Preliminary Results of Spatial Modelling of GPS/Levelling Heights: A Local Quasi-Geoid/Geoid for the Lisbon Area

  • A. P. FalcãoEmail author
  • J. Matos
  • A. Gonçalves
  • J. Casaca
  • J. Sousa
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 135)


Taking GPS-measured ellipsoidal heights with in situ measured gravity values, levelling-measured heights, and knowing the difference between normal gravity potential and geoidal potential, the calculation of normal heights is possible. The difference between normal and ellipsoidal heights allows the computation of gravity anomalies and geoid undulation, and thus the calculation of quasi-geoid and geoid surfaces, to serve practical applications such as large scale map production and engineering applications.

In this work an evaluation of the spatial interpolation techniques used in the quasi-geoid/ geoid local calculation methods is presented. Deterministic interpolators (Inverse Power of Distance – IPD and Radial Basis Functions– RBF), and probabilistic interpolators (Ordinary Kriging – OrdK and Kriging with External Drift – KED) were tested. The sample used in this study is from a 34 km × 28 km area including Lisbon, which includes 25 levelling heights and gravity values measured by the Instituto Geográfico Português, and the related ellipsoidal heights, measured with a LEICA AX1200 double-frequency GPS receiver.


Quasi-geoid Normal heights Interpolation techniques 



Authors would like to thank Instituto Geográfico Português for data availability.


  1. Boucher, C. and Z. Altamimi (2007). Specifications for reference frame fixing in the analysis of a EUREF GPS campaign. Technical Note.Google Scholar
  2. Casaca, J. and A.P. Falcão (2007). A gravidade normal e as altitudes normais. In: Actas da V Conferência Nacional de Cartografia e Geodesia. Lisboa, Portugal, April 19–20.Google Scholar
  3. Featherstone, W. and M. Kuhn (2006). Height systems and vertical datums: a review in the Australian context. J. Spatial Sci., 51(1):21–42.CrossRefGoogle Scholar
  4. Featherstone, W.E., M.C. Dentith, and J.F. Kirby (1998). Strategies for the accurate determination of orthometric heights from GPS. Survey Review, No 34, 267.Google Scholar
  5. Fotopoulos, G. (2003). An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data, PHD thesis, Department of Geomatics Engineering. University of Calgary, Alberta. Canada.Google Scholar
  6. Hannah, J. (2001). An assessement of New Zealand’s height systems and options for a futures height datum. Prepared for the Surveyor General land Information New Zealand. University of Otago.Google Scholar
  7. Heiskanen, W. and H. Moritz (1967). Physical geodesy. W. H. Freeman and Company, San Francisco, USA.Google Scholar
  8. Jekeli, C. (2000). Heights, the geopotential, and vertical datums. Technical Report 459. Ohio Sea Grant Development Program, NOAA.Google Scholar
  9. NOAA (1998). National height modernization study. Executive summary of a report to congress available from the National Geodetic Survey.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • A. P. Falcão
    • 1
    Email author
  • J. Matos
    • 1
  • A. Gonçalves
    • 1
  • J. Casaca
    • 2
  • J. Sousa
    • 3
  1. 1.Departamento de Engenharia Civil e Arquitectura (DECivil)Instituto Superior Técnico, Universidade Técnica de LisboaLisboaPortugal
  2. 2.Laboratório Nacional de Engenharia CivilLisboaPortugal
  3. 3.Departamento de Engenharia de Minas e Georrecursos (DEMG)Instituto Superior Técnico, Universidade Técnica de LisboaLisboaPortugal

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