ECMWFSlide 19th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation:

Perturbing the background state to represent

model uncertainties

Carla Cardinali

Nedjeljka Zagar , Gabor Radnoti, Roberto Buizza

ECMWFSlide 29th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation:

Perturbing the background state to represent model

uncertainties

- EDA perturbing y and xb

- Comparisons with EDA with different model error representation

and EDA where only data error is represented

- Diagnostics on the B derived from all different EDA

- EDAs performance in the EPS

- Conclusion

( )a q b

x Ky I KH x

data uncertainties model uncertainties

outline

ECMWFSlide 39th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation

perturbing the background state to represent model

uncertainties

εo has the magnitude of σo

εb has the magnitude < b

and the B correlation

Control Analysis

Member 1

y ± ε1o

Member 2

y ± ε2o

Member 3

y ± ε3o

Member 1

xb ± ε1b

y ± ε1o

Member 2

xb ± ε2b

y ± ε2o

Member 10

ECMWFSlide 49th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation

Experiment set-up

Realization:10 member

Resolution: T399T159L91

Period: 20081005-20081115

Model error representation:

-BS Spectral Stochastic Kinetic Energy Backscatter scheme (Berner et

al. 2009)

-ST Stochastic representation of model error associated to

parametrized physical processes tendencies (Buizza et al. 1999)

-Xb Perturbed background with gaussian random correlated

perturbation

-OBS (Infl) Perturbed observation with gaussian random perturbation

and inflated background error variances

Systematic kinetic energy loss

numerical integrations and

parametrization

Infl

Infl

εb= 0.5 σb

ECMWFSlide 59th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation

XbST

BSOBS

Zonal averaged cross section u-comp ensemble spread Spread(EDA) = E(

(mi-m)2

i=1

N

å

N -1)

ECMWFSlide 69th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation: Xb

εb= σb

εb= 0.5 σb

ECMWFSlide 7

Ensemble Data Assimilation: u-spread

-80

-60

-40

-20

0

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91

Rela

tiv

e U

-Sp

read

Decre

ase %

model levels

OBS BS ST

9th-Adjoint Workshop Cefalu' (I) 2011

-80

-60

-40

-20

0

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91

Rela

tiv

e U

-Sp

read

Decre

ase %

model levels

OBS BS ST Xb_half

Xb_half

εb = 0.5 σb

ECMWFSlide 89th-Adjoint Workshop Cefalu' (I) 2011

Ensemble Data Assimilation: Baroclinic development

6-h fc valid on 21 October 12 UTC

850 hPa vorticity spread

OBSST

BS Xb

ECMWFSlide 9

EDA: Energetic diagnosis of the ensemble spread

9th-Adjoint Workshop Cefalu' (I) 2011

En = gHn cn cn

*

Sn

=1

N -1(E

v ,i- E

v)2

i=1

N

åé

ëê

ù

ûú

1/2

Χν non-dim complex proj. coef.

ν=ν(k,n,vert.mode,wave type)

H equivalent depth coupling hor+vert motion

Balanced flow EIG WIG

Tropical spreadTropical&Strato spread

5

zonal

meridional

smaller vertical scale

in the low troposphere

ECMWFSlide 109th-Adjoint Workshop Cefalu' (I) 2011

Observation Space Diagnostic

B computed from EDAs Desroziers et al. 2005

HBHT = E(dba(db

o)T) dba =Hxa-Hxb db

o = y-Hxb

VarianceConsinstencyCheck= estimated - assigned HB HT HBHT

AMSU-A

Wind Observations

-12

-10

-8

-6

-4

-2

0

2

13 12 11 10 9 8 7 6 5

VC

C

Channel

Obs BS ST XB

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

< 300 300-700 > 700

VC

C

hPa

Obs BS ST Xb

ECMWFSlide 119th-Adjoint Workshop Cefalu' (I) 2011

Observation Space Diagnostic

Observation Influence Cardinali et al. 2004

T TaHx

K Hy

1 1 1 1T TK = (B + H R H) H R

-80

-70

-60

-50

-40

-30

-20

-10

0

AMSU-A AIRS IASI AMSU-B HIRS SSM/I SCAT ConvWind

Rre

lati

ve D

FS

Decre

ase %

OBS BS ST

ECMWFSlide 129th-Adjoint Workshop Cefalu' (I) 2011

EDAs used to generate initial perturbations for the EPS

EPS 51 members ST perturbations

T399L62 0-10 day

T255L62 11-15 day

ECMWFSlide 139th-Adjoint Workshop Cefalu' (I) 2011

EDAs used to generate initial perturbations for the EPS

ECMWFSlide 149th-Adjoint Workshop Cefalu' (I) 2011

Perturbing the background state versus Others:

Perturbing the background state add more spread in the tropics and

extra-tropics

Increase of spread in the stratosphere

Increase of spread in less observed areas and dynamically active areas

When the B is computed from the EDAs largest OI is achieved

Results from EPS show larger spread in the Tropics and in the Extra-

Tropics

Very easy to maintain does not require tuning from one model-cycle to

an other

To determine the correct perturbation amplitude the following

comparisons are planned:

OBS ensemble spread versus innovation vector spread of the

Control analysis