Optimal Control Theory Applied to an Objective Analysis of a Tidal Current Mapping by HF Radar

Abstract

Optimal control can provide a tool to perform an optimization of a tidal model via a data assimilation operation. A pilot study is presented here to test the theoretical and numerical feasibility of an assimilation of HF radar current measurements in a simplified tidal model of limited extent. The aim is, on one hand, to filter and smooth data, and, on the other, to identify ad hoc boundary forcing and friction coefficient, in order to ensure the ?best? fit between data and model results. Simultaneous use of the model and its adjoint permits us to handle a gradient descent algorithm to minimize, in a least square sense, model and data misfits. A few tools of functional analysis are progressively introduced, so that most of the results are first derived and interpreted in the framework of a continuous formulation. Their counterpart discretized versions are obtained in ultimate stages of the calculus. A sample of computer experiments is carried out to test the validity of the proposed optimization-assimilation algorithm.