EGU24-327, updated on 08 Mar 2024
EGU General Assembly 2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Using Inverse GNSS Methods for the Determination of C20 and C30 Gravity Field Coefficients for the Support of GRACE Solutions   

Adrian Nowak, Radosław Zajdel, Filip Gałdyn, and Krzysztof Sośnica
Adrian Nowak et al.
  • Wrocław University of Environmental and Life Sciences, Institute of Geodesy and Geoinformatics, Poland (

The distribution of atmospheric, hydrological, and oceanic mass loads on the lithosphere affects the deformation of the Earth's surface over time. Monitoring of the relative displacements of the dense global network of permanent Global Navigation Satellite System (GNSS) stations enables the direct measurement of these loads on a global scale. The application of inverse GNSS methods provides an independent tool to retrieve the time variable gravity (TVG) models of the Earth system and to support hydrogeodesy studies, including the monitoring of the water storage cycle or polar ice mass loss.

The goal of this study is to investigate the effectiveness of using inverse GNSS methods to provide independent C20 and C30 coefficients. These coefficients are essential for deriving highly accurate Gravity Recovery and Climate Experiment (GRACE)-based TVG models. In this study, surface mass variations of low-degree TVG coefficients are derived from the displacements of continuously tracking GNSS sites based on the 21 years (2000-2021) of the Center for Orbit Determination in Europe solutions of the 3rd data reprocessing campaign of the International GNSS Service in the framework of the preparation of the International Terrestrial Reference Frame 2020. The geometrical displacements of the GNSS stations calculated by inverse methods are compared with changes in the gravity field based on independent estimates obtained from the GRACE and GRACE Follow-On (GRACE-FO) satellite missions and the Satellite Laser Ranging (SLR).

As an alternative to the solutions provided by SLR, it is shown that the C20 and C30 coefficients can be derived based on GNSS station displacements. The challenge of the inverse GNSS approach is to properly choose the maximum degree of TVG expansion. Compared with the SLR-based solution, the most consistent GNSS estimate of the temporal gravity variation rate of the C20 coefficient (−1.73 ± 0.10 × 10−11/year) and annual variation (4.7 ± 0.6 × 10−11/43.9° ± 7.5°) was obtained by expansion of the spherical harmonics to degree and order of 8. The GNSS-based C30 series is superior to the SLR-based estimates before the launch of the Laser Relativity Satellite. From August 2016, when the C30 estimates are essential for correcting the GRACE solutions, the root mean square between GNSS and SLR solutions is 4.2 × 10−11. GNSS could potentially support GRACE/GRACE-FO solutions that face problems in deriving C20 and C30, which are fundamental to estimates of ice mass changes in the polar regions. Recovery of mass change in the Antarctic ice sheet from April 2002 to December 2020 based on the coefficients replaced by GNSS estimates results in a linear trend of −111 ± 3 Gt/year. In comparison, the trend for the SLR-based replacement from Technical Note 14 shows a trend of −114 ± 2 Gt/year.

How to cite: Nowak, A., Zajdel, R., Gałdyn, F., and Sośnica, K.: Using Inverse GNSS Methods for the Determination of C20 and C30 Gravity Field Coefficients for the Support of GRACE Solutions   , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-327,, 2024.