IAG 150 Years pp 305-311 | Cite as

Height System Unification Based on the Fixed GBVP Approach

Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 143)


In general, any national or regional height reference system is related to an individual vertical datum, defined by one or several tide gauges. The discrepancies of these local vertical datums cause height datum offsets in a range of about ±1–2 m at a global scale. For the purpose of height system unification, global geopotential models derived from homogeneous satellite data provide an important contribution. However, to achieve a unification of high precision, the use of local terrestrial gravity data in the framework of a Geodetic Boundary Value Problem (GBVP) is required. By solving the GBVP at GNSS/leveling benchmarks, the unknown height datum offsets can be estimated in a least squares adjustment. In contrast to previous studies, related to the scalar free GBVP based on gravity anomalies, this paper discusses the alternative use and benefit of the fixed GBVP. This modern formulation of the GBVP is related to gravity disturbances, using the surface of the Earth as boundary surface. In contrast to gravity anomalies, gravity disturbances are not affected by the discrepancies of the local height datum. Therefore, in comparison to a scalar free GBVP approach, the proposed method is not affected by indirect bias terms, which will simplify a height system unification. In this paper, the theory of the fixed GBVP approach is developed and formulas in spherical approximation are derived. Moreover, the method is validated using a closed loop simulation based on the global geopotential model EGM2008, showing mm-accuracy of the estimated height datum offsets.


Height system unification Geodetic boundary value problem (GBVP) Hotine’s integral formula 



The authors acknowledge the financial support provided by the German Research Foundation (DFG) under grant number HE1433/20-1. Furthermore, we would like to thank three anonymous reviewers as well as the associated editor and the Editor-in-Chief for their valuable comments, which helped to improve the manuscript.


  1. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geod 85(8):457–473. doi:10.1007/s00190-011-0444-4 CrossRefGoogle Scholar
  2. Colombo OL (1980) A world vertical network. Rep 296, Dep. of Geodetic Science, Ohio State University, Columbus, USAGoogle Scholar
  3. Featherstone WE (2013) Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral. J Geod 87(5):487–500. doi:10.1007/s00190-013-0612-9 CrossRefGoogle Scholar
  4. Forsberg R, Tscherning CC (1997) Topographic effects in gravity field modelling for BVP. In: IAG symposia, vol 65, pp 239–272. doi:10.1007/BFb0011707 Google Scholar
  5. Gatti A, Reguzzoni M, Venuti G (2013) The height datum problem and the role of satellite gravity models. J Geod 87(1):15–22. doi:10.1007/s00190-012-0574-3 CrossRefGoogle Scholar
  6. Gerlach C, Rummel R (2013) Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geod 87(1):57–67. doi:10.1007/s00190-012-0579-y CrossRefGoogle Scholar
  7. Gruber T, Gerlach C, Haagmans R (2012) Intercontinental height datum connection with GOCE and GPS-levelling data. J Geod Sci 2(4):270–280. doi:10.2478/v10156-012-0001-y Google Scholar
  8. Heck B (1990) An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull Géod 64(1):88–108. doi:10.1007/BF02530617 CrossRefGoogle Scholar
  9. Heck B (2004) Problems in the definition of vertical reference frames. In: IAG symposia, vol 127, pp 164–173. doi:10.1007/978-3-662-10735-5_22 Google Scholar
  10. Heck B (2011) A Brovar-type solution of the fixed geodetic boundary-value problem. Stud Geophys Geod 55(3):441–454. doi:10.1007/s11200-011-0025-2 CrossRefGoogle Scholar
  11. Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: IAG symposia, vol 104, pp 116–128. doi:10.1007/978-1-4684-7098-7_14 Google Scholar
  12. Heiskanen WA, Moritz H (1967) Physical geodesy. WH Freeman, San Francisco, USAGoogle Scholar
  13. Hotine M (1969) Mathematical geodesy. ESSA Monograph 2, US Dep. of Commerce, Washington, USAGoogle Scholar
  14. Ihde J, Sánchez L (2005) A unified global height reference system as a basis for IGGOS. J Geodyn 40(4–5):400–413. doi:10.1016/j.jog.2005.06.015 CrossRefGoogle Scholar
  15. Müßle M, Heck B, Seitz K, Grombein T (2014) On the effect of planar approximation in the geodetic boundary value problem. Stud Geophys Geod 58(4):536–555. doi:10.1007/s11200-013-0249-4 CrossRefGoogle Scholar
  16. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008. J Geophys Res 117, B04406. doi:10.1029/2011JB008916 CrossRefGoogle Scholar
  17. Rapp RH (1988) The need and prospects for a world vertical datum. In: IAG symposia, vol 2, pp 432–445Google Scholar
  18. Rülke A, Liebsch G, Sacher M, Schäfer U, Schirmer U, Ihde J (2012) Unification of European height system realizations. J Geod Sci 2(4):343–354. doi:10.2478/v10156-011-0048-1 Google Scholar
  19. Rummel R (2002) Global unification of height systems and GOCE. In: IAG symposia, vol 123, pp 13–20. doi:10.1007/978-3-662-04827-6_3 Google Scholar
  20. Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Géod 62(4):477–498. doi:10.1007/BF02520239 CrossRefGoogle Scholar
  21. Sánchez L (2009) Strategy to establish a global vertical reference system. In: IAG symposia, vol 134, pp 273–278. doi:10.1007/978-3-642-00860-3_42 Google Scholar
  22. Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149(3):768–775. doi:10.1046/j.1365-246X.2002.01680.x Google Scholar
  23. Schwarz HR (1989) Numerical analysis: a comprehensive introduction. Wiley, Chichester, UKGoogle Scholar
  24. Xu P (1992) A quality investigation of global vertical datum connection. Geophys J Int 110(2):361–370. doi:10.1111/j.1365-246X.1992.tb00880.x CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Geodetic Institute, Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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