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GRACE Level-3 Monthly Solutions

Description of data product

Equivalent water heights (EWH) are derived from monthly level-2 solutions of the Gravity Recovery and Climate Experiment (GRACE) satellite mission and of the GRACE-Follow On satellite mission, by relating changes in gravity to changes in the mass distribution in a thin surface layer, loading the Earth elastically. Gravity changes due to solid Earth phenomena, such as they occur after bigger earthquakes and due to glacial isostatic adjustment (GIA), have been removed during our processing.
The animation shows the global monthly variation of the EWH in mm with respect to a multi-year mean (January 2003 - September 2019), as well as the time series of mass changes integrated over Antarctica, Greenland and Amazonas river basin.


Data processing

Spherical harmonic coefficients

Spherical harmonic (SH) coefficients, a level-2 data product of GRACE, are commonly used to describe the monthly gravity field of the Earth. For generating this level-3 data product, the monthly solutions from TU Graz are used complete to degree and order 96 (Mayer-Gürr et al, 2018).

Low-degree coefficients

As GRACE cannot sense the changes in geocenter motion, the SH coefficients of degree-1 (C10, C11, S11), which are proportional to the geocenter motion, are typically determined by alternative means. Here, we use the data provided by NASA JPL following the approach proposed by Swenson et al (2008) that combines GRACE data and the output of a numerical ocean model.
We have also replaced the C20 coefficient by a time series provided by NASA JPL, as recommended in Cheng et al (2011).


Degree-dependend correlated noise, which manifests itself in north-south stripes, renders it difficult to analyze small-scale regional mass variations. Methods to mitigate this problem range from a Gaussian isotropic filter by Swenson and Wahr (2006) to anisotropic filters, such as the DDK filter by Kusche et al (2009). Here, the DDK3 filter is applied.

Glacial isostatic adjustment

The ongoing response of the viscoelastic Earth to the changing ice loads after the Last Glacial Maximum (LGM) results in long-term gravity changes that are not related to present-day hydrological mass transports and are typically removed in the data processing using modeled values. Here, a GIA model based on the ICE5-G ice load history (Peltier, 2004) and provided by NASA JPL (A et al, 2013) is utilized.


GRACE senses the change of Earth's gravity field due to internal mass dislocation and surface/ocean bottom displacement caused by large earthquakes. The residual geoid heights in the earthquake area comprise environmental effects (semiannual and annual variations and tidal effects) as well as the impact of the earthquake, which is modeled as the sum of the coseismic effect and the exponential post-seismic relaxation following Einarsson et al (2010). The estimated values for the earthquake are subtracted from the global geoid change of the GRACE gravity field model, correcting the time series after the event. The residual geoid change is in turn transformed to EWH via SH coefficients.

Following earthquake signals with magnitude over 9.0 are removed:
  • West Coast of Northern Sumatra, Indonesia on 24 Dec 2004
  • near the East Coast of Honshu, off Tohoku, Japan on 11 Mar 2011


The EWH time-series obtained here is used among others in following projects.


The main objective of the GlobalCDA project is to improve our understanding of global freshwater resources and to obtain better estimates of continental water fluxes and storages by combining state-of-the-art hydrological modeling and multiple new and optimally processed geodetic and remote sensing data in an ensemble-based calibration and data assimilation (C/DA) approach.

More information:


The GlobeDrought project aims at the development of a web-based drought information system. The impact of drought on water resources, crop productivity, food trade and the need for international food aid will be examined using a combination of observational data and model outputs.

More information:


The monthly EWH in Netdcf-4 format can be downloaded here.



A, G., Wahr, J., Zhong, S. (2013): Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada. Geophysical Journal International, 192, pp. 557—572.
Cheng, M., J. C. Ries, and B. D. Tapley (2011) Variations of the Earth's figure axis from satellite laser ranging and GRACE. Journal of Geophysical Research, Vol. 116, Article B01409.
Einarsson, I., Hoechner, A., Wang, R. and  Kusche, J. (2010) Gravity changes due to the Sumatra-Andaman and Nias earthquakes as detected by the GRACE satellites: a reexamination. Geophysical Journal International, Vol. 183, pages 733–747.   
Kusche, J., R. Schmidt, S. Petrovic and R. Rietbroek (2009) Decorrelated GRACE time variable gravity solutions by GFZ, and their validation using a hydrological model. Journal of Geodesy, Vol. 83, Issue 10, pages 903–913.
Mayer-Gürr, T., Behzadpour, S., Ellmer, M., Klinger, B., Kvas, A., Strasser, S., & Zehentner, N. (2018). ITSG-Grace2018: The new GRACE time series from TU Graz. Abstract from GRACE / GRACE-FO Science Team Meeting 2018, Potsdam, Germany.
Peltier, W. R. (2004) Global Glacial Isostasy and the Surface of the Ice-Age Earth: The ICE-5G(VM2) model and GRACE. Annual Review of Earth and Planetary Sciences, Vol. 32, pages 111-149.
Swenson, S. C. and J. Wahr. (2006) Post-processing removal of correlated errors in GRACE data. Geophysical Research Letters, Vol. 33, L08402.
Swenson S. C., D. P. Chambers, and J. Wahr (2008) Estimating geocenter variations from a combination of GRACE and ocean model output. Journal of Geophysical Research-Solid Earth, Vol. 113, Issue: B8, Article B08410.