Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Amjadiparvar B, Rangelova E, Sideris MG, Véronneau M (2013a) North American height datums and their offsets: the effect of GOCE omission errors and systematic levelling effects. J Appl Geod 7(1):39–50

    Google Scholar 

  • Amjadiparvar B, Rangelova E, Sideris MG (2013b) North American height datums and their offsets: evaluation of the GOCE-based global geopotential models in Canada and the USA. J Appl Geod 7(3):191–203

    Google Scholar 

  • Amos MJ, Featherstone WE (2009) Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations. J Geod 83:57–68

    Article  Google Scholar 

  • Ardalan AA, Safari A (2005) Global height datum unification: a new approach in gravity potential space. J Geod 79:512–523

    Article  Google Scholar 

  • Ardalan AA, Karimi R, Poutanen M (2010) A bias-free geodetic boundary value problem approach to height datum unification. J Geod 84:123–134

    Article  Google Scholar 

  • Ardalan AA, Grafarend EW (2004) High-resolution regional geoid computation without applying Stokes’s formula: a case study of the Iranian geoid. J Geod 78:138–156

    Google Scholar 

  • Balasubramania N (1994) Definition and realization of a global vertical datum. The Ohio State University, OSU Report No. 427, Columbus

  • Bessel FW (1837) Über den Einfluss der Unregelmässigkeiten der Figur der Erde auf geodätische Arbeiten und ihre Vergleichung mit den Astronomischen Bestimmungen. Astronomische Nachrichten 14:269

    Article  Google Scholar 

  • Bruinsma SL, Förste C, Abrikosov O, Marty J-C, Rio M-H, Mulet S, Bonvalot S (2013) The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett 40:3607–3612

    Article  Google Scholar 

  • Cannon JB (1929) Adjustment of the precise level net of Canada 1928. Publication no. 28, Geodetic Survey Division, Earth Sciences Sector, Natural Resources Canada, Ottawa

  • Cannon JB (1935) Recent adjustments of the precise level net of Canada. Publication no. 56, Geodetic Survey Division, Earth Sciences Sector, Natural Resources Canada, Ottawa, Canada

  • Colombo O (1980) A world vertical network. The Ohio State University, OSU report no. 296, Columbus

  • Craymer MR, Lapelle E (1997) The GPS supernet: an integration of GPS projects across Canada. Internal report, Geodetic Survey Division, Geomatics Canada, Ottawa

  • Denker H (2001) On the effect of datum inconsistencies of gravity and position on the European geoid computations. In: Proceedings IAG scientific assembly, Budapest, Hungary, 2–7 Sep., on CD-ROM

  • Denker H (2013) Regional gravity field modeling: theory and practical results. In: Xu G (ed) Sciences of geodesy—II. Springer, Berlin, pp 185–291

  • ESA (1999) Gravity field and steady-state ocean circulation mission. In: Report for mission selection of the four candidate Earth Explorer missions, ESA SP-1233(1)

  • Filmer MS, Featherstone WE (2012) Three viable options for a new Australian vertical datum. J Spat Sci 57(1):19–36

    Article  Google Scholar 

  • Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. The Ohio State University, OSU report no. 355, Columbus

  • Gatti A, Reguzzoni M, Venuti G (2013) The height datum problem and the role of satellite gravity models. J Geod 87:15–22

    Article  Google Scholar 

  • Gauss CF (1828) Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona. Vandenhoek und Ruprech, Göttingen

    Google Scholar 

  • Gerlach C, Fecher T (2012) Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets. J Geod Sci 2(4):247–256

    Google Scholar 

  • Gerlach C, Rummel R (2013) Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geod 87:57–67

    Article  Google Scholar 

  • Gruber T, Gerlach C, Haagmans R (2012) Intercontinental height datum connection with GOCE and GPS-levelling data. J Geod Sci 2(4):270–280

    Google Scholar 

  • Hayden T, Amjadiparvar B, Rangelova E, Sideris MG (2012) Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models. J Geod Sci 2(4):257–269

    Google Scholar 

  • Hayden T, Rangelova E, Sideris MG, Véronneau M (2014) Contribution of tide gauges for the determination of W0 in Canada. In: Marti U (ed) Gravity, geoid and height systems, IAG symposia series, vol 141. Springer, Berlin. pp 241–248

  • Hayden T (2013) Geopotential of the geoid-based North American vertical datum. University of Calgary, MSc thesis, UCGE report no. 20381, Department of Geomatics Engineering, Calgary

  • Heck B (1989) A contribution to the scalar free boundary value problem of physical geodesy. Manu Geod 14:87–99

    Google Scholar 

  • Heck B (1990) An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull Geod 64:88–108

    Article  Google Scholar 

  • Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Sea surface topography and the geoid, IAG symposia series, vol 104. Springer, Berlin, pp 116–128

  • Helmert FR (1884) Die mathematischen und physikalischen Theorieen der höheren Geodäsie, v. 2. BG Teubner, Leipzig. Reprinted (1962) BG Teubner, Leipzig. Also (1962) Minerva GMBH, Frankfurt-Main

  • Hirt C, Featherstone W, Marti U (2010) Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data. J Geod 84:557–567

    Article  Google Scholar 

  • Hofmann-Wellenhof B, Moritz H (2006) Physical geodesy, 2nd edn. Springer, Wien. ISBN 10 3-211-33544-7

  • Huang J, Véronneau M (2013) Canadian gravimetric geoid model 2010. J Geod 87:771–790

    Article  Google Scholar 

  • Ihde J, Adam J, Gurtner W, Harsson BG, Sacher M, Schlüter W, Wöppelmann G (2000) The height solution of the European vertical reference network (EUVN). In: Veröffentlichungen der Bayerischen Kommission fur die Internationale Erdmessung, Bayerische Akademie der Wissenschaften, Nr. 61, 132–145, München

  • Jekeli C (2000) Heights, the geopotential, and vertical datums. The Ohio State University, OSU report no. 459, Columbus

  • Kotsakis C, Katsambalos K, Ampatzidis D (2012) Estimation of the zero-height geopotential level WoLVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands. J Geod 86:423–439

    Article  Google Scholar 

  • Lamothe P, Véronneau M, Goadsby M, Berg R (2013) Canada’s new vertical datum. Ontario Professional Surveyor, vol 56. No 4 Fall 2013. http://www.aols.org/sites/default/files/OPS%20Fall2013WebVersion.pdf

  • Listing JB (1873) Über unsere jetzige Kenntnis der Gestalt und Größe der Erde. Dietrichsche Verlagsbuchhandlung, Göttingen

    Google Scholar 

  • LP DAAC (2004) Global 30 arc-second elevation data set GTOPO30. Land Process Distributed Active Archive Center, Sioux Falls. http://edcdaac.usgs.gov/gtopo30/gtopo30.asp

  • Mäkinen J, Ihde J (2008) The permanent tide in height systems. In: Sideris MG (ed) Observing our changing earth, IAG symposia series, vol 133. Springer, Berlin, pp 81–87

  • Mikhail EM, Ackermann F (1976) Observations and lease squares. IEP-A Dun-Donnelley Publisher, New York

    Google Scholar 

  • Moritz H (2000) Geodetic reference system 1980. J Geod 7:128–133

    Article  Google Scholar 

  • Pail R, Bruinsma S, Migliaccio F, Foerste C, Goiginger H, Schuh WD, Hoeck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sanso F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843

    Article  Google Scholar 

  • Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development of the earth gravitational model 2008 (EGM2008). J Geophys Res 117:B04406

    Google Scholar 

  • Petit G, Luzum B (eds) (2010) IERS conventions 2010. IERS technical note 36. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt a.M

  • Prasanna HMI, Chen W (2012) Geoid modeling using a high resolution geopotential model and terrain data: a case study in Canadian Rockies. J Appl Geod 6(2):89–101

    Google Scholar 

  • Rangelova E, van der Wal W, Sideris MG (2012) How significant is the dynamic component of the North American vertical datum? J Geod Sci 2(4):281–289

    Google Scholar 

  • Rapp RH, Balasubramania N (1992) A conceptual formulation of a world height system. The Ohio State University, OSU report no. 421, Columbus

  • Rapp RH (1997) Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. J Geod 71:282–289

    Article  Google Scholar 

  • Roman D, Weston ND (2012) Beyond GEOID12: implementing a new vertical datum for North America. In: FIG proceedings 2012, Rome, Italy, 6–10 May 2012. http://www.fig.net/pub/fig2012/papers/ts04b/TS04B_weston_5691.pdf

  • Rummel R (2000) Global integrated geodetic and geodynamic observing system (GIGGOS). In: Rummel R, Drewes H, Bosch W, Hornik H (eds) Towards an integrated global geodetic observing system (IGGOS), IAG symposia series, vol 120. Springer, Berlin, pp 253-260

  • Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Geod 62:477–498

    Article  Google Scholar 

  • Rummel R, Ilk KH (1995) Height datum connection-the ocean part. Allgemeine Vermessungsnachrichten 8–9:321–330

    Google Scholar 

  • Rülke A, Liebsch G, Sacher M, Schäfer U, Schirmer U, Ihde J (2012) Unification of European height system realizations. J Geod Sci 2(4):343–354

    Google Scholar 

  • Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149(3):768–775

    Google Scholar 

  • Sanso F, Sideris MG Eds (2013) Geoid determination. In: Lecture notes in earth system science, vol 110. Springer, Berlin

  • Sánchez L (2007) Definition and realization of the SIRGAS vertical reference system within a globally unified height system. In: Tregoning P, Rizos C (eds) Dynamic planet, IAG symposia series, vol 130. Springer, Berlin, pp 638–645

  • Sánchez L (2008) Approach for the establishment of a global vertical reference level. In: Xu P, Liu J, Dermanis A (eds) VI Hotine-Marussi symposium on theoretical and computational geodesy, IAG symposia series, vol 132. Springer, Berlin, pp 119–125

  • Sánchez L (2009) Strategy to establish a global vertical reference system. In: Drewes H (ed) Geodetic reference systems, IAG symposia series, vol 134. Springer, Berlin, pp 273–278

  • Sánchez L, Bosch W (2009) The role of the TIGA project in the unification of classical height systems. In: Drewes H (ed) Geodetic reference systems, IAG symposia series, vol 134. Springer, Berlin, pp 285–290

  • Sánchez L, Brunini C (2009) Achievements and challenges of SIRGAS. In: Drewes H (ed) Geodetic reference systems, IAG symposia series, vol 134. Springer, Berlin, pp 161–166

  • Sideris MG, Rangelova E, Amjadiparvar B (2014) First results on height systems unification in North America using GOCE. In: Marti U (ed) Gravity, geoid and height systems, IAG symposia series, vol 141. Springer, Berlin, pp 221–227

  • Sideris MG, Amjadiparvar B, Rangelova E, Huang J, Véronneau M (2015) Evaluation of release-3, 4 and 5 GOCE-based global geopotential models in North America, In Proc of 5th International GOCE user workshop, (CD-ROM). ESA Publications Division, European Space Agency, Noordwijk

    Google Scholar 

  • Thompson KR, Huang J, Véronneau M, Wright DG, Lu Y (2009) Mean surface topography of the northwest Atlantic: comparison of estimates based on satellite, terrestrial gravity, and oceanographic observations. J Geophys Res 114:C07015

    Google Scholar 

  • Véronneau M, Héroux P (2006) Canadian height reference system modernization: rational, status and plans. Report natural resources of Canada. http://www.geod.nrcan.gc.ca/hm/pdf/geocongres_e.pdf

  • Véronneau M, Huang J, Smith DA, Roman DR (2014a) Canada’s new vertical datum: CGVD2013 (Part 1). XYHT magazine, October 2014, pp 43–45. http://e-ditionsbyfry.com/Olive/ODE/XYHT/Default.aspx?href=XYHT/2014/10/01

  • Véronneau M, Huang J, Smith DA, Roman DR (2014b) Canada’s new vertical datum: CGVD2013 (Part 2). XYHT magazine, November 2014, pp 41–43. http://e-ditionsbyfry.com/Olive/ODE/XYHT/Default.aspx?href=XYHT/2014/11/01

  • Wang YM, Saleh J, Li X, Roman D (2012) The US gravimetric geoid of 2009 (USGG 2009): model development and evaluation. J Geod 86:165–180

    Article  Google Scholar 

  • Woodworth PL, Hughes CW, Bingham RJ, Gruber T (2012) Towards worldwide height system unification using ocean information. J Geod Sci 2(4):302–318

    Google Scholar 

  • Xu P (1990) Monitoring the sea level rise. Delft Rep (New Ser) 90:1

    Google Scholar 

  • Xu P (1992) A quality investigation of global vertical datum connection. Geophys J Int 110(2):361–370

    Article  Google Scholar 

  • Xu P, Rummel R (1991) A quality investigation of global vertical datum connection, Netherlands Geodetic Commission

  • Zhang L, Li F, Chen W, Zhang C (2009) Height datum unification between Shenzhen and Hong Kong using the solution of the linearized fixed-gravimetric boundary value problem. J Geod 83:411–417

    Article  Google Scholar 

  • Zilkoski D, Richards J, Young G (1992) Results of the general adjustment of the North American vertical datum of 1988. Surv Land Inf Syst 52(3):133–149

    Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

    B. Amjadiparvar, E. Rangelova & M. G. Sideris

Authors
  1. B. Amjadiparvar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Rangelova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. G. Sideris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Amjadiparvar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amjadiparvar, B., Rangelova, E. & Sideris, M.G. The GBVP approach for vertical datum unification: recent results in North America. J Geod 90, 45–63 (2016). https://doi.org/10.1007/s00190-015-0855-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00190-015-0855-8

Keywords

Search

Navigation