| A general procedure of adjoint data assimilation for atmosphere-ocean coupled systems was developed. A simple equatorial coupled atmosphere-ocean model, with the atmosphere and the ocean each represented by a single-layer linear shallow water model, was then used to explore the effects of data type (wind or sea level height (SLH)), data sparsity, noise, and initial guess on the retrieval of model parameters and initial conditions.; Six parameters (two Rayleigh damping coefficients, two Newtonian cooling coefficients, and two coupling parameters) of the simple model were estimated with its initial conditions specified. By assimilating the wind and SLH data, the temporal sparsity of the data was found to be more detrimental for parameter estimation than their spatial sparsity, and sparse wind data were more detrimental than sparse SLH data. Longer assimilation windows improved the parameter estimation, but the best window length for the wind data was not the best for the SLH data. A priori information for individual parameters as implemented in the cost function was useful in providing information for the size of the parameters and in enhancing the convexity of the cost function, but not as a substitute for inadequate data.; Three initial oceanic fields (SLH and two horizontal current components) in the simple coupled model were estimated with the six parameters specified. By assimilating either the wind or SLH data, it was found that the SLH data were more efficient in retrieving the oceanic initial conditions than the wind data, and the initial SLH field was more accurately retrieved than the initial currents. The current fields were sensitive to the temporal density of data, especially with wind data, where once a day would be the minimum density needed for a satisfactory retrieval. The error in the magnitude of the initial guess was readily corrected, while the large phase error was not even with both the wind and SLH available. Assimilation of noisy data showed that the retrieval of the initial conditions was far more sensitive to noise in the SLH data than in the wind data. |
