Optimization Approach to the Treatment of Open Boundary Conditions

Abstract

A solution to an optimization problem is developed that deals with minimizing a measure of difference between the values of observed and predicted variables at an open ocean boundary. Minimization is based on the change of the flux of energy through the open boundary. It is shown that many of the longwave radiation conditions that are commonly used in ocean modeling can be derived using this optimization criteria. However, the minimization process is seen to produce a modification of these radiation conditions in that they are multiplied by a coefficient, which allows the conditions to adapt to a change in the flux of energy penetrating the boundary. An example of the numerical implementation is presented for the Reid and Bodine boundary formulation. For a standing wave problem with an analytical solution, use of the modified Reid and Bodine formulation is seen to eliminate almost entirely errors in the predicted amplitudes and phases. Overall, this approach is seen to allow a modeler to generate different types of boundary conditions based on observations as well as the inclinations of the modeler.