THE RIGID LIDS CONTRIBUTION TO THE ILL-CONDITIONING OF OCEANIC INVERSE PROBLEMS

Fitting oceanographic general circulation models to data is a difficul t computational undertaking. This paper addresses difficulties stemmin g from the rigid lid approximation. Adjusting the barotropic stream fu nction to achieve the fit, in effect, requires the solution of a hidde n elliptical equation, the resolution-dependent difficulty of the elli ptical problem manifest in the optimization problem. Adjusting the ind ependent (subsuface) baroclinic velocity variables also contributes to the ill-conditioning of the least squares computation, but Lagrange m ultipliers can be used to adjust all baroclinic velocity variables (su rface and subsurface) symmetrically. Similarly, Lagrange multipliers c an be used to adjust the total velocity variables, thereby circumventi ng the use of barotropic stream function and baroclinic velocities; de termining the multipliers at each optimization iteration requires the solution of an elliptical partial differential equation, the solution of which can be thought of as a preconditioning transformation.