Remarks on the Role of Height Datum in Altimetry-Gravimetry Boundary-Value Problems

  • Fausto Sacerdote
  • Fernando Sansò
Part of the Space Sciences Series of ISSI book series (SSSI, volume 17)


The problem of global geoid determination is usually solved using satellite altimetry data on the oceans, together with an oceanographic model of sea surface topography, and gravity anomaly data on the continents. Such data, however, enable to obtain only potential differences with respect to a reference surface whose absolute potential is unknown. This situation suggests to modify the classical mixed boundary-value problem of physical geodesy by inserting into the boundary conditions an unknown additive constant, that must be determined by imposing a suitable additional constraint. Yet, such formulation of the boundary-value problem, from the point of view of its mathematical properties, is not unconditionally well-posed, and. furthermore, does not reflect faithfully the available physical model, as the present knowledge of ocean circulation docs not allow to connect along coastlines the reference surfaces defined on the oceans and on the continents. The introduction of two different unknown additive constants, one for the oceans and one for the earth, to be determined by imposing two additional constraints, gives rise to a more faithful picture of the present physical knowledge, and, at the same lime, to a new well-posed formulation of the boundary-value problem.


height datum geoid. boundary-value problems 


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  1. Heiskanen, \V, and Moritz, H.: 1967, Physical Geodesy, W.H. Freeman and Co., San Francisco, 364 pp.Google Scholar
  2. Lehmann, R.: 20(H), Aliimeiry-Gravimeiry Problems with Free Vertical Datum’, Journal of Geodesy 74, 327–334.Google Scholar
  3. Pedlosky, J.: 1996. Ocean Circulation Theory, Springer Verlag, Heidelberg, 438 pp.CrossRefGoogle Scholar
  4. Sacerdote, F. and Sansô, F.: 1987, ‘Further Remarks on the Altimetry-Gravimetry Problems’, Bull. Geod. 61, 65–82.CrossRefGoogle Scholar
  5. Sacerdote, F. and Sansô, F.: 2001, “IVn: A story of the height datum problem’, in Festschrift W. forge, Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover 241, 49–56.Google Scholar
  6. Svensson. L.: 1985. ‘Some Remarks on the Altimetry-Gravimetry Problem’, Proc. of the I Hotine- Marussi Symposium on Math. Geodesy, 559–582.Google Scholar
  7. Svensson. L.: 1991, ‘The Boundary Equation Approach to the Geoid’, in (R. H, Rapp and F. S an su (eds.), Determination of the Geoid–Present and Future, [AG Symposia 106, Springer-Verlag, pp. 357–364.Google Scholar
  8. Wunsch. C.: 1993, ‘Physics of the Ocean Circulation’, in R. Rummel and F. Sansô (eds.). Satellite Altimetry in Geodesy and Oceanography, Lecture Notes in Earth Sciences 50. Springer-Verlag, pp. 9–98.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Fausto Sacerdote
    • 1
  • Fernando Sansò
    • 2
  1. 1.Dipartimento di Ingegneria CivileUniversità di FirenzeItaly
  2. 2.DIIAR - Facoltà di Ingegneria di ComoPolitecnico di MilanoItaly

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