Abstract
Vertical datum definition is identical with the choice of a potential (or height) value for the fundamental bench mark. Also the connection of two adjacent vertical datums poses no principal problem as long as the potential (or height) value of two bench marks of the two systems is known and they can be connected by levelling. Only the unification of large vertical datums and the connection of vertical datums separated by an ocean remains difficult.
Two vertical datums can be connected indirectly by means of a combination of precise geocentric positions of two points, as derived by space techniques, their potential (or height) value in the respective height datum and their geoid height difference. The latter requires the solution of the linear geodetic boundary value problem under the assumption that potential and gravity anomalies refer to a variety of height datums. The unknown off-sets between the various datums appear in the solution inside and outside the Stokes integral and can be estimated in a least squares adjustment, if geocentric positions, levelled heights and adequate gravity material are available for all datum zones. The problem can in principle also be solved involving only two datums, in case a precise global gravity field becomes available purely from satellite methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.E. ALBERDA: Report on the Adjustment of the United European Levelling Net and Related Computations, Netherlands Geodetic Commission, New Series, 1, 2, 1963.
W. BAARDA: A Connection Between Geometric and Gravimetric Geodesy, A First Sketch. NGC, New Series, 6, 4, 1979.
E.I. BALAZS: Local Mean Sea Level in Relation to Geodetic Levelling Along the United States Coastlines, National Geodetic Survey, Rockville, Md., 1973.
O.L. COLOMBO: A World Vertical Network, Dept. Geodetic Science, 296, The Ohio State University, Columbus, 1980.
O.L. COLOMBO: Levelling with the Help of Space Techniques, in proc. 3rd Int. Symp. on the North American Vertical Datum, National Geodetic Information Center, NOAA, Rockville, 1985.
Th. ENGELIS, R.H. RAPP: Global Ocean Circulation Pattern Based on SEASAT Altimeter Data and the GEM L2 Gravity Field, 18th General Assembly, IUGG, Hamburg, 1983.
I. FISCHER: Mean Sea Level and the Marine Geoid—An Analysis of Concepts, Marine Geodesy, 1, 1, 1978.
D.P. HAJELA: Accuracy Estimates of Gravity Potential Differences Between Western Europe and United States Through LAGEOS Satellite Laser Ranging Network, Dept. Geodetic Science, 345, The Ohio State University, Columbus, 1983.
W. HEISKANEN, H. MORITZ: Physical Geodesy, Freeman, San Francisco, 1967.
IAPSO Advisory Committee on Tides and Mean Sea Level: Changes in Relative Mean Sea Level, EOS Transactions, AGU, 66, 45, pp. 754–756, 1985.
J.J. KOK: The United European Levelling Network (UELN-73), Report on the Symp. IAG Subcommission for RETrig (ed.: K. Poder), pp. 106–116, Muenchen, 1985.
T. KRARUP: Letters on Molodenski's Problem, Communication to the members of IAG Special Study Group 4.31, Copenhagen 1971.
P. LASKOWSKI: The Effect of Vertical Datum Inconsistencies on the Determination of Gravity Related Quantities, Dept. Geodetic Science, 349, The Ohio State University, Columbus, 1983.
D. LELGEMANN: On the Definition of the Listing Geoid Taking into Consideration Different Height Systems, 3rd Int. Symp. Geodesy and Physics of the Earth, Potsdam, 1977.
R.S. MATHER: The Influence of Stationary Sea Surface Topography on Geodetic Considerations, in proc. Symp. Earth's Gravitational Field & Secular Variations in Position, pp. 585–599, Canberra, 1973.
H. MORITZ: Precise Gravimetric Geodesy, Dept. Geodetic Science, 219. The Ohio State University, Columbus, 1974.
R.H. RAPP, R. RUMMEL: Comparison of Doppler Derived Undulations with Gravimetric Undulations Considering the Zero-Order Undulation of the Geoid, proc. of Int. Geodetic Symposium Satellite Doppler Positioning, vol. 1, pp. 389–397, Las Cruces, 1976.
R.H. RAPP: The Need and Prospects for a World Vertical Datum, proc. of the IAG Symposia 18th General Assembly, IUGG, vol. 2, pp. 432–445, Hamburg, 1983.
R.H. RAPP, J. WHITCOMB, R. MITCHELL, P. VANICEK, O.W. Williams, B.D. TAPLEY, Report of the Vertical Datum Subcommittee of the Committee on Geodesy, Board on Earth Sciences, National Research Council, 1984.
R. RUMMEL, P. TEUNISSEN: A Connection Between Geometric and Gravimetric Geodesy—Some Remarks on the Role of the Gravity Field, in: Daar heb ik veertig jaar over nagedacht ..., vol. 2, pp. 602–622, Delft, 1982.
R. RUMMEL: From the Observational Model to Gravity Parameter Estimation, proc. Local Gravity Field Approximation (ed.: K.-P. Schwartz), pp. 67–106, Beijing, 1984.
R. RUMMEL, P. TEUNISSEN: Geodetic Boundary Value Problem and Linear Inference, Intern. Symp. Figure and Dynamics of the Earth, Moon and Planets, vol. 1, pp. 227–264, Prague, 1986.
D.E. SMITH, D.C. CHRISTODOULIDIS, R. KOLENKIEWICZ, P.J. DUNN, S.M. KLOSKO, M.H. TORRENCE, S. FRICKE, S. BLACKWELL: A Global Geodetic Reference Frame from LAEGOS Ranging, Journ. Geoph. Res., 90, B11, pp. 9221–9233, 1985.
D. SMITH, R. KOLENKIEWICZ, M.H. TORRENCE, P. DUNN Geophysical Parameters Obtained During a Decade of LAGEOS Tracking, Int. Symp. Figure and Dynamics of the Earth, Moon and Planets, vol. 1, pp. 73–84, Prague, 1986.
W. STURGES: Sea Level Slope Along Continental Boundaries, Journ. Geoph. Res., 79, pp. 825–830, 1974.
A. WAALEWIJN: Drie Eeuwen Normaal Amsterdams Peil, hoofddirectie van de waterstaat, 48, Den Haag, 1986.
J. ZEGER: Aufbau eines Neuen Höhensystems in Österreich, Allg. Vermessungs-Nachrichten, 8–9, pp. 299–310, 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rummel, R., Teunissen, P. Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull. Geodesique 62, 477–498 (1988). https://doi.org/10.1007/BF02520239
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02520239