Tongji-GMMG2025C: A High-Resolution Global Gravity Field Solution Integrated from Heterogeneous Gravity Data via a Grid-based VCE Method

Abstract. In this study, we present Tongji-GMMG2025C, a high-resolution global gravity field solution complete to degree and order (d/o) 2190. The solution combines GRACE and GOCE satellite gravity information with five marine gravity datasets derived from satellite altimetry, four topographic gravity field models, pseudo terrestrial observations generated from EGM2008 up to d/o 719, high-resolution Antarctic gravity anomaly grids (AntGG2021), and Arctic Gravity Project (ArcGP) datasets. Grid-level variance component estimation (VCE) is used to combine the marine and topographic datasets separately. The Tongji-GMMG2021S satellite-based full normal equation system is then combined with a terrestrial block-diagonal normal equation derived from global 5’×5’ gravity anomaly grids. As a multi-source integrated solution, Tongji-GMMG2025C demonstrates lower residual statistics than single-source based solutions, exhibiting improvements of 0.01~0.21 mGal in measured free-air gravity anomalies and shipborne gravity anomaly enhancements of 0.08~0.54 mGal. Comparison with other existing gravity field solutions EGM2008, EIGEN-6C4, SGG-UGM-2, and XGM2019e reveals a good performance of our new combination solution Tongji-GMMG2025C and the closest agreement with XGM2019e. In oceanographic applications, Tongji-GMMG2025C achieves a root mean square error (RMSE) of 75.27 cm/s in geostrophic current determination relative to the DTU22MDT, outperforming EIGEN-6C4 by over 4.87 cm/s. Continental geoid evaluations in data-sparse regions yield accuracies of 38.94 cm (surrounding Brazil), 34.45 cm (surrounding Africa), and 50.60 cm (surrounding India), representing a 24 % improvement over EGM2008 in the surrounding Brazil region. Validation against millions of shipborne gravity measurements indicates that Tongji-GMMG2025C performs favourably, particularly in the 0~10 km coastal zone, where it achieves an accuracy of 6.99 mGal, outperforming existing models by 9 % to 24 %. Similarly, the model establishes an accuracy improvement of approximately 40 % compared to EGM2008 over Antarctica. These results demonstrate that Tongji-GMMG2025C may provide useful complementary gravity information in data-sparse regions. The Tongji-GMMG2025C solution is available at https://doi.org/10.5281/zenodo.22667828 (Xuan et al., 2026).