stochastic representations of model uncertainties in the ifs · pdf file ·...
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![Page 1: Stochastic representations of model uncertainties in the IFS · PDF file · 2016-10-18Streamfunction forcing = [bD]1=2 F( ;˚;˙;t), ... 3-dim evolving pattern, respectively Total](https://reader034.vdocuments.site/reader034/viewer/2022051722/5aa10adb7f8b9a62178efdfa/html5/thumbnails/1.jpg)
Stochastic representations of model uncertainties in the IFS
Martin Leutbecher, Pirkka Ollinaho, Sarah-Jane Lock, Simon Lang,Peter Bechtold, Anton Beljaars, Alessio Bozzo, Richard Forbes,
Thomas Haiden, Robin Hogan and Irina Sandu
ECMWF/WWRP workshop April 2016
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 1
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Model uncertainty representations in the IFS
• Operational in medium/extended-range and seasonal ensembles (ENS, SEAS)• SPPT (Stochastically Perturbed Parametrisation Tendencies) with 3-scales• SKEB (Stochastic Kinetic Energy Backscatter)
• Operational in ensemble of data assimilations (EDA)• SPPT with 1-scale (fast & small-scale)
• Research• modifications of SPPT (cf. talks by Weisheimer and Christensen)• Development of a new scheme “SPP”: Stochastically Perturbed Parameterisations• ENS with SPP versus ENS with SPPT• EDA with SPP• EDA with 3-scale SPPT
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 2
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Model uncertainty representations in the IFS
• Operational in medium/extended-range and seasonal ensembles (ENS, SEAS)• SPPT (Stochastically Perturbed Parametrisation Tendencies) with 3-scales• SKEB (Stochastic Kinetic Energy Backscatter)
• Operational in ensemble of data assimilations (EDA)• SPPT with 1-scale (fast & small-scale)
• Research• modifications of SPPT (cf. talks by Weisheimer and Christensen)• Development of a new scheme “SPP”: Stochastically Perturbed Parameterisations• ENS with SPP versus ENS with SPPT• EDA with SPP• EDA with 3-scale SPPT
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 2
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Stochastic Kinetic Energy Backscatter (SKEB)
• Rationale: A fraction of the dissipated energy is backscattered upscale and acts asstreamfunction forcing for the resolved-scale flow (Shutts and Palmer 2004,Shutts 2005, Berner et al. 2009)
• Streamfunction forcing = [bD]1/2 F (λ, φ, σ, t),where b,D,F denote the backscatter ratio, the (smoothed) total dissipation rateand the 3-dim evolving pattern, respectively
• Total dissipation rate: sum of• “Numerical” dissipation: Loss of KE by numerical diffusion + interpolation in
semi-Lagrangian advection; estimated from biharmonic diffusion• an estimate of the deep convective KE production
• Resolution upgrade (32→ 19 km) in March 2016:Spectral viscosity approach for cubic octahedral grid is inconsist with biharmonicdiffusion assumed by SKEB and used previously with the linear grid ( ⇒contribution from numerical dissipation deactivated, i.e. SKEB → SCB ⇒ SKEBis less active )
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 3
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Stochastic Kinetic Energy Backscatter (SKEB)
• Rationale: A fraction of the dissipated energy is backscattered upscale and acts asstreamfunction forcing for the resolved-scale flow (Shutts and Palmer 2004,Shutts 2005, Berner et al. 2009)
• Streamfunction forcing = [bD]1/2 F (λ, φ, σ, t),where b,D,F denote the backscatter ratio, the (smoothed) total dissipation rateand the 3-dim evolving pattern, respectively
• Total dissipation rate: sum of• “Numerical” dissipation: Loss of KE by numerical diffusion + interpolation in
semi-Lagrangian advection; estimated from biharmonic diffusion• an estimate of the deep convective KE production
• Resolution upgrade (32→ 19 km) in March 2016:Spectral viscosity approach for cubic octahedral grid is inconsist with biharmonicdiffusion assumed by SKEB and used previously with the linear grid ( ⇒contribution from numerical dissipation deactivated, i.e. SKEB → SCB ⇒ SKEBis less active )
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 3
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Stochastically Perturbed Parameterization Tendencies(SPPT)
• Total physics tendencies P perturbed by ∆P = µrP, with r a random pattern andµ a tapering profile (0 in BL and stratosphere, 1 in free troposphere)
• Improved version of the original SPPT scheme (stochastic physics, Buizza, Miller& Palmer, 1999)
• Random pattern r(lat, lon, t) uses AR-1 processes in spectral space and is“continuous” in space and time
• Multi-scale pattern with three components:τ =6h, 3 d, 30 d and L =500 km, 1000 km, 2000 km with standard deviations ofσ =0.52, 0.18, 0.06, respectively
• Gaussian distribution (limited to range [−1, 1] )• Same pattern r for T , q, u, v
• see Tech Memo 598, Palmer et al. (2009) and Shutts et al (2011), ECMWFNewsletter 129
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 4
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Stochastically Perturbed Parameterization Tendencies(SPPT)
• Total physics tendencies P perturbed by ∆P = µrP, with r a random pattern andµ a tapering profile (0 in BL and stratosphere, 1 in free troposphere)
• Improved version of the original SPPT scheme (stochastic physics, Buizza, Miller& Palmer, 1999)
• Random pattern r(lat, lon, t) uses AR-1 processes in spectral space and is“continuous” in space and time
• Multi-scale pattern with three components:τ =6h, 3 d, 30 d and L =500 km, 1000 km, 2000 km with standard deviations ofσ =0.52, 0.18, 0.06, respectively
• Gaussian distribution (limited to range [−1, 1] )• Same pattern r for T , q, u, v
• see Tech Memo 598, Palmer et al. (2009) and Shutts et al (2011), ECMWFNewsletter 129
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 4
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SPPT patterncomposed of 3 random fields
stdev=0.52 0.18 0.06
5
Multi-scale SPPT
500 km6 h
1000 km3 d
2000 km30 d
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 5
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What happens without representation of modeluncertainties?
Ensemble standard deviation
0
2
4
6
8
10
12
14
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em
u200hPa, Northern Extra-tropics
IP only
SPPT
SPPT+SKEB
0
2
4
6
8
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em
u200hPa, Tropics
IP only
SPPT
SPPT+SKEB
TL399/255, resolution change at D15, 20 members
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 6
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What happens without representation of modeluncertainties?Probabilistic skill (I)
0
2
4
6
8
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
ContinuousRankedProbabilityScore
u200hPa, Northern Extra-tropics
IP only
SPPT
SPPT+SKEB
0
1
2
3
4
5
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
ContinuousRankedProbabilityScore
u200hPa, Tropics
IP only
SPPT
SPPT+SKEB
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 7
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What happens without representation of modeluncertainties?Probabilistic skill (II)
2
3
4
DS
2M
OM
EN
TS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
ContinuousIgnoranceScoreGaussianNN
u200hPa, Northern Extra-tropics
IP only
SPPT
SPPT+SKEB 3
4
DS
2M
OM
EN
TS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
ContinuousIgnoranceScoreGaussianNN
u200hPa, Tropics
IP only
SPPT
SPPT+SKEB
Proper two-moment score of Dawid and Sebastiani (1999) ≡ log-score of Gaussian distribution withthe two moments given by ensemble mean and ensemble variance
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 8
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Planned and potential upgrades of SPPT
• fix global integral of perturbed tendency to the value of the unperturbed tendencyto address lack of conservation (Antje Weisheimer, Simon Lang and Jost vonHardenberg)
• independent patterns for different processes / groups of processes (iSPPT:Hannah Christensen and Sarah-Jane Lock)
• re-assessment of supersaturation limiter (Sarah-Jane Lock)
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 9
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Towards process-level specification of uncertaintiesAim: Improve physical consistency of model uncertainty representation
Subgrid-scaleorographic drag
Turbulent diffusion
Deepconvection
Cloud
Shallowconvection
Long-waveflux
Short-waveflux
Latentheatflux
Non-orographicwave drag
Sensibleheat flux
Short-waveradiation
Cloud
O3 Chemistry
Wind Waves
CH4 OxidationLong-waveradiation
Ocean model
Surface
IFS documentation
• Flux perturbations at TOAand sfc that are consistentwith tendency perturbation inatmospheric column
• Conservation of water
• No ad hoc tapering in BL andstratosphere
• Include multi-variate aspectsof uncertainties
• Embed stochasticity within IFS physics
• Local stochastic perturbations toparameters and variables with specifiedspatial and temporal correlations
• Target uncertainties that matter
• Stochastic parameterisation convergesto deterministic IFS physics in limit ofvanishing variance
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 10
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Towards process-level specification of uncertaintiesAim: Improve physical consistency of model uncertainty representation
Subgrid-scaleorographic drag
Turbulent diffusion
Deepconvection
Cloud
Shallowconvection
Long-waveflux
Short-waveflux
Latentheatflux
Non-orographicwave drag
Sensibleheat flux
Short-waveradiation
Cloud
O3 Chemistry
Wind Waves
CH4 OxidationLong-waveradiation
Ocean model
Surface
IFS documentation
• Flux perturbations at TOAand sfc that are consistentwith tendency perturbation inatmospheric column
• Conservation of water
• No ad hoc tapering in BL andstratosphere
• Include multi-variate aspectsof uncertainties
• Embed stochasticity within IFS physics
• Local stochastic perturbations toparameters and variables with specifiedspatial and temporal correlations
• Target uncertainties that matter
• Stochastic parameterisation convergesto deterministic IFS physics in limit ofvanishing variance
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 10
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Stochastically Perturbed Parametrisations (SPP)The distributions sampled by SPP
Stochastic parameterisation samplesparameter ξj by a log-normaldistribution
ξj = ξ̂j exp (Ψj)
with unperturbed parameter ξ̂j
Ψj ∼ N (µj , σ2j )
µ = 0⇒ median of ξj is equal to ξ̂j0 1 2 3 4 5
ξj/ξ̂j
0.0
0.2
0.4
0.6
0.8
1.0
1.2
pd
f
cloud vert. decorrel. height (McICA)
fractional stdev. hor. distr. water content
effective radius of cloud water /ice
Development started with parameter perturbationsthat target the cloud-radiation interaction
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 11
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The distributions sampled by SPPturbulent diffusion and subgrid oro. cloud and large-scale precipitation
0 1 2 3 4 5
ξj/ξ̂j
0.0
0.5
1.0
1.5
2.0
2.5
pd
f
transfer coeff. momentum (oc)
transfer coeff. momentum (lnd)
turbulent orogr. form drag
stdev subgrid orography
vert. mixing length scale, stable BL
0 1 2 3 4 5
ξj/ξ̂j
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
pd
f
RH threshold stratiform condensation
diff. coeff. for evaporation of turb. mixing
crit. cloud water content
threshold for snow autoconversion
radiation convection
0 1 2 3 4 5
ξj/ξ̂j
0.0
0.2
0.4
0.6
0.8
1.0
1.2
pd
f
cloud vert. decorrel. height (McICA)
fractional stdev. hor. distr. water content
effective radius of cloud water /ice
aerosol vert. distrib. scale height
aerosol optical thickness
0 1 2 3 4 5
ξj/ξ̂j
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
pd
f
entrainment rate
shallow entr. rate
detrainment rate
conversion cloud-rain
adjustment time scale
conv. momentum transport
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 12
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Correlation scales matterEnsemble standard deviation and CRPS
0
2
4
6
RM
S
0 3 6 9 12 15fc-step (d)
2013120400-2014112100 (23)
spread_em
u200hPa, Tropics
IP_only
PPL
PPInf
PPM
0
1
2
3
4
CR
PS
0 3 6 9 12 15fc-step (d)
2013120400-2014112100 (23)
ContinuousRankedProbabilityScore
u200hPa, Tropics
IP_only
PPL
PPInf
PPM
Exp L (km) τ (h)
PPM 500 6PPL 2000 72
PPInf ∞ ∞
horizontal correlation length scale Lcorrelation time τfor pattern ΨOllinaho et al. (2016, submitted to QJ)
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 13
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Amplitude matters tooEnsemble standard deviation and CRPS
0
2
4
6
RM
S
0 3 6 9 12 15fc-step (d)
2013120400-2014112100 (23)
spread_em
u200hPa, Tropics
IP_only
PPL
PPL0.5
0
1
2
3
4
CR
PS
0 3 6 9 12 15fc-step (d)
2013120400-2014112100 (23)
ContinuousRankedProbabilityScore
u200hPa, Tropics
IP_only
PPL
PPL0.5
PPL0.5 has all standard deviations σj halved compared to PPL.The correlation scales are 2000 km and 72 h in both experiments.
Ollinaho et al. (2016, submitted to QJ)
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 14
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Intercomparison of SPP and SPPTEnsemble stdev of 0–3 h temperature tendencies (K[3 h]−1)
SPPT SPP
no initialpertns.TL255,
20 member
← level 64∼ 500 hPa
← level 9110m above
surface
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 15
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Comparing ensembles of temperature tendenciesSPP versus SPPT (no initial perturbations)
0.0 0.9 1.8 2.7
20
40
60
80
STD
EV
TR
0.0 0.9 1.8
20
40
60
80
NH
0-3h SPPT 0-3h SPP
0.0 0.5 1.0
20
40
60
80
CO
RR
STD
EV
0.0 0.5 1.0
20
40
60
80
• Stdev of 0–3 h tendency
• SPP induces larger (smaller)tendency perturbations in(above) BL than SPPT
• regions where tendencies aremost uncertain become moresimilar with increasing leadtime (bottom: corr stdev)
• 6 boreal winter cases; Unit(top panels): K/(3 h)
Ollinaho et al. (2016,submitted to QJ)
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 16
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Comparing ensembles of temperature tendenciesSPP versus SPPT (no initial perturbations)
0.0 0.9 1.8 2.7
20
40
60
80
STD
EV
TR
0.0 0.9 1.8
20
40
60
80
NH
21-24h SPPT 21-24h SPP
0.0 0.5 1.0
20
40
60
80
CO
RR
STD
EV
0.0 0.5 1.0
20
40
60
80
• Stdev of 21–24 h tendency
• SPP induces larger (smaller)tendency perturbations in(above) BL than SPPT
• regions where tendencies aremost uncertain become moresimilar with increasing leadtime (bottom: corr stdev)
• 6 boreal winter cases; Unit(top panels): K/(3 h)
Ollinaho et al. (2016,submitted to QJ)
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 16
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Change of ensemble stdev: 200 hPa zonal windSPP versus SPPT relative to initial perturbation only
-0.1
0.1
0.3
0.5
0.7
0.9
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em [sign p=0.0500]
u200hPa, Northern Extra-tropics
IP only
SPPT
SPP
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em [sign p=0.0500]
u200hPa, Tropics
IP only
SPPT
SPP
TCo255/159, resolution change at D15,20 member
Exp L (km) τ (h)
SPP 2000 72SPPT 3-scale 3-scale
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 17
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Change of CRPS: 200 hPa zonal windSPP versus SPPT relative to initial perturbation only
-0.2
-0.1
0
0.1
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
fairContinuousRankedProbabilityScore [sign p=0.0500]
u200hPa, Northern Extra-tropics
IP only
SPPT
SPP
-0.4
-0.3
-0.2
-0.1
0
0.1
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
fairContinuousRankedProbabilityScore [sign p=0.0500]
u200hPa, Tropics
IP only
SPPT
SPP
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 18
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Change of CRPS: 200 hPa zonal windSPP+SPPT1 and . . . relative to initial perturbation only
-0.2
-0.1
0
0.1
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
fairContinuousRankedProbabilityScore [sign p=0.0500]
u200hPa, Northern Extra-tropics
IP only
SPPT
SPP
SPPT1+SPP
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
CR
PS
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
fairContinuousRankedProbabilityScore [sign p=0.0500]
u200hPa, Tropics
IP only
SPPT
SPP
SPPT1+SPP
Exp L (km) τ (h)
SPP 2000 72SPPT1 500 6
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 19
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Impact on model climate
W20
0
W70
0
W92
515
10
5
0
5
10
15
RM
SE C
HA
NG
E (
%)
TR WINDS
TP(1
)
TP(2
)
PRECIPITATION
TCC
CLOUD COVER
TCW
V(1)
TCW
V(2)
TCWV
TTR
TSR
RADIATION
SPPSPPT
Relative change of RMSerror of annual meanfields with respect tounperturbed forecasts.
ERA-Interim (tropicalwinds) and satellite obs.are used as reference.
Model configuration:uncoupled TL255, 4 startdates, initial monthomitted.
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 20
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EDA first guess (3 h) stdev: Meridional wind (m s−1)
90°S60°S30°S0°N30°N60°N90°N
20
40
60
80
100
120
-0.5 -0.42 -0.33 -0.25 -0.17 -0.08 -0.01 0.01 0.08 0.17 0.25 0.33 0.42 0.5
SPPT − noTenPert
90°S60°S30°S0°N30°N60°N90°N
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.5
noTenPert
SPPT:oper.1-scale
SPPT3 andSPP
propagaterandom
fields acrosscycles
90°S60°S30°S0°N30°N60°N90°N
20
40
60
80
100
120
-0.5 -0.42 -0.33 -0.25 -0.17 -0.08 -0.01 0.01 0.08 0.17 0.25 0.33 0.42 0.5
SPPT3 − noTenPert
90°S60°S30°S0°N30°N60°N90°N
20
40
60
80
100
120
-0.5 -0.42 -0.33 -0.25 -0.17 -0.08 -0.01 0.01 0.08 0.17 0.25 0.33 0.42 0.5
SPP − noTenPert
mean over16 12-hourassimilationcycles inJune 2015
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 21
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Summary
• The operational schemes SPPT (+SKEB) contribute significantly to theprobabilistic skill in medium range and extended range
• A new stochastic scheme has been developed for representing model uncertaintiesat the process level in IFS: The SPP scheme provides a framework to buildstochastic parameterisations that are guided by existing deterministicparameterisations
• A first attempt to represent model uncertainties in the main physical processes in aphysically consistent way.
• Further extensions of SPP are envisaged and ideas are welcome
• Proximity to processes implies a scheme that is less parsimonious than SPPT.
• Further development could benefit from validating the ensemble for variables thatare close to the processes.
• Initial operational implementation could consider a combination of SPPT and SPP
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 22
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Current ECMWF ideas on future plansFor working group discussions
• Move towards consistent approach to represent model uncertainties inassimilations and forecasts at all lead times
• Process-oriented diagnostics of ensembles(e.g. radiative fluxes, precipitation, skin temperature)
• Ideas for extending scope of SPP:• thermodynamic coupling between surface and atmosphere• vertical mixing above boundary layer• atmospheric composition: trace gas sources/sinks
• How to evolve from current SKEB?Stochastic Convective Backscatter (SCB, Shutts 2015)and/or stochastic dynamical core
Vacancy VN16-13 at ECMWF for Scientist to work on specification of global surfacecharacteristics for land, ocean, biosphere and cryosphere and model uncertainty, seehttp://www.ecmwf.int/en/about/jobs/jobs-ecmwf
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 23
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Current ECMWF ideas on future plansFor working group discussions
• Move towards consistent approach to represent model uncertainties inassimilations and forecasts at all lead times
• Process-oriented diagnostics of ensembles(e.g. radiative fluxes, precipitation, skin temperature)
• Ideas for extending scope of SPP:• thermodynamic coupling between surface and atmosphere• vertical mixing above boundary layer• atmospheric composition: trace gas sources/sinks
• How to evolve from current SKEB?Stochastic Convective Backscatter (SCB, Shutts 2015)and/or stochastic dynamical core
Vacancy VN16-13 at ECMWF for Scientist to work on specification of global surfacecharacteristics for land, ocean, biosphere and cryosphere and model uncertainty, seehttp://www.ecmwf.int/en/about/jobs/jobs-ecmwf
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 23
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extra slides . . .
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 24
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What happens without representation of modeluncertainties?
Ensemble standard deviation
0
2
4
6
8
10
12
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em
u200hPa, Northern Extra-tropics
IP only
SPPT
SPPT+SKEB
0
2
4
6
8
RM
S
0 5 10 15 20 25 30fc-step (d)
2013120100-2014112600 (46)
spread_em
u200hPa, Tropics
IP only
SPPT
SPPT+SKEB
TCo255/159, resolution change at D15, 20 members
M. Leutbecher et al. Stochastic representations of model uncertainties in the IFS ECMWF/WWRP workshop April 2016 25