Abstract : In this paper, we present an overview of various data assimilation methods, in order to identify the initial condition of a geophysical system and reconstruct its evolution in time and space. We first present the well known four dimensional variational adjoint method, the 4D-VAR algorithm, and then the four dimensional variational dual method, the 4D-PSAS algorithm, extended to nonlinear models. We present then an improved sequential data assimilation algorithm, the SEEK filter. We finally introduce a new simple algorithm, the Back and Forth Nudging. Some theoretical and numerical results about the BFN algorithm are finally given.
