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Andrew Tangborn, Robert Cooper, Steven Pawson, and Zhibin Sun

estimation problems, the Kalman filter gives a minimum variance solution by minimizing a cost function that gives weights to the forecast and observations according to their relative covariances ( Cohn 1997 ). The forecast error covariance, 𝗣 f , is evolved by the linearized dynamics and therefore contains current information on error variance and the correlations between different locations. In carrying out assimilation, nonzero correlations are used to spread the corrections to the forecast to grid

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Olivier Pannekoucke

complex domains (e.g., in ocean modeling with coasts). But in their current formalism, neither the recursive filters nor the diffusion operator are able to represent the nonseparability of statistics. However, an improvement of the spectral formulation, designed with the spherical wavelets, has been proposed by Fisher and Andersson (2001 ; see also Fisher 2003) . This correlation model is heterogeneous and nonseparable. An equivalent wavelet diagonal assumption has been considered by Deckmyn and

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