|Stochastic Systems Group|
Prof. T. Michael Chin
University of Miami and Jet Propulsion Laboratory
The state dimension of a typical atmospheric and oceanic general circulation model has on the order of 10 thousand to 10 million variables. Constraining the state trajectory by some available observation data (the problem of "data assimilation") tends to be an enormous computational task due to the state dimension, especially when a standard optimization formulation (e.g., quadratic cost minimization) is used. Efficient and effective dimension-reduction schemes are necessary for practical solution. In particular, a number of such schemes have been developed for the Kalman filter algorithm. This presentation tends to focus on one that reduces the implicit (or the "information form") Kalman filter. It parameterizes the huge covariance matrix (associated with the model state) using an approximate whitening operator. Its complementary role to the afore-mentioned explicit/standard reduction schemes, its performance on reconstruction of meso-scale ocean surface features, and some open technical issues are discussed in a highly informal fashion.
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