Abstract
AbstractThe Singular Evolutive Extended Kalman (SEEK) filter introduced by Pham et al. is applied to a primitive‐equation model in order to reconstruct the mesoscale circulation typical of the mid‐latitude ocean from altimetric data. The SEEK filter is a variant of the Kalman‐filter algorithm based on two concepts: the order reduction of the initial‐error covariance matrix, and the dynamical evolution of the reduced‐order basis. This makes the method potentially suitable for problems with a high number of degrees of freedom.Previous work has shown the ability of a steady version of the filter to improve the vertical structure of the ocean thermocline in the case of the quasi‐linear dynamics associated with the equatorial tropical Pacific Ocean, and the need to combine the dynamical evolution of the basis with an adaptive scheme in a mid‐latitude ocean model of the Gulf Stream region.This work examines the potential advantages of the dynamical evolution of the basis functions with simple assimilation experiments. It demonstrates the ability of the method to propagate in time the statistical properties of the system when the filter is initialized properly. However, the lack of robustness of the filter is investigated theoretically and experimentally, showing the need to consider variants of the method when the filter is not properly initialized.
Highlights
During the last decade, the observation of the ocean from space has led to an unprecedented amount of oceanographic data
The Singular Evolutive Extended Kalman (SEEK) filter introduced by Pham et al (1998) is one of these simplifications
The first set of empirical orthogonal functions (EOFs) accounts for the variance of the model during the time period corresponding to the synthetic observations to be assimilated
Summary
The observation of the ocean from space has led to an unprecedented amount of oceanographic data. Only r eigenvectors are needed on the assimilation algorithm instead of the full covariance matrix This hypothesis is equivalent to the condition of order reduction, in which the state vector may be expressed as (4). In the context of a sequential scheme, Cane et al (1996) project the KF equations onto an EOF basis in order to construct an analog of the Kalman filter for the principal components In their application, the time evolution of the principal components of a small perturbation of the state vector, ax, is computed as follows:. In the SEEK filter, Pham et al (1998) take a different approach to Eq (5), by allowing the dynamical model to modify the directions defined by the columns of ST, i.e. i.e. the linear evolution of the current state of the system is expressed by the evolution of each one of the members of the subspace basis.
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