1. Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Model Error and Parameter Estimation Joint NCAR/MMM CSU/CIRA Data Assimilation Workshop Boulder, CO, September 19, 2005 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu Outline  State augmentation approach  Issues of model error estimation - Degrees of freedom of model error - Information content of available data  Current research projects  Future research directions and collaborations

2. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu - Dynamical model for standard model state x State Augmentation Approach - Dynamical model for model error (bias) b - Dynamical model for empirical parameters  Define augmented state vector w Find optimal solution (augmented analysis) w a by minimizing J (MLEF method): And augmented dynamical model F ,. (Zupanski and Zupanski 2005, MWR)

3. Issues of Model Error (and Parameter) Estimation Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu State augmentation increases the size of the control variable  More Degrees of Freedom (DOF)! Do we need more ensembles? Do we need more observations? What is the number of the effective DOF of an ensemble-based data assimilation and model error estimation system?

4. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu What is the number of the effective DOF? Ensemble Data Assimilation + State Augmentation + Information theory Answer can be obtained by using the following 3 components within a general framework: Shannon information content, or entropy reduction Degrees of freedom (DOF) for signal (Rodgers 2000; Zupanski et al. 2005) C - information matrix in ensemble subspace

5. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu Information Content Analysis GEOS-5 Single Column Model N state =80; N obs =80 d s measures effective DOF of an ensemble-based data assimilation system (e.g., MLEF). Useful for addressing DOF of the model error.

6. NEGLECT BIASBIAS ESTIMATION (vector size=101) BIAS ESTIMATION (vector size=10)NON-BIASED MODEL BIAS ESTIMATION, KdVB model It is beneficial to reduce degrees of freedom of the model error.

7. Current Research Projects  Precipitation Assimilation (NASA) Apply MLEF to NASA GEOS-5 column precipitation model Address model error and parameter estimation (In collaboration with A. Hou, S. Zhang - NASA/GMAO, C. Kummerow - CSU/Atmos. Sci. Dept.)  GOES-R Risk Reduction (NOAA/NESDIS) Evaluate the impact of GOES-R measurements in applications to severe weather and tropical cyclones Information content of GOES-R measurements (In collaboration with M. DeMaria - CIRA/NOAA/NESDIS, T. Vonder Haar, L. Grasso, M. Zupanski - CSU/CIRA)  Carbon Cycle Data Assimilation (NASA) Apply MLEF to various carbon models (LPDM, SiB3, PCTM, and SiB- CASA-RAMS) Assimilate carbon concentrations globally and locally Address model error and parameter estimation (In collaboration with S. Denning, M. Uliasz, K. Gurney, L. Prihodko, R. Lokupitiya, I. Baker, K. Schaefer - CSU/Atmos. Sci. Dept., M. Zupanski - CSU/CIRA) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

8. Future Research Directions and Collaborations Model bias and parameter estimation requires collaboration Learning about model errors and uncertainties of different dynamical models Developing diagnostic tools for new model development Information content analysis Quantify value added of new observations (e.g., GPM, CloudSat, GOES-R, OCO) Determine effective DOF of an ensemble-based data assimilation system Cross-over the existing scientific boundaries Apply ensemble-based framework to different science disciplines (e.g., atmospheric, oceanic, ecological, hydrological sciences) General, adaptive, algorithmically simple algorithm opens new possibilities Discuss issues for collaboration with NCAR/MMM Model errors and parameter estimation for WRF model Information content analysis - effective DOF of WRF data assimilation system Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu