Terrain-corrected differential GNSS gravity potential leveling method and its application to elevation determination in mountainous areas

Abstract To address the difficulties in conventional elevation surveying caused by the strong topographic relief in mountainous areas and the dual constraints imposed on GNSS gravity potential leveling by the selection of the absolute gravity potential reference and local short wavelength terrain effects, a terrain corrected differential GNSS gravity potential leveling method is proposed. The proposed method takes the normal height difference between two points as the quantity to be determined and directly determines the height difference of a survey segment through a differential strategy, thereby reducing the influence of common systematic errors at the two endpoints and weakening the dependence on the absolute gravity potential reference. Considering the significant local short wavelength terrain effects in mountainous areas, a residual terrain model is constructed using a high resolution digital elevation model. The Helmert second condensation method is employed to process the terrain mass, and the residual terrain potential is calculated based on the prism–plate model. The difference in residual terrain potential between the two endpoints is then taken as the terrain correction for the survey segment to compensate for the local short wavelength terrain effects that are not adequately represented by the global gravity field model. 28 height difference segments in the reservoir area of the Cihaxia Hydropower Station in southern Qinghai Province were used for testing, with precise trigonometric leveling results adopted as the reference. The results show that, within the GNSS gravity potential leveling framework, the differential determination of height differences achieves a higher accuracy (RMS = 0.218 m) than the single point determination (RMS = 0.341 m). The terrain corrected differential GNSS gravity potential leveling method further improves the accuracy to RMS = 0.062 m, which is significantly better than that without terrain correction (RMS = 0.218 m) and substantially reduces the systematic bias of approximately − 0.22 m. The proposed method can improve the accuracy of normal height difference determination for survey segments in complex mountainous areas and provides a feasible technical approach for elevation control surveying in reservoir areas.