Optimal Spectral Decomposition (OSD) for Ocean Data Assimilation

Optimal spectral decomposition (OSD) is applied to ocean data assimilation with variable (temperature, salinity, or velocity) anomalies (relative to background or modeled values) decomposed into generalized Fourier series, such that any anomaly is represented by a linear combination of products of basis functions and corresponding spectral coefficients. It has three steps: 1) determination of the basis functions, 2) optimal mode truncation, and 3) update of the spectral coefficients from innovation (observational increment). The basis functions, depending only on the topography of the ocean basin, are the eigenvectors of the Laplacian operator with the same lateral boundary conditions as the assimilated variable anomalies. The Vapnik–Chervonkis dimension is used to determine the optimalmode truncation.After that, themodel field updates due to innovation through solving a set of a linear algebraic equations of the spectral coefficients. The strength andweakness of the OSD method are demonstrated through a twin experiment using the Parallel Ocean Program (POP) model.