Analysis of Sparse and Noisy Ocean Current Data Using Flow Decomposition. Part II: Applications to Eulerian and Lagrangian Data

Part 2The capability of the reconstruction scheme developed in Part I is demonstrated here through three practical applications. First, the nonlinear regression model is used to reproduce the upper-layer three-dimensional circulation of the eastern Black Sea from model data distorted by white and red noises. Second, the quasigeostrophic approximation is used to reconstruct the shallow water circulation pattern in an open domain with various sampling strategies. Third, the large-scale circulation in the Southern Ocean is reproduced from the First Global Atmospheric Research Program (GARP) Global Experiment (FGGE) drifter data with noncontrollable noise statistics. All three cases confirm that the theoretical approach is robust to various noise-to-signal ratios, number of observations, and station disposition. Using the simplified open boundary condition for analyzing long-term observational data is recommended because the nonlinear regression procedure requires considerable computer resources.This research was sponsored by the Office of Naval Research, Naval Oceanographic Office, and the Naval Postgraduate School.Leonid Ivanov also thanks the International Field Office of the Office of Naval Research for support under the Grant N00014-02-1-4058. This work was partially conducted by Leonid Ivanov while he held a National Research Council Research Associateship Award at the Naval Postgraduate School, and while he visited the University of Delaware

Analysis of sparse and noisy ocean current data using flow decomposition Part 1: Theory

Part 1A new approach is developed to reconstruct a three-dimensional incompressible flow from noisy data in an open domain using a two-scalar (toroidal and poloidal) spectral representation. The results are presented in two parts: theory (first part) and application (second part). In Part I, 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 k, (c) spectral expansion of k, (d) calculation of basis functions for each of the scalar potentials, and (e) determination of coefficients in the spectral decomposition of both velocity and k 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 k 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. In Part II, the capability of the method is demonstrated through reconstructing a 2D wind-driven circulation in a rotating channel, a baroclinic circulation in the eastern Black Sea, and a large-scale surface circulation in the Southern Ocean.This research was sponsored by the Office of Naval Research, Naval Oceanographic Office, and the Naval Postgraduate School. Leonid Ivanov, Tatyana Korzhova, Tatyana Margolina, and Oleg Melnichenko thank U.S. Civilian Research and Development Foundation for sup- port received through Award UG-2079

Reconstruction of Shelf Circulation in Northern Gulf of Mexico from Drifter Buoy Data

Joint Assembles of the International Association for Physical Sciences of the Oceans, International Association for Biological Oceanography, Mar del Plata, Argentina, 22-26 October 200