Time-resolved satellite gravimetry has revolutionized understanding of mass transport in the Earth system. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) has enabled monitoring of the terrestrial water cycle, ice sheet and glacier mass balance, sea level change and ocean bottom pressure variations, as well as understanding responses to changes in the global climate system. Initially a pioneering experiment of geodesy, the time-variable observations have matured into reliable mass transport products, allowing assessment and forecast of a number of important climate trends, and improvements in service applications such as the United States Drought Monitor. With the successful launch of the GRACE Follow-On mission, a multi-decadal record of mass variability in the Earth system is within reach.

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Data availability

The GRACE data used in this paper are freely available from the websites of the Science Data Systems Centres. The GRACE gravity field data products (Level 2 data) as well as supporting documentation may be accessed at http://podaac.jpl.nasa.gov/grace and http://isdc.gfz-potsdam.de/grace. User-friendly, gridded maps of mass change (Level 3 data) are available from https://grace.jpl.nasa.gov/ (JPL), http://www2.csr.utexas.edu/grace/ (CSR) and http://gravis.gfz-potsdam.de/home (GFZ). GRACE Follow-On data will be provided through the same portals once available. The reader is encouraged to use all data sets available.

A list of GRACE-related publications is available under https://grace.jpl.nasa.gov/publications/ and https://www.gfz-potsdam.de/en/grace/. Videos of the GRACE-Follow On pre-launch briefing and the launch are available under https://www.youtube.com/watch?v=qYJt-6uHVcM and https://www.youtube.com/watch?v=I_0GgKfwCSk, respectively (both sources last accessed September 15, 2018).

The figures and updates to published values presented in this paper are based on the following data sets and processing.

Figure 1: the plot is based on the 1-arc degree mascon solution by CSR RL05M5. A linear trend, annual and semi-annual model is fit to each pixel for the entire mission duration, assuming temporally uniform uncertainties. The temporal linear part of that fit is mapped in a and b the standard deviation shown in c is calculated after the removal of the temporal linear trend. The trends have been corrected for glacial-isostatic adjustment using the ICE5G model of Peltier et al.13 computed by A et al.125.

Figure 2 and ‘Ice sheets and glaciers’: time series of ice-sheet mass change are based on GRACE Level 2 data of CSR RL05 obtained with an inversion approach based on forward modelling19,126. For Antarctica the GIA correction is AGE1 (ref. 126) (48 ± 28 Gt yr–1), for Greenland it is GGG1D (ref. 127)(17 Gt yr–1). Uncertainties are calculated based on the formal monthly uncertainties provided by the processing centres, scaled by the root mean square (RMS) residual after subtracting temporal fluctuations longer than three months. Temporal linear trends for the entire GRACE period are estimated using uncertainty-weighted least squares. Annual balances are estimated using an unweighted piecewise linear model with breakpoints on 1 January. Uncertainties for the temporal linear trends and the annual balances are obtained by error propagation.

Figure 3 and ‘Terrestrial water storage’: time series of the zonal mean of terrestrial water storage anomalies in mid-latitudes are based on CSR RL05M Mascons5. Uncertainties are calculated as RMS residual of the zonal mean after subtracting the linear trend, offset, annual and sub-annual temporal components and fluctuations longer than five months. The RMS uncertainty (2 cm equivalent water height along the latitude, 2σ) is then used to scale the formal, time-dependent uncertainties provided by the processing centre CSR. Then the temporal model is refit and propagated uncertainties are calculated. The annual amplitude is shown on the right part of the figure. The anomalies shown in the left part of the figure are the residuals with respect to the fitted temporal model.

Figure 4 and ‘Sea-level change and ocean dynamics’: Global Mean Sea-level (GMSL) and its components. GSML from altimetry is based on data provided by the University of Colorado (http://sealevel/colorado.edu)89. Ocean mass changes are derived from GRACE Level 2 data of three processing centres (CSR RL05, JPL RL05 and GFZ RL05) using an averaging kernel method and scaling100, available from the University of South Florida (http://xena.marine.usf.edu/~chambers/SatLab/Home.html). Global mean steric sea level anomalies are based on Argo data provided by the National Oceanic and Atmospheric Administration (NOAA; https://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/basin_fsl_data.html). To unify the temporal sampling, we adopt three-month (seasonal) averages, which is limited by the sampling period of the Argo data obtained from NOAA. These were computed after first fitting and removing annual and semi-annual sinusoids from the altimetry and GRACE monthly averages. An annual and semi-annual sinusoid was also estimated and removed from the three-month thermometric time-series for consistency. The correction for glacial-isostatic adjustment to the GRACE data is based on the ICE5G ice model13, computed by A et al.125. Further details can be found in Chambers et al.94.

Additional information

Journal peer review information: Nature Climate Change thanks Bryant Loomis and other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


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The authors acknowledge the influence of J. M. Wahr (formerly of the University of Colorado Boulder, USA) making fundamental contributions, both in theoretical concept and in measurement applications, to the success of the GRACE mission.

C.D., H.D. und F.F. acknowledge funding of the development of the GRACE-Follow On Science Data System by the German Federal Ministry of Education and Research (BMBF) under grant 03F0654A. I.S. acknowledges funding by the Helmholtz Climate Initiative REKLIM (Regional Climate Change), a joint research project of the Helmholtz Association of German Research Centres (HGF) and the German Research Foundation (DFG) through grant SA 1734/4-1. A.G. received funding from the NASA Cryosphere Science program. M.E.T. was supported by CSR discretionary funds.

Author information


  1. Center for Space Research, University of Texas, Austin, TX, USA

    • Byron D. Tapley
    • , Srinivas Bettadpur
    • , Himanshu Save
    •  & Mark E. Tamisiea
  2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    • Michael M. Watkins
    • , Felix W. Landerer
    • , John T. Reager
    • , Alex S. Gardner
    • , Erik R. Ivins
    • , Carmen Boening
    • , David N. Wiese
    •  & Isabella Velicogna
  3. Department of Geodesy, GFZ German Research Centre for Geosciences, Telegrafenberg, Potsdam, Germany

    • Frank Flechtner
    • , Christoph Reigber
    • , Christoph Dahle
    •  & Henryk Dobslaw
  4. Hydrological Sciences Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA

    • Matthew Rodell
  5. Division of Climate Sciences, Alfred Wegener Institute, Bremerhaven, Germany

    • Ingo Sasgen
  6. Global Institute for Water Security, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

    • James S. Famiglietti
  7. College of Marine Science, University of South Florida, St. Petersburg, FL, USA

    • Don P. Chambers
  8. Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, CO, USA

    • Sean C. Swenson
  9. Department of Geodesy and Geoinformation Science, Technical University Berlin, Berlin, Germany

    • Frank Flechtner


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All authors contributed the writing and editing of the paper; introductory text (B.D.T., C. R., S.B., M.W. and I.S.), ‘Ice sheets and glaciers’ (I.S., A.G. and I.V.), ‘Terrestrial Water Storage’ (J.F., M.R., J.T.R, and S.S.), ‘Sea-level change and ocean dynamics’ (D.C., F.L., C.B., H.D. and I.S.), ‘Climate service applications’ (F.F., C.D., D.W. and M. R.) and ‘Future of mass transport observations’ (B.D.T., F.L., M.W., F.F. and I.S.); overall editing and internal review E.R.I. and M.E.T; Box 1 (NASA/JPL, I. S.); Fig. 1 (H.S.), Fig. 2 (I.S.), Fig. 3 (I.S. and M.R.), Fig. 4 (D.C. and I.S.) and Fig. 5 (M.R.). I.S. handled implementing the comments of peer reviewers.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Ingo Sasgen.

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