The prediction process can be viewed as the relaxation of the initial condition probability distribution toward the climatological or equilibrium distribution (the degree of disequilibrium measures the "usefulness" of the prediction). We use a realistic atmospheric model and very large ensembles to study this process in detail. A particular focus will be on the utilization of information theoretic functionals on these two distributions. We shall also discuss various measures of information flow and discuss in particular the information flow between the initial conditions and predictions. At the beginning of the presentation a personal perspective on challenges in model initialization and prediction from a mathematical viewpoint will be given
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