Rigorous Evaluation of Gravity Field Functionals from Satellite-Only Gravitational Models Within Topography

Currently, extensive work is being done in the field of geodesy on producing better gravitational models using purely space-based techniques. With the large datasets spanning a long timeframe, thanks to the GOCE and GRACE missions, it is now possible to compute high quality global gravitational models and publish them in a convenient form: spherical harmonics. For regional geoid modeling, this is advantageous as these models provide a useful reference which can be improved with terrestrial observations. In order for these global models to be usable below the topographical surface, certain considerations are required; topographical masses cause the function that describes the gravity potential to be non-harmonic in the space between the topographical surface and the geoid. This violates the mathematical assumptions behind solid spherical harmonics. This paper aims to look at the error caused by evaluating solid spherical harmonics when topography is present. It thus provides a more rigorous methodology than the commonly used approach of computing the quasigeoid and then applying an approximate correction term for the geoid-quasigeoid separation. It is therefore well-suited for the Stokes-Helmert approach to high-precision regional geoid computation. Comparisons between the more rigorous methodology and the generally used algorithm are made in order to study the error that is committed. With a range of 23.6 cm and a standard deviation of 0.8 cm, this is a non-trivial error if the ultimate goal is to compute a regional geoid with an accuracy of better than 1 cm.