Definition
A height system is a one-dimensional coordinate system used to express the metric distance (height) of a point or object above a reference surface (i.e. the zero-height surface) along a well-defined path. The metric distance is also known as vertical coordinate, elevation or altitude. Each height system has an associated vertical datum that defines the reference surface and provides a unique relationship between the zero-height level and the heights determined at the earth’s surface. Thus, any height system is basically composed of (1) a reference surface that materialises the zero-height level (vertical datum) and (2) a vertical coordinate or type of height. The realisation of the height system is given by a vertical network, i.e. a set of points whose heights are of the same type as defined in (2) and refer to the datum defined in (1).
Introduction
Geodetic reference systems are needed to describe the position (or motion) of a point (or object) on or near the earth’s...
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References and Reading
Angermann D, Gruber T, Gerstl M, Heinkelmann R, Hugentobler U, Sánchez L, Steigenberger P (2016) GGOS Bureau of Products and Standards: Inventory of standards and conventions used for the generation of IAG products. The Geodesists’ Handbook 2016, Journal of Geodesy, 90(10), 1095-1156, https://doi.org/10.1007/s00190-016-0948-z
Angermann D, Gruber T, Gerstl M, Heinkelmann R, Hugentobler U, Sánchez L, Steigenberger P (2020) Bureau of Products and Standards: Inventory of standards and conventions used for the generation of IAG products. The Geodesists' Handbook 2020, Journal of Geodesy, 94(11), 221–292, https://doi.org/10.1007/s00190-020-01434-z
Balasubramania N (1994) Definition and realization of a global vertical datum. The Ohio State University, Department of Geodetic Science and Surveying, OSU Report No. 427. 112 pp.
Bjerhammar A (1985) On a relativistic geodesy. Bull Géod 59:207–220, https://doi.org/10.1007/BF02520327
Colombo OL (1980) A world vertical network. Report No. 296, Dept. of Geodetic Science and Surveying, The Ohio State University, Columbus.
Delva P, Denker H, Lion G (2019) Chronometric Geodesy: Methods and Applications. In: Puetzfeld D, Lämmerzahl C (Eds.) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_2
Denker H (2013) Regional gravity field modeling: Theory and practical results. In: Xu, G. (Ed.): Sciences of Geodesy – II: Innovations and Future Developments, p. 185-291, https://doi.org/10.1007/978-3-642-28000-9_5
Denker H, Timmen L, Voigt C et al. (2018) Geodetic methods to determine the relativistic redshift at the level of 10−18 in the context of international timescales: a review and practical results. J Geod 92, 487–516, https://doi.org/10.1007/s00190-017-1075-1
Drewes H, Kuglitsch F, Ádám J, Rózsa S (2016) Geodesist’s Handbook 2016, J Geod 90, 907, https://doi.org/10.1007/s00190-016-0948-z
Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model, Physics of the Earth and Planetary Interiors, 25(4): 297–356, https://doi.org/10.1016/0031-9201(81)90046-7
Ebbing J, Haas P, Ferraccioli F, et al. (2018) Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging, Sci Rep 8, 16356, https://doi.org/10.1038/s41598-018-34733-9
Foroughi I, Vaníček P, Sheng M, Kingdon RW, Santos MC (2017) In defense of the classical height system, Geophys J Int 211(2): 1154–1161, https://doi.org/10.1093/gji/ggx366
Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data, IAG Symposia, 104: 116-128, https://doi.org/10.1007/978-1-4684-7098-7_14.
Helmert FR (1890) Die Schwerkraft im Hochgebirge, Insbesondere in den Tyroler Alpen, Veröff. Königl. Preuss Geod Inst No. 1, Berlin.
Hofmann-Wellenhof B, Moritz H (2005) Physical Geodesy. Springer, New York
Ihde J, Sánchez L (2005) A unified global height reference system as a basis for IGGOS, J Geodyn 40: 400 – 413, https://doi.org/10.1016/j.jog.2005.06.015
Ihde J, Sánchez L, Barzaghi R, Drewes H, Foerste C, Gruber T, Liebsch G, Marti U, Pail R, Sideris M (2017) Definition and proposed realization of the International Height Reference System (IHRS). Surveys in Geophysics, 38(3), 549-570, https://doi.org/10.1007/s10712-017-9409-3
Khafid (1998) On the unification of Indonesian Local Heights, DGK, Reihe C, Heft 488, München
Kutterer H, Neilan R, Bianco G (2012) Global Geodetic Observing System (GGOS). In: Drewes H, Hornik H, Ádám J, Rózsa S (Eds.). The geodesist's handbook 2012. J Geod 86 (10): 915 – 926, https://doi.org/10.1007/s00190-012-0584-1
Leismann M, Klees R, Beckers, H. (1992) Untersuchungen verschiedener Höhensysteme, dargestellt an einer Testschleife in Reihnland-Pfalz. Deutsche Geodätische Kommission, Reihe B, Heft 296, München (In German)
Mäkinen J (2021) The permanent tide and the International Height Reference Frame IHRF, J Geod 95, 106, https://doi.org/10.1007/s00190-021-01541-5
Mehlstäubler TE, Grosche G, Lisdat C, Schmidt PO, Denker H (2018) Atomic clocks for geodesy, Rep. Prog. Phys. 81 064401, https://doi.org/10.1088/1361-6633/aab409
Molodensky MS, Yeremeev VF, Yurkina MI (1960) Methods for study of the external gravitational field and figure of the Earth. Trudy Ts NIIGAiK 131 Geodezizdat, Moscow, Russia (English translation by Israel Program for Scientific Translation, Jerusalem 1962)
Moritz H (2000) Geodetic Reference System 1980, J Geod 74: 128-133, https://doi.org/10.1007/s001900050278
Odera PA, Fukuda Y (2015) Comparison of Helmert and rigorous orthometric heights over Japan. Earth Planet Sp 67, 27, https://doi.org/10.1186/s40623-015-0194-2
Petit G, Luzum B Eds. (2010) IERS Conventions (2010). IERS Technical Note No. 36. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt a. M.
Rapp R (1983) The need and prospects for a world vertical datum, Proceedings of the International Association of Geodesy, IUGG General Assembly Hamburg. Vol. 2: 432 – 445.
Rapp R (1995) A world vertical datum proposal, Allgemeine Vermessungsnachrichten (AVN), 1028-9: 297 – 204.
Rapp R, Balasubramania N (1992) A conceptual formulation of a world height system, The Ohio State University, Department of Geodetic Science and Surveying, OSU Report No. 421. 55 pp.
Rummel R (2001) Global Unification of Height Systems and GOCE, IAG Symposia 123:12-19, https://doi.org/10.1007/978-3-662-04827-6_3
Rummel R, Gruber T, Ihde J, Liebsch G, Rülke A, Schäfer U, Sideris M, Rangelova E, Woodworth P, Hughes C (2014) STSE-GOCE+, Height system unification with GOCE, Doc. No. GO-HSU-PL-002, Issue 1, 24-02-2014.
Rummel R, Ilk KH (1995) Height datum connection – the ocean part. Allgemeine Vermessungsnachrichten (AVN). 102 8-9: 321 – 296.
Rummel R, Teunissen P (1988) Height Datum Definition, Height Datum Connection and the Role of the Geodetic Boundary Value Problem. Bulletin Géodésique 62, 477–498, https://doi.org/10.1007/BF02520239
Sacerdote F, Sansò F (2004) Geodetic boundary-value problems and the height datum problem, IAG Symposia 127: 174.178, https://doi.org/10.1007/978-3-662-10735-5_23
Sacher M, Liebsch G (2020) EVRF2019 as new realization of EVRS, available at https://evrs.bkg.bund.de/SharedDocs/Downloads/EVRS/EN/Publications/EVRF2019_FinalReport.pdf?__blob=publicationFile&v=3, accessed on 2023-05-09
Sánchez L, Sideris MG (2017). Vertical datum unification for the International Height Reference System (IHRS). Geophysical Journal International, 209(2), 570-586, https://doi.org/10.1093/gji/ggx025
Sánchez L, Ågren J, Huang J, Wang YM, Mäkinen J, Pail R, Barzaghi R, Vergos GS, Ahlgren K, Liu Q (2021) Strategy for the realisation of the International Height Reference System (IHRS), J Geod, 95(3), https://doi.org/10.1007/s00190-021-01481-0
Sánchez L, Čunderlík R, Dayoub N, Mikula K, Minarechová Z, Šíma Z, Vatrt V, Vojtíšková M (2016) A conventional value for the geoid reference potential W0, J Geod, 90(9): 815-835, https://doi.org/10.1007/s00190-016-0913-x
Sansò F (2018) The Analysis of the Geodetic Boundary Value Problem: State and Perspectives. In: Freeden W, Nashed M (Eds) Handbook of Mathematical Geodesy. Geosystems Mathematics, Birkhäuser, Cham, https://doi.org/10.1007/978-3-319-57181-2_5
Sansò F, Sideris M (2017) Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions, Springer, Cham, https://doi.org/10.1007/978-3-319-46358-2
Santos MC, Vaniček P, Featherstone WE, Kingdon R, Ellmann A, Martin B-A, Kuhn M, Tenzer R (2006) The relation between rigorous and Helmert’s definitions of orthometric heights, J Geod 80: 691– 704, Springer, https://doi.org/10.1007/s00190-006-0086-0
Tenzer R, Vaniček P, Santos M, Featherstone WE, Kuhn M (2005a) The rigorous determination of orthometric heights, J Geod 79: 82 – 92, Springer, https://doi.org/10.1007/s00190-005-0445-2
Tenzer R, Vaníček P, Santos M, Featherstone WE, Kuhn M (2005b) Rigorous orthometric heights. J Geodesy 79:1432–1394. https://doi.org/10.1007/s001-005-0445-2
Torge W, Müller J (2012) Geodesy, Berlin, Boston: De Gruyter, https://doi.org/10.1515/9783110250008
Van Camp MF, Dos Santos P, Murböck M, Petit G, Müller J (2021), Lasers and ultracold atoms for a changing Earth, Eos, 102, https://doi.org/10.1029/2021EO210673
Van Onselen K (1997) Quality investigation of vertical datum connection, Delft University of Technology, DEOS Report No. 97.3. 98 pp.
WLS (2017) Updating the International Great Lakes Datum (IGLD) Vertical Control – Water Levels Subcommittee, Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data, September 2017, http://www.naref.org/igld/pubs/IGLD_Update_20170929_opt.pdf
Wziontek H, Bonvalot S, Falk R, Gabalda G, Mäkinen J, Pálinkás̆ V, Rülke A, Vitushkin L (2021) Status of the International Gravity Reference System and Frame. J Geod 95, 7, https://doi.org/10.1007/s00190-020-01438-9
Xu P, Rummel R (1991) A quality investigation of global vertical datum connection, Netherlands Geodetic Commission, Publications on Geodesy. N. 34.
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Sánchez, L. (2024). Height Systems. In: Sideris, M.G. (eds) Encyclopedia of Geodesy. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_49-1
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