Abstract. This paper deals with a new data assimilation algorithm, called the Back and Forth Nudging. The standard nudging technique consists in adding to the equations of the model a relaxation term that is supposed to force the observations to the model. The BFN algorithm consists of repeating forward and backward resolutions of the model with relaxation (or nudging) terms, that have opposite signs in the direct and inverse resolutions, so as to make the backward evolution numerically stable. This algorithm has first been tested on the standard Lorenz model, with discrete observations (perfect or noisy) and it has been compared with the 4D-VAR method. Then the same type of study has been performed on the viscous Burgers equation and the comparison with the variational method has been focused on the evolution in time of the error between the reference trajectory and the identified one, for a period being split into one assimilation period and one prediction time. The possible use of the BFN algorithm as an initialization of the 4D-VAR method has also been pointed out. Finally the algorithm has been tested on a layered quasi- geostrophic model with sea-surface height observations. The comparison of the behaviour of the two algorithms has been performed in the case of perfect or noisy observations, and also for imperfect models. Finally a conclusion on the relative performance of the two algorithms has been proposed.
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