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

Abstract

This study investigates prospects for establishing a geoid-based vertical datum in South Africa and aligning it 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 derived 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 standard deviations of ±5.1 and ±3.9 cm on quasigeoid and geoid models, respectively. The spheroidal orthometric height system referred to the land levelling datum (LLD) used over South Africa provided a better fit with the quasigeoid (±6.3 cm) than with the geoid (±7.6 cm). In addition, the study determined linear vertical datum offsets between the IHRS and variants of the local vertical datum (LLD, local quasigeoid and local geoid) on four tide gauge benchmarks (TGBMs) around South Africa. Empirical tests on a few benchmarks observed around each TGBM followed. The linear offsets at each TGBM, between each local height system and the global vertical datum (IHRS), revealed similar trends for the quasigeoid and geoid, but not for the LLD. The transformed heights (on the IHRS) were used to determine datum offsets based on benchmarks around each TGBM. Compared to the other three TGBMs (PEL, ELN and DBN), the results show the smallest mean offset around the TGBM in Cape Town. They also indicate that either normal or orthometric height systems should be adopted over South Africa and that the TGBM at CPT should be adopted when transforming a selected local height system to the IHRS.