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 develop ment 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 attenu ated by the system. This not only reduces the implementation cost but may also improve the filter stability as well. These 'directions of co rrection' evolve with time according to the model evolution, which con stitutes the most original feature of this filter and distinguishes it from other sequential assimilation methods based on the projection on to a fixed basis of functions. A method for initializing the filter ba sed 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 gi ven. Although this is only a simple test case designed to assess the f easibility of the method, the results are very encouraging. (C) 1998 E lsevier Science B.V. All rights reserved.