Applications of information theory in ensemble data assimilation

We apply information theory within an ensemble-based data assimilation approach and define information matrix in ensemble subspace. The information matrix in ensemble subspace employs a flow-dependent forecast error covariance and it is of relatively small dimensions (equal to the ensemble size). The information matrix in ensemble subspace can be directly linked to the information matrix typically used in non-ensemble-based data assimilation methods, such as the Kalman Filter (KF) and the three-dimensional variational (3D-Var) methods, which provides a framework for consistent comparisons of information measures between different data assimilation methods. We evaluate information measures, such as degrees of freedom for signal, within the Maximum Likelihood Ensemble Filter (MLEF) data assimilation approach and compare them with those obtained using the KF approach and the 3D-Var approach. We assimilate model-simulated observations and use the Goddard Earth Observing System Single Column Model (GEOS-5 SCM) as a dynamical forecast model. The experimental results demonstrate that the proposed framework is useful for comparing information measures obtained in different data assimilation approaches. These comparisons indicate that using a flow-dependent forecast error covariance matrix (e.g. as in the KF and the MLEF experiments) is fundamentally important for adequately describing prior knowledge about the true model state when calculating information measures of assimilated observations. We also demonstrate that data assimilation results obtained using the KF and the MLEF approach (when ensemble size is larger than 10 ensemble members) are superior to the results of the 3D-Var approach. Copyright (C) 2007 Royal Meteorological Society.