An extended Kalman filter to assimilate satellite altimeter data into a nonlinear numerical model of the tropical Pacific Ocean: Method and validation

A new implementation of the extended Kalman filter scheme is developed for the purpose of assimilating observations into a high-resolution nonlinear numerical model of the tropical Pacific Ocean. It is characterized by two successive stages: (1) approximation of 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 naturally attenuated by the system (in this respect it is quite similar to the approach adopted by Cane et al. [1996]), and (2) modification of these directions over time according to the model dynamics, thus reflecting the evolutive nature of the filter. The filter is initialized by a method based on the empirical orthogonal functions obtained from free runs of the model. The reduction of the error covariance matrix avoids the overwhelming burden of computing the temporal evolution of the prediction error with all the degrees of freedom of the full state vector. This assimilation scheme is implemented in the Gent and Cane [1989] primitive equation reduced gravity model. This model has the advantage of using a σ coordinate in the vertical which allows a geographical refinement of the vertical resolution for thermocline gradients. It is forced by the Florida State University database winds, and the Chen et al. [1994] hybrid scheme parameterization is assumed for the mixed layer. The domain of application is the tropical Pacific Ocean basin between 120°E and 80°W longitude and 30°S and 30°N latitude. The resolution is finest at the equator and steadily increases away from the equator. In a first application, validation twin experiments are conducted in which observations are assumed to be synthetic altimeter data sampled according to the TOPEX/POSEIDON mission features. The method is shown to be efficient under various conditions and, in particular, to be capable of transferring information in the vertical from the surface-only altimeter data to the deepest ocean layers and therefore of adequately constraining the thermal and the velocity profiles within the 300 or 400 m upper ocean. In a second application, real TOPEX/POSEIDON data are used and the results evaluated against independent in situ data, namely, Tropical Ocean-Global Atmosphere (TOGA)/TAO mooring observations. Improvements in the model behavior are clear in terms of the time variability of the tropical ocean. It therefore seems that the reduced state Kalman filter with empirical orthogonal function (EOF) initialization can be applied with success to such a primitive equation model of the Pacific for the assimilation of altimeter data. However, at this stage the evolutivity of the filter seems to have a limited impact on the performances, which was not the case for tests in the strongly nonlinear midlatitudes [Pham et al., 1998a].

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