Optimal control of open boundary conditions for a numerical tidal model

Abstract

Abstract A major difficulty faced by numerical models of tidal flows concerns the treatment of open boundaries. It is shown that effective control of the open boundary conditions in a depth-averaged numerical tidal model can be achieved by assimilation of data from tide gauges in the interior of the region occupied by the water body. The tidal model considered is a semi-linearized one in which kinematic nonlinearities are neglected but nonlinear bottom friction is included, and the numerical scheme consists of a two-level leapfrog method. The adjoint scheme is constructed on the assumption that a certain norm of the difference between computed and observed elevations at the tide gauges should be minimized. The numerical minimization is completed using the BFGS quasi-Newton algorithm. The effectiveness of the procedure is verified on three test problems, the first involving flow in a long narrow inlet, the second, flow in a rectangular gulf with one open side and the third, flow in a bay with a long open boundary.