Fitting a finite element tidal model to sparse data: application to the Straits of Dover

Abstract

The major difficulty faced by numerical models of tidal dynamics in the limited-area shelf basins concerns the treatment of open boundaries. We show that effective control of the open boundary conditions in a depth-averaged numerical model can be achieved by assimilation of data from coastal tide gauges in the interior of the basin, distant from its open boundaries. We use variational assimilation of sea level data at a number of coastal locations into a quasi-linearized finite element tidal model, and a “weak” formulation of the dynamical constraints. The effectiveness of the procedure is verified on a test problem involving tidal wave propagation in a zonally oriented, narrow, rotating channel with two open boundaries. The assimilation technique was then successfully applied to the reconstruction of the M 2 tide in the Dover Straits using coastal tidal measurements in the ports. A rigorous error analysis is performed using the explicit inversion of the Hessian matrix, associated with the assimilation scheme. As a result, an error chart for the amplitude of the optimized sea surface elevation is obtained.