OPTIMAL ASSIMILATION OF CURRENT AND SURFACE ELEVATION DATA IN A 2-DIMENSIONAL NUMERICAL TIDAL MODEL

It is shown that the parameters in a two-dimensional (depth-averaged) numerical tidal model can be estimated is a semilinearized one in whic h kinematic nonlinearities are neglected but nonlinear bottom friction is included. The parameters estimated are the bottom friction coeffic ient, the water depth, and the wind dr ag coefficient, the first two o f which are assumed to be position-dependent and are approximated by p iecewise linear interpolations between certain nodal values. The adjoi nt method is used to construct the gradient of a cost function defined as a certain norm of the difference between computed and observed cur rents and surface elevations. Minimization of the cost function is per formed using Nash's truncated Newton algorithm. On the basis of a numb er of tests, it is shown that very effective estimation of the nodal v alues of the parameters can be achieved using either current or elevat ion data or both. When random errors are introduced into the data, the estimated parameters are quite sensitive to the magnitude of the erro rs when only one of the data types is assimilated, but they are less s ensitive when both are used. The sensitivity to data errors is signifi cantly reduced by assimilating a longer data record.