Studia Geophysica et Geodaetica

, Volume 43, Issue 4, pp 327–337 | Cite as

Geoidal Geopotential and World Height System

  • Milan Burša
  • Jan Kouba
  • Muneendra Kumar
  • Achim Müller
  • Karel Raděj
  • Scott A. True
  • Viliam Vatrt
  • Marie Vojtíšková


The geoidal geopotential value of W 0 = 62 636 856.0 ± 0.5m 2 s −2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W 0 -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W 0 -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W 0 ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W 0 ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: −55.1 cm, −11.0 cm, +42.4 cm, −11.1 cm and +1.8 cm, respectively.

Geoidal Geopotential World Height System 


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  1. AUSLIG, 1998: Australian GPS/leveling data, private comm., (webb page: Scholar
  2. AVISO/CALVAL yearly Report; 1999: TOPEX/POSEIDON Cycles 1 to 231 (1993–1999), AVINT-011-316-CN Edition 1.0 pp 66.Google Scholar
  3. Bessel F.W.; 1837: Ueber den Einfluss der Unregelmaessigkeiten der Figur der Erde auf geodaetische Arbeiten und ihre Vergleichung mit den Astronomischen Bestimmungen. Astronomische Nachrichten, T. 14,No 269, 329–331.Google Scholar
  4. Burša M., Kouba J., Müller A., Raděj K., True S.A., Vatrt V., Vojtíšková M.; 1998a: Mean Earth's equipotential surface from TOPEX/POSEIDON altimetry, Studia geoph. et geod., 42, 459–466.Google Scholar
  5. Burša M., Kouba J., Müller A., Raděj K., True S.A., Vatrt V., Vojtíšková M.; 1998b: Determination of geopotential differences between local vertical datums and realization of a world height system, Proceeding of Inter, IAG Symp Towards an Integrated Global Geodetic Observing System, Munich Oct 5–9, in print.Google Scholar
  6. Burša M., Kouba J., Raděj K., True S.A., Vatrt V., Vojtíšková M.; 1999: Determination of the geopotential at the tide gauge defining the North American Vertical Datum 1988 (NAVD88), Geomatica, in print.Google Scholar
  7. Chen R., Kakkuri J.; 1995: Result of the Baltic Sea Level 1993 GPS Campaign, Reports Finnish Geodetic Inst., 95:2 Final Results of the Baltic Sea Level 1993 GPS Campaign, Res. Works of the SSG 5.147 of the IAG, ed. by Juhanik Kakurri, 21–30.Google Scholar
  8. Forsberg R.; 1997: Scandinavian GPS/leveling data, personal comm.Google Scholar
  9. Fukushima T.; 1994: Time ephemeris. In: Kinoshita H, Nakai H (eds)Proc 26 th Symp Celestial Mechanics. Jan 12–13 1994. Tokyo, Japan, 149–159.Google Scholar
  10. Gauss, C.F., Bestimmung des Breitenunterschiedes zwischen den Sternwaten von Goettingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector, Vanderschoeck und Ruprecht, Goettingen, 48–50, 1828.Google Scholar
  11. Heiskanen W.A., Moritz H.; 1967: Physical Geodesy. San Francisco and London.Google Scholar
  12. Hellings R.W., Adams P.J., Anderson J.D., Keesy M.S., Lau E.L., Standish E.M., Canuto V.M., Goldman I.; 1983: Experimental Test of the Variability of G Using Viking Lander Ranging Data, Physical Review Letters, 51,No 18, 13609–1612.Google Scholar
  13. IAG SC3 Final Report; 1995: Travaux de L'Association Internationale de Géodésie, 30, 370–384, IAG, Paris.Google Scholar
  14. Lemoine, F.G., D.E. Smith, L. Kunz, R. Smith, E.C. Pavlis, N.K. Pavlis, S.M. Klosko, D.S. Chinn, M.H. Torrence, R.G. Williamson, C.M. Cox, K.E. Rachlin, Y.M. Wang, S.C. Kenyon, R. Salman, R. Trimmer, R.H. Rapp, R.S. Nerem, The Development of the NASA GSFC and NIMA Joint Geopotential Model, Proc. Int. Symp. Gravity, Geoid and Marine Geodesy, (GRAGEOMAR 1995), Univ. of Tokyo, Japan, Sep.30–Oct.5, Springer VLG, 461–469, 1997. NASA report number NASA/TP-1998-20686+1, 1998.Google Scholar
  15. Listing J.B. 1873: Ueber unsere jetzige Kenntniss der Gestalt und Groesse der Erde. Nachrichten von der Koenigl. Gesellschaft der Wissenschaften und der G.A. Universitaet zu Goettingen, No 3, Goettingen VLG der Dietrichschen Buchhandlung, 33–98.Google Scholar
  16. Mainville A.; 1997: The February 1997 GPS on BM data file from Canada, a distribution data set for 1482 stations in Canada, Geodetic Survey Division, Natural Resources Canada, Ottawa, Canada, May 9.Google Scholar
  17. Mather R.S., Rizos C., Morrison T.; 1978: On the Unification of Geodetic Levelling Datums Using Satellite Altimetry, NASA Techn.Memo 79533, Goddard Space Flight Center, Greenbelt Md.Google Scholar
  18. Ménard Y., Jeansou E:, Vincent P.: Calibration of the TOPEX/POSEIDON altimeters at Lampedusa: Additional Results at Harvest. J. Geophys. Res., 99, 487–504.Google Scholar
  19. Milbert D.G., 1995: Improvement of a high resolution geoid height model in the U.S. by GPS heights on NAVD88 benchmarks, IGeS Bull. N.4. New Geoids in the World, International Geoid Service, Milano, 13–36.Google Scholar
  20. Molodensky M.S., Eremeev V.F. and Yurkina M.I.; 1962: Methods for Study of the External Gravitational Field and Figure of the Earth (in Russian), Trudy TsNIIGAiK, Moscow, No 131, pp. 249. English transl.: Israel Program for Sci. Transl. Jerusalem, pp.248.Google Scholar
  21. Munk W.H., MacDonald C.J.F.; 1960: The rotation of the Earth. Cambridge University Press, London, 323 pp.Google Scholar
  22. NRC, 1997: Satellite Gravity and the Geosphere, Contributions to the Study of the Solid Earth and Its Fluid Envelope, Commission on Geosciences, Environment, and Resources, Chair Jean Dickey, National Academy Press, Washington, D.C., pp.112.Google Scholar
  23. Petit G.; 1998: Importance of common framework for realization of space-time reference systems. Proceeding of Inter. IAG Symp Towards an Integrated Global Geodetic Observing System, Munich Oct 5–9, in print.Google Scholar
  24. Pizzetti P.; 1894: Sull'espresione della gravitá alla superficie del geoide supposto ellisoidico. Atte Aead Naz Lincei, Rendl C1 Sci Fis Mat Nat 3:166–172,.Google Scholar
  25. Ries J.C., Eanes R.J., Shum C.K., Watkins M.M.; 1992: Progress in the Determination of the Gravitational Coefficient of the Earth, Geophys. Res. Letters, 19,No. 6, 271–274,.Google Scholar
  26. Rummel R., Teunissen P.J.G.; 1988: Height datum definition, height data connection and the role of the geodetic boundary value problem. Bull. Géod. vol. 62,no 4, p.477–498.Google Scholar
  27. Yurkina, M.I.; 1996: Gravity Potential at the Major Vertical Datum as Primary Geodetic Constant, Studia geoph. et geod., 40, 9–13.Google Scholar

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© StudiaGeo s.r.o. 1999

Authors and Affiliations

  • Milan Burša
  • Jan Kouba
  • Muneendra Kumar
  • Achim Müller
  • Karel Raděj
  • Scott A. True
  • Viliam Vatrt
  • Marie Vojtíšková

There are no affiliations available

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