On the estimation of a multi-resolution representation of the gravity field based on spherical harmonics and wavelets

The gravitational potential of the Earth is usually modeled by means of a series expansion in terms of spherical harmonics. However, the computation of the series coefficients requires preferably homogeneous distributed global data sets. Since one of the most important features of wavelet functions is the ability to localize both in the spatial and in the frequency domain, regional and local structures may be modeled by means of a spherical wavelet expansion. In general, applying wavelet theory a given input data set is decomposed into a certain number of frequency-dependent detail signals, which can be interpreted as the building blocks of a multi-resolution representation. On the other hand, there is no doubt that the low-frequency part of the geopotential can be modeled appropriately by means of spherical harmonics. Hence, the main idea of this paper is to derive a combined model consisting of an expansion in spherical harmonics for the low-frequency part and an expansion in spherical wavelets for the remaining medium and high-frequency parts of the gravity field. Furthermore, an appropriate parameter estimation procedure is outlined to solve for the unknown model coefficients.     

Comparison of Multimission Altimetric Sea-Surface Heights with Tide Gauge Observations in the Southern Baltic Sea

One possible technique to validate the observations of altimeter missions is the comparison with sea-surface heights measured by tide gauges. In our investigation, we compared observations of the two tide gauge stations, Sassnitz and Warnemünde, which are located at the southern coast of the Baltic Sea, with sea-surface heights obtained from the altimeter missions Geosat, ERS-1, ERS-2, and TOPEX/Poseidon. For this purpose, the compared sea-surface heights were related to a common reference system and extrapolated to a common location. GPS observations, leveling data, regional geoid information, sea-surface topography, and postglacial rebound were included in the analysis. Considering the uncertainties of all model components, a more reliable estimation of the error budget (source, type, and magnitude of the errors) was performed. The obtained absolute altimeter biases are (-243 - 32) mm for Geosat, (467 - 19) mm for ERS-1, (76 - 19) mm for ERS-2, and (13 - 18) mm for TOPEX.