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1B.17 ASSESSING THE IMPACT OF OBSERVATIONS AND MODEL ERRORS IN THE ENSEMBLE DATA ASSIMILATION FRAMEWORK D. Zupanski 1, A. Y. Hou 2, S. Zhang 2, M. Zupanski 1, and C. D. Kummerow 1 1 Colorado State University, Fort Collins, CO 2 NASA Goddard Space Flight Center, Greenbelt, MD Introduction A general framework that links together information theory and ensemble data assimilation is presented. Ensemble data assimilation component provides information matrix in ensemble subspace, calculated using a flow-dependent forecast error covariance. Information theory component provides mathematical formalism for calculation of various measures of information (e.g., degrees of freedom for signal, entropy reduction). The general framework is examined in application to NASA GEOS-5 column precipitation model. Methodology Maximum Likelihood Ensemble Filter (MLEF, Zupanski 2005; Zupanski and Zupanski 2005) Developed using ideas from Variational data assimilation (3DVAR, 4DVAR) Iterated Kalman Filters Ensemble Transform Kalman Filter (ETKF, Bishop et al. 2001) Minimize cost function J Change of variable -augmented control variable of dim Nstate >>Nens (includes initial conditions, model error, empirical parameters) -control variable in ensemble space of dim Nens Analysis error covariance Forecast error covariance Degrees of freedom (DOF) for signal d s (Rodgers 2000) Experiments with the NASA/GEOS-5 column model Single column version of the GOES-5 GCM GOES-5 includes a finite-volume dynamical core and full physics package The model is driven by external data (ARM observations) Model simulated “observations” with random noise 40 level model, two control variables: T and Q 10, 20, or 40 ensemble members 40 or 80 observations of T and Q 50 data assimilation cycles 6-h data assimilation interval One iteration of the minimization Impact of model error is not included in the experiments presented Increasing ensemble size generally reduces analysis errors, except in the initial cycles for Q. Acknowledgements This research is partially funded by NASA grants: , NAG , and NNG04GI25G. References Bishop, C. H., B. J. Etherton, and S. Majumjar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part 1: Theoretical aspects. Mon. Wea. Rev., 129, 420–436. Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. World Scientific, 238 pp. Shannon, C. E., and Weaver W., 1949: The Mathematical Theory of Communication. University of Illinois Press, 144 pp. Zupanski D. and M. Zupanski, 2005: Model error estimation employing ensemble data assimilation approach. Submitted to Mon. Wea. Rev. [available at ftp://ftp.cira.colostate.edu/Zupanski/manuscripts/MLEF_model_err.Feb200 5.pdf]. Zupanski, M., 2005: Maximum likelihood ensemble filter: Theoretical aspects. Accepted to Mon. Wea. Rev. [Available at ftp://ftp.cira.colostate.edu/milija/papers/MLEF_MWR.pdf]. Shannon information content, or entropy reduction h (Shannon and Weaver 1949; Rodgers 2000) Increased information content in the initial 1-5 cycles due to initial adjustments in P f. Increased information content in the final 10 cycles (cycles 40 – 50) due to new observed information. T obs carry more information than Q obs. Eigenvalue spectrum of C provides additional useful information. Future work Evaluate this framework in application to complex 3-d atmospheric and other geophysical models. Estimate information content of various satellite observations. Columns b i f are calculated employing a non-linear forecast model M: Information matrix C, of dimension Nens X Nens, is a link between ensemble data assimilation and information theory: Columns of Z are defined as Measures of information -eigenvalues of C Innovation statistics is satisfactory for the experiment with 40 ensemble members.

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