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Open Access Published by De Gruyter Open Access October 15, 2013

Inverting GRACE gravity data for local climate effects

D. Fischer and V. Michel


The Amazon area is the largest water shed on Earth. Thus, it is of great importance to observe the water levels regularly. The satellite mission Gravity Recovery and Climate Experiment (GRACE) allows, since its launch in 2002, a monthly global overview of the water distribution on Earth, in particular floods and droughts. In recent years, the Amazon area has experienced a number of extreme weather situations in late summer (July through October), explicitly a drought in 2005 and one in 2010. Furthermore, one can identify the remains of a flood in spring 2009 in the summer season of 2009 as well, where the names of the seasons refer here to the northern hemisphere, though some events were also located on the southern hemisphere. Here we present corresponding results with respect to a recently introduced localized method called the RFMP (Regularized Functional Matching Pursuit) that can be applied to ill-posed inverse problems. In comparison to the usual processing of GRACE data as well as other data types (i.e., the volumetric soil moisture content given by the NOAA-CIRES Twentieth Century Global Reanalysis Version II and the average layer 1 soil moisture given by the GLDAS Noah Land Surface Model L4), we gain an improved spatial resolution with the novel method. We also observe that it is very difficult to validate inverted GRACE data with hydrological models due to, e.g., discrepancies among these models.


Amirbekyan A. and Michel V., 2008, Splines on the threedimensional ball and their application to seismic body wave tomography, Inverse Probl., 24, 1-25.10.1088/0266-5611/24/1/015022Search in Google Scholar

Berkel P., 2009, Multiscale methods for the combined inversion of normal mode and gravity variations, PhD thesis, Geomathematics Group, University of Kaiserslautern (Aachen: Shaker Verlag).Search in Google Scholar

Berkel P. and Michel V., 2010, On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method, Math. Geosci., 42, 795-816.10.1007/s11004-010-9297-2Search in Google Scholar

Chen J.L., Wilson C.R. and Tapley B.D., 2006, Satellite gravity measurements confirm accelerated melting of Greenland ice sheet, Science, 313, 1958-60.10.1126/science.1129007Search in Google Scholar PubMed

Chen J.L., Wilson C.R. and Tapley B.D., 2010, The 2009 exceptional Amazon flood and interannual terrestrial water storage change observed by GRACE, Water Resour. Res., 46, W12526.10.1029/2010WR009383Search in Google Scholar

Chen J.L., Wilson C.R., Tapley B.D., Blankenship D.D. and Young D., 2008, Antarctic regional ice loss rates from GRACE, Chen J.L., Wilson C.R., Tapley B.D. and Grand S., 2007, GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake, Geophys. Res. Lett., 34, L13302.10.1029/2007GL030356Search in Google Scholar

Chen J.L., Wilson C.R., Tapley B.D., Yang Z.L. and Niu G.Y., 2009, 2005 drought event in the Amazon river basin as measured by GRACE and estimated by climate models, J. Geophys. Res., 114, B05404.10.1029/2008JB006056Search in Google Scholar

Crowley J.W., Mitrovica J.X., Bailey R.C., Tamisiea M.E. and Davis J.L., 2006, Land water storage within the Congo Basin inferred from GRACE satellite gravity data, Geophys. Res. Lett., 33, L19402.10.1029/2006GL027070Search in Google Scholar

Fengler M.J., Freeden W., Kohlhaas A., Michel V. and Peters T., 2007, Wavelet modeling of regional and temporal variations of the Earth’s gravitational potential observed by GRACE, J. Geodesy, 81, 5-15.10.1007/s00190-006-0040-1Search in Google Scholar

Fengler M.J., Michel D. and Michel V., 2006, Harmonic spline-wavelets on the 3-dimensional ball and their application to the reconstruction of the Earth’s density distribution from gravitational data at arbitrarily shaped satellite orbits, ZAMM, 86, 856-73.10.1002/zamm.200510277Search in Google Scholar

Fischer D., 2011, Sparse regularization of a joint inversion of gravitational data and normal mode anomalies, PhD thesis, Geomathematics Group, University of Siegen (Munich: Verlag Dr. Hut).Search in Google Scholar

Fischer D. and Michel V., 2012, Sparse regularization of inverse gravimetry - case study: spatial and temporal mass variations in South America, Inverse Probl., 28, 065012.10.1088/0266-5611/28/6/065012Search in Google Scholar

Fischer D. and Michel V., 2013, Automatic best-basis selection for geophysical tomographic inverse problems, Geophys. J. Int., 193, 1291-1299.10.1093/gji/ggt038Search in Google Scholar

Freeden W., Gervens T. and Schreiner M., 1998, Constructive approximation on the sphere (with applications to geomathematics), Oxford University Press, Oxford.Search in Google Scholar

Freeden W. and Windheuser U., 1996, Spherical wavelet transform and its discretization, Adv. Comput. Math., 5, 51-94. 10.1007/BF02124735Search in Google Scholar

Center for Space Research, 2012, GRACE overview, University of Texas (Austin)., accessed 11 June 2012.Search in Google Scholar

Hu X.G., Chen J.L., Zhou Y.H., Huang C. and Liao X.H., 2006, Seasonal water storage change of the Yangtze River basin detected by GRACE, Sci. China Ser. D Earth Sci., 49, 483-91.10.1007/s11430-006-0483-5Search in Google Scholar

Joodaki G. and Nahavandchi H., 2012, Mass loss of the Greenland ice sheet from GRACE time-variable gravity measurements, Stud. Geophys. Geod., 56, 197-214.10.1007/s11200-010-0091-xSearch in Google Scholar

JPL: Jet Propulsion Laboratory, California Institute of Technology (Pasadena)., accessed 11 June 2012.Search in Google Scholar

Koch K.R. and Kusche J., 2002, Regularization of geopotential determination from satellite data by variance components, J. Geodesy, 76, 259-268.10.1007/s00190-002-0245-xSearch in Google Scholar

Kusche J., 2007, Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models, J. Geodesy, 81, 733-49.10.1007/s00190-007-0143-3Search in Google Scholar

Kusche J., Schmidt R., Petrovic S. and Rietbroek R., 2009, Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model, J. Geodesy, 83, 903-13.10.1007/s00190-009-0308-3Search in Google Scholar

Michel V., 2002, A multiscale approximation for operator equations in separable Hilbert spaces - case study: reconstruction and description of the Earth’s interior, habilitation thesis, Geomathematics Group, University of Kaiserslautern (Aachen: Shaker Verlag).Search in Google Scholar

Michel V., 2010, Tomography: problems and multiscale solutions, in: Freeden W., Nashed M.Z. and Sonar T. (eds.) Handbook of Geomathematics, Heidelberg, Springer, pp. 949-72.10.1007/978-3-642-01546-5_32Search in Google Scholar

Michel V., 2013, Lectures on constructive approximation - Fourier, spline, and wavelet methods on the real line, the sphere, and the ball, Birkhäuser, Boston.Search in Google Scholar

Michel V. and Fokas A.S., 2008, A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods, Inverse Probl., 24, 045091.10.1088/0266-5611/24/4/045019Search in Google Scholar

Rodell M. et al, 2004a, The global land data assimilation system, Bull. Am. Meteorol. Soc., 85, 381-94.10.1175/BAMS-85-3-381Search in Google Scholar

Rodell M., Familiglietti J.S., Chen J., Seneviratne S.I., Viterbo P., Holl S. and Wilson C.R., 2004b, Basin scale estimates of evaporation using GRACE and other observations, Geophys. Res. Lett., 31, L20504. 10.1029/2004GL020873Search in Google Scholar

Syed T.H., Famiglietti J.S., Chen J., Rodell M., Seneviratne S.I., Viterbo P. and Wilson C.R., 2005, Total basin discharge for the Amazon and Mississippi River basins from GRACE and a land-atmosphere water balance, Geophys. Res. Lett., 32, L24404.10.1029/2005GL024851Search in Google Scholar

Tapley B.D., Bettadpur S., Ries J.C., Thopson P.F. and Watkins M.M., 2004, GRACE measurements of mass variability in the Earth system, Science, 305, 503-5.10.1126/science.1099192Search in Google Scholar PubMed

Wahr J., Swenson S. and Velicogna I., 2006, The accuracy of GRACE mass estimates, Geophys. Res. Lett., 33, L06401.10.1029/2005GL025305Search in Google Scholar

Winsemius H.C., Savenije H.H.G., van de Giesen N.C., van den Hurk B.J.J.M., Zapreeva E.A. and Klees R., 2006, Assessment of gravity recovery and climate experiment (GRACE) temporal signature over the upper Zambezi, Water Resour. Res., 42, W12201.10.1029/2006WR005192Search in Google Scholar

Xu P., Shen Y., Fukuda, Y. and Liu, Y., 2006, Variance component estimation in linear inverse ill-posed models, J. Geodesy, 80, 69-81. 10.1007/s00190-006-0032-1Search in Google Scholar

Published Online: 2013-10-15
Published in Print: 2013-09-1

This content is open access.

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