Data Assimilation by Optimal Control Method in a 3D Coastal Oceanic Model: The Problem of Discretization

Abstract

A methodology to proceed from the continuous to the discrete formulation of a control problem is described. The aim of a boundary control procedure is to identify boundary forcing to ensure the best fit between data and model results by minimizing a function that measures model and data discrepancies. A continuous variational formulation involving the adjoint technique is used. To ensure the minimization of the ?cost function? in the discretized form as well as in its continuous form, particular discretizations are performed. The model considered at first is given by Burger?s equation. Then results are extended to a typical 3D multilayered ocean circulation model for a semienclosed basin Kelvin wave.