Dynamical evolution of the error statistics with the SEEK filter to assimilate altimetric data in eddy-resolving ocean models

The Singular Evolutive Extended Kalman (SEEK) filter introduced by Pham et al. is applied to a primitive equation model in order to reconstruct the me soscale circulation typical of the mid-latitude ocean from altimetric data, The SEEK filter is a variant of the Kalman-filter algorithm based on two c oncepts: the order reduction of the initial error covariance matrix, and th e dynamical evolution of the reduced-order basis. This makes the method pot entially 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 im prove the vertical structure of the ocean thermocline in the case of the qu asi-linear dynamics associated with the equatorial tropical Pacific Ocean, and the need to combine the dynamical evolution of the basis with an adapti ve scheme in a mid-latitude ocean model of the Gulf Stream region. This work examines the potential advantages of the dynamical evolution of t he basis functions with simple assimilation experiments. It demonstrates th e ability of the method to propagate in time the statistical properties of the system when the filter is initialized properly. However, the lack of ro bustness of the filter is investigated theoretically and experimentally, sh owing the need to consider variants of the method when the filter is not pr operly initialized.