Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model

A new data assimilation scheme has been elaborated for ocean circulation mo dels based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial error covariance matrix as a truncated series of orthogonal perturbations. This error sub-space evolves during the assimilation so as to capture the growing modes of the estimation error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filt er considers a time-independent error sub-space, the apprentice filter prog ressively enriches the error sub-space with the information learned from th e innovation vector after each analysis step, and the dynamical filter upda tes the error sub-space according to the model dynamics. The SEEK filter ha s been implemented to assimilate synthetic observations of the surface topo graphy in a non-linear, primitive equation model that uses density as verti cal coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a reso lution of 20 km in the horizontal, and 4 levels in the vertical. The concep t of twin experiments is used to demonstrate that the conventional SEEK fil ter must be complemented by a learning mechanism in order to model the misr epresented tail of the error covariance matrix. An approach based on the ve rtical physics of the isopycnal model, is shown particularly robust to cont rol the velocity field in deep layers with surface observations only. The c ost of the method makes it a suitable candidate for large-size assimilation problems and operational applications. (C) 1999 Elsevier Science B.V. All rights reserved.