Abstract
We present a multiresolution analysis of temporal and spatial variations of the Earth’s gravitational potential by the use of tensor product wavelets which are built up by Legendre and spherical wavelets for the time and space domain, respectively. The multiresolution is performed for satellite and hydrological data, and based on these results we compute correlation coefficients between both data sets, which help us to develop a filter for the extraction of an improved hydrology model from the satellite data.
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References
Beth S, Viell M (1998) Uni- und multivariate Legendre-Wavelets und ihre Anwendung zur Bestimmung des Brechungsindexgradienten. In: Freeden W (ed) Progress in Geodetic Science at GW 98, Shaker, pp 25–33
Freeden W (1999) Multiscale modelling of spaceborne geodata. Teubner, Stuttgart, Leipzig
Freeden W, Schneider F (1998a) An integrated wavelet concept of physical geodesy. J Geod 72:259–281
Freeden W, Schneider F (1998b) Regularization wavelets and multiresolution. Inverse Prob 14:225–243
Freeden W, Schreiner M (2009) Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup. Springer, Heidelberg
Freeden W, Gervens T, Schreiner M (1998) Constructive approximation on the sphere (with applications to geomathematics). Oxford Science Publication, Clarendon Press, Oxford
Louis AK, Maaß P, Rieder A (1998) Wavelets: Theorie und Anwendungen. Teubner, Stuttgart
Maier T (2003) Multiscale geomagnetic field modelling from satellite data: theoretical aspects and numerical applications. PhD Thesis, University of Kaiserslautern, Geomathematics Group
Mallat S (1989a) Multiresolution approximations and wavelet orthonormal bases of \({L}^{2}(\mathbb{R})\). Trans Am Math Soc 315:69–87
Mallat S (1989b) A theory for multiresolution signal decompostion. IEEE Trans Pattern Anal Machine Intell 11:674–693
Meyer Y (1992) Wavelets and operators. Cambridge University Press
Müller C (1966) Spherical harmonics, vol 17. Springer, Berlin
Nutz H, Wolf K (2008) Time-space multiscale analysis by use of tensor product wavelets and its application to hydrology and GRACE data. Studia Geophysica et Geodaetica 52: 321–339
Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33: L08402. doi:10.1029/ 2005GL025285
Swenson S, Wahr J, Milly PCD (2003) Estimated accuracies of regional water storage variations inferred from the gravity recovery and climate experiment (GRACE). Water Resour Res 39(8):1223. doi:10.1029/ 2002WR001808
Tapley BD, Reigber C (2001) The GRACE mission: status and future plans. EOS Trans AGU 82(47): Fall Meet Suppl G41, C-02
Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins MM (2004a) GRACE measurements of mass variability in the Earth system. Science 305:503–505
Tapley BD, Bettadpur S, Watkins MM, Reigber C (2004b) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31: L09607. doi:10.1029/2004GL019920
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Nutz, H., Wolf, K. (2010). Multiresolution Analysis of Hydrology and Satellite Gravitational Data. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01546-5_11
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DOI: https://doi.org/10.1007/978-3-642-01546-5_11
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