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

Abstract

The 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.

Observational studies on association between eastward equatorial jet and Indian Ocean dipole

“…To overcome this weakness, a recently developed Optimal Spectral Decomposition method (Chu et al, 2003a(Chu et al, , 2003b(Chu et al, , 2004 was used to reconstruct the OSCAR data at each time instance, which is represented by V(x, y, t), where (x, y) are horizontal coordinates, and t is time.…”

Climate Change: Anticipated Effects on High-Energy Laser Weapon Systems in Maritime Environments

“…A variable c(x, z, t) at depth z k is decomposed using the generalized Fourier series (Chu et al 2003a(Chu et al ,b, 2005a:…”

Determination of Mesoscale Surface Currents in Shallow-Water Regions According to the Data of High-Frequency Radar Measurements

“…In order to eliminate the existing arbitrariness in the definition of the potentials on the boundary, we use the approach developed in [10] for closed water basins and in [11,12] for the regions with open boundaries. For the sake of definiteness, the region S is regarded as simply connected and bounded by the coastal line G and the open boundary G′, i.e., by G ∪ G′.…”

“…In more detail, the boundary conditions (4) and (5) are discussed in [11,12]. Here, we only note that, according to condition (5), the tangential component of the velocity is a priori neglected along the open segment of the boundary.…”

“…In practical applications, it is necessary to determine the optimal number of terms in series (12). Both optimal numbers K opt and M opt depend on the rate of convergence of series (12) to the actual values of the potentials, on the level of noise distorting the data of radar measurements, and on the quality of the radar coverage determined by the uniformity of arrangement of points, where the data of radar measurements are available in S. It is clear that the procedure of truncation of series (12) is, in fact, a specific procedure of regularization, which enables one to get estimates stable under the influence of measurement noise and gaps in the radar coverage.…”