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Acta Geodaetica et Geophysica

, Volume 48, Issue 2, pp 199–208 | Cite as

On the reliability and error calibration of some recent Earth’s gravity models of GOCE with respect to EGM08

  • M. EshaghEmail author
Article

Abstract

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission is dedicated to recover spherical harmonic coefficients of the Earth’s gravity field to degree and order of about 250 using its satellite gradiometric data. Since these data are contaminated with coloured noise, therefore, their inversion will not be straightforward. Unsuccessful modelling of this noise will lead to biases in the harmonic coefficients presented in the Earth’s gravity models (EGMs). In this study, five of the recent EGMs of GOCE such as two direct, two time-wise and one space-wise solution are used to degree and order 240 and their reliability is investigated with respect to EGM08 which is assumed as a reliable EGM. The detected unreliable coefficients and their errors are replaced by the corresponding ones from EGM08 as a combination strategy. A condition adjustment model is organised for each two corresponding coefficients of GOCE EGMs and EGM08; and errors of the GOCE EGMs are calibrated based on a scaling factor, obtained from a posteriori variance factor. When the factor is less than 2.5 it will be multiplied to the error otherwise the error of EGM08 coefficient will be considered as the calibrated one. At the end, a simple geoid estimator is presented which considers the EGMs and their errors and its outcomes are compared with the corresponding geoid heights derived from the Global Positioning System (GPS) and the levelling data (GPS/levelling data), over Fennoscandia. This comparison shows that some of the combined-calibrated GOCE EGMs are closer to the GPS/levelling data than the original ones.

Keywords

A posteriori variance factor GOCE GPS/levelling EGM08 Degree of resolution Signal and error spectra Geoid Scaling factor 

Notes

Acknowledgements

The author is thankful to the Swedish National Space Board (SNSB) for supporting projects 98/09:1 and 82/11. The Land Survey of Sweden (LMV) and Dr. Jonas Ågren are acknowledged for providing the GPS/levelling data of Sweden, gravity and topographic data of Fennoscandia. Dr. Mette Weber is appreciated for providing the GPS/levelling data of Denmark, Professor Dag Solheim for Norwegian ones and Dr. Veikko Saaranen for those of Finland. Dr-Ing. Christian Gerlach is appreciated for reading and commenting to the draft version of the paper.

References

  1. Abdalla A, Fashir HH, Ali A, Faihead D (2012) Validation of recent GOCE/GRACE geopotential models over Khartoum state-Sudan. J Geod Sci 2(2):88–97 Google Scholar
  2. Bruinsma SL, Marty JC, Balmino G, Biancale R, Foerste C, Abrikosov O, Neumayer H (2010) GOCE gravity field recovery by means of the direct numerical method. In: The ESA living planet symposium, 27th June–2nd July 2010, Bergen, Norway. See also: earth.esa.int/GOCE Google Scholar
  3. ESA (1999) Gravity field and steady-state ocean circulation mission, ESA SP-1233(1). Report for mission selection of the four candidate Earth explorer missions, ESA Publications Division, p 217, July 1999 Google Scholar
  4. Eshagh M (2010) Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation. Contrib Geophys Geod 40(1):1–30 CrossRefGoogle Scholar
  5. Eshagh M (2012) A strategy towards an EGM08-based geoid model of Fennoscandia. J Appl Geophys 58:53–59 CrossRefGoogle Scholar
  6. Fotopoulos G (2005) Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetrical geoid height data. J Geod 79:111–123 CrossRefGoogle Scholar
  7. Goiginger H, Höck E, Rieser D, Mayer-Gürr T, Maier A, Krauss S, Pail R, Fecher T, Gruber T, Brockmann JM, Krasbutter I, Schuh W-D, Jäggi A, Prange L, Hausleitner W, Baur O, Kusche J (2011) The combined satellite-only global gravity field model GOCO02S. In: The 2011 general assembly of the European geosciences union, Vienna, Austria, April 4–8, 2011 Google Scholar
  8. Gruber T, Visser PNAM, Ackermann C, Hosse M (2011) Validation of GOCE gravity models by means of orbit residuals and geoid comparisons. J Geod 85:845–860 CrossRefGoogle Scholar
  9. Guimaraes GN, Matos ACOC, Biltzkow D (2012) An evaluation of recent GOCE geopotential models in Brazil. J Geod Sci 2(2):144–155 Google Scholar
  10. Heiskanen W, Moritz H (1967) Physical geodesy. Freeman, San Francisco Google Scholar
  11. Hirt C, Gruber T, Featherstone WE (2011) Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights. J Geoid 85:723–740 CrossRefGoogle Scholar
  12. Janak J, Pitonak M (2011) Comparison and testing of GOCE global gravity models in central Europe. J Geod Sci 1(4):333–347 Google Scholar
  13. Kiamehr R, Eshagh M (2008) Estimating variance components of ellipsoidal, orthometric and geoidal heights through the GPS/leveling network in Iran. J Earth Space Phys 34(3):1–13 Google Scholar
  14. Mayer-Gürr T, Rieser D, Höck E, Brockmann JM, Schuh W-D, Krasbutter I, Kusche J, Maier A, Krauss S, Hausleitner W, Baur O, Jäggi A, Meyer U, Prange L, Pail R, Fecher T, Gruber T (2012) The new combined satellite only model GOCO03s, Abstract, GGHS2012, Venice (Poster) Google Scholar
  15. Migliaccio F, Reguzzoni M, Sanso F, Tscherning CC, 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 the ESA living planet symposium. ESA publication SP-686, ESA/ESTEC. ISBN: 978-92-9221-250-6 Google Scholar
  16. Pail R, Goiginger H, Schuh WD, Hoeck E, Brockmann JM, Fecher T, Gruber T, Mayer Guerr T, Kusche J, Jaeggi A, Rieser D (2010) Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett 37:L20314 CrossRefGoogle Scholar
  17. Pail R, Bruinsma S, Migliaccio F, Foerste C, Goiginger H, Schuh WD, Hoeck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veichert M, Fecher T, Mayrhofer R, Krasbutter I, Sanso F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843 CrossRefGoogle Scholar
  18. Pavlis N, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2160: EGM08. In: The 2008 general assembly of the European geosciences union, Vienna, Austria, April 13–18, 2008 Google Scholar
  19. Rao CR, Kleffe J (1988) Estimation of variance components and applications. North-Holland, Amsterdam Google Scholar
  20. Reguzzoni M, Tselfes N (2009) Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J Geod 83:13–29 CrossRefGoogle Scholar
  21. Sjöberg LE (1980) Least squares combination of satellite harmonics and integral formulas in physical geodesy. Gerlands Beitr Geophys 89:371–377 Google Scholar
  22. Sjöberg LE (1981) Least squares combination of satellite and terrestrial data in physical geodesy. Ann Geophys 37:25–30 Google Scholar
  23. Sjöberg LE (1987) The estimation of the power spectrum and reliability of models of the Earth’s gravity field by intercomparison of independent models. Manuscr Geod 12:104–112 Google Scholar
  24. Sprlak M, Gerlach C, Pettersen BR (2012) Validation of GOCE global gravity field models using terrestrial gravity data in Norway. J Geod Sci 2(2):134–143 Google Scholar
  25. Tapley B, Ries J, Bettadpur S, Chambers D, Cheng M, Condi F, Gunter B, Kang Z, Nagel P, Pastor R, Pekker T, Poole S, Wang F (2005) GGM02-an improved Earth gravity field model from GRACE. J Geod 79:467–478 CrossRefGoogle Scholar
  26. Wanger CA, McAdoo DC (2012) Error calibration of geopotential harmonics of recent and past gravitational fields. J Geod 86:99–108 CrossRefGoogle Scholar
  27. Wenzel HG (1981) Zur Geoidbestimmung durch kombination von Schwereanomalien und einem Kugelfunktionsmodell mit hilfe von Integralformeln. ZfV 106(3):102–111 Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of Engineering ScienceUniversity WestTrollhättanSweden
  2. 2.Division of Geodesy and GeoinformaticsRoyal Institute of Technology (KTH)StockholmSweden

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