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The Height Datum Problem

  • Fernando SansòEmail author
  • Mirko Reguzzoni
  • Riccardo Barzaghi
Chapter
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)

Abstract

Normal and orthometric heights are among the most widespread height coordinate systems in use for geodetic purposes. Yet in principle they can be determined only by ground gravimetric measurements combined with levelling so that \(W\left( \text {P}\right) \) becomes available. Nevertheless, what the above measurements can really provide are at most potential differences, \(W\left( \text {P}_0\right) -W\left( \text {P}\right) \), for instance with respect to an origin point \(\text {P}_0\) of which however the absolute value \(W\left( \text {P}_0\right) \) is unknown. When \(\text {P}_0\) is a tide gauge, we know that we can assume \(W\left( \text {P}_0\right) \sim W_0\) with an error \(\delta W_0\) such that \(\displaystyle {\left| \frac{\delta W_0}{\gamma }\right| < 2\,\text {m}}\) (cfr. Sect. 4.6); when \(\text {P}_0\) is a point of known ellipsoidal height, e.g. a GNSS permanent station, we can always assume that \(h^* \cong \widetilde{h}^* = h - \displaystyle {\frac{T_b}{\gamma }}\), where \(T_b\) is some global model that has been computed with biases and so it has an error which however is almost surely included in the above range.

References

  1. Abramowitz M., Stegun I.A. (1964). Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York.Google Scholar
  2. Barzaghi R., Carrion D., Reguzzoni M., Venuti G. (2016). A feasibility study on the unification of the Italian height systems using GNSS-leveling data and global satellite gravity models. In: Rizos C., Willis P. (eds), IAG 150 Years, International Association of Geodesy Symposia, 143:281–288, Springer, Cham.Google Scholar
  3. Betti B., Carrion D., Sacerdote F., Venuti G. (2016). The observation equation of spirit leveling in Molodensky’s context. In: Sneeuw N., Novàk P., Crespi M., Sansò F. (eds), VIII Hotine-Marussi Symposium on Mathematical Geodesy, International Association of Geodesy Symposia, 142:213–219. Springer, Cham.Google Scholar
  4. Gatti A., Reguzzoni M., Venuti G. (2013). The height datum problem and the role of satellite gravity models. Journal of Geodesy, 87(1):15–22.CrossRefGoogle Scholar
  5. Gerlach C., Fecher T. (2012). Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets. Journal of Geodetic Science, 2(4):247–256.Google Scholar
  6. Gilardoni M., Reguzzoni M., Sampietro D., Sansò F. (2013). Combining EGM2008 with GOCE gravity models. Bollettino di Geofisica Teorica ed Applicata, 54(4):285–302.Google Scholar
  7. Gilardoni M., Reguzzoni M., Sampietro D. (2016). GECO: a global gravity model by locally combining GOCE data and EGM2008. Studia Geophysica et Geodaetica, 60(2):228–247.CrossRefGoogle Scholar
  8. Hirt C., Kuhn M. (2012). Evaluation of high-degree series expansions of the topographic potential to higher-order powers, Journal of Geophysical Research: Solid Earth, 117, B12407.CrossRefGoogle Scholar
  9. Mayer-Gürr, T., Rieser D., Höck E., Brockmann J.M., Schuh W-D., Krasbutter I., Kusche J., Maier S., Krauss S., Hausleitner W., Baur O., Jäggi A., Meyer U., Prange L., Pail R., Fechner T., Gruber, T. (2012). The new combined satellite only model GOCO03s. Presentation at International Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, Italy.Google Scholar
  10. Mayer-Gürr T., Pail R., Gruber T., Fecher T., Rexer M., Schuh W.-D., Kusche J., Brockmann J.-M., Rieser D., Zehentner N., Kvas A., Klinger B., Baur O., Höck E., Krauss S., Jäggi A. (2015). The combined satellite gravity field model GOCO05s. Presentation at EGU 2015, Vienna, Austria.Google Scholar
  11. Pail R., Goiginger H., Schuh W.-D., Höck E., Brockmann J.M., 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. Geophysical Research Letters, 37(20):L20314.CrossRefGoogle Scholar
  12. Pail R., Bruinsma S., Migliaccio F., Förste C., Goiginger H., Schuh W.-D., Höck E., Reguzzoni M., Brockmann J.M., Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sansò F., Tscherning C.C. (2011). First GOCE gravity field models derived by three different approaches. Journal of Geodesy, 85(11):819–843.CrossRefGoogle Scholar
  13. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117(B4):B04406.CrossRefGoogle Scholar
  14. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. (2013). Correction to “The development and valuation of the Earth Gravitational Model 2008 (EGM2008)”. Journal of Geophysical Research: Solid Earth, 118(5):2633.Google Scholar
  15. Rapp, R.H. (1989). Combination of Satellite, Altimetric and Terrestrial Gravity Data. In: Sansò F., Rummel R. (Eds.), Theory of Satellite Geodesy and Gravity Field Determination, Lecture Notes in Earth Sciences, 25. Springer-Verlag, Berlin, Heidelberg, pp. 261–284.Google Scholar
  16. Reguzzoni M., Sansò F. (2012). On the combination of high-resolution and satellite-only global gravity models. Journal of Geodesy, 86(6):393–408.CrossRefGoogle Scholar
  17. Reguzzoni M., Venuti G. (2018). Local versus global height datum adjustment. Presentation at the IX Hotine-Marussi Symposium, Rome, June 2018.Google Scholar
  18. Reguzzoni M., Venuti G., de Lacy M.C., Carrion D., Barzaghi R., Borque M.J., Gil A.J., Vaquero P.A. (2018). The use of GNSS/levelling and gravity data for the Spanish height system unification. In: Vergos G.S., Pail R., Barzaghi R. (eds), International Symposium on Gravity, Geoid and Height Systems 2016, International Association of Geodesy Symposia, 148, Springer, Cham.Google Scholar
  19. Reigber C., Jochmann H., Wünsch J., Petrovic S., Schwintzer P., Barthelmes F., Neumayer K.-H., König R., Förste C., Balmino G., Biancale R., Lemoine J.-M., Loyer S., Perosanz F. (2004). Earth Gravity Field and Seasonal Variability from CHAMP. In: Reigber C., Lühr H., Schwintzer P., Wickert J. (Eds.), Earth Observation with CHAMP-Results from Three Years in Orbit. Springer, Berlin, Heidelberg, pp. 25–30.Google Scholar
  20. Sansò F., Sideris M.G. (2013). Geoid determination: Theory and methods. Lecture Notes in Earth System Sciences, Vol. 110. Springer-Verlag, Berlin, Heidelberg.Google Scholar
  21. Tapley B.D., Bettadpur S., Watkins M., Reigber C. (2004). The gravity recovery and climate experiment: Mission overview and early results. Geophysical Research Letters, 31(9):L09607.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fernando Sansò
    • 1
    Email author
  • Mirko Reguzzoni
    • 1
  • Riccardo Barzaghi
    • 1
  1. 1.Department of Civil and Environmental Engineering (DICA)Politecnico di MilanoMilanItaly

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