ClimaticChange11 ID: 418062
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NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDSWITHINTHEEARTHSCLIMATESYSTEMJOSÉA.RIAL,ROGERA.PIELKESR.,MARTINBENISTONMARTINCLAUSSEN,JOSEPCANADELL,PETERCOX,HERMANNHELDNATHALIEDENOBLET-DUCOUDRÉ,RONALDPRINN ClimaticChange1138,2004.©2004KluwerAcademicPublishers.PrintedintheNetherlands. JOSÉA.RIALETAL.thethermohalinecirculationoftheNorthAtlanticocean,suggesttheexistenceofthresholds,multipleequilibria,andotherfeaturesthatmayresultinepisodesofrapidchange(StockerandSchmittner,1997).AsdescribedinKabatetal.(2003),theEarthsclimatesystemincludesthenaturalspheres(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.LINEARANDNONLINEARSYSTEMSEvenanelementarydescriptionofEarthsclimatesystemmustdealwiththefactthatitiscomposedoftheabovesubsystemsallinterconnectedandopen,allowinguxesofmass,energyandmomentumfromandtoeachother(seeFigure1).SincetheEarthitselfisaclosedsystem,theseuxeseventuallycyclethrough,sothatoutputsre-enterthesystemtobecomeinputs,creatingfeedbacksandfeedbackchains.Eventually,eachsubsystemaffectstheresponseofeveryothersubsystemandoftheclimateasawhole.Itisthiscrosstalkamongthedifferentpartsoftheclimatethatengendersthedisproportionaterelationsbetweeninputandoutputtypicalofanonlinearsystem.Thephrasethewholeismorethanthesumofitspartsunderscoresthefailureoftheprincipleofsuperpositioninanonlinearsystemsuchastheclimate.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,anoscillatorylinearsystemsfrequencyalwaysequalsthatoftheforcing,whilethespectralresponseofanonlinearsystemtooscillatoryexternalforcingusuallyexhibitsfrequenciesnotpresentintheforcing(suchascombinationtones),phaseandfrequencycoupling,synchronizationandotherindicationsofnonlinearityoftendetectedinpastclimatedata(e.g.,Pisiasetal.,1990).1.2.CHAOSANDCOMPLEXITYThus,nonlinearitygivesrisetounexpectedstructuresandeventsintheformofabrupttransitionsacrossthresholds,unexpectedoscillations,andchaos(KaplanandGlass,1995).Actually,theclimatesystemisnotonlychaotic,itisalsocomplex(Rind,1999),inthesensethatitiscomposedofmanypartswhose JOSÉA.RIALETAL.interactionscan,throughaprocessstillnotcompletelyunderstood(Cowanetal.,1999),provokespontaneousself-organizationandtheemergenceofcoherent,col-lectivephenomenathatcanbedescribedonlyathigherlevelsthanthoseoftheindividualparts(GoldenfeldandKadanoff,1999).Therefore,itisusefultoestab-lishforclarityssakethatchaosandcomplexityaredifferentaspectsofnonlinearresponse.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.PAPERORGANIZATIONThegoalofthispaperistodiscusskeyissuesandquestionsrelatedtononlinearityintheEarthsclimatesystemanditsimplicationsinglobalclimatechangeresearch.First,wediscussexamplesofnonlinearclimateresponsefromobservationsofabruptclimatechangedetectedinbothpre-historicandrecenttimeseries(Exam-ples2.12.5).Nextwediscussmodelsofcoupledoceanandatmospheremediatedbychaoticdynamics(Examples3.13.2).Finallywelookatnonlinearitiesinthecarboncycleandtheeffectsofbiogeochemicalfeedbacksinmodelsofpresentandfutureclimatechange(Examples4.14.4).Aftertheexamples,weaddressscaleandmethodologicalissuesasrelatedtosomeofthechallengesinpredictingtheconsequencesofhumanactionsontheEarthsclimatesystem.Forexample,giventhenearlycertainoccurrenceofsuddentransitionsbetweenclimatestates,ispredictionperseachievable?Wesuggestanalternativeandhighlyrobustapproachusingintegratedassessmentswithintheframeworkofvulnerabilitystudies,thedetailsofwhichwethendiscussandjustify.Toconcludeweprovideaseriesofrecommendationsforresearchpriorities,includingelucidatingpotentialsourcesofnonlinearity,identifyingkeyfeedbacksandlinkagesintheEarthsclimatesystem,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(secularchangesinEarthsorbitaleccentricity,spinaxis,andprecession)appearstobestronglynonlinear.Forinstance,itiswellknownthatwhilethemaindrivingfrequencyoftheiceagesisabout100ky(1ky=1,000years)thetimingbetweenconsecutiveglacialperiodshasbeensteadilyincreasingfrom80kyto120kyoverthelast500ky(Raymo,1997;Petitetal.,1999).Thisfeature,plusthenearabsenceofalargeresponseatthestrongesteccentricityforcingperiod(413ky)andthepresenceofsignicantvarianceatfrequenciesnotpresentintheorbitalforcing,arestrongevidenceofnonlinearityintheclimatesresponsetoorbitalforcing(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,couldhaveshiftedtheclimatesystemssensitivitytoforcingatlowerfrequency.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?TheDansgaardOeschger(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(90006000yearsago),NorthAfricawaswetterandtheSaharawasmuchsmallerthantoday(Prenticeetal.,2000).Annualgrassesandshrubscoveredthedesert,andtheSahelreachedasfaras23N(Claussenetal.,1999),over500kmnorthofitspresentlocation.DuringtheHoloceneoptimumaslightlyincreasedtiltoftheEarthsspinaxisandperihelioninJulyledtostrongerinsolationoftheNorth-ernHemisphereduringsummertherebystrengtheningtheNorthAfricansummermonsoon(KutzbachandGuetter,1986).However,theNorthAfricanclimateissensitivetochangesinlandsurfacesalbedo,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)timeseriesofGreenlandsicecoresknownastheDansgaard-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(20N30Nand15W50E)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,reectingalongmemory,yetthereareoccasionallargerapidshiftsintheannualows.Sveinssonetal.(2003)showthatitispossibletosimulatestatisticallysimilartimeseriespatternsofstreamowsthatmayoccurinthefuture,andanalyzethevulnerabilityofexistingandprojectedwatersupplysystemsinthisregion.AsevidentinthetimeseriesoutowsfromtheequatoriallakesmeasuredattheMongallastationfortheperiod19151983(Figure6),itisnotnecessarytoemployanytypeofstatisticalanalysistorecognizethatsomethingpeculiarhappenedwiththeoutowtimeseriesaround1962.Somehydrologistshavearguedthatsuchasuddenshiftintheoutowmayhavebeentheresultofthelakesoperation(e.g.,Yevjevich,personalcommunication).However,others(e.g.,Lamb,1966,Figure1)havedocumentedthatLakeVictorialevelsalsoshowasimilarsuddenshiftduringthesametimeperiod.Furtheranalysisshowedthattheperiod19611964hasbeenthewettestconsecutiveperiodfortheentirehistoricalprecipitationrecord(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,Africafortheperiod19071999showingacomplexpatternofhighandlowows.Theautocorrelationfunctionshowstheeffectoflongmemory(modiedfromSveinssonetal.2003). Figure6.TimeseriesofannualoutowsfromtheAfricanequatoriallakesmeasuredattheMongallastationfortheperiod19151983,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.Associatedareasofdeepconvectionmigratewiththepropagationofthewarmsurfacewater,whicharetheprincipalenergysourceforconvection.TheareaofanomalouslywarmsurfacewateratthepeakofanElNiñoepisodecanreach30millionkm,roughly3timesthesizeofCanada,andcon-sequentlythesensibleandlatentheatexchangeattheocean-atmosphereinterfaceissufcienttoperturbclimaticpatternsglobally.Thisperturbationoccursinthreesimultaneoussteps:verticaltransferofenergy,heatandmoisturethroughthedeepconvection,horizontalpropagationthroughatmosphericowsathighelevationsand,intime,anoverowintothemid-latitudesynopticsystemsthatcanrein-forceorweakensurfacepressurepatternsanddeectthejetstreamsfromtheirusualtrajectories.ThecoldphaseofENSO,commonlyreferredtoasLaNiña,occurssometimes(butnotalways)attheendofanElNiñoevent.AnomalouslycoldwatersinvadethetropicalPacicregion,andthestrengthofLaNiñacaninsomeinstancesreversethepreviouslydiscussedanomalypatterns,i.e.,byreversingrespectiveprecipitationordroughtpatternsthatoccurduringanElNiñoevent.FromamechanisticpointofviewENSOsirregularoscillationscanbeunder-stoodasthoseofalow-orderchaoticsystem(Pacicocean-atmosphereoscillator)drivenbytheseasonalcycle(Tzipermanetal.,1994).Sincechaoticsystemsarenottotallyunpredictable,atleastnotfortheshorttimescale,itmayeventuallybepossibletoestimatearangeofpredictabilityforENSOwithinwhichmodelscanforecastwithprecisionitsshort-termevolution.3.2.THEPACIFICDECADALOSCILLATIONOnecloseclimateprocesstoENSOisthePacicDecadalOscillation(PDO),whichisanatmosphere-oceanphenomenonassociatedwithpersistent,bimodalclimatepatternsintheNorthPacicOcean.ThePDOisanumericalindexbasedonseasurfacetemperatures(SSTs)inaspecicregionoftheNorthPacic(Mantuaetal.,1997),whichshowssuddenshiftingpatternswithmeanlevelsswitchingfrompositivetonegativeandviceversaintimescalesofabout2050years(Salas NONLINEARITIES,FEEDBACKSANDCRITICALTHRESHOLDS Figure7.AutocorrelationfunctionandpowerspectrumobtainedforthetimeseriesofannualPDOindicesfortheperiod19001999.Thetimeseriesdepictsabruptshiftsinadditiontolowfrequencyvariationsthatappearnon-stationary.Mostofthepowerisatperiodsaround50years.Thespec-trumalsoshowsclearperiodicitiesataround5.7years(adaptedfromSalasandPielke(2002).WithpermissionfromJohnWiley&Sons,Inc.).andPielke,2002).InFigure7theautocorrelationfunctionandspectrumreecttheeffectofashiftinglowfrequencypattern.Suchshiftingpatternsillustratethenonstationarityoftheclimatesystem,inthattheassumptionofthestabilityofso-calledclimatenormalsdoesnotadequatelyrepresenttherealclimatesystem.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/GEMTMnonlinearcoupledmodelresultstheseasonaldomain-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,FEEDBACKSANDCRITICALTHRESHOLDSeventswerefarstrongerandfasterthananythingcurrentGCMworkpredictsforthenextfewcenturies.Thus,areasonablequestiontoaskis:Couldpresentglobalwarmingbejustthebeginningofoneofthosenatural,abruptwarmingepisodes,perhapsexacerbated(ortriggered)byanthropogenicCOemissions?SincethereisnoreliablemechanismthatexplainsorpredictstheD/O,itisnotclearwhetherthewarmingeventsoccuronlyduringaniceageorcanalsooccurduringaninterglacial,suchasthepresent.OtherlimitationsinpredictiveskillforavarietyofenvironmentalissueshavebeenrecentlydiscussedinSarewitzetal.(2000),sopredictionoffutureenvironmentalchangeseemsdaunting,atleastatHence,itappearsthatoneshouldnotrelyonpredictionastheprimarypol-icyapproachtoassessthepotentialimpactoffutureregionalandglobalclimatechange.Weargueinsteadthatintegratedassessmentswithintheframeworkofvulnerability(IAV)offerthebestsolution,wherebyriskassessmentanddisasterpreventionbecomethealternativetoprediction.IntheWorkingGroupIIReportoftheIPCC,vulnerabilityisdenedasthedegreetowhichasystemissusceptibleto,orunabletocopewith,adverseef-fectsofclimatechange,includingclimatevariabilityandextremes(McCarthy,2001).Thevulnerabilityofaparticularsystemis,ofcourse,afunctionofboththemagnitudeandrateofclimatechangeaswellasthecurrentstateofthesystem(i.e.,itsadaptivecapacity).Usingthismethodology,impactmodelsareappliedtoassessthespectrumofpotentialchangesinenvironmentalforcingsthatresultindeleteriouseffectsonaparticularsystem.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,includewhatifscenariossuchas:Thedustbowlyearsofthe1930sweretooccuragainintheUnitedStates;TheLittleIceAgeweretoreoccurinWesternEurope; JOSÉA.RIALETAL.AnabruptwarmingonthescaleoftheD/O(Figure3a)wastooccur;orMajorvolcaniceruptionssimilartoTamborain1815weretotakeplace?Theconsequences(and,whenpossible,theprobabilities)oftheseeventsneedtobeassessedinthecontextofcurrentsocioeconomicandculturalconditions.6.RecommendedResearchAreasWehaveprovidedexamplestoillustratethatinputsandoutputswithintheEarthsclimatesystemarenotproportionate,thatchangeisoftenepisodicandabruptnotgradualandcontinuousandmultipleequilibriaarethenorm,nottheexceptionconsistentwiththepresumednonlinearnatureofEarthsclimatesystem.Actu-ally,thattheEarthsclimatesystemrespondsnonlinearlyto(internalorexternal)forcingseemswidelyaccepted.However,whatsortofnonlinearitiesarethere,howstrong,andwhetherdrivenbyastronomicalforcing,byinternalfeedbacks,orbybothisfarlessclear,andonlypoorlyunderstood.Giventhis,itisimperativefortheresearchcommunitytoadoptaresearchstrategythatembracesthenonlinearclimateparadigmby,forinstance,learningtoidentifythesymptomsofnonlinearityinthedata,andtousethemoderntheoreticalandpracticalmeans(models,dataprocessing)ofdiagnosingmajorclimaticthreatstosociety.Therefore,wehaveagreedonalistofdesirableresearchstrategiessomeofwhicharespecic,employingintegratedassessmentswithintheframeworkofavulnerabilityapproach,andsomeofwhicharegeneral.Thelistisnotintendedtobeexhaustivebuthopefullyillustrativeofthemanychallenges(andopportunities)fac-ingtheEarthsclimatesystemresearchcommunity.Accordingly,werecommendExplorethelimitstoclimatepredictabilityandsearchforswitchesandchokepoints(orhotspots)ofenvironmentalchangeandvariability.Constructmodelstoexplainthenonlinearresponseoftheclimatesystemtochangesininsolationforcingduetoorbitalparameterchanges,anobjectivebestapproachedfromthepaleoclimateperspective.Improveourvisionoftheclimatesfuturethroughabetterunderstandingofitshistory.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).PromoteresearchtoimprovetechniquesthatmeasuredirectlyorindirectlythespectralvariabilityoftheSunsirradianceoutputatdecadalandmillennialUnderstandthephysicsoftheoceanthermohalinecirculation(THC),whosecollapsemaybeoneimportantcauseofmajorclimaticchangeinWesternEuropeandNorthAmerica(Rahmstorf,2000).Performsensitivityexperimentswithglobalclimatemodelstoevaluatetheresponseoftheclimatesystemtobiosphericinteractions(includingvegetationdynamics,andtheeffectassociatedwiththeanthropogenicinputofcarbondioxideandnitrogencompounds),themicrophysicaleffectsoncloudsandprecipitationduetoanthropogenicaerosolemissions,andland-usechangeincludingfragmentationofecosystems.ExistingexperimentstoexploretheseeffectsincludeCoxetal.(2000),Eastmanetal.(2001b),andPielke(2001a,b).Investigatethebenetsandrisksoflarge-scaledeliberatehumaninterventionintheclimatesystem.Forexample,carbonsequestration,associatedwithland-managementpracticescouldbeastrategytoremoveCOfromtheat-mosphere.ThisshouldincludetheconcurrenteffectonwatervaporuxesintotheatmosphereandthenetirradiancereceivedattheEarthssurface(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.WeenthusiasticallyendorseJohnLawtons(2001)callforestablishingspecicprogramsonEarthSystemScience(ESS)atvariousinstitutionsanduniversi-ties,inordertoprovideupcominggenerationsofscientistswithinsightintothecomplexity,theinterdisciplinarynatureandthecrucialimportanceofthesethemesforthefutureofhumanity.ThegreatestchallengeistobuildastrongresearchinfrastructurethatdenesESS,andasLawtonnotes,thegreatestbarrieratpresentisthelackoforganizationsreadytonurturethisnewdiscipline.AcknowledgementsThispaperresultedfromaWorkshopentitledNonlinearResponsestoGlobalEnvironmentalChange:CriticalThresholdsandFeedbacksIGBPNonlinearInitiative,organizedbytheInternationalBiosphere-GeosphereProgram(IGBP)May2627th,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.,385Alley,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,20052010.AspenGlobalChangeInstitute:1998,ElementsofChange1997:SessionOne:ScalingfromSite-SpecicObservationstoGlobalModelGrids.Beniston,M.:1997,VariationsofSnowDepthandDurationintheSwissAlpsovertheLast50Years:LinkstoChangesinLarge-ScaleClimaticForcings,Clim.Change,281300.Beniston,M.andJungo,P.:2002,ShiftsintheDistributionsofPressure,TemperatureandMoistureandChangesintheTypicalWeatherPatternsintheAlpineRegioninResponsetotheBehavioroftheNorthAtlanticOscillation,Theor.Appl.Climatol.,2942.Berger,A.andLoutre,M.F.:1991,InsolationValuesfortheClimateoftheLast10MillionofYears,Quat.Sci.Rev.(4),297317.Betts,R.A.:2000,OffsetofthePotentialCarbonSinkfromBorealForestationbyDecreasesinAlbedo,Nature,187190.Bonan,G.B.,Pollard,D.,andThompson,S.L.:1992,EffectsofBorealForestVegetationonGlobalClimate,Nature,716718. 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