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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/[email protected]
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/[email protected]
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/[email protected]
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/[email protected]
From Zupanski and Zupanski 2003 (submitted to MWR)
EnsDA experiments with KdVB modelAnalysis error covariance matrix
Dusanka Zupanski, CIRA/[email protected]
![J T P-1 H M )] T R 1 H M )] 1 Carbon data assimilation ... · Carbon data assimilation using Maximum Likelihood Ensemble filter (MLEF) Dusanka Zupanski1, A. Scott Denning2, ... Zupanski](https://img.pdfslide.us/doc/110x75/5b4b7f377f8b9a691e8cdb8e/j-t-p-1-h-m-t-r-1-h-m-1-carbon-data-assimilation-carbon-data-assimilation.jpg)
