Low-dimensional dynamical system model for observed coherent structures in ocean satellite data

The dynamics of coherent structures present in real-world
environmental data is analyzed. The method developed in this Paper
combines the power of the Proper Orthogonal Decomposition (POD)
technique to identify these coherent structures in experimental
data sets, and its optimality in providing Galerkin basis for
projecting and reducing complex dynamical models. The POD basis
used is the one obtained from the experimental data. We apply the
procedure to analyze coherent structures
in an oceanic setting, the ones
arising from
instabilities of the Algerian current, in the western
Mediterranean Sea. Data are from satellite altimetry providing Sea
Surface Height, and the model is a two-layer quasigeostrophic
system. A four-dimensional dynamical system is obtained that
correctly describe the observed coherent structures (moving
eddies). Finally, a bifurcation analysis is performed on the
reduced model.