MODEL ERROR ESTIMATION IN ENSEMBLE DATA ASSIMILATION FRAMEWORK Dusanka Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University.

MODEL ERROR ESTIMATION INMODEL ERROR ESTIMATION INENSEMBLE DATA ASSIMILATION ENSEMBLE DATA ASSIMILATION

FRAMEWORKFRAMEWORK

Dusanka ZupanskiDusanka ZupanskiCooperative Institute for Research in the AtmosphereCooperative Institute for Research in the Atmosphere

Colorado State UniversityColorado State UniversityFort Collins, CO 80523-1375Fort Collins, CO 80523-1375

Acknowledgements:M. Zupanski, MLEF

Dusanka Zupanski, CIRA/CSUZupanski@CIRA.colostate.edu

DoD Center for Geosciences/Atmospheric Research at Colorado State University, Nov. 17-18, 2003

4DVAR framework

Forecast error covariance

Data assimilation(Init. Cond. and Model Error adjust.)

Observations First guess

Init. Cond. and Model Error opt. estimates

Forecast error covariance

Data assimilation(Init. Cond. and Model Error adjust.)

Observations First guess

Init. Cond. and Model Error opt. estimates

Ens. forecasting

Analysis error Covariance

(in ensemble subspace)

EnsDA framework

In EnsDA framework model error does not depend on assumptions regarding forecast error covariance;

data assimilation problem is solved in ensemble subspace

Dusanka Zupanski, CIRA/CSUZupanski@CIRA.colostate.edu

State augmentation approach (a model bias example)

1-n1-n

1-n

k1-n

n1-n

n

nn FF

Mw

Φ

x

bΦ

Φx

Φ

xw

)1(

bias model ; conditions initial ; , k0k0k bxbxz

Control variable for the analysis cycle k:

Solve EnKF equations (or MLEF) equations in terms of control variable z and forecast model F :

TaaTaf ])(][)([ 2/12/1 PFPFFFPP

Dusanka Zupanski, CIRA/CSUZupanski@CIRA.colostate.edu

IMPACT OF STATE DEPENDENT MODEL ERROR

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

1 11 21 31 41 51 61 71 81 91

Cycle No.

RM

S e

rro

r

correct_model

no_err

param_err

serial_err

EnsDA experiments withKorteweg-de Vries-Burgers (KdVB) model- one-dimensional model- includes non-linear advection, diffusion and dispersion

From Zupanski and Zupanski 2003 (submitted to MWR)

Dusanka Zupanski, CIRA/CSUZupanski@CIRA.colostate.edu

From Zupanski and Zupanski 2003 (submitted to MWR)

EnsDA experiments with KdVB modelAnalysis error covariance matrix

Dusanka Zupanski, CIRA/CSUZupanski@CIRA.colostate.edu