South Africa’s vertical datum offset to IHRS W ₀ from spheroidal-orthometric heights and satellite-only global geopotential models

This paper estimates the zero-level geopotential of South Africa’s Land Levelling Datum (LLD) and its offset to the International Height Reference System (IHRS) using a height-geopotential combination tailored to the country’s spheroidal-orthometric height practice. Geopotential at GNSS/levelling benchmarks is synthesized directly from satellite-only Global Geopotential Models (GGMs), GOSG02S, WHU-SWPU-GOGR2022S, and Tongji-GMMG2021S, by summing gravitational and centrifugal potentials at each GPS/levelling station’s geocentric position. The estimator forms pointwise values of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:msubsup> <m:mi>W</m:mi> <m:mn>0</m:mn> <m:mtext>LVD</m:mtext> </m:msubsup> </m:mrow> </m:math> W₀LVD , with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:msup> <m:mover accent="true"> <m:mi>γ</m:mi> <m:mo>̄</m:mo> </m:mover> <m:mo>*</m:mo> </m:msup> </m:mrow> </m:math> γ ̄ the Vignal mean-normal gravity consistent with South African height datum, and averages these over a quality-controlled national network (138 stations) under harmonized frame, tide system, and epoch. The three GGMs yield tightly clustered <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:msubsup> <m:mi>W</m:mi> <m:mn>0</m:mn> <m:mtext>LVD</m:mtext> </m:msubsup> </m:mrow> </m:math> W₀LVD estimates: 62,636,857.5890, 62,636,857.6179, 62,636,857.6551 m 2 s −2 , implying a consistent potential offset δW ≈ 4.221 m 2 s −2 relative to the IHRS conventional value. Converted using <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:msup> <m:mover accent="true"> <m:mi>γ</m:mi> <m:mo>̄</m:mo> </m:mover> <m:mo>*</m:mo> </m:msup> </m:mrow> </m:math> γ ̄ , this corresponds to a national height shift of δh ≈ 0.431 m. Diagnostic checks show near-unity normalization of synthesized potentials and negligible spatial variability in the height conversion (sitewise SD ∼ 0.1 mm; weak latitude trend). The inter-model spread in δW ∼ 0.07 m 2 s −2 (<1 cm in height), indicating robust, model-insensitive results at sub-decimetre level. Main residual uncertainties stem from short-wavelength omission in satellite-only GGMs, legacy levelling distortions, spheroidal-orthometric approximations, and remaining tide/epoch nuances. A single national conversion ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:mi>δ</m:mi> <m:msubsup> <m:mi>h</m:mi> <m:mtext>LLD</m:mtext> <m:mi>S</m:mi> </m:msubsup> <m:mo>≈</m:mo> <m:mn>0.431</m:mn> <m:mtext> </m:mtext> <m:mi mathvariant="normal">m</m:mi> </m:mrow> </m:math> δ hLLDS≈ 0.4310.17emm ) is therefore recommended for transforming LLD heights to IHRS-compatible vertical coordinates, with optional millimetric sitewise refinements.