Empirical investigations towards establishing a geoid-based vertical datum over South Africa

Abstract

This study investigates prospects for establishment of a geoid-based vertical datum in South Africa, aligning with the International Height Reference System (IHRS) to modernise and unify vertical positioning. Employing the SAGEOID10 quasigeoid model alongside 138 GPS/levelling data points, this research evaluates the compatibility of spheroidal orthometric, normal, and orthometric height systems with the current quasigeoid and geoid models. The assessment is carried out using vertical datum offsets modelled at 100 and validated at 38 GPS/levelling points by applying a four-parameter planar model.  The cross-validation results show that the normal and orthometric height systems provide a best fit with a standards deviation of ±5.1 and ±3.9 cm, on quasigeoid and geoid models respectively. Spheroidal orthometric height system referred to the land levelling datum (LLD) used over South Africa provided a best fit with the quasigeoid (±6.3 cm) than the geoid (±7.6 cm). In addition, the study determined linear vertical datum offsets between IHRS and variants of the local vertical datum (LLD, local quasigeoid and local geoid) on four TGBMs around South Africa, followed by empirical tests on a few benchmarks observed around each TGBM. Linear offset at each TGBM, between each local height system and the global vertical datum (IHRS) reveal similar trends for the quasigeoid and geoid, but not LLD. The transformed heights (on the IHRS) are used in determining datum offsets based on benchmarks around each TGBM. Results show smallest mean offset around the TGBM in Cape Town compared to the other three TGBMs (PEL, ELN and DBN). These results show that either normal or orthometric height systems should be adopted over South Africa. The results also show that TGBM at CPT should be adopted when transforming selected local height system to the IHRS.