TRACKING NONLINEAR SOLUTIONS WITH SIMULATED ALTIMETRIC DATA IN A SHALLOW-WATER MODEL

Low-frequency variability of western boundary currents (WBCs) is perva sive in both observations and numerical models of the oceans. Because advection is of the essence in WBCs, nonlinearities are thought to be important in causing their variability. In numerical models, this vari ability can be distorted by our incomplete knowledge oi the system's d ynamics, manifested in model errors. A reduced-gravity shallow-water m odel is used to study the interaction of model error with nonlinearity . Here our focus is on a purely periodic solution and a weakly aperiod ic one. For the periodic case, the noise-corrupted system loses its pe riodicity due to nonlinear processes. For the aperiodic case, the inte rmittent occurrences of two relatively persistent states-a straight je t with high total energy and a meandering one with low total energy-in the perturbed model are almost out of phase with the unperturbed one. For both casts, the simulation errors are trapped in the WBC region, where the nonlinear dynamics is most vigorous. Satellite altimeters me asure sea surface height globally in space and almost synoptically in Lime. They provide an opportunity to track WBC variability through its pronounced sea surface signature. By assimilating simulated Geosat da ta into the stochastically perturbed model with the improved optimal i nterpolation method, the authors can faithfully track the periodic beh avior that had been lost and capture the correct occurrences of two re latively persistent patterns for the aperiodic cast. The simulation er rors accumulating in the WBC region are suppressed, thus improving the system's predictability. The domain-averaged rms errors reach a stati stical equilibrium below the observational error level. Comparison exp eriments using simulated Geosat and TOPEX/POSEIDON tracks show that sp atially dense sampling yields lower rms errors than temporally frequen t sampling For the present model. A criterion defining spatial oversam pling-that is, diminishing returns-is also addressed.