Height Datum Unification with the Boundary Value Problem Approach

Abstract

Two levelling-based vertical datums have been used in North America, namely CGVD28 in Canada and NAVD88 in the USA and Mexico. The unification of these levelling-based vertical datums is of great interest to the scientific and user communities. In this thesis, the geodetic boundary value problem (GBVP) approach is studied as a rigorous method for connecting vertical datums through computed datum offsets from a global equipotential surface defined by means of a GOCE-based geoid. The so-called indirect bias term, the effect of the GOCE geoid omission error, the effect of the systematic levelling datum errors and distortions, and the effect of the data errors on the datum unification are four important factors affecting the practical implementation of this approach. These factors are investigated numerically using the GNSS-levelling and tide gauge stations. The results show that the indirect bias term can be omitted if a GOCE-based global geopotential model is used in geoid computation. The omission of the indirect bias term simplifies the linear system of equations for the estimation of the datum offset. Because of the existing systematic levelling errors and distortions in the Canadian and US levelling networks, the datum offsets are investigated in eight smaller regions along the Canadian and US coastal areas. Using GNSS-levelling stations in the US coastal regions, the mean datum offset can be estimated with a 1 cm error if the GOCE geoid omission error is taken into account using local gravity and topographic information. In the Canadian Atlantic and Pacific regions, the datum offsets can be estimated with 2.3 and 3.5 cm uncertainty, respectively, using GNSS-levelling stations. However, due to the very limited number of tide gauge stations, the datum offset error can reach one decimetre in the Pacific regions. With the available GNSS-levelling stations in Alaska and Mexico, the datum offsets can be estimated with less than 3 cm error. The numerical investigations of this study provide, for the first time, the datum offsets between North American vertical datums and their associated errors with which the offsets can be estimated.