Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model


We have analyzed recent gravity recovery and climate experiment (GRACE) RL04 monthly gravity solutions, using a new decorrelating post-processing approach. We find very good agreement with mass anomalies derived from a global hydrological model. The post-processed GRACE solutions exhibit only little amplitude damping and an almost negligible phase shift and period distortion for relevant hydrological basins. Furthermore, these post-processed GRACE solutions have been inspected in terms of data fit with respect to the original inter-satellite ranging and to SLR and GPS observations. This kind of comparison is new. We find variations of the data fit due to solution post-processing only within very narrow limits. This confirms our suspicion that GRACE data do not firmly ‘pinpoint’ the standard unconstrained solutions. Regarding the original Kusche (J Geod 81:733–749, 2007) decorrelation and smoothing method, a simplified (order-convolution) approach has been developed. This simplified approach allows to realize a higher resolution—as necessary, e.g., for generating computed GRACE observations—and needs far less coefficients to be stored.

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  1. Chambers D, Wahr J, Nerem RS (2004) Preliminary observations of global ocean mass variations with GRACE. Geophys Res Lett 33. doi:10.1029/2004GL020461

  2. Colombo OL (1986) Notes on the mapping of the gravity field using satellite data. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy. Lecture notes in earth Sciences, vol 7. Springer, Berlin

  3. Davis J, Tamisea M, Elósegui P, Mitrovica J, Hill E (2008) A statistical filtering approach for Gravity Recovery and Climate Experiment (GRACE) gravity data. J Geophys Res/Solid Earth 113: B04410. doi:10.1029/2007JB005043

    Article  Google Scholar 

  4. Döll P, Kaspar F, Lehner B (2003) A global hydrological model for deriving water availability indicators: model tuning and validation. J Hydrol 270(1–2): 105–134

    Article  Google Scholar 

  5. Fenoglio-Marc L, Kusche J, Becker M (2006) Mass variation in the Mediterranean Sea and its validation by altimetry, steric and hydrologic fields. Geophys Res Lett 33. doi:10.1029/2006GL026851

  6. Flechtner F (2007) GFZ Level-2 processing standards document for level-2 product release 0004, GRACE 327-743, Rev. 1.0

  7. Güntner A (2008) Improvement of global hydrological models using GRACE data. Surv Geophys. doi:10.1007/s10712-008-9038-y

  8. Gunter B, Ries J, Bettadpur S, Tapley B (2006) A simulation study of the errors of omission and commission for GRACE RL01 gravity fields. J Geod. doi:10.1007/s00190-006-0083-3

  9. Han S-C, Simons F (2008) Spatiospectral localization of global geopotential fields from the gravity recovery and climate experiment (GRACE) reveals the coseismic gravity change owing to the 2004 Sumatra–Andaman earthquake. J Geophys Res/Solid Earth 113: B01405. doi:10.1029/2007JB004927

    Article  Google Scholar 

  10. Klees R, Revtova E, Gunter B, Ditmar P, Oudman E, Winsemius H, Savenije H (2008) The design of an optimal filter for monthly GRACE gravity models. Geophys J Int. doi:10.1011/j.1365-246X.2008.03922.x

  11. Kusche J (2007) Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J Geod 81: 733–749. doi:10.1007/s00190-007-0143-3

    Article  Google Scholar 

  12. Parker RL (1994) Geophysical inverse theory. Princeton University Press, New Jersey

    Google Scholar 

  13. Petrovic S, Schmidt R, Wünsch J, Barthelmes F, Güntner A, Rothacher M (2007) Towards a characterization of temporal gravity field variations in GRACE observations and global hydrology models. J Mapping 18: 199–204

    Google Scholar 

  14. Schmidt R, Schwintzer P, Flechtner F, Reigber C, Güntner A, Döll P, Ramillien G, Cazenave A, Petrovic S, Jochmann H, Wünsch J (2006) GRACE observations of changes in continental water storage. Glob Planet Change 50(1–2): 112–126

    Article  Google Scholar 

  15. Schmidt R, Petrovic S, Güntner A, Barthelmes F, Wünsch J, Kusche J (2008a) Periodic components of water storage changes from GRACE and global hydrology models. J Geophys Res/Solid Earth. doi:10.1029/2007JB005363

  16. Schmidt R, Flechtner F, Meyer U, Neumayer K-H, Dahle C, König R, Kusche J (2008b) Hydrological signals observed by the GRACE satellites. Surv Geophys. doi:10.1007/s10712-008-9033-3

  17. Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33: L08402. doi:10.1029/2005GL025285

    Article  Google Scholar 

  18. Swenson S, Wahr J (2007) Multi-sensor analysis of water storage variations in the Caspian Sea. Geophys Res Lett 34: L16401. doi:10.1029/2007GL030733

    Article  Google Scholar 

  19. Tapley B, Bettadpur S, Ries J, Thompson P, Watkins M (2004a) GRACE measurements of mass variability in the Earth system. Science 305: 503–505

    Article  Google Scholar 

  20. Tapley B, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: Mission overview and early results. Geophys Res Lett 31: L09607. doi:10.1029/2004GL019920

    Article  Google Scholar 

  21. Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: hydrological and oceanic effects and their possible detection using GRACE. J Geophy Res/Solid Earth 108(B12):30,205–30,229

  22. Wouters B, Schrama EJO (2007) Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics. Geophys Res Lett 34: L23711. doi:10.1029/2007GL032098

    Article  Google Scholar 

  23. Velicogna I, Wahr J (2006) Measurements of time-variable gravity show mass loss in Antarctica. Science 311: 1754

    Article  Google Scholar 

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Kusche, J., Schmidt, R., Petrovic, S. et al. Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. J Geod 83, 903–913 (2009).

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  • Time-variable gravity
  • Smoothing
  • Decorrelation
  • Hydrological model validation