A New Ocean Data Assimilation Scheme—Optimal Spectral Decomposition (OSD)

The optimal spectral decomposition (OSD) method is applied to ocean data assimilation with fields (e.g., temperature, salinity, and velocity) decomposed into generalized Fourier series, such that any ocean field is represented by linear combination of the products of basis functions (or modes) and corresponding spectral coefficients. The OSD data assimilation method has three steps: (1) determination of the basis functions, (2) optimal mode truncation, and (3) update of the spectral coefficients from innovation (or called observational increment). The basis functions only depend on the topography of the ocean basin and boundary conditions. For a rectangular basin, the basis functions are the sinusoidal functions. For a realistic ocean basin, the basis functions can be the eigen functions of the Laplace operator. The Vapnik-Chervonkis cost function is used to determine the optimal mode truncation. After the mode truncation, the model field updates due to innovation through solving a set of a linear algebraic equations of the spectral coefficients. Major benefits using the OSD data assimilation method include: (a) effective utilization of the ocean topographic data, (b) utilization of lateral boundary conditions of the assimilated variables, (c) no requirement of any a-priori information on a background error covariance field, and (d) orthonormal and predetermined basis functions which are independent on the assimilated variable. The capability of the OSD method is demonstrated through a twin-experiment using the Parallel Ocean Program (POP) model.