A popular method to process ocean data is the optimum interpolation (OI). Using the OI method (Gandin 1965), the background field (or called first-guess field) and autocorrelation function (or decorrelation scale) should be given. For the velocity field, both background field and decorrelation scale are unknown. For the temperature or salinity field, the decorrelation scale is unknown. Usually, the decorrelation scale is user defined in the OI application. Therefore, the estimated fields are dependent on the decorrelation scale.
Without knowing the background field and decorrelation scale, the optimal spectral decomposition (OSD) method can process sparse and noisy data (Chu et al., 2003 a, b). Any field (temperature, salinity, or velocity) can be decomposed into generalized Fourier series using the OSD method. The three dimensional field is then represented by linear combination of the products of basis functions (or called modes) and corresponding Fourier coefficients. If a rectangular closed ocean basin is considered, the basis functions are sinusoidal functions. If a realistic ocean basin is considered, the basis functions are the eigenvalues of the three-dimensional Laplace operator with real topography. After the decomposition, the three-dimensional field is represented by a set of Fourier coefficients. This method has three components: (1) determination of the basis functions, (2) optimal mode truncation, and (3) determination of the Fourier coefficients.
Streamfunction for the mid-depth (~1000 m) circulation is calculated using the OSD method for every three months. Three major patterns of the streamfunction in the North Atlantic tropics are found: (1) a cyclonic gyre with the northward branch in the east and the southward branch in the west (AAIW moving northward along the western coast of Africa), (2) double-gyre structure with a cyclonic gyre in the east and an anticyclonic gyre in the west (AAIW moving northward along the western coast of Africa and the Brazilian coast), and (3) double-gyre structure with an anticyclonic gyre in the east and a cyclonic gyre in the west (AAIW moving northward in the middle of the Atlantic Ocean). The streamfunction has rapid change in 2004. It reveals Pattern-1 in March-May, changes to Pattern-2 in June-August, and shifts to Pattern-3 in September-November. The effects of rapid AAIW path change on THC and in turn the climate are also presented.
Chu, P.C., L.M. Ivanov, T.P. Korzhova, T.M. Margolina, and O.M. Melnichenko, 2003: 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, 2003: 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.