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ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 1
Ensemble Data Assimilation:Perturbing the background state to represent model
uncertainties
Carla Cardinali Gabor Radnotiand
Roberto Buizza
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 2
Ensemble Data Assimilation:Perturbing the background state to represent model
uncertainties
- EnDA perturbing y and xb
- Comparisons with EnDA with different model errorrepresentation and EnDA where only data error is represented
- Diagnostics on the B derived from all different EnDA
- EnDAs performance in the EPS
- Conclusion
( )a q b x Ky I KH x
data uncertainties model uncertainties
outline
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 3
Ensemble Data Assimilationperturbing the background state to represent model
uncertainties
Control Analysis
Member 1y ± ε1
o
Member 2y ± ε2
o
Member 3y ± ε3
o
Member 1xb ± ε1
by ± ε1
o
Member 2xb ± ε2
by ± ε2
o
εo has the magnitude of σo
εb has the magnitude of band the structure of B
Member 10
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 4
Ensemble Data Assimilation:perturbing the background state to represent model
uncertainties
2 2 2
2 2 2
( ) ( ), ( )
( ) ( ), ( )Q R
Q R
t t t
t t t
To be compared with
2 2 2
2 2 2
1
2 2 2 22 2
1
2 2 22 2
( ) ( ), ( )
( ) ( ), ( )
1 1( ) ( ) ( ) ( ) ( )
( ) ( )
1 1( ) ( ) , ( )
( ) ( )
B R
B R
T TB Q A Q
B R
TQ R
B R
t t t
t t t
t t L t L t tt t
t t tt t
L L
L L
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 5
Ensemble Data AssimilationExperiment set-up
Realization:10 memberResolution: T399T159L91Period: 20081005-20081115Model error representation:-BS Spectral Stochastic Kinetic Energy Backscatter scheme (Berner etal. 2009)-ST Stochastic representation of model error associated toparametrized physical processes tendencies (Buizza et al. 1999)-PXb Perturbed background with gaussian random correlatedperturbation-O Perturbed observation with gaussian random perturbation-OInfl Perturbed observation with gaussian random perturbation andinflated background error variances
Systematic kinetic energy lossnumerical integrations andparametrization
Infl
Infl
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 6
Ensemble Data Assimilation: spread U L10
PXb ST
BS OInfl
O
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 7
Ensemble Data Assimilation: spread U L78
PXb ST
BS OInfl
O
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 8
Ensemble Data Assimilation: spread T L10
PXbST
BS OInfl
O
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 9
Ensemble Data Assimilation: AMSUA ch 6 Desroziers et al. 2005
PXb
ST BS
HBH = E(dba(db
o)T) dba =Hxa-Hxb db
o = y-Hxb
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 10
Ensemble Data Assimilation: AMV >700 hPa Desroziers et al. 2005
PXb
ST BS
HBH = E(dba(db
o)T) dba =Hxa-Hxb db
o = y-Hxb
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 11
EnDA: Observation Influence AMSUA ch6 Cardinali et al. 2004
T Ta
HxK Hy
PXb ST
BS
1 1 1 1T T K = (B + H R H) H R
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 12
T850 - TRT850 - NH
1. EDA[PXb], EDA[ST], EDA[BS],EDA[ST,BS]: STD/EM Roberto Buizza
In terms of T850, EDA[PXb] has the largest spread and EDA[BS] thesmallest for the whole forecast range. Adding BS to ST has anegligible impact.
In terms of rmse of the ensemble-mean, EDA[PXb] and EDA[ST] havesimilar scores, both lower than EDA[BS] over NH in the medium-range, and over the tropics from ~ day 4.
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 13
T850 - TRT850 - NH
1. EDA[PXb], EDA[ST], EDA[BS],EDA[ST,BS]: RPSS Roberto Buizza
In terms of RPSS for T850, EDA[BS] has the lowest scores. EDA[PXb],EDA[ST] and EDA[ST,BS] have very similar scores, better over bothNH and the tropics. This is probably a consequence of the better-tuned ensemble spread.
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 14
T850 - TRT850 - NH
1. EDA[PXb], EDA[ST], EDA[BS],EDA[ST,BS]: IGN Roberto Buizza
The ignorance score, which is more sensitive to the tail of the forecastprobability distribution function, shows more differences betweenthe experiments. In terms of IGN for T850, EDA[BS] has the lowestscores, followed by EDA[ST] and EDA[ST,BS], with EDA[PXb]showing the best results over both NH and the tropics.
ECMWF8th-Adjoint Workshop Tannersville (US) 2009 Slide 15
Perturbing the background state versus Others:Preliminary Conclusion
Perturbing the background state add more spread in the tropics andextra-tropics
-The increase of spread is observed in areas where the model isknown to be wrong
-The increase of spread is linked with the dynamic activity
Very easy to maintain does not require tuning from one model-cycle toan other
The diagnostic performed on the B matrix computed from differentEnDA shows NO differences
-Need of further investigation on the B matrix computation (Derber etBouttier 1998), in particular to the applied balance operator
Preliminary results from EPS show larger spread in the Tropics and inthe Extra-Tropics