a singular evolutive extended kalman filter for data assimilation in oceanography：一个奇异的演变扩展卡尔曼滤波器在海洋数据同化.pdfVIP

Journal of Marine Systems 16 1998 323–340 A singular evolutive extended Kalman filter for data assimilation in oceanography Dinh Tuan Pham a, , Jacques Verron b , Marie Christine Roubaud a a Laboratoire de Modelisation et Calcul, Projet Idopt, INRIA JNPG UJF CNRS, B.P. 53X, 38041 Grenoble Cedex, France ´ ´ b ´ Laboratoire des Ecoulements Geophysiques et Industriels, UMR 5519 CNRS, UJF, INPG, B.P. 53X, 38041 Grenoble Cedex, France ´ ´ Received 23 September 1996; accepted 12 November 1997 Abstract 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 correction’ 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