Optimal estimation of parameters for a two‐dimensional hydrodynamical model of the Arabian Gulf

Abstract

The parameters of a two‐dimensional numerical tidal model of the Arabian Gulf are estimated by optimal assimilation of data from tide gauges at several of the Saudi Aramco tide stations. The parameters estimated are the bottom drag coefficient and a correction to the bathymetry and are in general allowed to be position dependent. Significant improvements in the predictions of the model are obtained. The method used is based on the minimization of a cost function measuring the difference between the observed and computed water heights at the tide stations, the gradient of the cost function being computed by the adjoint method. The parameter functions are approximated by piecewise constant or piecewise linear approximations, and the cost function is minimized using the quasi‐Newton algorithm CONMIN. It is found in general that in order to obtain stable estimates, it is necessary to include in the cost function a term that penalizes large variations in the parameter functions. Techniques are developed to reduce the storage demands of the algorithm sufficiently to permit the assimilation of 29 days of tidal data.