Implementing a Dynamic Geoid as a Vertical Datum for Orthometric Heights in Canada

Abstract

The geoid heights in Canada are subject to secular dynamic changes caused by the slow glacial isostatic adjustment of the viscoelastic Earth. As a result, the reference surface for orthometric heights changes with time at a level that is an order of magnitude smaller than the rate of change of heights. The objective of this paper is to provide a feasibility study on implementing the geoid as a dynamic vertical datum. For this purpose, the most accurate GPS ellipsoidal heights from the CBN (Canadian Base Network), orthometric heights from the most recent minimally constrained adjustment of the primary vertical control network and the latest geoid model for Canada are used. In this approach, the dynamic geoid is treated in the context of the combined adjustment of the ellipsoidal, orthometric and geoid heights. In this paper, it is shown that the present-day accuracy of the three height components precludes the implementation of the dynamic vertical datum, and the accuracy of the orthometric heights appears to be the limiting factor. By means of a simulated example, we demonstrate that the dynamic vertical datum requires an accuracy of 1.0–1.5 cm for each of the three height components. Provided this level of accuracy is reached, the vertical reference surface must be adjusted for the secular geodynamic effect after 8–10 years have elapsed from the reference epoch. For comparison, vertical crustal motion can cause significant systematic discrepancies among the ellipsoidal, orthometric, and geoid heights over a 2-year time interval.