Abstract
Abstract Kalman filter theory shows great promise when applied to the assimilation of atmospheric observations. Previous work has concentrated on extratropical dynamics, and tropical aspects have not yet been seriously tackled. In this article, a Kalman filter is applied to the linearized shallow water equations on an equatorial beta plane. The system or model error is constructed from the slow eigenmodes of the model and is based on an expansion in parabolic cylinder functions. The resulting second‐moment statistics are discussed in some detail. The Kalman filter is applied to a special observation network that allows the diagonalization of the system. Following Daley and Ménard (1993), it is then possible to obtain the complete space and time solution for the second‐moment forecast and analysis error statistics. The slow (low‐frequency) and fast (high‐frequency) error statistics are examined separately for both the optimal and suboptimal cases.
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