The quasigeoid as a vertical datum

The quasigeoid is popular in many parts of a world as a vertical reference surface that is usually in close proximity to the geoid. It has been important historically as a practical replacement for the geoid, because the quasigeoid can be calculated without knowledge of density variations within topography. A large and still growing body of work exists examining the means of calculating the quasigeoid, and its relationship to the geoid. But can the quasigeoid be treated as a useful vertical reference surface, or should it be treated instead as an approximation of the geoid?

The position of the quasigeoid is given by the height anomaly at the topographical surface. As a consequence, it will contain folds, edges or vertices, reflecting those of the topography. These properties are undesirable in a surface used for height referencing, because they allow multiple heights or multiple slopes for any point, creating ambiguity. We demonstrate from basic principles the theoretical limitations of the quasigeoid in providing a useful vertical reference surface, and estimate the magnitude of errors associated with such applications.

It is common to object that either (a) a quasigeoid model will not contain these issues in a practical applications, because it will be associated with some smoothed model of topography, or (b) that the quasigeoid is still the best choice for a vertical reference surface, because of issues in geoid computation associated with numerical conditioning or with uncertainty about the topographical density. We argue that the theoretical problems with the definition of the quasigeoid cannot be resolved by smoothing applied in a particular solution, and that in any case the geoid defines an unambiguous height reference that can be determine to sufficient accuracy in almost all cases.