This data product provides monthly values of the spherical harmonic coefficients of the gravity field complete to degree and order 5 (+C61/S61), derived from satellite laser ranging to five geodetic satellites, computed by Minkang Cheng, John Ries and Byron Tapley (2011).

This is an experimental product. The data are provided for experienced users who wish to assess the quality of the product.

The coefficients of degree 1 and 2 have clear physical interpretations. The degree 1 coefficients are formally converted from the estimated vector from the origin of ITRF2014 to the position of the geocenter (the center of mass of the Earth), which reflects the degree-1 mass loading. The degree 2, order 0 coefficient is related to the Earth’s oblateness. The degree 2, order 1 coefficients are related to the relative position of the principal figure axis of the Earth relative to the rotational axis, while the degree-2, order-2 coefficients determine the Earth’s equatorial ellipticity.

Annual variation of surface mass change from the monthly 5x5 harmonics (Ries
Annual variation of surface mass change from the monthly 5x5 harmonics (Ries & Cheng, CSR, 2018).
The coefficients are given as variations relative to the mean gravity field GGM05C, which is provided in the data file. All coefficients are normalized. The estimates with AOD restored should be added to GGM05C to obtain the full signal.

Each month’s information consists of 22 lines with a header giving the epoch and the 5x5 (+6,1) variations. The next 21 lines contain the delta C and S coefficients without and with the GRACE Atmosphere and Ocean De-aliasing product (AOD) restored (the AOD was included during processing). The variations and their sigmas are scaled by 1.0e10. The format and contents are provided in the file header information. The epoch in Modified Julian Date is provided again with each degree and order pair to make it easy to extract selected harmonics. The degree 1 terms are obtained by converting the estimated geocenter translation to gravity harmonics.

Data Access

The data can be downloaded here.


Acknowledgement and Citation

This research is sponsored by the NASA GRACE Science Team (NASA Grant NNX16AF20G) and the NASA MEaSUREs program (JPL contract JPL1616713). When using these data, please acknowledge receiving the data from "https://grace.jpl.nasa.gov/data/get-data/ ", and cite:

Cheng, M., J. C. Ries, and B. D. Tapley (2011) Variations of the Earth's figure axis from satellite laser ranging and GRACE, J. Geophys. Res., 116, B01409, 2011, DOI:10.1029/2010JB000850.

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