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ImprovingtheSPPTSchemeusingHigh-Resolu8onModelSimula8ons

ECMWF/WWRPWorkshoponModelUncertainty,13thApril2016

HannahChristensen1,Sarah-JaneLock2,AndrewDawson1,TimPalmer1

[email protected]

1.  Atmospheric,OceanicandPlanetaryPhysics,Univ.Oxford2.  EuropeanCentreforMediumRangeWeatherForecasts

PredictabilityofWeatherandClimateatOxford

•  DevelopmentandanalysisofstochasNcparametrisaNonschemesinEarth-Systemmodels

•  Inexacthardwareinnumericalweatherandclimatemodels–  DoubleprecisionasadefaultisovercauNous–whethermodelsarestochasNcordeterminisNc

–  Reducingprecisionforthesmallscalescanleadtosignificantenergysavings

22bits=1sign,11exponent,10significand20bits=1sign,11exponent,8significand

HannahChristensen ImprovingtheSPPTschemeusinghigh-resoluNonsimulaNons

IFSinSinglePrecision

•  EnsembleforecastsatT399arealmostidenNcal,butwith40%speedup

Dübenetal,MWR2015.Vanaetal,submi]edtoGRL


AScaleSelecNveApproach

•  SmallscaledynamicsareinherentlyuncertainduetoparametrisaNonschemes,viscosity,missingdata,iniNalisaNon,…

•  Wecanpushthesmallscalesharderthanthelargescales•  Thesmallestscalesarethemostexpensiveones•  Ourvision:aglobalcirculaNonmodelwhichusesjusttherightlevel

ofprecision,reducingnumericalprecisionwithscales•  e.g.possibleapproach:aspectralmodelusingsingleprecisionfor

wavenumbers0-500,andhalfprecisionforwavenumbers500-2000


AScaleSelecNveApproach

•  SmallscaledynamicsareinherentlyuncertainduetoparametrisaNonschemes,viscosity,missingdata,iniNalisaNon,…

•  Wecanpushthesmallscalesharderthanthelargescales•  Thesmallestscalesarethemostexpensiveones•  Ourvision:aglobalcirculaNonmodelwhichusesjusttherightlevel

ofprecision,reducingnumericalprecisionwithscales•  e.g.possibleapproach:aspectralmodelusingsingleprecisionfor

wavenumbers0-500,andhalfprecisionforwavenumbers500-2000

PleaseseePeterDüben’sposterformoredetails!


ImprovingtheSPPTSchemeusingHigh-ResoluNonModelSimulaNons

SPPTisoneofthemostwidelyusedstochas8cparametrisa8onschemes

•  SPPT:‘StochasNcallyPerturbedParametrisaNonTendencies’•  HolisNcapproachforrepresenNnguncertaintyinallsub-gridphysics

parametrisaNons•  SPPTschemeusedinweather,seasonalandclimatemodels

Implemented/testedin:–  UKMetOffice–  ECMWFIFS(med.range&System4)–  JapanMeteorologicalAgency–  AROME

–  COSMO–  WRF–  CESM–  EC-Earth


Beneficialimpactonreliabilityofforecasts,meansquareerror,andclimatologyofmodel

RMSE

Ensemblespread

-56 -48 -40 -32 -24 -16 -8 8 16 24 32 40 48 56 -28 -24 -20 -16 -12 -8 -4 4 8 12 16 20 24 28

stochphysOFF – reanalysis S4 – reanalysis S4 – stochphysOFF

OLR bias DJF 1981-2010

-56 -48 -40 -32 -24 -16 -8 8 16 24 32 40 48 56 -28 -24 -20 -16 -12 -8 -4 4 8 12 16 20 24 28

stochphysOFF – reanalysis S4 – reanalysis S4 – stochphysOFF

OLR bias DJF 1981-2010

ReliabilityofT850inIFSMedium-rangeforecastsê

ReducingOLRbiasinSystem4seasonalforecastsè

ImprovingENSOvariabilityinCCSM4ê

Shu]setal,2011

Christensen,Berner,ColemanandPalmer,submi]edtoJ.Climate,2016

Weisheimeretal,2014,PhilTrans

T850,tropics

CTRL–OBS STOCHASTIC(SYS4)–OBS


ImprovingENSOvariabilityinCCSM4

Christensen,Berner,ColemanandPalmer,submi]edtoJ.Climate,2016

•  BecauseofmulNplicaNvenatureofSPPT–  AddiNvenoisescheme(SKEB)doesnothavethesameimpact

•  TestedaddiNveandmulNplicaNvenoiseinsimple‘DelayedOscillator’modelofENSO–  EquivalentresultasinCCSM4–  addiNvenoiseamplifiedENSOwhereasmulNplicaNvenoisereducedthe

amplitude


T = D+ (1+ e) Pii=1

6

∑AllIFSphysicsschemesareperturbedusingsamepaOern:

1.RadiaNon2.Turbulence&GravityWaveDrag3.ConvecNon4.Cloud5.Non-OrographicGrav.WaveDrag6.MethaneOxidaNon

Fourvariablesperturbed:T,U,V,q

Perturba8onconstantver8cally,taperedinBLandstratosphere

SPPT T–TotaltendencyD–DynamicstendencyP–Parametrisa8ontendency

SPPT:StochasNcallyPerturbedParametrisaNonTendencies

Palmeretal,2009.ECMWFTechMemo598


TesNng“IndependentSPPT”inIFS

T = D+ (1+ ei )Pii=1

6

∑iSPPT

•  PerturbIFSphysicsschemeswithindependentrandomfields–  Assumeserrorsfromdifferentschemesareuncorrelated–  SetnoisemagnitudeandcorrelaNonsseparatelyforeachscheme–  Abletoonlytapercertainschemesifdesired–  Startwithsameσ,φasoperaNonalSPPT

SPPTT–TotaltendencyD–DynamicstendencyP–Parametrisa8ontendency

T = D+ (1+ e) Pii=1

6

∑


TesNng“IndependentSPPT”inIFS

•  Seriesofexperiments–  CY41R1atTL255 (12startdates)–  CY42R1atTCO255 (48startdates)

•  21ensemblemembers•  AntjeWeisheimer’sglobalmoisturefixon

•  StandardSPPT: (111111)•  IndependentSPPT: (123456)•  ParNallyindependentSPPT: (123343)

(112212)

1.RadiaNon2.Turbulence&Grav.WaveDrag3.ConvecNon4.Cloud5.Non-OrogGrav.WaveDrag6.MethaneOxidaNon

nomenclature:assigneachindependent

pa]ernanumber


iSPPT:significantimprovementintheTropics

lead time / hrs0 100 200

RM

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RM

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2no SPPTSPPTiSPPT123343112212


RM

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CY41R1TL255

dashed:spreadsolid:error


ImpactisinregionswithsignificantconvecNon


RM

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RM

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RM

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RM

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RM

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TropicalregionswithsignificantconvecNon

Tropicalregionswithli]leconvecNon



Two-pa]ernschemeimprovesoverSPPT&iSPPT

CY42R1TCO255

123456

123343

112212

111111

Ø  be]erthanoperaNonalSPPTandfulliSPPTØ  largespreadincreaseintropics,smaller

increaseinextratropicsØ  errorreducNonintropics,neutralinNET,

smallincreaseinSET

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

CR

PS

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)fairContinuousRankedProbabilityScore [sign p=0.0500]

t850hPa, Northern Extra-tropics

[11111

[11221

[12334

[12345

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Southern Extra-tropics

[11111

[11221

[12334

[12345

-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

CRPSiSPPT-CRPSSPPT

CRPS(iSPPT)–CRPS(SPPT3)



Ø  be]erthanoperaNonalSPPTandfulliSPPTØ  largespreadincreaseintropics,smaller

increaseinextratropicsØ  errorreducNonintropics,neutral/slight

reducNoninNETandSET

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.05

-0.03

-0.01

0.01

0.03

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.03

-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t200hPa, Tropics

[11111

[11221

[12334

[12345

123456

123343

112212

111111-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

CY42R1TCO255

CRPSiSPPT-CRPSSPPT


iSPPT:onlysmalldegradaNoninS.ExtraTropics


RM

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1.5(a) T 850


RM

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RM

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•  BUTcanweimproveSPPTmoresystemaNcally?•  CanwejusNfySPPT?Canweexplainwhyitdoessuchagoodjob?•  CanweidenNfywhereitdoesn’tdoagoodjobandwhy?

•  SPPTschemeincludesseveralassumpNons–  MulNplicaNvenoise–  Allschemestreatedthesame:uncertaintyintendencyproporNonaltototaltendency(cf.iSPPT:errorsfromschemesuncorrelated)

–  SpecifiesstandarddeviaNons,temporalandspaNalcorrelaNonswithnophysicalreasonforchoices

•  Q:Canweconstrainsomeofthecharacteris8csofthestochas8ctermusinghigh-resolu8onmodeloutput?

–  FollowinginthefootstepsofShu]sandPalmer2007(J.Clim.),Shu]sandCalladoPallares2014(PhilTransR.Soc.A)…

iSPPTseemsapromisingapproach


UsetheCASCADEdatasetas‘truth’CompareIFSSCMtothistruth

TRMMthankstoChrisHolloway,U.Reading

CASCADE4km3DSmagOLR


Coarsegrainingexperiments1.CoarsegrainCASCADEtomodelgridtoprovideICsandforcingdataforIFSSCMatT639=30km

2.EvolveinNme:SCMdt=15min

3.CompareSCMtoCASCADEatlaterNme

CASCADESCM


Analysingthedata:mulNplicaNvenoise?

Allveryeasytosaythis…

∑=

++=5

1)1(i

iPeDTSPPT:

Calculate‘true’totaltendencyfromCASCADE AssumeSCMdynamics

tendencyis‘correct’

ConsidererrorinSCMphysicstendencies

T −D = (1+ e) Pii=1

5

∑Compare‘true’

physicstendency… …toparametrisedphysicstendency


ConsiderTtendencyat850hPa


CAS tendency-0.5 0 0.5 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1CAS tendency-0.5 0 0.5 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = -0.034996σ = 0.055631

-0.25 < T tend < -0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.0016507σ = 0.048906

-0.01 < T tend < 0.01


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.091291σ = 0.053567

0.01 < T tend < 0.25


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.32825σ = 0.097988

0.25 < T tend < 0.5


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.59714σ = 0.19639

0.5 < T tend < 0.75


0.05

0.1

0.15

0.2

0.25

0.3

0.35µ = 0.86272σ = 0.31746

0.75 < T tend < 1

μ=-0.03σ=0.05

μ=0.002σ=0.04

μ=0.09σ=0.05

μ=0.33σ=0.10

μ=0.60σ=0.20

μ=0.86σ=0.32

SCMparametrisedtendency Histograms:CASCADEtendency


Analysingthedata:characterisNcsofe


∑=

++=5

1)1(i

iPeDTSPPT:

Calculate‘true’totaltendencyfromCASCADE AssumeSCMdynamics

tendencyis‘correct’

ConsidererrorinSCMphysicstendencies

T −D− Pii=1

5

∑ = e Pii=1

5

∑SOLVEi.e.FollowingtheassumpNonsofSPPT,canwemeasurethestaNsNcalcharacterisNcsoftheperturbaNone

DonotusedatafromBLorstratosphere(tapered)

TqUV


e.g.eforasingleNmestep


T −D− Pii=1

5

∑ = e Pii=1

5

∑ CalculateeasafuncNonofposiNonforasingleNmestep

500km



Considerdifferentschemes

T −D− Pii=1

5

∑ = eiPii=1

5

∑


•  SPPTisaskilfulapproachforrepresenNnguncertaintyinweatherandclimatemodels

•  iSPPTimprovestropicalreliabilityofSPPTinmediumrange–  Twopa]erniSPPTappearsparNcularlyskilfulintropicsandextra

tropics

•  Usecoarse-grainingtomeasureerrorcharacterisNcsofdifferentschemes–  MulNplicaNvenoiseappearsareasonablemodelforuncertaintyin

tendencies–  BUTdifferenterrorcharacterisNcsfordifferentschemesmoNvates

treaNngtheparametrisaNonschemesseparately–  IfconvecNonisnottriggered,theerrorcharacterisNcsoftheother

schemeschangeTheseareearlyresults!Futurework:refinetechniquesusedtocalculateerror,calculatestaNsNcalproperNesoferrorterm

Conclusions


Thanksforlistening!

•  UKMetOfficeatmosphericmodelsetup•  Semi-Lagrangian,non-hydrostaNcdynamics•  Cloud-systemresolving(4km,70levels)one-waynestedgrid•  Largetropicaldomain(15,500kmx4,500km)•  PrescribedconstantSSTandupdatedlateralboundary

condiNonsfromECMWF25kmforecastanalysesfortheYearofTropicalConvecNon(YOTC)

•  3DSmagorinskymixing•  ConvecNonschemeswitchedonbutclosuresuchthat

convecNonschemeisonlyacNveinlowCAPEenvironments(tendstoproduceshallow/congestus)

CASCADE:modelsetup

Sometechnicaldetails

•  Coarsenusingasimple‘tophat’funcNon

•  SpaNallyaveragefirst,beforeinterpolaNngfromCASCADEtoSCMlevels

•  CASCADEdataonlyevery1hr,solinearlyinterpolaNngbetween

•  SCMhashighertopthanCASCADEdata:fillinusingERAreanalysis

•  UsestandardIFSboundaryfiles(orography,landcoveretc)

•  Automaterunning75,000SCMsperNmestep

Calculateeseparatelyfordifferentvariables

500km

500km

•  PerformedbyAlfonsCalladoPallaresandGlennShu]s–  DefinetendenciesfromIFS@T1279(16km)tobe“truth”–  Comparetotendenciesfromforecast:IFS@T159(130km)–  Use24x12-hourforecastsfromidenNcaliniNalcondiNons–  CoarsegrainbothresoluNonsinNme(12hrtriangularfilter)andspace(to500kmgrid)

–  Calculatemeanand standarddeviaNon ofT1279tendencies condiNonedonthe T159tendencies

Coarsegrainingexperiments

T1279

T1279

T1279

T159

tendency

pdf.

Coarsegrainingexperiments

figfromA.Callado-PallaresandG.Shu]s

iSPPT:significantimprovementintheTropics


RM

S

0.5

1

1.5(a) T 850


RM

S

1

1.5

2

2.5

3

3.5

(b) U 850


RM

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50

100

150

(c) Z 500


RM

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8(d) U 200

1 1.5 21

1.2

1.4

1.6

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CY41R1TL255


-0.08

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(a)


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(b)


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(g)


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(h)


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(i)


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(j)


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(l)


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-0.15

-0.1

-0.05

0

(b)


-0.8

-0.6

-0.4

-0.2

0

(c)


-0.1

-0.05

0

(d)


-0.2

-0.15

-0.1

-0.05

0

0.05(e)


-0.4

-0.3

-0.2

-0.1

0

0.1(f)


-0.3

-0.2

-0.1

0

0.1

(g)


-0.4

-0.2

0

(h)


-0.6

-0.4

-0.2

0

0.2

(i)


-0.1

-0.05

0

(j)


-0.2

-0.15

-0.1

-0.05

0

0.05(k)


-0.4

-0.2

0

(l)


-0.08

-0.06

-0.04

-0.02

0

0.02

(a)


-0.15

-0.1

-0.05

0

(b)


-0.8

-0.6

-0.4

-0.2

0

(c)


-0.1

-0.05

0

(d)


-0.2

-0.15

-0.1

-0.05

0

0.05(e)


-0.4

-0.3

-0.2

-0.1

0

0.1(f)


-0.3

-0.2

-0.1

0

0.1

(g)


-0.4

-0.2

0

(h)


-0.6

-0.4

-0.2

0

0.2

(i)


-0.1

-0.05

0

(j)


-0.2

-0.15

-0.1

-0.05

0

0.05(k)


-0.4

-0.2

0

(l)


-0.08

-0.06

-0.04

-0.02

0

0.02

(a)


-0.15

-0.1

-0.05

0

(b)


-0.8

-0.6

-0.4

-0.2

0

(c)


-0.1

-0.05

0

(d)


-0.2

-0.15

-0.1

-0.05

0

0.05(e)


-0.4

-0.3

-0.2

-0.1

0

0.1(f)


-0.3

-0.2

-0.1

0

0.1

(g)


-0.4

-0.2

0

(h)


-0.6

-0.4

-0.2

0

0.2

(i)


-0.1

-0.05

0

(j)


-0.2

-0.15

-0.1

-0.05

0

0.05(k)


-0.4

-0.2

0

(l)

T850 U850

Z500 U200

RPSS

RPSS

RPSS

RPSS

T850CRPS

CY42R1TCO255

123456

123343

112212

111111

…but(112212)schemeØ  reasonablygoodinextra-tropics,Ø  largeimprovementinthetropics

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

CRPS

T850RMSEinensemblemean

CY42R1TCO255

123456

123343

112212

111111


-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.07

0.09

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.07

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.03

-0.02

-0.01

0

0.01

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]

t850hPa, Tropics

[11111

[11221

[12334

[12345

RMSE

T850RMSensemblespread

CY42R1TCO255

123456

123343

112212

111111


-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

-0.01

0.01

0.03

0.05

0.07

0.09

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.04

-0.02

0

0.02

0.04

0.06

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]


[11111

[11221

[12334

[12345

0

0.03

0.06

0.09

0.12

0.15

0.18

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]

t850hPa, Tropics

[11111

[11221

[12334

[12345

RMSS


CY42R1TCO255


-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.05

-0.03

-0.01

0.01

0.03

CR

PS

0 3 6 9 12 15fc-step (d)



[11111

[11221

[12334

[12345

-0.03

-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t200hPa, Tropics

[11111

[11221

[12334

[12345

CRPS

123456

123343

112212

111111-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345


CY42R1TCO255


RMSE

123456

123343

112212

111111-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.09

-0.07

-0.05

-0.03

-0.01

0.01

0.03

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.04

-0.03

-0.02

-0.01

0

0.01

RM

SE

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)rmse_em [sign p=0.0500]

t200hPa, Tropics

[11111

[11221

[12334

[12345


CY42R1TCO255


RMSS

123456

123343

112212

111111-0.02

-0.01

0

CR

PS

0 3 6 9 12 15fc-step (d)


t850hPa, Tropics

[11111

[11221

[12334

[12345

-0.02

0

0.02

0.04

0.06

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]


[11111

[11221

[12334

[12345

-0.03

-0.01

0.01

0.03

0.05

0.07

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]


[11111

[11221

[12334

[12345

0

0.02

0.04

0.06

0.08

RM

S

0 3 6 9 12 15fc-step (d)

2013120100-2014112600 (46)spread_em [sign p=0.0500]

t200hPa, Tropics

[11111

[11221

[12334

[12345

Inexacthardwareinnumericalweatherandclimatemodels

•  DoubleprecisionasadefaultisovercauNous–whethermodelsarestochasNcordeterminisNc

•  Reducingprecisionforthesmallscalescanleadtosignificantenergysavings

0 2 4 6 8

10 12 14 16 18 20

0 1 2 3 4 5 6

fore

cast

erro

r g

eopo

tent

ial h

eigh

t [m

]

time in days

double precision; 235 km res.double precision; 260 km res.

8 bit; 235 km res.10 bit; 235 km res.

22bits=1sign,11exponent,10significand20bits=1sign,11exponent,8significand

ExperimentswithIGCM

P.Dueben

Improving the SPPT Scheme using High-Resolu8on Model ... › sites › default › files ›...

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Transcript of Improving the SPPT Scheme using High-Resolu8on Model ... › sites › default › files ›...