)proposedthefollowingmechanism.Thepresent-dayclimatestateischaracterizedbyawarm(switched-on)modeofthethermohalinecirculation(THC)beinginterpretedasanequilibriumstateoftheunderlyingdynamics.Althoughasecondstablestateexistsforthepresent-dayclimate(seeFigure3b)representingamodeleadingtomuchcoldertemperaturesovernorthernEurope(switched-offTHC),atransitionbetweenthetwohasnotoccurredduringtheHolocenebecauseoftherelativelylargebasinofattractionof JOSÉA.RIALETAL.thewarmmode.Quitethecontrary,duringthelastglacialperiod,astable(cold)andamarginallyunstable(warm)modeexistedforthedynamicsoftheTHCwithamuchsmallerbasinofattractionforthecoldmode.UtilizingCLIMBER2.3,aclimatemodelofintermediatecomplexity(whoseframeworkisillustratedinFigure1),itcanbeshownthatarelativelysmallperturbationofthefreshwaterinputathighlatitudesissufcienttoswitchthesystemintothemarginallyun-stablemodewhoselifetimeisoftheorderofseveralhundredyears.AsinusoidalmodulationwithamplitudemuchsmallerthantheboundariesF1/F2inFigure3bdoesnotinduceswitchinginthepresent-dayclimatebutdoesresultinperiodicswitchingunderglacialconditions.Preliminaryresultsindicatethatinthepres-enceofnoise,thisdrivingamplitudecanbefurtherreduced,resultinginaippingbehaviortypicalofthenonlineareffectcalledstochasticresonance(GanopolskyandRahmstorf,2001).Finally,theD/Oeventscanbeexplainedifamildperiodicforcing(ofunknownorigin)oftheTHCplusnoiseisassumed.ThisexternaltriggerbecomesampliedduetothecoexistenceofastablestateandamarginallyunstablemodeintheTHCsystem.Suchcoexistenceisimpossibleinalinearsystem;hence,nonlinearityisanecessaryconditionforswitchingbehavior.2.4.THEABRUPTDESERTIFICATIONOFTHESPaleoclimaticreconstructionssuggestthatduringtheHoloceneclimateoptimum(9000–6000yearsago),NorthAfricawaswetterandtheSaharawasmuchsmallerthantoday(Prenticeetal.,2000).Annualgrassesandshrubscoveredthedesert,andtheSahelreachedasfaras23N(Claussenetal.,1999),over500kmnorthofitspresentlocation.DuringtheHoloceneoptimumaslightlyincreasedtiltoftheEarth’sspinaxisandperihelioninJulyledtostrongerinsolationoftheNorth-ernHemisphereduringsummertherebystrengtheningtheNorthAfricansummermonsoon(KutzbachandGuetter,1986).However,theNorthAfricanclimateissensitivetochangesinlandsurface’salbedo,whichcanresultfromvegetationremoval.Infact,CharneyandStone(1975)recognizedthathighalbedoresultingfromvegetationremovalcanenhancedesertexpansionbyreducingrainfall,whichfurtherreducesvegetation,inastrong,desert-expandingpositivebiogeophysicalfeedback.ThismechanismoffersapossibleexplanationforclimatechangesintheSaharaandparticularlyforincreaseddroughtintheSahelanditssouthwardmigrationinlateHolocene.Actually,whenusingpresent-dayland-coverasinitialcondition,modelsbasedsolelyonatmosphericprocessesdonotyieldanincreaseinprecipitationlargeenoughtoleadtoasubstantialreductionintheSahara6000yearsago(Joussaumeetal.,1999).However,whenfeedbacksbetweenatmosphereandvegetationareincorporated,themodelssimulateavegetationdistributioningoodagreementwithpaleobotanicreconstructions(ClaussenandGayler,1997;deNoblet-Ducoudreetal.,2000;Dohertyetal.,2000).Summarizing,precessionalforcingledtoanenhancementoftheAfricanmonsoon,creatingconditionsthatwerethenampliedmainlybyatmosphere-vegetationfeedbacks,andtoalesser NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure3a.Perhapsthemostpuzzlingfeatureofrecentpaleoclimaterecords,highlyrelevanttounder-standingfutureglobalclimatechange,isthefast-warming/slow-coolingsequencefoundinthestableisotopeuctuations(O)timeseriesofGreenland’sicecoresknownastheDansgaard-Oeschger(D/O)oscillations(Jouzeletal.,1994;Alleyetal.,1999).TheD/Otypicallyshowverysudden,Cwarmingepisodeslastingafewcenturiesorperhapsevenafewdecades,followedbymillenniaofrelativelyslowcooling.Remarkably,reconstructedseasurfacetemperatures(SST)inthetropicalAtlantic(Figure2b)mimictheD/Orecordinthe30kato60kainterval,andsimilarrecordingsarefoundinthesubtropicalPacicandtropicalIndianoceans.Thelongestperiodofthesignalintheinsetisasubmultipleoftheprecessionforcingandevidenceofprecessionforcingexistselsewhereintherecord(Rial,2003).TheordinalsnearselectedpeakscorrespondtonumberedinterstadialsandYDistheYoungerDryasevent(Dansgaardetal.,1993). JOSÉA.RIALETAL. Figure3b.Climate(temperature)stabilityasafunctionoffreshwaterinputathighlatitudesintheNorthAtlantic(ModiedfromPaillard,2001).extentbyatmosphere-oceaninteraction(Ganopolskietal.,1998;Braconnotetal.,1999).Theseleadtomultipleequilibriumstates(Claussen,1997)withthepossibil-ityofabruptchangeswhenthresholdsarecrossed(Brovkinetal.,1998),asshowninFigure4(modiedfromClaussenetal.(1999)andDeMenocaletal.(2000)).ThisgureshowsamodelsimulationofanabruptdeclineinprecipitationintheSahara(20N–30Nand15W–50E)around5,500yearsagothatissupported NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure4.Simulationoftransientdevelopmentofprecipitation(B),andvegetationfraction(C)asresponsetochangesininsolation(Adepictsinsolationchangesonaverageoverthenorthernhemi-sphereduringborealsummer).ResultsfromClaussenetal.(1999)(B,C)arecomparedwithdataofterrigenousmaterialandestimateduxofmaterialinNorthAtlanticcoresofftheNorthAfricancoast(D)bydeMenocaletal.(2000).ThegureisreproducedfromFigure2.8,inKabatetal.(2003),withpermission.byobservationsfromsedimentcoresofftheNorthAfricancoast.Therapidchangecontrastsmarkedlywiththeslowdecreaseininsolation.2.5.ABRUPTSHIFTSANDTRENDSOFHYDROCLIMATICTIMESERIESHereweillustrateabruptshiftsandtrendsofhydroclimatictimeseriesthatoccuratdecadaltimescales,ascomparedtohundredsandthousandsofyearsinthepreviousexamples.Theeffectofthesechangesontheenvironmentandsocietyareofcurrentconcernbecauseoftheiroccurrenceduringourlifetime.AnexampleofcomplextimeserieswithmultidecadaltrendsaretheannualowsoftheNiger JOSÉA.RIALETAL.RiveratKoulikoro(Figure5)andtheoutowsfromtheAfricanequatoriallakes(Figure6).AsdepictedinFigure5,theNigerRiverseriesischaracterizedbyaslowdecayingautocorrelationfunction,reectingalong‘memory’,yetthereareoccasionallargerapidshiftsintheannualows.Sveinssonetal.(2003)showthatitispossibletosimulatestatisticallysimilartimeseriespatternsofstreamowsthatmayoccurinthefuture,andanalyzethevulnerabilityofexistingandprojectedwatersupplysystemsinthisregion.AsevidentinthetimeseriesoutowsfromtheequatoriallakesmeasuredattheMongallastationfortheperiod1915–1983(Figure6),itisnotnecessarytoemployanytypeofstatisticalanalysistorecognizethatsomethingpeculiarhappenedwiththeoutowtimeseriesaround1962.Somehydrologistshavearguedthatsuchasuddenshiftintheoutowmayhavebeentheresultofthelakes’operation(e.g.,Yevjevich,personalcommunication).However,others(e.g.,Lamb,1966,Figure1)havedocumentedthatLakeVictorialevelsalsoshowasimilarsuddenshiftduringthesametimeperiod.Furtheranalysisshowedthattheperiod1961–1964hasbeenthewettestconsecutiveperiodfortheentirehistoricalprecipitationrecord(Salasetal.,1981).Quitelikelynotonlyextremeprecipitationovertheequatoriallakes(e.g.,themajorwaterinputtoLakeVictoriaisfromprecipitationoverthelakeitself)butalsoincreasesinthecatchmentrunoffanddecreasesinthelakeevaporationandlandevaporation/transpiration(asare-sultofincreasedcloudinessofheavyrainyperiodsduringthesametimeperiod)mighthavecontributedtotheoccurrenceofsuchsignicantandabruptshiftsintheEquatoriallakeslevelsandlakeoutows.3.NonlinearIrregularOscillationsandChaosinOcean-AtmosphereInteractions3.1.NORTHATLANTICOSCILLATIONANDELNIÑOSOUTHERNOSCILLATIONTheNorthAtlanticOscillation(NAO)isalarge-scalealternationofatmosphericpressureelds(i.e.,atmosphericmass)withcentersofactionneartheIcelandicLowandtheAzoresHigh.Whensea-levelpressureislowerthanaverageintheIce-landiclowpressurecenter,itishigherthanaverageneartheAzores,andvice-versa;whichcanbedescribedasasortofsee-sawoscillatingbehaviorofthesystem.LikeENSO(ElNiño/SouthernOscillation),theNAOrepresentsoneofthemostimportantmodesofdecadal-scalevariabilityoftheclimatesystem,andaccountsforupto50%ofsea-levelpressurevariabilityonbothsidesoftheAtlantic(Hurrell,1995).TheNAOexertsastronginuenceonprecipitationandtemperatureonboththeeasternthirdofNorthAmericaandwesternhalfofEurope,particularlyduringwintermonths,andisresponsibleformanyclimaticanomalies(Beniston,1997;Hurrell,1995).TheNorthAtlanticOscillationindexiscomputedasadifferenceofsea-levelpressurebetweentheAzores(orLisbon,Portugal)andIceland.Itisameasure NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure5.TimeseriesofannualstreamowsoftheNigerRiver,Africafortheperiod1907–1999showingacomplexpatternofhighandlowows.Theautocorrelationfunctionshowstheeffectoflongmemory(modiedfromSveinssonetal.2003). Figure6.TimeseriesofannualoutowsfromtheAfricanequatoriallakesmeasuredattheMongallastationfortheperiod1915–1983,showinganabruptshiftaround1961andslowdecayingdownwardtrend(adaptedfromSalasetal.(1981).Withpermission). JOSÉA.RIALETAL.ofthestrengthofzonalowsovertheNorthAtlantic.ApositiveanomalyoftheNAOindexrepresentsawarmphaseoftheoscillation,withdrierandwarmerthanaverageconditionsinthesouthernhalfofEurope.WhentheNAOindexisstronglypositive,thereisageneralreductioninatmosphericmoistureathighelevationsintheAlps(seee.g.,BenistonandJungo,2002).BecauseofthehighlypositivenatureoftheNAOindexinthelatterpartofthe20thcentury,itisspeculatedherethatasignicantpartoftheobservedwarmingintheAlpsresultsfromshiftsintemperatureextremesinducedbythebehavioroftheNAO.Thesechangesarecapableofhavingprofoundimpactsonsnow,hydrology,andmountainvegetation.ENSOrepresentsanonlinearinterplayofcoupledocean-atmospherephenom-ena(e.g.,Tziperman,1994).ElNiñoisthewarmphaseofENSO,wherebyaweakeningoftheprevailingeasterlytradewindsintheequatorialPacicallowstheeastwardpropagationofwarmsurfacewaterthatnormallyaccumulatetothewestofthePacicbasin.Associatedareasofdeepconvection‘migrate’withthepropagationofthewarmsurfacewater,whicharetheprincipalenergysourceforconvection.TheareaofanomalouslywarmsurfacewateratthepeakofanElNiñoepisodecanreach30millionkm,roughly3timesthesizeofCanada,andcon-sequentlythesensibleandlatentheatexchangeattheocean-atmosphereinterfaceissufcienttoperturbclimaticpatternsglobally.Thisperturbationoccursinthreesimultaneoussteps:verticaltransferofenergy,heatandmoisturethroughthedeepconvection,horizontalpropagationthroughatmosphericowsathighelevationsand,intime,an‘overow’intothemid-latitudesynopticsystemsthatcanrein-forceorweakensurfacepressurepatternsanddeectthejetstreamsfromtheirusualtrajectories.ThecoldphaseofENSO,commonlyreferredtoasLaNiña,occurssometimes(butnotalways)attheendofanElNiñoevent.AnomalouslycoldwatersinvadethetropicalPacicregion,andthestrengthofLaNiñacaninsomeinstancesreversethepreviouslydiscussedanomalypatterns,i.e.,byreversingrespectiveprecipitationordroughtpatternsthatoccurduringanElNiñoevent.FromamechanisticpointofviewENSO’sirregularoscillationscanbeunder-stoodasthoseofalow-orderchaoticsystem(Pacicocean-atmosphereoscillator)drivenbytheseasonalcycle(Tzipermanetal.,1994).Sincechaoticsystemsarenottotallyunpredictable,atleastnotfortheshorttimescale,itmayeventuallybepossibletoestimatearangeofpredictabilityforENSOwithinwhichmodelscanforecastwithprecisionitsshort-termevolution.3.2.THEPACIFICDECADALOSCILLATIONOnecloseclimateprocesstoENSOisthePacicDecadalOscillation(PDO),whichisanatmosphere-oceanphenomenonassociatedwithpersistent,bimodalclimatepatternsintheNorthPacicOcean.ThePDOisanumericalindexbasedonseasurfacetemperatures(SSTs)inaspecicregionoftheNorthPacic(Mantuaetal.,1997),whichshowssuddenshiftingpatternswithmeanlevelsswitchingfrompositivetonegativeandviceversaintimescalesofabout20–50years(Salas NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure7.AutocorrelationfunctionandpowerspectrumobtainedforthetimeseriesofannualPDOindicesfortheperiod1900–1999.Thetimeseriesdepictsabruptshiftsinadditiontolowfrequencyvariationsthatappearnon-stationary.Mostofthepowerisatperiodsaround50years.Thespec-trumalsoshowsclearperiodicitiesataround5.7years(adaptedfromSalasandPielke(2002).WithpermissionfromJohnWiley&Sons,Inc.).andPielke,2002).InFigure7theautocorrelationfunctionandspectrumreecttheeffectofashiftinglowfrequencypattern.Suchshiftingpatternsillustratethenonstationarityoftheclimatesystem,inthattheassumptionofthestabilityofso-called‘climatenormals’doesnotadequatelyrepresenttherealclimatesystem.IncomparisonwithENSO,thephysicaldynamicsassociatedwiththePDOarenotwellunderstood,andthephaseofthePDOisgenerallynotpredictable,althoughitispossibletocreatescenariosdepictingsimilarshiftingPDOpatternsusingstochasticmethods(Sveinssonetal.,2003). JOSÉA.RIALETAL.4.NonlinearityandFeedbacksintheCarbonCycle4.1.ATMOSPHERECARBONCYCLENONLINEARFEEDBACKSTheocean,vegetation,andsoilonthelandarecurrentlyabsorbingabouthalfofthehumanemissionsofatmosphericcarbondioxide(CO),whichhassignicantim-plicationsforglobalclimatechange(Schimeletal.,2000).TheprocessesinvolvedinCOuptakebybothlandandoceanareknowntobesensitivetotheweatherandatmosphericCOconcentration,aswellasotherenvironmentalfactors,e.g.,humanperturbationstothenitrogencycle(Vitouseketal.,1997).Forexample,theuptakeofCObytheoceandependsuponthedifferenceintheCOconcentrationacrosstheocean-airinterface(whichtendstoincreaseasatmosphericCOrises),thesol-ubilityofCOinseawater(whichreducesastemperaturerises),andthetransportofCOtodepthintheocean(whichissuppressedbythermalstraticationandalsodependsontheoceancirculation(Sarmientoetal.,1998)).Likewise,COuptakebyplantstendstoincreasewithincreasingCO(dependingupontheavailabilityofnutrients,water,temperature,andothervariables,suchasozoneconcentration)(Körner,2000),butthebreakdownofsoilorganicmatter(SOM)isahighlynon-linearprocess,characterizedbyanumberofnonlinearfeedbackloopsinvolvingplants,microbes,SOM,andnutrientavailability.Cheng(1999)characterizedonesuchloopoperatinginforestsasfollows:(i)increasingCOuptakebyplantsleadstoanincreaseincarboninputstotherhizosphere(plantroots,soilmicroorganisms,soil);(ii)increasedsoilcarbonmayormaynotstimulateincreasesinmicrobialrespiration;(iii)alteredrhizosphererespirationmayeitherincreaseordecreaseSOMdecomposition;(iv)changesinSOMdecompositioncausechangesinsoilnutrientmineralizationandimmobilization;(v)changesinsoilnutrientdynam-icsaffecttreegrowth;and(vi)changesintreegrowthhavekeyimplicationsforglobalcarbonsequestering,andhence,climatechange.Supportingthis,Gilletal.(2002)reportedthatmineralizationratesinsoilsofaTexasgrasslanddecreasednonlinearlywithincreasingCO,andspeculatedthatsuchdecreasesinnitrogenavailabilitywilllikelyhaveadetrimentaleffectonlong-termplantproductivityand,ultimately,onecosystemcarbonstorage.4.2.LANDUSEVEGETATIONFEEDBACKSONTHEREGIONALSCALEEastmanetal.(2001a,b)haveshownthatland-usechange,grazing,andincreasedcarbondioxidecansignicantlyaltertheregionalclimatesysteminthecentralGreatPlainsoftheUnitedStates.Figure8showstheseeffectsonmaximumandminimumtemperature,rainfall,andabovegroundbiomassgrowthduringagrowingseasoninthisregion.Forexample,theeffectsofenhancedatmosphericconcentrationsofCOonplantgrowthonaseasonaltimescaleareshowntoamplifytheradiativeeffectofenhancedatmosphericCOontheregion.Thenon-lineareffectofvegetation-atmosphericfeedbackonthisscaleresultsinacomplexspatialandtemporalpatternofresponse.Notonlyisthereateleconnectionof NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure8.RAMS/GEMTMnonlinearcoupledmodelresults–theseasonaldomain-averaged(centralGreatPlains)for210daysduringthegrowingseason,contributionstomaximumdailytemperature,minimumdailytemperature,precipitation,andleafareaindex(LAI)dueto:naturalvegetation,radiation,andbiology(adaptedfromEastmanetal.(2001),withpermissionfromBlackwellPublishing).atmosphericconditionstolocationsdistantfromwherethelandfeedbackoccurs,butthelandscapeatdistantlocationsitselfisinuencedbythealteredweather.Inmanipulativevegetationexperimentswherecarbondioxideconcentrationsarearbitrarilyincreased,forexample,thisnonlinearfeedbackbetweentheatmosphereandlandsurfaceismissedsincethereisnofeedbacktotheregionalweather(withgreatervegetationcoverresultingingreatersummerrainfallandcoolermaximumtemperatures.)4.3.‘SATURATIONOFTHEATMOSPHERICOXIDATIONPROCESSTheremovalofalargenumberofgreenhouseandpollutinggasesfromtheat-mosphere(includingallhydrocarbons,carbonmonoxide(CO),nitrogenoxides(NO),sulfuroxides(SO))isaccomplishedthroughtheirreactionintheloweratmospherewiththehydroxylfreeradical(OH).Thisradicalisproducedbyprocessesinvolvingnitrogenoxides,ozone,watervaporandshort-wavelengthul-travioletradiation,andremovedbyreactionswiththeaforementionedgases.Allelsebeingequal,loweringemissionsofnitrogenoxidesand/orincreasingemis-sionsofcarbonmonoxideandmethane,coulderodeOHlevels,andtherefore JOSÉA.RIALETAL.increasethelifetimesoftheabovegreenhousegases(ThompsonandCicerone,1986;Prinnetal.,2001).Theatmosphericconcentrationofmethaneandothergreenhousegasesbecomesanonlinearfunctionofemissionratesincethereactionprocessitselfisdependentontheiratmosphericconcentrations,whichinturnisdependentontheemissions.Suchcombinationsofemissionchangesthereforeconstituteapositivefeedbackonclimatechange.4.4.METHANEPOSITIVEFEEDBACKPROCESSESMethaneisthethirdmostimportantgreenhousegas(afterwatervaporandcar-bondioxide).Twoofitssources,orpotentialsources,exhibitnonlinearbehavior.Methanogensinthewetlandsbecomeincreasinglyactivewithwarmingabovethefreezingpoint,whilemethaneclathratehydratesinsubmarineandsubtundralde-positsbecomemethanesourcesabovetheirknownstabilitytemperatures(Prinnetal.,1999;Buffett,2000).Atmosphericmethaneisalreadyasignicantconsumeroftheverychemical(hydroxylradicalOH)whichremovesit.Allelsebeingequal,increasedmethaneemissionsfromwetlandsandnewemissionsfromclathrateswillthereforelowerOHandincreasethelifetime(andhencegreenhouseforcing)ofmethaneaboveitscurrentvalues(Prather,1996).Thus,formethane,thetwosourcesaboveandtheOHsinkbehaveinawaythatcanconstituteasignicantpositivefeedbackonwarming.5.ConsequencesofaComplex,NonlinearEarthSystemInspiteofthenecessarilyincompletesetofexamplesdiscussedabovewehopetohavecontributedtoconveysomeofthechallengesthatresearchersfaceinaeldwherethedynamicsarestillbeingunderstood.Theexampleswechoseillustratetheexistenceofawidediversityofnonlinearinteractionsthatresultsintherecog-nizablevariabilityofclimaticprocesses,butwehaveonlytouchedthesurface.Ifspatialdomainandlong-distanceinteractionsareincluded,thereismuchmoretoinvestigate.Forexample,large-scaleatmosphericcirculationpatternsexertama-jorinuenceonlocalweather.Conversely,thunderstormdevelopmentexemplieshowsmall-scaleclimateprocessescanupscaletoaffectlarge-scaleatmosphericcirculationsatlongdistancesfromthesourceofthedisturbance(i.e.,teleconnec-tions).Anotherexampleistheland-usechangeinthetropics,whichnonlinearlyinuencesthunderstormpatternsthatpropagateworldwide(Chaseetal.,2000;Zhaoetal.,2000;Pielke,2001b;Pielkeetal.,2002).Ontheotherhand,ourexamplesleadtoaninevitableconclusion:sincetheclimatesystemiscomplex,occasionallychaotic,dominatedbyabruptchangesanddrivenbycompetingfeedbackswithlargelyunknownthresholds,climatepredic-tionisdifcult,ifnotimpracticable.RecallforinstancetheabruptD/Owarmingevents(Figure3a)ofthelasticeage,whichindicateregionalwarmingofoverCinGreenland(about4CatthelatitudeofBermuda).Thesenaturalwarming NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSeventswerefarstronger–andfaster–thananythingcurrentGCMworkpredictsforthenextfewcenturies.Thus,areasonablequestiontoaskis:Couldpresentglobalwarmingbejustthebeginningofoneofthosenatural,abruptwarmingepisodes,perhapsexacerbated(ortriggered)byanthropogenicCOemissions?SincethereisnoreliablemechanismthatexplainsorpredictstheD/O,itisnotclearwhetherthewarmingeventsoccuronlyduringaniceageorcanalsooccurduringaninterglacial,suchasthepresent.OtherlimitationsinpredictiveskillforavarietyofenvironmentalissueshavebeenrecentlydiscussedinSarewitzetal.(2000),sopredictionoffutureenvironmentalchangeseemsdaunting,atleastatHence,itappearsthatoneshouldnotrelyonpredictionastheprimarypol-icyapproachtoassessthepotentialimpactoffutureregionalandglobalclimatechange.Weargueinsteadthatintegratedassessmentswithintheframeworkofvulnerability(IAV)offerthebestsolution,wherebyriskassessmentanddisasterpreventionbecomethealternativetoprediction.IntheWorkingGroupIIReportoftheIPCC,vulnerabilityisdenedas‘thedegreetowhichasystemissusceptibleto,orunabletocopewith,adverseef-fectsofclimatechange,includingclimatevariabilityandextremes’(McCarthy,2001).Thevulnerabilityofaparticularsystemis,ofcourse,afunctionofboththemagnitudeandrateofclimatechangeaswellasthecurrentstateofthesystem(i.e.,itsadaptivecapacity).Usingthismethodology,‘impactmodels’areappliedtoassessthespectrumofpotentialchangesinenvironmentalforcingsthatresultindeleteriouseffectsonaparticularsystem.Thisquanticationofthevulnerabilityofasystemcanprovideinsightintotherelativeimportanceofclimate,withrespecttootherenvironmentalinuences.Forexample,Vörösmartyetal.(2000)usetheIAVapproachtodemonstratethatpopulationgrowthisamuchgreaterthreattopotablewatersuppliesthantheIPCC-predictedclimatechange.OtherexamplesarereportedinKabatetal.(2003),includingthemathematicalformalismtoinvestigatevulnerability.Thevalueofavulnerabilityassessmentisthattheapproachfocusesontheintegratedeffectofthespectrumofforcingsandfeedbacksonasystem(e.gwaterresources).Insteadofattemptingtopredictthefuturestateofasystem,therisktoaresourcefromallenvironmental(orother)threatsisdeterminedincludingthepresenceofthresholdsandtheirresiliency.Preventionsubstitutesprediction.Globalandregionalprojectionsbasedonmodels,thepaleoclimaticandpaleo-environmentalrecords,thehistoricalrecord,andworst-caseperturbationsofthehistoricalrecordcanbeusedtoestimatewhichvulnerabilitieshaveareasonablelikelihoodofoccurringandeventuallyhowtocopewiththem.Examplesoftheapplicationofthevulnerabilityapproach,whichcanbeusedtoassesstheresilienceandsensitivityofdifferentcountriesandculturestoenvironmentaldisturbance,include‘whatif’scenariossuchas:The‘dustbowl’yearsofthe1930sweretooccuragainintheUnitedStates;The‘LittleIceAge’weretoreoccurinWesternEurope; JOSÉA.RIALETAL.AnabruptwarmingonthescaleoftheD/O(Figure3a)wastooccur;orMajorvolcaniceruptionssimilartoTamborain1815weretotakeplace?Theconsequences(and,whenpossible,theprobabilities)oftheseeventsneedtobeassessedinthecontextofcurrentsocioeconomicandculturalconditions.6.RecommendedResearchAreasWehaveprovidedexamplestoillustratethatinputsandoutputswithintheEarth’sclimatesystemarenotproportionate,thatchangeisoftenepisodicandabrupt–notgradualandcontinuous–andmultipleequilibriaarethenorm,nottheexception–consistentwiththepresumednonlinearnatureofEarth’sclimatesystem.Actu-ally,thattheEarth’sclimatesystemrespondsnonlinearlyto(internalorexternal)forcingseemswidelyaccepted.However,whatsortofnonlinearitiesarethere,howstrong,andwhetherdrivenbyastronomicalforcing,byinternalfeedbacks,orbybothisfarlessclear,andonlypoorlyunderstood.Giventhis,itisimperativefortheresearchcommunitytoadoptaresearchstrategythatembracesthenonlinearclimateparadigmby,forinstance,learningtoidentifythesymptomsofnonlinearityinthedata,andtousethemoderntheoreticalandpracticalmeans(models,dataprocessing)ofdiagnosingmajorclimaticthreatstosociety.Therefore,wehaveagreedonalistofdesirableresearchstrategies–someofwhicharespecic,employingintegratedassessmentswithintheframeworkofavulnerabilityapproach,andsomeofwhicharegeneral.Thelistisnotintendedtobeexhaustivebuthopefullyillustrativeofthemanychallenges(andopportunities)fac-ingtheEarth’sclimatesystemresearchcommunity.Accordingly,werecommendExplorethelimitstoclimatepredictabilityandsearchforswitchesandchokepoints(orhotspots)ofenvironmentalchangeandvariability.Constructmodelstoexplainthenonlinearresponseoftheclimatesystemtochangesininsolationforcingduetoorbitalparameterchanges,anobjectivebestapproachedfromthepaleoclimateperspective.Improveourvisionoftheclimate’sfuturethroughabetterunderstandingofitshistory.Paleoclimateandhydroclimaterecordsexhibitabruptchangesintheformofrapidwarmingevents,theirregularoscillationsofENSO,catastrophicoods,sustaineddroughts,andmanyothernonlinearresponsecharacteristics.Extracting,identifying,categorizing,modelingandunderstandingthesenon-linearitieswillgreatlyhelpourabilitytounderstandthepresentandfuturestateoftheclimate.DevelopGCMscoupledtolow-dimensionalenergybalanceicesheet/litho-spherehybridmodels(e.g.,DecontoandPollard,2003)thatcansimulatetheinteractionbetweenhydrosphere,atmosphereandlandoverawiderangeofspatial(continentaltoglobal)andtemporal(centennial,millennia)scales. NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSUnderstandtheglobalconnectivityandvariabilityofocean-atmospherecou-pledphenomena,suchastheNorthPacicOscillation(NPO),thePacicDecadalOscillation(PDO),theArcticOscillation(AO),theNorthAtlanticOscillation(NAO),andtheElNiño/SouthernOscillation(ENSO).PromoteresearchtoimprovetechniquesthatmeasuredirectlyorindirectlythespectralvariabilityoftheSun’sirradianceoutputatdecadalandmillennialUnderstandthephysicsoftheoceanthermohalinecirculation(THC),whosecollapsemaybeoneimportantcauseofmajorclimaticchangeinWesternEuropeandNorthAmerica(Rahmstorf,2000).Performsensitivityexperimentswithglobalclimatemodelstoevaluatetheresponseoftheclimatesystemtobiosphericinteractions(includingvegetationdynamics,andtheeffectassociatedwiththeanthropogenicinputofcarbondioxideandnitrogencompounds),themicrophysicaleffectsoncloudsandprecipitationduetoanthropogenicaerosolemissions,andland-usechangeincludingfragmentationofecosystems.ExistingexperimentstoexploretheseeffectsincludeCoxetal.(2000),Eastmanetal.(2001b),andPielke(2001a,b).Investigatethebenetsandrisksoflarge-scaledeliberatehumaninterventionintheclimatesystem.Forexample,carbonsequestration,associatedwithland-managementpracticescouldbeastrategytoremoveCOfromtheat-mosphere.ThisshouldincludetheconcurrenteffectonwatervaporuxesintotheatmosphereandthenetirradiancereceivedattheEarth’ssurface(e.g.,Betts,2000;Claussen,2001;Pielke,2001c).Anotherexampleistheeffectoftheconstructionoflarge-scalewatersystemsandthecontroloflargelakessuchasLakeVictoriaandtheGreatLakesonregionalclimatesystems.Identifylocationsorregionsthatareparticularlysensitivetooreasilyim-pactedbytheplanetaryclimatesystem.TheAmazonrainforestanditsuvialregime(Coxetal.,2000;WerthandAvissar,2002),SoutheastAsia(Chaseetal.,2000),theNorthAtlanticOcean(Rahmstorf,2000),theArcticOcean(Foleyetal.,1994),theborealforest(Bonanetal.,1992),andtheNileRiversystemareexamplesofsuchsensitivelocations.Investigateinincreasingdetail,nonlinearinteractionsinvolvingchangesinbiosphericemissionsofchemicallyandradiativelyimportanttracegases,changesinatmosphericchemistryaffectingthelifetimesofthesegases,andresultantchangesinradiativeforcing.ExamplesofsuchinvestigationsusingsimpliedmodelsincludeHomesandEllis(1999)andPrinnetal.(1999).Toconclude,werecommendthedevelopmentofneweducationalinitiativesonenvironmental/climatescience.Thecomplexityoftheclimatesystem,itsmyr-iadofparts,interactions,feedbacksandunsolvedmysteriesneedsresearchersabletotranscendtheirownspecialties,jumpoverandbuildbridgesacrossar-ticialdisciplinaryboundaries.Hence,afundamentalrequirementforthefutureenvironmentalist/climatologistisarmgraspofthemathematicsandphysicsof JOSÉA.RIALETAL.nonlinearityandofthemethodsandgoalsofinterdisciplinaryclimatescience.WeenthusiasticallyendorseJohnLawton’s(2001)callforestablishingspecicprogramson‘EarthSystemScience’(ESS)atvariousinstitutionsanduniversi-ties,inordertoprovideupcominggenerationsofscientistswithinsightintothecomplexity,theinterdisciplinarynatureandthecrucialimportanceofthesethemesforthefutureofhumanity.ThegreatestchallengeistobuildastrongresearchinfrastructurethatdenesESS,andasLawtonnotes,thegreatestbarrieratpresentisthelackoforganizationsreadytonurturethisnewdiscipline.AcknowledgementsThispaperresultedfromaWorkshopentitled‘NonlinearResponsestoGlobalEnvironmentalChange:CriticalThresholdsandFeedbacks–IGBPNonlinearInitiative’,organizedbytheInternationalBiosphere-GeosphereProgram(IGBP)May26–27th,2001,DukeUniversity,Durham,NorthCarolina.Thispapercon-tributestothenewIGBPNonlinearInitiativeandtotheeffortsofindividualcoreprojectsonthistopicincludingBAHC,GCTE,PAGES,andGAIM.SupportforthisresearchincludesthatobtainedfromUSGSGrant#99CRAG005andSA9005CS0014.JARwaspartiallysupportedbyNSFgrant#ATM0241274(Paleocli-mateprogram).Weappreciatethedetailedcommentsofananonymousreviewer,theeditingskillsofDallasJ.StaleyandtheincisivecommentsofMayaElkibbi.ReferencesAlley,R.B.,Clark,P.U.,Keiwin,L.D.,andWebb,R.S.:1999,‘MakingSenseofMillennialScaleClimateChange’,inClark,P.U.,Webb,R.S.,andKeiwin,L.D.(eds.),MechanismsofGlobalClimateChangeatMillennialTimeScalesAmer.Geophys.Union,Geophys.Monogr.,385–Alley,R.B.,Marotzke,J.,Nordhaus,W.D.,Overpeck,J.T.,Peteet,D.M.,PielkeJr.,R.A.,Pier-Rehumbert,R.T.,Rhines,P.B.,Stocker,T.F.,Talley,L.D.,andWallace,J.M.:2003,‘AbruptClimateChange’,Science,2005–2010.AspenGlobalChangeInstitute:1998,‘ElementsofChange1997:SessionOne:ScalingfromSite-SpecicObservationstoGlobalModelGrids’.Beniston,M.:1997,‘VariationsofSnowDepthandDurationintheSwissAlpsovertheLast50Years:LinkstoChangesinLarge-ScaleClimaticForcings’,Clim.Change,281–300.Beniston,M.andJungo,P.:2002,‘ShiftsintheDistributionsofPressure,TemperatureandMoistureandChangesintheTypicalWeatherPatternsintheAlpineRegioninResponsetotheBehavioroftheNorthAtlanticOscillation’,Theor.Appl.Climatol.,29–42.Berger,A.andLoutre,M.F.:1991,‘InsolationValuesfortheClimateoftheLast10MillionofYears’,Quat.Sci.Rev.(4),297–317.Betts,R.A.:2000,‘OffsetofthePotentialCarbonSinkfromBorealForestationbyDecreasesinAlbedo’,Nature,187–190.Bonan,G.B.,Pollard,D.,andThompson,S.L.:1992,‘EffectsofBorealForestVegetationonGlobalClimate’,Nature,716–718. NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSBraconnot,P.,Joussaume,S.,Marti,O.,anddeNoblet-Ducoudre,N.:1999,‘SynergisticFeedbacksfromOceanandVegetationontheAfricanMonsoonResponsetoMid-HoloceneInsolation’,Geophys.Res.Lett.,2481–2484.Brovkin,V.,Claussen,M.,Petoukhov,V.,andGanopolski,A.:1998,‘OntheStabilityoftheAtmosphere-VegetationSystemintheSahara/SahelRegion’,J.Geophys.Res.,31613–Buffett,B.A.:2000,‘ClathrateHydrates’,Ann.Rev.EarthPlanet.Sci.,477–508.Chase,T.N.,Pielke,R.A.,Kittel,T.G.F.,Nemani,R.R.,andRunning,S.W.:2000,‘SimulatedImpactsofHistoricalLandCoverChangesonGlobalClimate’,Clim.Dyn.,93–105.Cherney,J.andStone,P.H.:1975,‘DroughtintheSahara:ABiogeophysicalFeedbackMechanism’,Science,434–435.Cheng,W.X.:1999,‘RhizosphereFeedbacksinElevatedCOTreePhysiol.,313–320.Clark,P.U.,Alley,R.B.,andPollard,D.:1999,‘NorthernHemisphereIceSheetInuencesonGlobalClimateChange’,Science,1104–1111.Clark,P.U.,Pisias,N.G.,Stocker,T.F.,andWeaver,A.J.:2002,‘TheRoleoftheThermohalineCirculationinAbruptClimateChange,Nature,863–869.Claussen,M.:1997,‘ModellingBiogeophysicalFeedbackintheAfricanandIndianMonsoonRegion’,Clim.Dyn.,247–257.Claussen,M.:2001,‘EarthSystemModels’,inEhlers,E.andKrafft,T.(eds.),UnderstandingtheEarthSystem:Compartments,ProcessesandInteractions,Springer-Verlag,Heidelberg,pp.145–Claussen,M.andGayler,V.:1997,‘TheGreeningofSaharaduringtheMid-Holocene:ResultsofanInteractiveAtmosphere-BiomeModel’,GlobalEcol.Biogeog.Lett.,369–377.Claussen,M.,Kubatzki,C.,Brovkin,V.,Ganopolski,A.,Hoelzmann,P.,andPachur,H.J.:1999,‘SimulationofanAbruptChangeinSaharanVegetationattheEndoftheMid-Holocene’,Geophys.Res.Lett.,2037–2040.Claussen,M.,Mysak,L.A.,Weaver,A.J.,Crucix,M.,Fichefet,T.,Loutre,M.-F.,Weber,S.L.,Alcamo,J.,Alexeev,V.A.,Berger,A.,Calov,R.,Ganopolski,A.,Goosse,H.,Lohmann,G.,Lunkeit,F.,Mokhov,I.I.,Petoukhov,V.,Stone,P.,andWang,Z.:2002,‘EarthSystemsModelsofIntermediateComplexity:ClosingtheGapintheSpectrumofClimateSystemModels’,Dyn.,579–586.Cowan,G.A.,Pines,D.,andMeltzer,D.:1999,Complexity,Metaphors,ModelsandReality,PerseusBooks,SantaFeInstitute.Cox,P.M.,Betts,R.A.,Jones,C.D.,Spall,S.A.,andTotterdell,I.J.:2000,‘AccelerationofGlobalWarmingDuetoCarbon-CycleFeedbacksinaCoupledClimateModel’,Nature,184–187.Cronin,T.M.(1999):PrinciplesofPaleoclimatology,ColumbiaU.Press,NewYork.DeConto,R.andPollard,D.:2003,‘RapidCenozoicGlaciationofAntarcticaInducedbyDecliningAtmosphericCONature,245–249.deMenocal,P.B.,Ortiz,J.,Guilderson,T.,Adkins,J.,Sarnthein,M.,Baker,L.,andYarusinsky,M.:2000,‘AbruptOnsetandTerminationoftheAfricanHumidPeriod:RapidClimateResponsetoGradualInsolationForcing’,Quat.Sci.Rev.,347–361.deNoblet-Ducoudre,N.andClaussen,M.:2001,‘Mid-HoloceneGreeningoftheSahara:FirstResultsoftheGAIM6000YearBPExperimentwithTwoAsynchronouslyCoupledAtmosphere/BiomeModels’,Clim.Dyn.,643–659.Doherty,R.,Kutzbach,J.,Foley,J.,andPollard,D.:2000,‘FullyCoupledClimate/DynamicalVegetationModelSimulationsoverNorthernAfricaduringtheMid-Holocene’,Clim.Dyn.Eastman,J.L.,Coughenour,M.B.,andPielke,R.A.Sr.:2001a,‘TheEffectsofCOandLandscapeChangeUsingaCoupledPlantandMeteorologicalModel’,GlobalChangeBiol.,797–815.Eastman,J.L.,Coughenour,M.B.,andPielke,R.A.Sr.:2001b,‘DoesGrazingAffectRegionalClimate’,J.Hydrometeor.,243–253. JOSÉA.RIALETAL.Foley,J.,Kutzbach,J.E.,Coe,M.T.,andLevis,S.:1994,‘FeedbacksbetweenClimateandBorealForestsduringtheHoloceneEpoch’,Nature,52–54.Gallagher,R.andAppenzeller,T.:1999,‘BeyondReductionism:IntroductiontoSpecialSectiononComplexSystems’,Science,79–109.Ganopolski,A.,Kubatzki,C.,Claussen,M.,Brovkin,V.,andPetoukhov,V.:1998,‘TheInuenceofVegetation-Atmosphere-OceanInteractiononClimateduringtheMid-Holocene’,ScienceGanopolski,A.andRahmstorf,S.:2001,‘RapidChangesofGlacialClimateSimulatedinaCoupledClimateModel’,Nature,153–158.Ghil,M.:1994,‘Cryothermodyamics:TheChaoticDynamicsofPaleoclimate’,PhysicaD,130–Gill,R.A.,Polley,H.W.,Johnson,L.J.,Maherali,H.,andJackson,R.:2002,‘NonlinearGrasslandsResponsestoPastandFutureAtmosphericCONature,279–282.Goldenfeld,N.andKadanoff,L.P.:1999,‘SimpleLessonsfromComplexity’,Science,87–89.GRIPProjectMembers:1993,‘ClimateInstabilityduringtheLastInterglacialPeriodRecordedintheGRIPIceCore’,Nature,203–207.Homes,K.J.andEllisa,J.H.:1999,‘AnIntegratedAssessmentModelingFrameworkforAssessingPrimaryandSecondaryImpactsfromCarbonDioxideStabilizationScenarios’,Environ.Model.Assess.,45–63.Hurrell,J.W.:1995,‘DecadalTrendsintheNorthAtlanticOscillationRegionalTemperaturesandPrecipitation’,Science,676–679Imbrie,J.,Berger,A.,Boyle,E.A.,Clemens,S.C.,Duffy,A.,Howard,W.R.,Kukla,G.,Kutzbach,J.,Martinson,D.G.,McIntyre,A.,Mix,A.C.,Molno,B.,Morley,J.J.,Peterson,L.C.,Pisias,N.G.,Prell,W.L.,Raymo,M.E.,Shackleton,N.J.,andToggweiler,J.R.:1993,‘OntheStructureandOriginofMajorGlaciationCycles2.The100,000-YearCycle’,Paleoceanography(6),699–735.Joussaume,S.,Taylor,K.E.,Braconnot,P.,Mitchell,J.F.B.,Kutzbach,J.E.,Harrison,S.P.,Prentice,I.C.,Broccoli,A.J.,Abe-Ouchi,A.,Bartlein,P.J.,Bonels,C.,Dong,B.,Guiot,J.,Herterich,K.,Hewit,C.D.,Jolly,D.,Kim,J.W.,Kislov,A.,Kitoh,A.,Loutre,M.F.,Masson,V.,McAvaney,B.,McFarlane,N.,deNoblet,N.,Peltier,W.R.,Peterschmitt,J.Y.,Pollard,D.,Rind,D.,Royer,J.F.,Schlesinger,M.E.,Syktus,J.,Thompson,S.,Valdes,P.,Vettoretti,G.,Webb,R.S.,andWyputta,U.:1999,‘MonsoonChangesfor6000YearsAgo:Resultsof18SimulationsfromthePaleoclimateModelingIntercomparisonProject(PMIP)’,Geophys.Res.Lett.,859–862.Kabat,P.,Claussen,M.,Dirmeyer,P.A.,Gash,J.H.C.,BravodeGuenni,L.,Meybeck,M.,PielkeSr.,R.A.,Vörösmarty,C.J.,Hutjes,R.W.A.,andLütkemeier,S.(eds.):2003,Vegetation,Water,HumansandtheClimate:ANewPerspectiveonanInteractiveSystem,Springer,Berlin,Heidelberg,NewYork,approx.550pp.,inpress.Kaplan,D.andGlass,L.:1995,UnderstandingNonlinearDynamics,Springer-Verlag,NewYork.Kim,Y.C.andPowers,E.J.:1978,‘DigitalBispectralAnalysisofSelf-ExcitedFluctuationSpectra’,Phys.Fluids,1452–1453.Körner,C.:2000,‘BiosphereResponsestoCOEnrichment’,Ecol.Appl.,1590–1619.Kutzbach,J.E.andGuetter,P.J.:1986,‘TheInuenceofChangingOrbitalParametersandSurfaceBoundaryConditionsonClimateSimulationsforthePast18,000Years’,J.Atmos.Sci.,1726–Lawton,J.H.:2001,‘EarthSystemScience’,Science,1965.Lamb,H.H.:1966,‘Climateinthe1960s’,Geogr.J.,183–212.Lorenz,E.N.:1963,‘DeterministicNonperiodicFlow’,J.Atmos.Sci.,130–141Mantua,N.J.,Hare,S.R.,Zhang,Y.,Wallace,J.M.,andFrancis,R.C.:1997,‘APacicInterdecadalClimateOscillationwithImpactsonSalmonProduction’,Bull.Amer.Meteorol.Soc.,1069– NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSMay,R.M.:1976,‘SimpleMathematicalModelswithVeryComplicatedDynamicalBehavior’,Nature,459–467.McCarthy,J.J.,Canziani,O.F.,Leary,N.A.,Dokken,D.J.,andWhite,K.S.(eds.):2001,ClimateChange2001:Impacts,AdaptationandVulnerability,ContributionofWorkingGroupIItotheThirdAssessmentReportoftheIntergovernmentalPanelonClimateChange(IPCC),CambridgeUniversityPress,Cambridge.Mudelsee,M.andSchultz,M.:1997,‘TheMid-PleistoceneClimateTransition:Onsetofthe100kaCycleLagsIceVolumeBuild-upby280ka’,EarthPlanet.Sci.Lett.,117–123.Nobes,D.C.,Bloomer,S.F.,Mienert,J.,andWestall,F.:1991,‘MilankovitchCyclesandNonlinearResponseintheQuaternaryRecordintheAtlanticSectoroftheSouthOceans’,ProceedingsODPScienticResults,551–576.Paillard,D.:2001,‘GlacialHiccups’,Nature,147–148.Petit,J.R.,Jouzel,J.,Raynaud,D.,andBarkov,N.I.:1999,‘ClimateandAtmosphericHistoryofthePast420,000YearsfromtheVostokIceCore,Antarctica’,Nature,429–436.PielkeSr.,R.A.:2001a,‘EarthSystemModeling–AnIntegratedAssessmentToolforEnviron-mentalStudies’,inMatsuno,T.andKida,H.(eds.),PresentandFutureofModelingGlobalEnvironmentalChange:TowardIntegratedModeling,TerraScienticPublishingCompany,Tokyo,Japan,pp.311–337.PielkeSr.,R.A.:2001b,‘InuenceoftheSpatialDistributionofVegetationandSoilsonthePredictionofCumulusConvectiveRainfall’,Rev.Geophys.,151–177.PielkeSr.,R.A.:2001c,‘CarbonSequestration:TheNeedforanIntegratedClimateSystemApproach’,Bull.Amer.Meteor.Soc.,2021.PielkeSr.,R.A.,Marland,G.,Betts,R.A.,Chase,T.N.,Eastman,J.L.,Niles,J.O.,Niyogi,D.,andRunning,S.:2002,‘TheInuenceofLand-UseChangeandLandscapeDynamicsontheClimateSystem-RelevancetoClimateChangePolicybeyondtheRadiativeEffectofGreenhouseGases’,Phil.Trans.A.SpecialThemeIssue,1705–1719.Pisias,N.G.,Mix,A.C.,andZahn,R.:1990,‘NonlinearResponseintheGlobalClimateSystem:EvidencefromBenthicOxygenIsotopicRecordinCoreRC13–110’,Paleoceanography(2),Prentice,I.C.,Jolly,D.,andBIOME6000members:2000,‘Mid-HoloceneandGlacial-MaximumVegetationGeographyoftheNorthernContinentsandAfrica’,J.Biogeogr.,507–519.Prather,M.J.:1996,‘NaturalModesandTimeScalesinAtmosphericChemistry:Theory,GWPsforandCO,andRunawayGrowth’,Geophys.Res.Lett.,2597–2600.Prinn,R.G.,Jacoby,H.D.,Sokolov,A.,Wang,C.,Xiao,X.,Yang,Z.,Eckaus,R.S.,Stone,P.H.,Ellerman,A.D.,Melillo,J.M.,Fitzmaurice,J.,Kicklighter,D.W.,Holian,G.L.,andLiu,Y.:1999,‘IntegratedGlobalSystemModelforClimatePolicyAssessment:FeedbacksandSensitivityStudies’,Clim.Change,469–546.Prinn,R.G.,Huang,J.,Weiss,R.F.,Cunnold,D.M.,Fraser,P.J.,Simmonds,P.G.,Harth,C.,Salameh,P.,O’Doherty,S.,Wang,R.H.J.,Porter,L.,andMiller,B.R.:2001,‘EvidenceforSubstantialVariationsofAtmosphericHydroxylRadicalsintheLastTwoDecades’,Science,1882–1888.Rahmstorf,S.:2000,‘TheThermohalineOceanCirculation:ASystemwithDangerousThresholds?’,Clim.Change,247–256.Rahmstorf,S.:2001,‘AbruptClimateChange’,inSteele,J.,Thorpe,S.,andTurekian,K.(eds.),EncyclopediaofOceanSciences,AcademicPress,London,pp.1–6.Raymo,M.E.:1997,‘TheTimingofMajorClimateTerminations’,Paleoceanography,577–585.Rial,J.A.:1999,‘PacemakingtheIceAgesbyFrequencyModulationofEarth’sOrbitalEccentric-ity’,Science,564–568.Rial,J.A.:2003,‘AbruptClimateChange:ChaosandOrderatOrbitalandMillennialScales’,Glob.Plan.Change,inpress.Rind,D.:1999,‘ComplexityandClimate’,Science,105–107. JOSÉA.RIALETAL.Sachs,J.P.andLehman,S.:1999,‘SubtropicalNorthAtlanticTemperatures60,000to30,000YearsAgo,Science,756–759.Salas,J.D.andPielkeSr.,R.A.:2002,‘StochasticCharacteristicsandModelingofHydroclimaticProcesses’,Chapter32inPotter,T.andColman,B.(eds.),HandbookofWeather,Climate,andWater,JohnWileyandSons,inpress.Salas,J.D.,Obeysekera,J.T.B.,andBoes,D.C.:1981,inSingh,V.P.(ed.),ModelingoftheEquato-rialLakesOutows,inStatisticalAnalysisofRainfallandRunoff,WaterResourcesPublications,Littleton,CO,pp.431–440.Sarewitz,D.,PielkeJr.,R.A.,andByerlyJr.,R.:2000,Prediction,Science,DecisionMakingandtheFutureofNature,IslandPress,Washington,DC,p.405.Sarmiento,J.L.,Hughes,T.M.C.,Stouffer,R.J.(etal.):1999,‘SimulatedResponseoftheOceanCarbonCycletoAnthropogenicClimateWarming’,Nature,245–249.Schellnhuber,H.J.:1999,‘EarthSystemAnalysisandtheSecondCopernicanRevolution’,Nature,C19–C26.Schimel,D.,Melillo,J.,Tian,H.Q.,McGuire,A.D.,Kicklighter,D.,Kittel,T.,Rosenblum,N.,Running,S.,Thorton,P.,Ojima,D.,Parton,W.,Kelly,R.,Sykes,M.,Neilson,R.,andRizzo,B.:2000,‘ContributionofIncreasingCOandClimatetoCarbonStoragebyEcosystemsintheUnitedStates’,Science,2004–2006.Stocker,T.F.andSchmittner,A.:1997,‘InuenceofCOEmissionRatesontheStabilityoftheThermohalineCirculation’,Science,862–865.Sveinsson,O.G.,Salas,J.D.,Boes,D.C.,andPielkeSr.,R.A.:2003,‘ModelingofLongTermVariabilityofClimaticandHydrologicProcesses’,J.Hydrometeor.,489–505.Thompson,A.M.andCicerone,R.J.:1986,‘PossiblePerturbationstoAtmosphericCO,CH,andJ.Geophys.Res.,10853–10864.Tziperman,E.,Stone,L.,Cane,M.A.,andJarosh,H.:1994,‘ElNiñoChaos:OverlappingofReso-nancesbetweentheSeasonalCycleandthePacicOcean-AtmosphereOscillator’,ScienceVitusenko,P.M.,Mooney,H.A.,Lubchenco,J.,andMelillo,J.M.:1997,‘HumanDominationofEarth’sEcosystems’,Science,494–499.Vörösmarty,C.J.P.,Green,P.,Salisbury,J.,andLammers,R.B.:2000,‘GlobalWaterResources:VulnerabilityfromClimateChangeAcidPopulationGrowth’,Science,284–288.Watson,A.J.andLovelock,J.E.:1984,‘BiologicalHomeostasisoftheGlobalRnvironment:TheParableofDaisyworld’,Tellus,284–289.Werth,D.andAvissar,R.:2002,‘TheLocalandGlobalEffectsofAmazonDeforestation’,Geophys.Res.,D20,8087,doi:10.1029/2001JD000717.Zhao,M.,Pitman,A.J.,andChase,T.:2000,‘TheImpactofLandCoverChangeontheAtmosphericCirculation’,Clim.Dyn.,467–477.(Received11March2002;inrevisedform1October2003)