Computing the Steady Oceanic Circulation Using an Optimization Approach

Abstract

The traditional method for computing the steady oceanic circulation has been by stepping an oceanic model forward in time until transients are damped by friction. An alternative method, which has the potential for being more economical is to minimize the sum of the squares of the residuals of the steady model equations. A variety of algorithms might be considered for computing the minimum; attention here is focused on preconditioned conjugate-gradient descent with the gradient computed using an adjoint model. The choice of varibles, i.e. the preconditioning transformation used in the optimization process, is found to be critical to the efficiency of the method. An appropriate preconditioning transformation can be suggested by a heuristic analysis similar to that commonly used to test the stability of numerical models. The method is demonstrated within the context of the barotropic vorticity equation.