Studia Geophysica et Geodaetica

, Volume 60, Issue 4, pp 622–643 | Cite as

RTM-based omission error corrections for global geopotential models: Case study in Central Europe

  • Zuzana ĎuríčkováEmail author
  • Juraj Janák


The aim of this paper is to evaluate the effects of residual terrain model (RTM) on potential and on gravity and to point out how significant can the omission error of global geopotential models (GGMs) be and how it can influence their testing. The RTM for Central Europe is computed in the spherical approximation. The topography is modelled by spherical tesseroids and the gravitational effect of the topography is obtained as a sum of their partial gravitational effects. A detailed picture of RTM in Slovakia is shown. The testing of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) global geopotential models in Central Europe published earlier is re-evaluated with the more rigorous omission error estimation. Experimental results show significantly better agreement between the gravity anomalies computed from global geopotential models with the omission-error estimation and gravity anomalies obtained from the direct measurements. On the other hand, for height anomalies such an improvement is not observed. The results are discussed in context of the other previously published studies.


residual terrain model topographic effects gravity anomaly height anomaly GOCE 


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  1. Altamimi Z., Collilieux X., Legrand J., Garayt B. and Boucher C., 2007. ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters. J. Geophys. Res., 112, B09401, DOI: 10.1029/2007JB004949.CrossRefGoogle Scholar
  2. Boucher C. and Altamimi Z., 1992. The EUREF terrestrial reference system and its first realizations. Veröffentlichungen der Bayerischen Kommission für die Internationale Erdmessung, 52, 205–213, München, Germany.Google Scholar
  3. Bruinsma S.L., Marty J.C. and Balmino G., 2004. Numerical simulation of the gravity field recovery from GOCE mission data. In: Proceedings of the 2nd International GOCE User Workshop. ESA SP-569, European Space Agency, Noordwijk, The Netherlands, ISBN 92-9092-880-8 ( Scholar
  4. Bruinsma S.L., Marty J.C., Balmino G., Biancale R., Förste C., Abrikosov O. and Neumeyer H., 2010. GOCE gravity field recovery by means of the direct numerical method. In: Lacoste-Francis H. (Ed.), Proceedings of ESA Living Planet Symposium. ESA SP-686, European Space Agency, Noordwijk, The Netherlands, ISBN 978-92-9221-250-6.Google Scholar
  5. Bruinsma S.L., Foerste C., Abrikosov O., Marty J.C., Rio M.H., Mulet S. and Bonvalot S., 2013. The new ESA satellite-only gravity field model via the direct approach. Geophys. Res. Lett., 40, 3607–3612, DOI: 10.1002/grl.50716.CrossRefGoogle Scholar
  6. Bucha B. and Janák J., 2013. A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders. Comput. Geosci., 56, 186–196, DOI: 10.1016/j.cageo.2013.03.012.CrossRefGoogle Scholar
  7. Farr T.G., Rosen P.A., Caro E., Crippen R., Duren R., Hensley S., Kobrick M., Paller M., Rodriguez E., Roth L., Seal D., Shaffer S., Shimada J., Umland J., Werner M., Oskin M., Burbank D. and Alsdorf D., 2007. The shuttle radar topography mission. Rev. Geophys., 45, RG2004, DOI: 10.1029/2005RG000183.CrossRefGoogle Scholar
  8. Forsberg R., 1984. A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity field Modelling. Report 355. Department of Geodetic Science and Surveying, Ohio State University, Columbus, OH.Google Scholar
  9. Forsberg R., 1994. Terrain Effects in Geoid Computations. Lecture Notes for the International School for the Determination and Use of the Geoid. IGeS-DIIAR - Politecnico di Milano, Milano, Italy.Google Scholar
  10. Förste C., Bruinsma S.L., Abrikosov O., Lemoine J.M., Marty J.C., Flechtner F., Balmino G., Barthelmes F. and Biancale R., 2014. EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services ( Scholar
  11. Grombein T., Seitz K. and Heck B., 2013. Optimized formulas for the gravitational field of a tesseroid. J. Geodesy, 87, 645–660, DOI: 10.1007/s00190-013-0636-1.CrossRefGoogle Scholar
  12. Heck B., 2003. On Helmert’s methods of condensation. J. Geodesy, 77, 155–170.CrossRefGoogle Scholar
  13. Heck B. and Seitz K., 2007. A comparison of the tesseroid, prism and point mass approaches for mass reductions in gravity field modelling. J. Geodesy, 81, 121–136.CrossRefGoogle Scholar
  14. Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. Freeman, San Francisco, CA.Google Scholar
  15. Hirt C., Kuhn M., Claessens S., Pail R., Seitz K. and Gruber T., 2014. Study of the Earth's shortscale gravity field using the ERTM2160 gravity model. Comput. Geosci., 73, 71–80, DOI: 10.1016/j.cageo.2014.09.00.CrossRefGoogle Scholar
  16. Hirt C., Claessens S., Fecher T., Kuhn M., Pail R. and Rexer M., 2013. New ultra-high resolution picture of Earth’s gravity field. Geophys. Res. Lett., 40, 1–5. DOI: 10.1002/grl.50838.CrossRefGoogle Scholar
  17. Hirt C., 2013. RTM gravity forward-modeling using topography/bathymetry data to improve highdegree global geopotential models in the coastal zone. Mar. Geod., 36, 183–202. DOI: 10.1080/01490419.2013779334.CrossRefGoogle Scholar
  18. Hirt C., Featherstone W. E. and Marti U., 2010. Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data. J. Geodesy, 84, 557–567.CrossRefGoogle Scholar
  19. Janák J. and Pitonák M., 2011. Comparison and testing of GOCE global gravity models in Central Europe. J. Geod.c Sci., 1, 333–347.Google Scholar
  20. Kadlec M., 2011. Refining Gravity Field Parameters by Residual Terrain Modelling. Ph.D. Thesis. University of West Bohemia, Pilsen, Czech Republic.Google Scholar
  21. Kaula W.M., 1959. Statistical and harmonic analysis of gravity. J. Geophys. Res., 64, 2401–2421.CrossRefGoogle Scholar
  22. Klobušiak M. and Pecár J., 2004. Model and algorithm of effective processing of gravity measurements performed with a group of absolute and relative gravimeters. Geodetický a kartografický obzor, 50(92), 99–110 (in Slovak).Google Scholar
  23. Mader K., 1951. Das Newtonsche Raumpotential prismatischer Körper und seine Ableitungen bis zur dritten Ordnung. Österreichische Zeitschrift für Vermessungswesen, Sonderheft 11 (in German).Google Scholar
  24. Martinec Z., 1998. Boundary Value Problems for Gravimetric Determination of a Precise Geoid. Lecture Notes in Earth Sciences, 73. Springer-Verlag, Berlin, Germany.Google Scholar
  25. Martinec Z. and Vanícek S., 1994. The indirect effect of topography in the Stokes-Helmert technique for a spherical approximation of the geoid. Manuscr. Geod., 19, 213–219.Google Scholar
  26. Migliaccio F., Reguzzoni M., Sansó F., Tscherning C.C. and Veicherts M., 2010. GOCE data analysis: the space-wise approach and the first space-wise gravity field model. In: Lacoste-Francis H. (Ed.), Proceedings of ESA Living Planet Symposium. ESA SP-686, European Space Agency, Noordwijk, The Netherlands, ISBN 978-92-9221-250-6 ( Scholar
  27. Migliaccio F., Reguzzoni M., Gatti A., Sanso F. and Herceg M., 2011. A GOCE-only global gravity field model by the space-wise approach. In: Proceedings of the 4th International GOCE User Workshop. ESA SP-696, European Space Agency, Noordwijk, The Netherlands, ISBN 978- 92-9092-260-5.Google Scholar
  28. Mikuška J., Pašteka R. and Marušiak I., 2006. Estimation of distant relief effect in gravimetry. Geophysics, 71, J59–J69.CrossRefGoogle Scholar
  29. Nagy D., 1966. The gravitational attraction of a right rectangular prism. Geophysics, 31, 362–371.CrossRefGoogle Scholar
  30. Nagy D., Papp G. and Benedek J., 2000. The gravitational potential and its derivatives for the prism. J. Geodesy, 74, 552–560, DOI: 10.1007/s001900000116.CrossRefGoogle Scholar
  31. Nagy D., Papp G. and Benedek J., 2002. Corrections to “The gravitational potential and its derivatives for the prism”. J. Geodesy, 76, 475, DOI: 10.1007/s00190-002-0264-7).CrossRefGoogle Scholar
  32. Novák P., Vanícek P., Martinec Z. and Véronneau M., 2001. Effects of the spherical terrain on gravity and the geoid. J. Geodesy, 75, 491–504, DOI: 10.1007/s001900100201.CrossRefGoogle Scholar
  33. Omang O.C., Tscherning C.C. and Forsberg R., 2012. Generalizing the harmonic reduction procedure in residual topographic modeling. In: Sneeuw N., Novák P., Crespiand, Sansò (Eds.), Proceedings of the VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, 137, 233–238. Springer-Verlag, Heidelberg, Germany.CrossRefGoogle Scholar
  34. Pail R., Goiginger H., Mayrhofer R., Schuh W.-D., Brockmann J.M., Krasbutter I., Höck E. and Fecher T., 2010. GOCE global gravity field model derived from orbit and gradiometry data applying the time-wise method. In: Lacoste-Francis H. (Ed.), Proceedings of ESA Living Planet Symposium. ESA SP-686, European Space Agency, Noordwijk, The Netherlands, ISBN 978-92-9221-250-6 ( Scholar
  35. Pail R., Bruinsma S.L., Migliaccio F., Foerste C., Goiginger H., Schuh W.D, Hoeck E, Reguzzoni M., Brockmann J.M, Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sanso F. and Tscherning C.C., 2011. First GOCE gravity field models derived by three different approaches. J. Geodesy, 85, 819–843, DOI: 10.1007/s00190-011-0467-x.CrossRefGoogle Scholar
  36. Pavlis N.K., Factor J.K. and Holmes S.A., 2007. Terrain-related gravimetric quantities computed for the next EGM. Proceedings of the 1st International Symposium of the International Gravity Field Service “Gravity field of the Earth”. Harita Dergisi, Special Issue 18, General Command of Mapping, Istanbul, Turkey, 318–323 ( Scholar
  37. Pavlis N.K., Holmes S.A., Kenyon S.C. and Factor J.K., 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res., 117, B04406, DOI: 10.1029/2011JB008916CrossRefGoogle Scholar
  38. Rülke A., Liebsch G., Sacher M., Schäfer U., Schirmer U. and Ihde J., 2012. Unification of European height system realizations. J. Geod. Sci., 2, 343–354, DOI: 10.2478/v10156-011-0048-1.Google Scholar
  39. Tsoulis D., 1999. Analytical and Numerical Methods in Gravity Feld Modelling of Ideal and Real Masses. Deutsche Geodätische Kommission, Reihe C, Heft Nr 510, München, Germany.Google Scholar
  40. Vanícek P., Tenzer R., Sjöberg L.E., Martinec Z. and Featherstone W.E., 2004. New views of the spherical Bouguer gravity anomaly. Geophys. J. Int., 159, 460–472.CrossRefGoogle Scholar
  41. Vykutil J., 1959. Computation of gravity corrections to levelling in Baltic vertical datum. Geodetický a kartografický obzor, 5(47), 145–149 (in Czech).Google Scholar
  42. Wild-Pfeiffer F., 2007. Auswirkungen topographisch-isostatischer Massen auf die Satellitengradiometrie. Deutsche Geodätische Kommission, C604, München, Germany (in German).Google Scholar
  43. Wild-Pfeiffer F., 2008. A comparison of different mass elements for use in gravity gradiometry. J. Geodesy, 82, 637–653, DOI: 10.1007/s00190-008-0219-8.CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2016

Authors and Affiliations

  1. 1.Department of Theoretical Geodesy, Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovakia

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