A singular evolutive extended Kalman filter for data assimilation in oceanography

In this work, we propose a modified form of the extended Kalman filter (KF) for assimilating oceanic data into numerical models. Its development consists essentially of approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those directions for which the error is the most attenuated by the system. This not only reduces the implementation cost but may also improve the filter stability as well. These ‘directions of correctionʹ evolve with time according to the model evolution, which constitutes the most original feature of this filter and distinguishes it from other sequential assimilation methods based on the projection onto a fixed basis of functions. A method for initializing the filter based on the empirical orthogonal functions (EOF) is also described. An example of assimilation based on the quasi-geostrophic (QG) model for a square ocean domain with a certain wind stress forcing pattern is given. Although this is only a simple test case designed to assess the feasibility of the method, the results are very encouraging.