Prediction error sampling procedure based on dominant Schur decomposition. Application to state estimation in high dimensional oceanic model

摘要

Iterative procedure is described to generate patterns of dominant Schur vectors of the system dynamics. Their roles in estimating the filter gain is study. These patterns are produced by several integrations of the model from a set of perturbations. This approach is motivated by a number of interesting results on stability of the filter whose gain is approximated in a subspace of dominant Schur vectors. A simple method for the filter design is presented which is aimed at overcoming the most serious drawback of advanced filtering algorithms for high dimensional systems related to very high computational cost in evaluation of the filter gain.The resulting filter will be compared with the existing ones, showing its relevance from a practical point of view. In order to demonstrate its efficiency, the new filter is tested on various experiments. These experiments include the much studied problem of estimating the solution of the Lorenz system as well as that of assimilating sea surface height observations in a high dimensional oceanic model. It is shown that significant increases in efficiency can be obtained by using this filter and that the proposed filter is very promising for solving realistic assimilation problems in meteorology and oceanography.