## Contributions of the Geomathematics Group, TU Kaiserslautern, to the 2nd International GOCE User Workshop 2004 at ESA-ESRIN Frascati, Italy

• The following two papers present recent developments in multiscale ocean circulation modeling and multiscale gravitational field modeling that have been presented at the 2nd International GOCE User Workshop 2004 in Frascati. Part A - Multiscale Modeling of Ocean Circulation In this paper the applicability of multiscale methods to oceanography is demonstrated. More precisely, we use convolutions with certain locally supported kernels to approximate the dynamic topography and the geostrophic flow. As data sets the French CLS01 data are used for the mean sea surface topography and are compared to the EGM96 geoid. Since those two data sets have very different levels of spatial resolutions the necessity of an interpolating or approximating tool is evident. Compared to the standard spherical harmonics approach, the strongly space localizing kernels improve the possibilities of local data analysis here. Part B - Multiscale Modeling from EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, EGM96 Spherical wavelets have been developed by the Geomathematics Group Kaiserslautern for several years and have been successfully applied to georelevant problems. Wavelets can be considered as consecutive band-pass filters and allow local approximations. The wavelet transform can also be applied to spherical harmonic models of the Earth's gravitational field like the most up-to-date EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, and the well-known EGM96. Thereby, wavelet coefficients arise. In this paper it is the aim of the Geomathematics Group to make these data available to other interested groups. These wavelet coefficients allow not only the reconstruction of the wavelet approximations of the gravitational potential but also of the geoid, of the gravity anomalies and other important functionals of the gravitational field. Different types of wavelets are considered: bandlimited wavelets (here: Shannon and Cubic Polynomial (CuP)) as well as non-bandlimited ones (in our case: Abel-Poisson). For these types wavelet coefficients are computed and wavelet variances are given. The data format of the wavelet coefficients is also included.

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Verfasserangaben: Martin Gutting, Dominik Michel urn:nbn:de:hbz:386-kluedo-15337 Schriften zur Funktionalanalysis und Geomathematik (10) Preprint Englisch 2004 2004 Technische Universität Kaiserslautern 30.04.2004 Approximation ; Geostrophisches Gleichgewicht ; Gravitationsfeld; Mehrskalenanalyse ; Wavelet Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 31-XX POTENTIAL THEORY (For probabilistic potential theory, see 60J45) / 31Bxx Higher-dimensional theory / 31B05 Harmonic, subharmonic, superharmonic functions 42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems 65-XX NUMERICAL ANALYSIS / 65Txx Numerical methods in Fourier analysis / 65T60 Wavelets 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A05 Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A30 Geodesy, mapping problems Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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