Analysis of remotely sensed ocean data by the optimal spectral decomposition (OSD) method

A new data analysis/assimilation scheme, optimal spectral decomposition (OSD), has been developed to reanalyze fields from noisy and sparse data in a domain with open boundary conditions using two scalar representations for a three-dimensional incompressible flow. The reanalysis procedure is divided into two steps: (a) specification of basis functions in the spectral decomposition from knowledge of boundary geometry and velocity and (b) determination of coefficients in the spectral decomposition for the circulation solving linear or nonlinear regression equations. The basis functions are the eigenfunctions of the Laplacian operator with mixed boundary conditions. The optimization process is used to obtain unique and stable solutions on the base of an iteration procedure with special regularization (the filtration. The capability is demonstrated using various examples.