1. Model Error and Parameter Estimation Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Joint NCAR/MMM CSU/CIRA Data Assimilation Workshop Boulder, CO, September 19, 2005 • 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 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

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

3. Issues of Model Error (and Parameter) Estimation 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? Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

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

5. Information Content AnalysisGEOS-5 Single Column Model Nstate =80; Nobs =80 ds measures effective DOF of an ensemble-based data assimilation system (e.g., MLEF). Useful for addressing DOF of the model error. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

6. BIAS ESTIMATION, KdVB model NEGLECT BIAS BIAS ESTIMATION (vector size=101) BIAS ESTIMATION (vector size=10) NON-BIASED 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