Ensemble data assimilation and information theory

Some of the most demanding goals of Numerical Weather Prediction (NWP) and new observing missions are (1) to determine analysis and forecast uncertainties, and (2) to estimate information content of new observations. Achieving these goals within a unified methodology is desirable since these two goals are not independent: information content of new observations is dependent on the prior knowledge about the atmospheric state, which is often defined in terms of analysis and forecast uncertainty. Ensemble based data assimilation approaches have a capability to update forecast error covariance, thus having a potential for appropriately addressing the first goal. Information theory provides a theoretical framework for addressing the second goal. In this study we examine a unified approach employing both ensemble data assimilation and information theory. A framework formulated as Maximum Likelihood Ensemble Filter (MLEF) will be used in this study as an example of the ensemble data assimilation approach. The MLEF framework provides maximum likelihood solution for the atmospheric state, model error, and empirical parameters, employing an iterative minimization of a cost function. It also calculates the analysis and forecast error covariance matrices as measures of the analysis and forecast uncertainty. In addition, information theory will be applied within the MLEF framework to determine information matrix in ensemble sub-space. This unified approach is examined in application to a relatively simple one-dimensional atmospheric model (a column version of NASA GEOS-5 model) and to a more complex 3-dimensional non-hydrostatic NWP model (RAMS). It will be demonstrated that the ensemble based data assimilation approaches if unified with the information theory can be effectively used to determine analysis and forecast uncertainties and to estimate information content of new observations.