A Partitioned Kalman Filter and Smoother

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Abstract
A new approach is advanced for approximating Kalman filtering and smoothing suitable for oceanic and atmospheric data assimilation. The method solves the larger estimation problem by partitioning it into a series of smaller calculations. Errors with small correlation distances are derived by regional approximations, and errors associated with independent processes are evaluated separately from one another. The overall uncertainty of the model state, as well as the Kalman filter and smoother, is approximated by the sum of the corresponding individual components. The resulting smaller dimensionality of each separate element renders application of Kalman filtering and smoothing to the larger problem much more practical than otherwise. In particular, the approximation makes high-resolution global eddy-resolving data assimilation computationally viable. The approach is described and its efficacy demonstrated using a simple one-dimensional shallow water model. Abstract A new approach is advanced for approximating Kalman filtering and smoothing suitable for oceanic and atmospheric data assimilation. The method solves the larger estimation problem by partitioning it into a series of smaller calculations. Errors with small correlation distances are derived by regional approximations, and errors associated with independent processes are evaluated separately from one another. The overall uncertainty of the model state, as well as the Kalman filter and smoother, is approximated by the sum of the corresponding individual components. The resulting smaller dimensionality of each separate element renders application of Kalman filtering and smoothing to the larger problem much more practical than otherwise. In particular, the approximation makes high-resolution global eddy-resolving data assimilation computationally viable. The approach is described and its efficacy demonstrated using a simple one-dimensional shallow water model.

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