Journal of Geodesy

, Volume 81, Issue 11, pp 733–749 | Cite as

Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models

  • Jürgen Kusche
Open Access
Original Article


We discuss a new method for approximately decorrelating and non-isotropically filtering the monthly gravity fields provided by the gravity recovery and climate experiment (GRACE) twin-satellite mission. The procedure is more efficient than conventional Gaussian-type isotropic filters in reducing stripes and spurious patterns, while retaining the signal magnitudes. One of the problems that users of GRACE level 2 monthly gravity field solutions fight is the effect of increasing noise in higher frequencies. Simply truncating the spherical harmonic solution at low degrees causes the loss of a significant portion of signal, which is not an option if one is interested in geophysical phenomena on a scale of few hundred to few thousand km. The common approach is to filter the published solutions, that is to convolve them with an isotropic kernel that allows an interpretation as smoothed averaging. The downside of this approach is an amplitude bias and the fact that it neither accounts for the variable data density that increases towards the poles where the orbits converge nor for the anisotropic error correlation structure that the solutions exhibit. Here a relatively simple regularization procedure will be outlined, which allows one to take the latter two effects into account, on the basis of published level 2 products. This leads to a series of approximate decorrelation transformations applied to the monthly solutions, which enable a successive smoothing to reduce the noise in the higher frequencies. This smoothing effect may be used to generate solutions that behave, on average over all possible directions, very close to Gaussian-type filtered ones. The localizing and smoothing properties of our non-isotropic kernels are compared with Gaussian kernels in terms of the kernel variance and the resulting amplitude bias for a standard signal. Examples involving real GRACE level 2 fields as well as geophysical models are used to demonstrate the techniques. With the new method, we find that the characteristic striping pattern in the GRACE solutions are much more reduced than Gaussian-filtered solutions of comparable signal amplitude and root mean square.


GRACE Time-variable gravity Smoothing Decorrelation 


  1. Bettadpur S (2004) UTCSR level-2 processing standards document for product release 01, GRACE Proj. Doc. JPL 327-742, rev. 1.1, Jet Propulsion Labarotary, PasadenaGoogle Scholar
  2. Chambers DP, Wahr J, Nerem RS (2004). Preliminary observations of global ocean mass variation with GRACE. Geophys Res Lett 31:L13310. doi:10.1029/2004GL020461CrossRefGoogle Scholar
  3. Chao BF (2005). On inversion for mass distribution from global (time-variable) gravity field. Geophys J Int 39:223–230Google Scholar
  4. Chen JL, Wilson CR, Famiglietti JS, Rodell M (2005) Spatial sensitivity of the gravity recovery and climate experiment (GRACE) time-variable gravity observations. J Geophys Res. doi:10.1029/2004JB003536Google Scholar
  5. Chen JL, Wilson CR, Famiglietti JS, Rodell M (2006) Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity. J Geod. doi:10.1007/s00190-006-0104-2Google Scholar
  6. Edmonds AR (1974). Angular momentum in quantum mechanics. Princeton University Press, PrincetonGoogle Scholar
  7. Farrell WE (1972). Deformation of the Earth by surface loads. Rev Geophys Space Phys 10(3):761–797Google Scholar
  8. Fengler MJ, Freeden W, Kohlhaas A, Michel V, Peters T (2006) Wavelet modelling of regional and temporal variations of the Earth’s gravitational potential observed by GRACE. J Geod. doi:10.1007/s00190-006-0040-1Google Scholar
  9. Flechtner F (2003) GFZ level-2 processing standards document for product release 01, GRACE Proj. Doc. JPL 327-743, rev. 1.0, Jet Propulsion Labaratory, PasadenaGoogle Scholar
  10. Freeden W, Gervens T, Schreiner M (1998). Constructive approximation on the sphere. Clarendon Press, OxfordGoogle Scholar
  11. Fenoglio-Marc L, Kusche J, Becker M (2006) Mass variation in the Mediterranean Sea from GRACE and its validation by altimetry, steric and hydrology fields. Geophys Res Lett 33:L19606. doi:10.1029/2006GL026851Google Scholar
  12. Han S-C, Shum CK, Jekeli C, Kuo C-Y, Wilson CR, Seo K-W (2005). Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement. Geophys J Int 163:18–25. doi:10.1111/j.1365-246X.2005.02756.xCrossRefGoogle Scholar
  13. Jekeli C (1981) Alternative methods to smooth the Earth’s gravity field. Report No. 327, Department of Geodetic Science, Ohio State University, OhioGoogle Scholar
  14. Jekeli C (1999). The determination of gravitational potential differences from satellite-to-satellite tracking. Cel Mech Dyn Astr 75:85–100CrossRefGoogle Scholar
  15. Klees R, Zapreeva EA, Winsemius HC, Savenije HHG (2006). The bias in GRACE estimates of continental water storage variations. Hydrol Earth System Sci Discussions 3: 3557–3594Google Scholar
  16. Narcowich FJ, Ward JD (1996). Nonstationary wavelets on the m-sphere for scattered data. Appl Comp Harm Anal 3: 324–336CrossRefGoogle Scholar
  17. Milly PCD, Shmakin AB (2002) Global modeling of land water and energy balances, Part I: The land dynamics (LaD) model. J Hydrometerol 3:283–299CrossRefGoogle Scholar
  18. Rodell M, Famiglietti JS, Chen J, Seneviratne SI, Viterbo P, Holl S, Wilson CR (2004) Basin scale estimates of evapotranspiration using GRACE and other observations. Geophys Res Lett 31:L20504. doi:10.1029/ 2004GL020873Google Scholar
  19. Sasgen I, Martinec Z, Fleming K (2006) Wiener optimal filtering of GRACE data. Stud Geophys Geod 50(4):499–508, doi:10.1007/s11200-006-0031-yCrossRefGoogle Scholar
  20. Schmidt M, Fengler M, Mayer-Gürr T, Eicker A, Kusche J, Sánchez L, Han S-C (2006). Regional gravity modelling in terms of spherical base functions. J Geod 81:17–38. doi:10.1007/s00190-006-0101-5CrossRefGoogle Scholar
  21. Schrama EJO, Visser P (2007). Accuracy assessment of the monthly GRACE geoids based upon a simulation. J Geod 81(1):67–80. doi:10.1007/s00190-006-0085-1CrossRefGoogle Scholar
  22. Schulten K, Gordon RG (1976). Recursive evaluation of 3j and 6j coefficients. Comp Phys Comm 11:269–278CrossRefGoogle Scholar
  23. Seo K-W, Wilson CR (2005) Simulated estimation of hydrological loads from GRACE. J Geod. doi:10.1007/s00190-004-0410-5Google Scholar
  24. Simons FJ, Dahlen FA (2006). Spherical Slepian functions and the polar gap in geodesy. Geophys. J Int 166(3):1039–1061. doi:10.1111/j.1365-245X.2006.03065.xCrossRefGoogle Scholar
  25. Stammer D, Davis R, Fu L-L, Fukomori I, Giering R, Lee T, Marotzke J, Marshall J, Menemnlis D, Niiler P, Wunsch C, Zlotnicky V (1999) The consortium for estimating the circulation and climate of the ocean (ECCO)— science goals and task plan. ECCO Report No. 1, 1999, The ECCO Consortium, La JollaGoogle Scholar
  26. Swenson S, Wahr J (2002) Methods for inferring regional surface-mass anomalies from gravity recovery and climate experiment (GRACE) measurements of time-variable gravity. J Geophys Res. doi:10.1029/2001JB000576Google Scholar
  27. Swenson S, Wahr J (2006). Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33:L08402. doi:10.1029/2005GL025285CrossRefGoogle Scholar
  28. 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:10.1029/2004GL019920CrossRefGoogle Scholar
  29. Velicogna I, Wahr J (2006) Measurements of time-variable gravity show mass loss in Antarctica. Scienceexpress, published online 2 March 2006. doi:10.1126/science.1123785Google Scholar
  30. 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 Geophys Res 103(B12):30205–30230CrossRefGoogle Scholar
  31. Wahr J, Swenson S, Velicogna I (2006). Accuracy of GRACE mass estimates. Geophys Res Lett 33:L06401. doi:10.1029/ 2005GL025305CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Delft Institute of Earth Observation and Space Systems (DEOS)Delft University of TechnologyGB DelftThe Netherlands
  2. 2.Department 1: Geodesy and Remote Sensing, TelegrafenbergGeoForschungsZentrum PotsdamPotsdamGermany

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