![]() The vertical offsets of NAVD88, AHD, and HKPD with respect to the global geoid are estimated as −0.809 ± 0.090, 0.082 ± 0.093, and −0.731 ± 0.030 m, respectively. Finally, as a result of the GBVP solution based on the combined DIR_R6/EGM2008 model, RTM, and residual gravity, the geopotential values of the North American Vertical Datum of 1988 (NAVD88), the Australian Height Datum (AHD), and the Hong Kong Principal Datum (HKPD) are estimated to be equal to 62636861.31 ± 0.96, 62653852.60 ± 0.6860.55 ± 0.29 m2s−2, respectively. In addition, to facilitate practical implementation of the GBVP approach, the effects of the indirect bias term, the spectral accuracy of the GGM, and the systematic levelling errors and distortions in estimations of the vertical datum parameters are investigated in this study. An additional consideration for the high-frequency gravity signals is induced by the topography, and the residual terrain model (RTM) is used to recover the omission errors effect of the combined GGM. To compensate for the omission error of GRACE/GOCE-based GGM, a weighting method is used to determine the combined GGM by combining the high-resolution EGM2008 model (Earth Gravitational Model 2008) and GRACE/GOCE-based GGM to effectively bridge the spectral gap between satellite and terrestrial data. The satellite missions of the GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Exploration) offer high accuracy medium–long gravity filed information, but GRACE/GOCE-based GGMs are restricted to medium–long wavelengths because the maximum degree of their spherical harmonic representation is limited, which is known as an omission error. In the RCR technique, a global geopotential model (GGM) is required to remove and restore the long wavelengths of the gravity field. For this purpose, the geodetic boundary value problem (GBVP) approach based on the remove-compute-restore (RCR) technique is used to determine the vertical datum parameters in this paper. Unification of the global vertical datum has been a key problem to be solved for geodesy over a long period, and the main challenge for a unified vertical datum system is to determine the vertical offset between the local vertical datum and the global vertical datum. The problem can in principle also be solved involving only two datums, in case a precise global gravity field becomes available purely from satellite methods. The unknown off-sets between the various datums appear in the solution inside and outside the Stokes integral and can be estimated in a least squares adjustment, if geocentric positions, levelled heights and adequate gravity material are available for all datum zones. The latter requires the solution of the linear geodetic boundary value problem under the assumption that potential and gravity anomalies refer to a variety of height datums. Two vertical datums can be connected indirectly by means of a combination of precise geocentric positions of two points, as derived by space techniques, their potential (or height) value in the respective height datum and their geoid height difference. Only the unification of large vertical datums and the connection of vertical datums separated by an ocean remains difficult. Also the connection of two adjacent vertical datums poses no principal problem as long as the potential (or height) value of two bench marks of the two systems is known and they can be connected by levelling. ![]() Vertical datum definition is identical with the choice of a potential (or height) value for the fundamental bench mark.
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