Local Multiscale Approximations of Geostrophic Oceanic Flow: Theoretical Background and Aspects of Scientific Computing

In modern geoscience, understanding the climate depends on the information about the oceans. Covering two-thirds of the Earth, oceans play an important role. Oceanic phenomena are, for example: oceanic circulation; water exchanges between atmosphere, land, and ocean; or temporal changes of the total water volume. All these features require new methods in constructive approximation, since they are regionally bounded and not globally observable. This article deals with a new and alternative method of handling data with locally supported basis functions, modeling them in a multiscale scheme involving a wavelet approximation and presenting the main results for the dynamic topography and the geostrophic flow, e.g., in the Northern Atlantic. Further, it is demonstrated that compressional rates of the occurring wavelet transforms can be achieved by using of locally supported wavelets and investigating the signal distribution within different frequency bands.