Towards a geoid consistent vertical datum in South Africa - Mphuthi, Matthews Siphiwe (School of Architecture, Planning and Geomatics, 2022)
Traditionally, vertical datums have been realised through mean sea level (MSL) data, at one or more tide gauge station(s), followed by a precise levelling procedure to establish a network of benchmarks. Most countries around the world are still using mean sea level based vertical datums, and South Africa is not an exception. However, these vertical datums suffer from a myriad of problems such as; numerous errors from the levelling networks and tide gauge sea level measurements, high cost of maintenance and upgrade, instability due to high MSL variability, inconsistency with data acquired by satellite and space-based measurement instruments and techniques, just to mention a few. Therefore there is a need to establish a geoid-based vertical datum to mitigate the limitations of mean sea level based vertical datum and to open further frontiers in geodesy, geophysics and geodynamics research, and related applications. Establishment of a national geoid-based vertical geodetic datum requires critical studies on the existing national height system(s) and related distortions, appropriate height system and related reference surface, offset between a local height datum and the intended reference surface, among others. The world is moving towards global unification of vertical datums to modernise the vertical positioning technique, an international height reference system (IHRS) would provide a globally unified height reference system. The horizontal positioning is already realised on the international terrestrial reference frame (ITRF) with high precision, and a similar approach for the realisation of a new vertical datum for South Africa is required. This study carries out analysis on the following aspects over South Africa: comparison between spheroidal, orthometric and normal height systems; accuracy of levelling network; vertical datum offset in relation to geoid, quasigeoid and the IHRS. It concludes by providing a unique framework for establishing a geoid-based vertical datum in South Africa. A numerical investigation of the correlation between the South African spheroidal, orthometric and normal height systems is conducted. It is determined that the spheroidal orthometric height system is more correlated with the normal height system (~ 21.3 cm on average) than the orthometric height system (~ 40.7 cm on average). A further numerical assessment was conducted to determine the magnitude of misclosures and the empirical value for the first order levelling network on the levelling loops. It was determined that majority of the levelling loops fall within the acceptable empirical value for the first order levelling network (c = 0.003). However, only one levelling loop does not fall within the acceptable range of misclosure for the first order levelling network, with a misclosure from spirit levelling measurement of −10.2 cm while the estimated acceptable misclosure is 9.7 cm. The vertical datum offset between the South African local vertical datum and global vertical datum was achieved by estimating the vertical datum offset and the geopotential values on the four fundamental benchmarks. A single-point-based geodetic boundary value problem (GBVP) approach was used following Molodensky's theory for estimating the height anomalies from the disturbing potential 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 0.585, −2.023, −2.597 and 2.105 m!s"! for Cape Town, Port Elizabeth, East London and Durban tide gauge benchmarks, respectively. The corresponding vertical datum offset between the international height reference system and the four fundamental benchmarks over South Africa are 5.973, −20.647, −26.518 , and 21.496 cm for Cape Town, Port Elizabeth, East London and Durban tide gauge benchmarks, respectively. The datum offsets between the land levelling datum (LLD) and the global vertical datum has been estimated, for the first time over South Africa, in this study. A preliminary geoid-based vertical datum in relation to the IHRS for South Africa was determined and evaluated using 138 GPS/levelling data points distributed over the country. However, since it would be difficult to identify exactly which data points are associated with a particular TGBM, the TGBM in Cape Town was held fixed for this analysis. During this analysis, the spheroidal orthometric height was unified to the IHRS (5#$%&#), an existing bias between the 5#$%&# and the local quasigeoid is estimated to be approximately 15.8 cm on average. An adequate data coverage is required to improve the quality of the determined vertical datum offset for the South African vertical datum in relation to the global vertical datum. It is proposed in this study that a normal height system should be adopted for South Africa, with the relevant reference surface being quasigeoid model. Some considerations to be taken during the implementation and adoption of a consistent geoid-based vertical datum in South Africa are discussed.