On the Geoid-Quasigeoid Separation in Mountain Areas

In modern precision height systems, two basic concepts of physical height definition are widely used: on the one hand the Stokes-Helmert concept of orthometric heights referred to the geoid, and on the other hand Molodensky's concept of normal heights to be used in combination with height anomalies or quasigeoid heights. The separation between the two reference surfaces - the geoid and the quasigeoid - is typically in the order of a few decimeters but can reach nearly 3 m in extreme cases. For a consistent use of both height concepts within a country, and in particular across borders of countries or regional vertical reference frames, the geoid-quasigeoid separation should be provided along with the vertical datum - with cm-accuracy and for every location (not only for benchmarks). The largest contribution to the geoid-quasigeoid separation is due to the distribution of topographic masses. We modeled the geoid-quasigeoid separation for test areas with very rough topography using a very fine grid resolution of 100 m and a rigorous treatment of topographic masses based on high-resolution digital terrain data. Results show that rigorous treatment of topographic masses leads to a rather small geoid-quasigeoid separation - only 30 cm at the highest summit - while results based on approximations are often larger by several decimeters. The accuracy of the topographic contribution to the geoid-quasigeoid separation is estimated to be 2-3 cm for areas with extreme topography if a modeling grid resolution of 200 m or less is used. We conclude that a consistent determination of the geoid and quasigeoid height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy.