Abstract
Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem.
Similar content being viewed by others
References
Andersen OB, Knudsen P (1998) Global marine gravity field from the ERS-1 and Geosat geodetic mission altimetry. J Geophys Res 103(C4): 8129–8137
Colombo OL (1980) A world vertical network. Tech. Rep. 296, Department of Geodetic Science and Surveying. Ohio State University, Columbus
Drinkwater MR, Floberghagen R, Haagmans R, Muzi D, Popescu A (2003) GOCE: ESA’s First Earth Explorer Core Mission. In: Beutler G et al (eds) Earth gravity field from Space—from sensors to Earth science. Space Sciences Series of ISSI, vol 17. Kluwer Academic Publishers, Dordrecht, pp 419–432
Forsberg R (2000) Draping of geoids to GPS observations, IGeS Geoid school, Johor, Malaysia. IGeS publications, Milan
Heck B (1989) A contribution to the scalar free boundary value problem of physical geodesy. Manuscripta Geodaetica 14(2): 87–99
Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco
Jekeli C (2000) Heights, the geopotential, and vertical datums. Tech. Rep. 459, Department of Civil and Environmental Engineering and Geodetic Science. Ohio State University, Columbus
Kotsakis C, Katsambalos K, Ampatzidis D (2012) Estimation of the zero-height geopotential level W L0 VD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands. J Geodesy 86(6):423–439
Krarup T (2006) Letters on Molodensky’s problem: III. A mathematical formulation of Molodensky’s problem. In: Borre K (ed) Mathematical foundation of geodesy: selected papers of Torben Krarup. Springer, Berlin
Lehmann R (2000) Altimetry-gravimetry problems with free vertical datum. J Geodesy 74(3–4): 327–334
Mayer-Gürr T (2006) Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. PhD thesis, Universitäts-und Landesbibliothek Bonn
Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010: the new GRACE gravity field release computed in Bonn. In: EGU General Assembly 2010, 2–7 May 2010, Vienna, Austria, vol 12, p 2446
Pail R, Goiginger H, Schuh WD, Höck E, Brockmann JM, Fecher T, Gruber T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D (2010) Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett 37(20): L20,314
Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayerhofer R, Kransbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geodesy 85(11): 819–843
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2160: EGM2008. In: EGU General Assembly 2008, 13–18 April 2008, Vienna, Austria
Rapp RH (1980) Precise definition of the geoid and its realization for vertical datum applications. In: Proceedings of the 2nd International Symposium on Problems Related to the Redefinition of the North American Vertical Geodetic Networks. Ottawa, Canada, pp 73–86
Rapp RH, Balasubramania N (1992) A conceptual formulation of a world height system. Tech. Rep. 421, Department of Geodetic Science and Surveying. Ohio State University, Columbus
Rummel R (2002) Global unification of height systems and GOCE. In: Sideris MG (ed) Gravity, Geoid and Geodynamics 2000, IAG Symposia, vol 123. Springer, Berlin, pp 13–20
Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bulletin Géodésique 62(4): 477–498
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, vol 132. Springer, Berlin, pp 119–125
Sansò F (1989) New estimates for the solution of Molodensky’s problem. Manuscripta Geodaetica 14(2): 68–76
Sansò F, Usai S (1995) Height datum and local geodetic datums in the theory of geodetic boundary value problems. Allgemeine Vermessung-Nachrichten (AVN) 102(8–9): 343–355
Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149(3): 768–775
Xu P, Rummel R (1991) A quality investigation of global vertical datum connection. Publications on Geodesy 34, Netherlands Geodetic Commission, Delft, The Netherlands. http://www.ncg.knaw.nl/Publicaties/Geodesy/pdf/34Xu.pdf
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gatti, A., Reguzzoni, M. & Venuti, G. The height datum problem and the role of satellite gravity models. J Geod 87, 15–22 (2013). https://doi.org/10.1007/s00190-012-0574-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-012-0574-3