A strict formula for geoid-to-quasigeoid separation

The paper presented by Flury and Rummel (J Geod 83:829–847, 2009) discusses an important topographic correction to the traditional formula for the quasigeoid-to-geoid separation. Nevertheless, as their formula is approximate, the reader may ask for its relation to the strict one (defined as the one consistent with Bruns’s formula and the boundary condition of physical geodesy), which is now derived. Although the result formally differs from that of Flury and Rummel, we show that the two formulas agree to the centimetre level all over the Earth. We also discuss the practical computation of the topographic correction.