Acta Geophysica

, Volume 61, Issue 1, pp 1–17 | Cite as

On regularized time varying gravity field models based on grace data and their comparison with hydrological models

  • Mehdi Eshagh
  • Jean-Michel Lemoine
  • Pascal Gegout
  • Richard Biancale
Research article


Determination of spherical harmonic coefficients of the Earth’s gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system is critical, as small errors of data will yield large variations in the result. Regularization is a method to solve such an unstable system of equations. In this study, direct methods of Tikhonov, truncated and damped singular value decomposition and iterative methods of ν, algebraic reconstruction technique, range restricted generalized minimum residual and conjugate gradient are used to solve the normal equations constructed based on range rate data of the gravity field and climate experiment (GRACE) for specific periods. Numerical studies show that the Tikhonov regularization and damped singular value decomposition methods for which the regularization parameter is estimated using quasioptimal criterion deliver the smoothest solutions. Each regularized solution is compared to the global land data assimilation system (GLDAS) hydrological model. The Tikhonov regularization with L-curve delivers a solution with high correlation with this model and a relatively small standard deviation over oceans. Among iterative methods, conjugate gradient is the most suited one for the same reasons and it has the shortest computation time.

Key words

gravity field and climate experiment hydrological model inversion range-rate smoothing 


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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2012

Authors and Affiliations

  • Mehdi Eshagh
    • 1
    • 2
  • Jean-Michel Lemoine
    • 3
  • Pascal Gegout
    • 3
  • Richard Biancale
    • 3
  1. 1.Division of Geodesy and GeoinformaticsRoyal Institute of Technology (KTH)StockholmSweden
  2. 2.Department of GeodesyK.N.Toosi University of TechnologyTehranIran
  3. 3.Department of Space Geodesy (GRGS)French Space Agency (CNES)ToulouseFrance

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