OPTIMAL ESTIMATION OF EDDY VISCOSITY AND FRICTION COEFFICIENTS FOR A QUASI-3-DIMENSIONAL NUMERICAL TIDAL MODEL

It is shown that the parameters in a quasi-three-dimensional numerical tidal model can be estimated accurately by assimilation of data fr om current meters and ride gauges. The tidal model considered is a semi- linearized one in which advective nonlinearities are neglected but non linear bottom friction is included. The parameters estimated are the e ddy viscosity, bottom friction coefficient water depth and wind drag c oefficient, the first three of which are allowed to be position-depend ent. The adjoint method is used to construct the gradient of a cost fu nction defined as a certain norm of the difference between computed an d observed current and surface elevations. On the basis of a number of tests, it is shown that very effective estimation of the nodal values of the parameters can be achieved using the current data either alone or in combination with elevation data. When random errors are introdu ced into the data, the estimated parameters are quite sensitive to the magnitude of the errors, and in particular the eddy viscosity is unst ably sensitive. The sensitivity of the viscosity can be stabilized by incorporating an appropriate penalty ten in the cost function or alter natively by reducing the number of estimated viscosity values via a fi nite element approximation. Once stabilized, the sensitivity of the es timates to data errors is significantly reduced by assimilating a long er data record.