Estimation of vertical datum offset for the South African vertical datum, in relation to the international height reference system

The vertical offset and the geopotential value over South Africa is estimated on the four fundamental benchmarks in relation to the international height reference system (IHRS). It is estimated to obtain discrepancies between the South African local vertical datum (W_P) and the global vertical datum (W_0). A single-point-based geodetic boundary value problem (GBVP) approach was used following Molodensky theory for estimating the height anomalies from the disturbing potential (T_P) using Bruns’s formula. The gravity potential at each tide gauge benchmark (TGBM) in South Africa deviates from the potential of the global reference surface by 0.589,-1.993,-2.593 and 2.154 m2s-2 for Cape Town, Port Elizabeth, East London and Durban, respectively. The corresponding vertical datum offsets between the international height reference system and the four fundamental benchmarks over South Africa are 6.013, -20.347, -26.478, and 21.996 cm for Cape Town, Port Elizabeth, East London and Durban, respectively. These offsets can be used for the unification of the South African vertical datum at the four tide gauge benchmarks in a manner that is consistent to the international height reference system.

Estimation of Vertical Datum Parameters Using the GBVP Approach Based on the Combined Global Geopotential Models

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. 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. In the RCR technique, a global geopotential model (GGM) is required to remove and restore the long wavelengths of the gravity field. 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. 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. 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. 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. 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 ± 0.95 and 62636860.55 ± 0.29 m2s−2, respectively. 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.

A Quasigeoid-Derived Transformation Model Accounting for Land Subsidence in the Mekong Delta towards Height System Unification in Vietnam

A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic transformation model to effectively fit the differences between the quasigeoid and GNSS/levelling heights was based on a third-order polynomial model. Second, the residual height anomalies have been interpolated to a grid employing Least-Squares Collocation. Finally, the distortions were restored to the residual grid. This model can be used for combination with a gravimetric quasigeoid model in GNSS levelling. The quality of GNSS/levelling data in Vietnam was analyzed and evaluated in this study. The annual subsidence rate from ALOS-1 was also used to analyze the effects of subsidence on the quality of GNSS/levelling data in the Mekong Delta. From this we made corrections to improve the accuracy of GNSS/levelling data in this region. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Based on this offset model, GNSS levelling can be carried out in most of Vietnam’s territory complying third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. This model in combination with the developed gravimetric quasigeoid model should also contribute to the modernization of Vietnam’s height system. We also used high-quality GNSS/levelling data and the determined quasigeoid model to determine the geopotential value W0 for the Vietnam Local Vertical Datum. The gravity potential of the Vietnam Local Vertical Datum is estimated equal to W 0 LVD = 62,636,846.81 ± 0.70 m2s−2 with the global equipotential surface realized by the conventional value W0 = 62,636,853.4 m2s−2.

Preliminary Unification of Kronsztadt86 Local Vertical Datum with Global Vertical Datum

The study concerns computation of the gravity potential difference between the Kronsztadt86 datum and the global vertical datum. This method is based on the use of ellipsoidal heights from satellite observations, normal heights obtained from the conducted leveling campaign and quasigeoid/ellipsoid separations computed based on the EGM2008 model. The obtained results indicate that there are substantial differences in the estimated value of the parameter ΔW, computed from three different satellite networks: POLREF, EUVN-DA and ASG-EUPOS. The parameter was determined with sufficient accuracy and the applied systematic error model has low efficiency. The computations reveal that the best value of ΔW for the territory of Poland is 0.43 m2s-2.

Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models

The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network.

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman Sea

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman SeaWe apply a novel approach for the gravimetric marine geoid modelling which utilise the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearised fixed gravimetric boundary-value problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The BEM approach is applied to determine the marine geoid model over the study area of the Southwest Pacific Ocean and Tasman Sea using DNSC08 marine gravity data. The comparison of the BEM-derived and EGM2008 geoid models reveals that the geoid height differences vary within -25 and 18 cm with the standard deviation of 6 cm. The DNSC08 sea surface topography data and the new marine geoid are then used for modelling of the mean dynamic topography (MDT) over the study area. The local vertical datum (LVD) offsets estimated at 15 tide-gauge stations in New Zealand are finally used for testing the coastal MDT. The average value of differences between the MDT and LVD offsets is 1 cm.