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

  • E. RangelovaEmail author
  • G. Fotopoulos
  • M. G. Sideris
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 135)


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.


Geoid-based vertical datum Dynamic geoid GNSS/levelling 



The authors gratefully acknowledge Geodetic Survey Division, Natural Resources, Canada for providing the GPS ellipsoidal, orthometric and CGG05 geoid heights. The two anonymous reviewers are also acknowledged for their insightful and helpful comments. Financial support is provided by GEOIDE NCE and NSERC, Canada.


  1. Fotopoulos, G. (2003). An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data. PhD thesis, University of Calgary, Department of Geomatics Engineering, Report No 20185.Google Scholar
  2. Fotopoulos, G. (2005). Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data. J. Geodesy, 79, 111–123.CrossRefGoogle Scholar
  3. Fotopoulos, G., M. Craymer, and E. Lapelle (2007). Epoch rectification of GPS on benchmarks in Canada. IUGG2007, Perugia, Italy, July 2–13, 2007.Google Scholar
  4. Heiskanen, H. and H. Moritz (1967). Physical Geodesy. Graz, Austria, (reprint 1999).Google Scholar
  5. Huang, J., G. Fotopoulos, M.K. Cheng, M. Véronneau, and M.G. Sideris (2006). On the estimation of the regional geoid error in Canada. In: Tregoning, P. and C. Rizos C (eds), IAG Symposia, Vol. 130, Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools, Cairns, Australia, August, 22–26, 2005.Google Scholar
  6. Peltier, W.R. (2004). Global glacial isostasy and the surface of the ice-age earth: The ICE-5G (VM2) model and GRACE. Annu. Rev. Earth Planet. Sci., 32, 111–149.CrossRefGoogle Scholar
  7. Rangelova, E. and M.G. Sideris (2008). Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America.J. Geodyn., doi:10.1016/j.jog.2008.03.006.Google Scholar
  8. Rangelova, E., W. Van der Wal, M.G. Sideris, and P. Wu (2008). Spatiotemporal analysis of the GRACE-derived mass variations in North America by means of multichannel singular spectrum analysis. In: IAG Symposia: Gravity, Geoid and Earth Observation 2008 (GGEO2008), Chania, Greece, 23–27, June.Google Scholar
  9. Schwarz, K.P., M.G. Sideris, and R. Forsberg (1987). Orthometric heights without leveling. J. Surv. Eng., 113(1), 28–40.CrossRefGoogle Scholar
  10. Véronneau, M. (2002). The Canadian gravimetric geoid model of 2000 (CGG2000). Report, Geodetic Survey Division, Earth Sciences Sector, Natural Resources Canada, Canada.Google Scholar
  11. Véronneau, M.,R. Duval, and J. Huang (2006). A gravimetric geoid model as a vertical datum for Canada. Geomatica, 60(2), 165–172.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Geomatics EngineeringSchulich School of Engineering, University of CalgaryCalgaryCanada
  2. 2.Faculty of Applied Sciences and Engineering, Department of Civil EngineeringUniversity of TorontoTorontoCanada

Personalised recommendations