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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