IMPROVING STEADY-STATE FIT OF DYNAMICS TO DATA USING ADJOINT EQUATIONFOR GRADIENT PRECONDITIONING

The steady-state fit of Arakawa and Lamb's shallow-water equation mode l to time-mean sea surface height (SSH) has been examined, seeking bet ter performance of the steady-state fit without requiring longer time integrations. It is shown that the minimization problem with steadines s penalties involving one time step is ill conditioned. The difficulty is due to disparity among components of the cost function gradient, w hen the cost function surface is characterized by steep slopes in some parameter directions and by Bat slopes in others. Preconditioning the gradient of cost function by means of an adjoint model is examined. R esults show improvement of condition number of the Hessian of the cost function and quality of the fit while retaining the economy of the on e-time-step approach. The method is extended to fitting the time-mean SSH from eddy-active simulations.