EnsembleofClimateModels

ClaudiaTebaldiClimateCentral

andDepartmentofSta7s7cs,UBC

RetoKnu>,ReinhardFurrer,RichardSmith,BrunoSanso’

Outline

Mul7‐modelensembles(MMEs)‐adescrip7onatfacevalue

WhattheyareandwhattheycanprovideWheretofindthemHowtheyareused(inpar7cularinIPCC‐AR4)

Mul7‐modelensemblesandfutureclimatechangeprojec7ons

Whatarethemainuncertain7esinfutureprojec7ons, evengivenaspecificemissionscenarioWhatMMEscancharacterizeandwhattheycannotMainissues,challengesandvalueofmul7‐modelanalysis

Anexampleofanalysis,summaryandwayforward

This unprecedented collection of recent model output is officially known as the "WCRP CMIP3 multi-model dataset." It is meant to serve IPCC's Working Group 1, which focuses on the physical climate system -- atmosphere, land surface, ocean and sea ice -- and the choice of variables archived at the PCMDI reflects this focus. A more comprehensive set of output for a given model may be available from the modeling center that produced it.

With the consent of participating climate modelling groups, the WGCM has declared the CMIP3 multi-model dataset open and free for non-commercial purposes. After registering and agreeing to the "terms of use," anyone can now obtain model output via the ESG data portal, ftp, or the OPeNDAP server.

As of January 2007, over 35 terabytes of data were in the archive and over 337 terabytes of data had been downloaded among the more than 1200 registered users. Over 250 journal articles, based at least in part on the dataset, have been published or have been accepted for peer-reviewed publication.

hSp://www‐pcmdi.llnl.gov/ipcc/about_ipcc.php

TheseareGeneralCircula7onModels

Theyrepresentfullycoupledocean‐atmosphere(andlandandice)processes.

Themostrecentensemblehasamedianhorizontalresolu7on~250Km.

Atypicalexperimentconsistofahandfulofrunsof250years’worthofsimulatedclimate(outputsavedas6‐hourly,daily,monthly…).

~2months’worthof(super)computer7meforasinglerun.

O`eneachexperimentconsistsofan“ensemble”ofruns(differentini7alcondi7ons).

Thewayeachmodeldiscre7zesitsdomain,theprocessesthatitchoosestorepresentexplicitly,thosethatitneedstoparameterize(andthevalueforthoseparameters*)formitsstructuraliden7ty.

Thereisnowrongorrightwaytodoit.Nomodelisthetruemodel.

Mul7‐modelensemblesgetatthisstructuraluncertainty.

Otheruncertain7esare:‐parameteruncertainty‐ini7alcondi7onsuncertainty‐boundaryuncertainty(SRESscenarios)

Perturbedphysicsensemblesdealwithparameteruncertaintywithinasinglemodel.

Themostrecentmul7‐modelensembleismadeofabout20state‐of‐the‐artGCMs

Whenitcomestofutureprojec7ons,eachmodelgivesitsownprojec7on.

Some7meonlyinabsolutevalue,some7meinsigntoo!

Agreementbecomeshardertogetthefinerthespa7alandtemporalscale.

S7pplingmeans90%ofmodelsormoreagreeinthesignofchange

S7pplingmeans90%ormoreofmodelsagreeinthesignofchange

Whatisbehindagreement/disagreement:Adistribu5onofprojectedchanges

Lookingatregionalaveragesoftemperaturechange

Whatisbehindagreement/disagreement:Adistribu5onofprojectedchanges

Lookingatregionalaveragesof%precipita7onchange

IPCC‐AR4WG1Chapter10and11,GlobalandRegionalFutureProjec7ons:

Mostoftheprojectedchangesareshownasmul7‐modelmeans.Inter‐modelstandarddevia7on/rangeiso`enusedasameasureoftheuncertainty

Whatarewelookingat?Whataretheuncertain7escharacterized?Whatarethosele`out?

Whymeans?Whystandarddevia7ons?

Theproblemofsynthesizingmul7plemodelsprojec7onshasaBayesianflavor:

Westartwithapriordistribu7on(ofmodels)whichdeterminestheirini7alweight.

Weobserveoutputandwecomparetherealquan77esofinterestbuildingalikelihood.

Combiningthetwowegetataposterior/finaldistribu7on.

Atthispointin7me,formostques7ons,thelikelihoodisnotrobustlyconstrainingthefinalresults,andthepriorremainsacrucialingredient.

So,whatisthepriorwearedealingwithwhenwelookatmul7plemodels,andwhatkindofsamplearethese20‐somethingmodelsweuseallthe7me?

WhatkindofsampleistheCMIP3ensemble?

 Acollec7onofbestguesses Likelymutuallydependent(modelssharecomponents) Notrandom,butnotsystema7ceither

Asimpleexampleandasimplefix

ThemodelmeanisbeEerthanasinglemodel

Butthereexistareaswhereerrorpersists

Modelerrorsarenotindependent

Histogramsofcorrela7oncoefficientsofallpossiblepairsofmodelbias(simulatedminusobservedfieldsofmeantemperature1980‐2000).

BehaviorofRMSerrorwithincreasingnumberofmodelsaveraged.

Theyarenotdesignedtosampleawiderangeofuncertainty

IPCC‐AR4wg1Ch10

Climatesensi7vityofCMIP3modelsisgreencurve

Ensemblemeansandensemblerangesareeasytointerpret,buttheyarenotjus7fiedbythenatureofthesample

Themodelshavesystema7candcommonerrors

Likely,theuncertaintyislargerthanwhatisrepresentedbytheensembleofbestguesses

Differen

tmod

elshavedifferen

tstren

gthsand

weaknesses Metricsof

performancefordifferentmodels(columns),acrossdifferentdiagnos7cs(rows).Blueisgood,Redisbad.Firsttwocolumnsareensemblemeanandmedian.

Gleckleretal.,(2008)JGR‐Atmos

Notallmodelsarecreatedequal

Shouldweusemodelperformanceinreplica5ngobservedclimateto“weigh”amodelmoreorless?

Whysta5s5calmodelingofclimatemodeloutput?

Simplemeansandstandarddevia7onsarenotsupportedbythenatureofthedata.

Throughsta7s7calmodelingofGCMdataandobserva7onswecancombineinforma7oninwaysthatbringvalida7onandperformancetobearonthefinalop7males7matesofwhatwearea`er:

Usually,es7matesoftemperatureorprecipita7onchangeforspecificregions/seasons/7meperiods.Usuallyaveragequan77es,sincebydefini7oncombiningmodelsproducesa“smoothed”versionofthequan7tywearea`er.

AnexampleofhowwecombineGCMoutput/observa5onstoproduceprobabilis5cprojec5onsofTemperatureandPrecipita5onchange

Theanalysisisperformedoverregionalanddecadalaverages,foragivenseason(e.g.,DJF)andaspecifiedemissionscenario.

Data

€

Ot =OtT

OtP

t =1950,1960,...2000

X jt =X jtT

X jtP

t =1950,1960,...,2000,2010,...,2100j =1,...,M

Observeddecadalmeansoftemperatureandprecipita7on

Modeleddecadalmeansoftemperatureandprecipita7on

Assump5onsbehindthesta5s5calmodel,inwords

• thetrueclimatesignal7meseries(bothtemperatureandprecipita7on)isapiecewiselineartrendwithanelbowat2000,toaccountforthepossibilitythatfuturetrendswillbedifferentfromcurrenttrends;

• superimposedtothepiecewiselineartrendsisabivariategaussiannoisewithafullcovariancematrix,whichintroducescorrela7onbetweentemperatureandprecipita7on;

• observeddecadalaveragesprovideagoodes7mateofthecurrentseriesandtheircorrela7on,andoftheiruncertainty;

• GCMsmayhavesystema7caddi7vebias,assumedconstantalongthelengthofthesimula7on;

• a`erthebiasineachGCMsimula7onisiden7fiedthereremainsvariabilityaroundthetrueclimatesignalthatismodelspecific.

Allunknownquan77es

haveuninforma7vepriordistribu7ons,andtheirjointposteriorises7matedthroughMCMC.

€

αT ,α P ,βT ,β P ,γT ,γ P ,d jT ,d j

P ,φ jT ,φ j

Pβxo,βxj

€

OtT ~ N µt

T ;ηT[ ]Ot

P ~ N µtP + βxo(Ot

T −µtT );ηP[ ]

X jtT ~ N µt

T + d jT ;φ j

T[ ]X jt

P ~ N µtP + βxj (X jt

T −µtT − d j

T ) + d jP ;φ j

P[ ]

µtT

µtP

=

αT + βT t + γT (t −T0)χ t

α P + β P t + γ P (t −T0)χ t

LikelihoodModel

1960 1980 2000 2020 2040 2060 2080 2100

2.0

2.2

2.4

2.6

2.8

decades

mm/day

1960 1980 2000 2020 2040 2060 2080 2100

12

14

16

18

20

decades

degre

es C

!"#$%&'('!))%*+,%")('!))

Temp. change, degrees C

% P

recip

change

1.5 2.0 2.5 3.0 3.5 4.0 4.5

05

10

0 5 10

0.0

00.0

50.1

00.1

50.2

00.2

5

% Precip change

% of baseline average

PD

F

1 2 3 4

0.0

0.5

1.0

1.5

Temperature change

degrees C

PD

F

GLOB, JJA

degrees C

mm

/day

12 14 16 18 20

2.0

2.2

2.4

2.6

2.8

Thisanalysis

Canquan7fysystema7cbiases,models’reliability.

Canprovideaprobabilis7c“bestguess”fortheclimatesignalasaweightedmeanbetweenobserva7onsandmodels’centraltendency.

Canprovideapredic7vedistribu7onfora“newmodel”,

ItisaninformedsynthesisofthedataYoucanacceptitassuchifyouagreewithitsassump7ons(likelihoodofthedata,priorsontheunknownparameters)

Whatdoesittellusabouttherealworld?

Conclusions

Combiningmul7‐modelensemblescanhelpquan7fyuncertain7esinfutureclimateprojec7ons,exploringandcomparingmodels’structuralcharacteris7cs.

Thenon‐systema7cnatureofthesampling,thein‐breedingamongthepopula7onofmodelsthecomplexi7esofchoosinganddrawinginferencefromdiagnos7cs,theimpossibilityofverifica7onpresentuniquechallengesintheformula7onofarigoroussta7s7calapproachatquan7fyingtheseuncertain7es.

Conclusions

Thingsareboundtobecomeevenmoreinteres7ng,withtheintroduc7onofmorecomplexGCMsandtheincreasingheterogeneityoftheseensembles;everincreasingdemandsoncompu7ngresourcesandtheconsequenttrade‐offsofresolu7onvsscenariosvsensemblesize.

Thewayforward:coordinatedexperiments,mul7‐modelplussingle‐modelensembles,process‐basedevalua7ontranslatedintometrics,representa7onofmodeldependencies,quan7fica7onofcommonbiases.

Allalong,transparencyandtwowaycommunica7onbetweenscien7stsandusers,stakeholders,policymakers.