Oceanic Data Analysis Using a General Circulation Model. Part II: A North Atlantic Model

A general circulation model and North Atlantic climatological data of temperature salinity, wind stress, evaporation minus precipitation, and air–sea heat fluxes are used to examine the possibility of solving inverse problems using a full-scale numerical GCM and real oceanographic data, combined through an optimization approach. In this study several solutions for the model inputs and the structure of the cost function as a function of the model inputs are examined to demonstrate two of the main difficulties confronting such large-case nonlinear inverse problems (about 30 000 unknowns and a similar number of constraints for the problem examined here). The first is the possible existence of local minima of the cost function, which prevents convergence of the optimization to the global minimum representing the desired optimal solution for the model inputs. The second difficulty, which seems the dominant one for many of the problem examined in this part as well as in Part I, is the ill conditioning of the inverse problem. Simple model equations are used to analyze the conditioning of the optimization problem and to analyze the role of both dissipation and waves in the model dynamics in conditioning the problem. The analysis suggests what might be an improved formulation of the cost function resulting in better conditioning of the problem. The relation between the optimization approach and the robust diagnostic method of Sarmiento and Bryan is explicitly demonstrated, and the solution obtained by combining the two methods is used to examine the performance of the GCM used here for the North Atlantic Ocean.