Journal of Geodesy

, Volume 90, Issue 1, pp 45–63 | Cite as

The GBVP approach for vertical datum unification: recent results in North America

  • B. AmjadiparvarEmail author
  • E. Rangelova
  • M. G. Sideris
Original Article


Two levelling-based vertical datums have been used in North America, namely CGVD28 in Canada and NAVD88 in the USA and Mexico. Although the two datums will be replaced by a common and continent-wide vertical datum in a few years, their connection and unification are of great interest to the scientific and user communities. In this paper, the geodetic boundary value problem (GBVP) approach is studied as a rigorous method for connecting two or more vertical datums through computed datum offsets from a global equipotential surface defined by 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 geodetic 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 in Canada, the USA, Alaska, and Mexico. The results show that the indirect bias term can be omitted if a GOCE-based global geopotential model is used in gravimetric geoid computations. The omission of the indirect bias term simplifies the linear system of equations for the estimation of the datum offset(s). 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 standard deviation if the GOCE geoid omission error is taken into account by means of the 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 standard deviation, respectively, using GNSS-levelling stations. However, due to the low number of tide gauge stations, the standard deviation of the CGVD28 and NAVD88 datum offsets can reach one decimetre in the Pacific regions. With the available GNSS-levelling stations in Alaska and Mexico, the NAVD88 datum offset can be estimated with a standard deviation below 3 cm. The numerical investigations of this study provide, for the first time, the datum offsets between North American vertical datums and their associated standard deviations with which the offsets can be estimated. The results of this study demonstrate the importance of the aforementioned four factors in the practical implementation of the GBVP approach for the unification of the levelling-based vertical datums.


Geodetic boundary value problem Vertical datum unification Indirect bias term GOCE Omission error  Levelling network 



This work is a contribution to the ESA STSE—GOCE+ Height System Unification with GOCE project. This work has been partially supported by a grant to the third author from Canada’s Natural Sciences and Engineering Research Council (NSERC). We thank the Canadian Geodetic Survey of NRCan and the National Geodetic Survey, NOAA, USA for providing the GNSS-levelling data sets in Canada and the USA, as well as the gravity data and their errors and David Avalos (INEGI, Mexico) for providing the GNSS-levellign data for Mexico. Also, within the frame of the GOCE+ project, Philip Woodwoth provided the data for the North American tide gauge stations, and Christian Gerlach provided the block-diagonal variance–covariance matrix of the GOCE DIR5 model and the software for error propagation. Finally, Marc Véronneau and Jianliang Huang from the Canadian Geodetic Survey are thanked especially for the invaluable consultation work related to the North American investigations in the GOCE+ project.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Geomatics EngineeringUniversity of CalgaryCalgaryCanada

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