Regularization and error characterization of GRACE mascons

  • B. D. LoomisEmail author
  • S. B. Luthcke
  • T. J. Sabaka
Original Article


We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.


GRACE Time-variable gravity Mascons Range-acceleration Regularization Model resolution Estimator bias 



Support for this work was provided by the NASA GRACE and GRACE Follow-On Science Team Grant NNH15ZDA001N. We acknowledge the quality of the GRACE Level-1B products produced by our colleagues at the Jet Propulsion Laboratory. We also acknowledge the numerous contributions of D.D. Rowlands, K.E. Rachlin, and J.B. Nicholas in developing the algorithms and software necessary to carry out this research, and we thank the three anonymous reviewers and the editors who provided valuable feedback toward improving this manuscript. The MEI is provided at


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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Geodesy and Geophysics LaboratoryNASA Goddard Space Flight CenterGreenbeltUSA

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