OPTIMAL ESTIMATION OF EDDY VISCOSITY FOR A QUASI-3-DIMENSIONAL NUMERICAL TIDAL AND STORM-SURGE MODEL

It is shown that the eddy viscosity profile in a quasi-three-dimension al numerical tidal and storm surge model can be estimated by assimilat ion of velocity data from one or more current meters located on the sa me vertical line. The computational model used is a simplified version of the so-called vertical/horizontal splitting algorithm proposed by Lardner and Cekirge. We have estimated eddy viscosity both as a consta nt and as a variable parameter. The numerical scheme consists of a two -level leapfrog method to solve the depth-averaged equations and a gen eralized Crank-Nicolson scheme to compute the vertical profile of the velocity field. The cost functional in the adjoint scheme consists of two terms. The first term is a certain norm of the difference between computed and observed velocity data and the second term measures the t otal variation in the eddy viscosity function. The latter term is not needed when the data are exact for the model but is necessary to smoot h out the instabilities associated with 'noisy' data. It is shown that a satisfactory minimization can be accomplished using either the Broy den-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm or Nash's t runcated Newton algorithm. Very effective estimation of eddy viscosity profiles is shown to be achieved even when the amount of data is quit e small.