ì

Regime-dependentpredictabilityandforecasterror

spectraofinitializedforecasts

Acknowledgements

ì  ThankstoLauraFerranti,SusannaCorti,YagaRichter,HannahChristensen

Regimesinclimate

ì  E.g.Vautard1990,KimotoandGhil,1993;Cortietal.1999

ì  Identificationofregimesandpreferredtransitions

ì  Climatestatisticperspective,oftenexpressedastransitionmatrix

Vautard1990Cortietal.1999 KimotoandGhil,1993

Flow-DependentVerificationoftheECMWFEnsembleovertheEuro-AtlanticSector

ì  ExtendedpredictabilityofstatesthatprojectatinitialtimeonNAO-

ì  Initializedforecasts

Ferrantietal.2015

ExperimentSetup

ì  Z500anomaliesì  ExtendedWinterOct-Marì  NAOregion20:80°N,90°W:40°Eì  PNAregion20:85°N,120°E:120°W

ì  Potentialpredictabilityindailyoutputof

CESM1.1(Largeensemble)ì  400yearsì  Notinitialized!ì  PerfectModelScenarioì  ProjectontoEOFphasespace

PacificNorthAmericanPattern

PNA-ì  RidgeoverWesternNorthAmericaandtrough

overEasternNorthAmericaì  Coldandmoistinthewestì  WarmanddryintheSouthEast

PNA+ì  RidgeoverWesternNorthAmericaandtrough

overEastersNorthAmericaì  Warmanddryinthewestì  ColdandwetintheSouthEast

LH

HH

L

Composites

EvolutionofstatesinEOFstatespace

SkillfromMean

ForecastDistributionp

Climatologicaldistributionq

Predictiveskillcomesfromthedifferenceoftheensemblemeanforecasttotheclimatologicalmean

Evolutionofclustermeans

v  PotentialpredictabilityfrommeanofEOF1outto15daysv  PotentialpredictabilityfrommeanofEOF3outto30daysv  Preferredregimetransitionsleadtodeviationsfromclimatology(e.g.withmax

atday7inEOF2)

Skillfromspread

ForecastDistributionp

Climatologicaldistributionq

Predictiveskillcomesfromthedifferenceoftheensemblemeanforecasttotheclimatologicalmean

ForecastDistributionp

Climatologicaldistributionq

Predictiveskillcomesfromdifferenceoftheforecastvariancewiththeclimatologicalvariance

x

Evolutionofclustervariance

v  PotentialpredictabilityfromvarianceofEOF1outto6daysforPNA+(8forPNA-);v  PotentialpredictabilityfromvarianceofEOF2/EOF3outto12daysforPNA-v  PreferredregimetransitionsleadtodecreaseinvarianceofEOF2/EOF3forthefirst

fewdays

Evolutionofclustervariance

v  PotentialpredictabilityfromvarianceofEOF1outto6daysforPNA+(8forPNA-);v  PotentialpredictabilityfromvarianceofEOF2/EOF3outto12daysforPNA-v  PreferredregimetransitionsleadtodecreaseinvarianceofEOF2/EOF3forthefirst

fewdays

=>Relativeentropy

RelativeentropyR(KullbackLeiblerdistance)•  Climatologicaldistributionq,Forecastdistributionp•  AsforlongleadtimesapproachesR->0•  E.g.Kleeman2002

•  Assuming1DGaussians

Evolutionofclustermean

Evolutionofclustervariance

Persistence

Nonlinearphase-spacedynamics

BranstatorandBerner,2007

Zonalandblockregimes

Evolutionofclustermeans

Anomalycorrelationinperfectmodelscenario

•  ACC=Correlationsbetweenforecastandverifyingobservations

•  Here:analogues(excluding>+/-2dfrominitialization)areusedasverifyingobservations

•  Conservativeestimate

ì  Extendedpotentialpredictabilityforstatesinitializedin+/-phasesofNAOandPNAby2-3days

ì  Preferredregimestransitionsindailydataì  Notjuststatisticalconcept,butreflectedasskillofinitialized

forecastsì  Morethanpersistence!!

Conclusions

Futurework

ì  Betterphasespace(optimalpersistencepattern?)

ì  Sensitivitytoresolutionì  Stochasticparameterizationì  Otherteleconnections,e.g.ElNino,MJO

Meansystematicerrorof500hPageopotentialheightfieldsinECMWFIFS

a)

-10

-6

-6

-6

-6

-2

-2

-2

-2

-2

-2

-2

-2

-2

2

2

2

2

2

2

6

66

Z500 Difference eto4-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214b)

-6

-6

-2

-2

-2

-2

-2

-2

2

2

2 2

2

2

2

2

Z500 Difference ezeu-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214

c)

-6 -2

-2

-2

-2

-2

-2

-2

2

2

2

2

2

2

2

2

Z500 Difference eut3-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214d)

-2 -2

-2

-2

-2

-2

-2

-2

2

2

Z500 Difference f8o8-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214

SKEBSLOWRES

•  Reductionofz500biasinallsimulationswithmodel-refinement

Berneretal.,2012

HIGHRES

a)

-10-6

-6

-6

-6

-2

-2

-2

-2

-2

-2

-2

-2

-2

2

2

2

2

2

2

6

66

Z500 Difference eto4-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214b)

-6

-6

-2

-2

-2

-2

-2

-2

2

2

2 2

2

2

2

2

Z500 Difference ezeu-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214

c)

-6 -2

-2

-2

-2

-2

-2

-2

2

2

2

2

2

2

2

2

Z500 Difference eut3-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214d)

-2 -2

-2

-2

-2

-2

-2

-2

2

2

Z500 Difference f8o8-er40 (12-3 1990-2005)

-14-12-10-8-6-4-22468101214

NAOandPNAinCESM

Berner,Sardeshmukh,Christensen,“OnthedynamicalmechnismsgoverningENSOIrregularity”

ThursdayP-C3-02

Berneretal.,J.Clim.2018

EOFs