1. MODEL ERROR ESTIMATION IN ENSEMBLE DATA ASSIMILATION FRAMEWORK Dusanka Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University Fort Collins, CO 80523-1375 Acknowledgements: M. Zupanski, MLEF Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu DoD Center for Geosciences/Atmospheric Research at Colorado State University, Nov. 17-18, 2003

2. 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

3. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu State augmentation approach (a model bias example) Control variable for the analysis cycle k: Solve EnKF equations (or MLEF) equations in terms of control variable z and forecast model F :

4. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu EnsDA experiments with Korteweg-de Vries-Burgers (KdVB) model - one-dimensional model - includes non-linear advection, diffusion and dispersion From Zupanski and Zupanski 2003 (submitted to MWR)

5. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu From Zupanski and Zupanski 2003 (submitted to MWR) EnsDA experiments with KdVB model Analysis error covariance matrix

6. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu