Why a Height Theory Must Be Rigorous and Physically Correct

Let us start with defining what we understand by a height system. A height system is a conglomerate of reference surface upon which height H = 0, and a recipe for how heights above that surface are obtained from observations. Two such systems, which we call the classical or Gauss-Stokes’s system and the Molodensky system, are used in practical height measurement. The reference surface used by the classical system is the Geoid and its usage is based on valid physical arguments. Determination of the height above the geoid requires data at the surface of the Earth obtained by levelling, gravimetry, sea level measurements, and topographical density from geological measurements. This system served us well when decimetre height accuracy was required and will continue doing so even now when one or even two orders of magnitude better accuracy is needed. On the other hand, Molodensky’s system uses the quasigeoid as a reference surface; this surface is ill suited for a global height system. This paper argues the case that the standard classical reference surface, the geoid, should be used in practice everywhere.