Oceanic Data Analysis Using a General Circulation Model. Part I: Simulations

This paper deals with the solution of inverse problems involving complex numerical models of the oceanic general circulation and large datasets. The goal of these inverse problems is to find values for model inputs consistent with a steady circulation and, at the same time, consistent with the available data. They are formulated as optimization problems, seeking values for the model's inputs that minimize a cost function measuring departures from steady state and from date. The two main objectives of this work are 1) to examine the feasibility of solving inverse problems involving a realistic numerical model of the oceanic general circulation and 2) to understand how the optimization uses various data to calculate the desired model parameters. The model considered here is similar to the primitive equation model of Bryan and of Cox, the principal difference being that here the horizontal momentum balance is essentially geostrophic. The model's inputs calculated by the optimization consist of surface fluxes of heat, water, and momentum, as well as the eddy-mixing parameters. In addition, optimal estimates for the hydrography are obtained by requiring the hydrography to be consistent with both other types of data and the model's dynamics. In the examples presented here, the data have been generated by the model from known inputs; in some cases, simulated noise has been added. The cost function is a sum of terms quadratic in the differences between the data and their model counterparts and terms quadratic in the temperature and salinity time rate of change as evaluated using the model equations. The different inverse problems considered differ in the choice of the model inputs calculated by the optimization and in the data used in the cost function. Optimal values of the model's inputs are computed using a conjugate-gradient minimization algorithm, with the gradient computed using the so-called adjoint method. In examples without added noise, solutions for the model inputs were found efficiently and accurately. This was not the case when simulated data with randomly generated noise was used. Amplification of noise was especially felt in regions of deep-water formation due to the strong vertical mixing in these regions. Away from deep-water formation regions, the performance of the optimization with noisy data was still not satisfactory, possibly due to bad conditioning of the problem. The conditioning of the optimization and the difficulties due to the noise amplification are further discussed in Part II of this work using real oceanographic data for the North Atlantic Ocean.