| Summary: | International audience A data assimilation method based on variational approach is presented. The novelty of the hybrid method consists in a coupling of the cost function of the variational approach with an optimal linear smoother issued from the singular evolutive extended Kalman filter (SEEK). The background error covariance matrix of the usual variational framework remains unchanged. In the hybrid method, however, at each transition between the assimilation windows, it is replaced with the one provided by the smoother. The latter is updated whenever new background states are produced. It can be shown that the background states issued from an appropriately constructed variational framework and some particular optimal linear smoother are mathematically equivalent. Hence the matrix injection into the cost function is done in a consistent manner. The hybrid method has been implemented in a shallow water model which mimics a double-gyre circulation in the North Atlantic. Realistic OSSEs have been performed. Comparisons illustrate superiority of the 4D-Var-smoother hybrid over an ordinary 4D-Var on the one hand and on the other over the 4D-Var-filter hybrid.
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