Singular evolutive Kalman filters for data assimilation in oceanography

We propose a Kalman type filter for assimilating oceanic data into a numerical model. It essentially consists in approximating the error covariance matrix by a singular low rank matrix which leads to making corrections only in those directions for which the error is not sufficiently attenuated by the system. These directions evolve the time according to the model evolution, yielding its adaptative nature to the filter. The filter has been applied in a realistic framework on the Pacific tropical ocean, yielding quite satisfactory results with simulated altimetric data, distributed according to the spatio-temporal sampling from the Topex/Poseidon satellite. (C) Academie des sciences/Elsevier, Paris.