Performance evaluation of high/ultra-high-degree global geopotential models over Vietnam using GNSS/leveling data

The availability of many high-degree Global Geopotential Models (GGMs), namely EGM2008, EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, XGM2019e_2159, and GGMPlus, challenges users regarding which model is best for Vietnam. This study, therefore, evaluates their performance by comparing them with GNSS/leveling data over Vietnam. Results show that their absolute and relative performances are largely independent of topographic conditions and geographical location and can be ranked into three classes: (1) XGM2019e_2159 has the highest accuracy, (2) the models EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, and GGMPlus, have a very similar level of medium accuracy, while (3) EGM2008 is found to be the least accurate. In an absolute sense, the differences between GNSS/leveling and EGM2008-based height anomalies have a standard deviation (STD) of 0.290 ± 0.010 m, whereas, for XGM2019e_2159, this is 0.156 ± 0.006 m. All other models have STDs of (0.18–0.19) ± 0.007 m. Regarding relative performance without fitting, all GGMs have comparable accuracies for baseline length of 5–20 km, while for baselines longer than 20 km, the STD of XGM2019e_2159 is 1.5 ppm–0.5 ppm (approximately 19%–40%) lower compared with EGM2008, and 0.5 ppm–0.25 ppm (approximately 7%–36%) lower compared with EIGEN6C4, GECO, SGG-UGM-1, SGG-UGM-2, and GGMPlus. In addition, the STDs decrease significantly from 20 to 12 ppm in the range of 5–10 km, slightly from 12 to 6 ppm for 10–35 km, very slightly from 6 to 2.5 ppm for 35–200 km, and then remain almost unchanged for longer baselines. After fitting, the relative accuracies of all GGMs are at the same level with negligible STD/RMSE values. Furthermore, only EGM2008 experiences significant regional differences, while other GGMs show more homogeneous spatial variation of absolute accuracy over Vietnam. These findings can contribute to the development of local quasigeoid models in Vietnam and may be helpful with the improvement of GGMs in the future.