22 years of time-variable gravity field determination from GRACE and GRACE Follow-On: the CNES/GRGS RL05 solution

Abstract

The GRACE and GRACE Follow-On (GRACE-FO) missions aim to track temporal changes in Earth's gravity field. Using data from these missions, CNES/GRGS has produced the “RL05” satellite-only series of geopotential solutions in spherical harmonics up to degree and order 90. These solutions are available at both monthly and 10-day temporal resolutions, covering the period from April 2002 to July 2025. These solutions were derived using a distinct processing strategy—particularly with respect to background models and solution stabilization techniques—compared to those adopted by most other groups involved in GRACE/GRACE-FO data processing. Nevertheless, the core parameter estimation approach remains fundamentally the same. The main differences with other processing centers are the combination of Satellite Laser Ranging (SLR) data from geodetic satellites with GRACE data at the normal equation level (and not as a substitution of low-degree SH coefficients) and the use of truncated singular value decomposition (TSVD) for the time-variable gravity (TVG) field solution. Examination of TVG time series over test areas such as the Caspian Sea and Iceland demonstrates the advantages of TSVD resolution over conventional unconstrained methods such as Cholesky decomposition, which require post-processing filtering. The DDK5 filter, for instance, produces a strong decrease in the restored signal from spherical harmonic degree 50, compared to approximately degree 70 for the TSVD solution. Our TSVD solution is also compared to mascon solutions, showing a commensurability of the signal content of the solutions, with the advantage of not relying on geophysical assumptions and of providing, on the oceans, a less constrained solution than mascons. Finally, an evaluation of the noise of these different solutions is carried out by estimating and comparing the errors of the solutions on the regions where the TVG signal is particularly weak. The noise is estimated at the level of 1.0 to 4.6 cm equivalent water height (EWH), depending on the resolution, for the DDK5-filtered RL06 solutions from CSR, JPL and GFZ, and at the level of 0.9–3.3 cm EWH for the COST-G, TUGRAZ and CNES-RL05-TSVD solutions.