Carla Cardinali Gabor Radnoti and Roberto Buizza...Carla Cardinali Gabor Radnoti and Roberto Buizza....

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


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


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


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


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


Ensemble Data Assimilation: spread U L10

PXb ST

BS OInfl

O


Ensemble Data Assimilation: spread U L78

PXb ST

BS OInfl

O


Ensemble Data Assimilation: spread T L10

PXbST

BS OInfl

O


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


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


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


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.


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.


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.


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

Carla Cardinali Gabor Radnoti and Roberto Buizza...Carla Cardinali Gabor Radnoti and Roberto Buizza....

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