Optimal Spectral Decomposition (OSD) for Analyzing Sparse and Noisy Ocean Data

Great advantages of optimal spectral decomposition (OSD) in analyzing sparse and noisy ocean data are demonstrated in this paper. Two-scalar (toroidal and poloidal) spectral representation is used to reconstruct three-dimensional ocean flow from noisy data in an open domain. This approach includes: (a) a boundary extension method to determine normal and tangential velocities at an open boundary, (b) establishment of homogeneous open boundary conditions for the two potentials with a spatially varying coefficient ê, (c) spectral expansion of ê, (d) calculation of basis functions for each of the scalar potentials, and (e) determination of coefficients in the spectral decomposition of both velocity and ê using linear or nonlinear regressions. The basis functions are the eigenfunctions of the Laplacian operator with homogeneous mixed boundary conditions and depend upon the spatially varying parameter ê at the open boundary. A cost function used for poor data statistics is introduced to determine the optimal number of basis functions. An optimization scheme with iteration and regularization is proposed to obtain unique and stable solutions. The capability of the method is demonstrated through analyzing noisy and sparse Eulerian and Lagrangian data. References Chu, P.C., L.M. Ivanov, T.P. Korzhova, T.M. Margolina, and O.M. Melnichenko, 2003a: Analysis of sparse and noisy ocean current data using flow decomposition. Part 1: Theory. Journal of Atmospheric and Oceanic Technology, 20 (4), 478-491. Chu, P.C., L.M. Ivanov, T.P. Korzhova, T.M. Margolina, and O.M. Melnichenko, 2003b: Analysis of sparse and noisy ocean current data using flow decomposition. Part 2: Application to Eulerian and Lagrangian data. Journal of Atmospheric and Oceanic Technology, 20 (4), 492-512.