Journal of Geodesy

, 85:791 | Cite as

GOCE gravitational gradients along the orbit

  • Johannes BoumanEmail author
  • Sophie Fiorot
  • Martin Fuchs
  • Thomas Gruber
  • Ernst Schrama
  • Christian Tscherning
  • Martin Veicherts
  • Pieter Visser
Original Article


GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is, the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V XX , V YY , V ZZ and V XZ are much more accurate than V XY and V YZ , and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed. We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V XX and V YY is approximately at the level of the requirement on the gravitational gradient trace, whereas the V ZZ error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients is good and that with this type of data valuable new gravity field information is obtained.


GOCE Gravitational gradients External calibration Tensor rotation 


  1. Arabelos D, Tscherning CC (1998) Calibration of satellite gradiometer data aided by ground gravity data. J Geod 72: 617–625CrossRefGoogle Scholar
  2. Bock H, Jäggi A, Meyer U, Visser P, van den IJssel J, van Helleputte T, Heinze M, Hugentobler U (2010) GPS derived orbits for the GOCE satellite. J Geod, GOCE special issue (submitted)Google Scholar
  3. Bouman J (2004) Quick-look outlier detection for GOCE gravity gradients. Newton’s Bull 2: 78–87Google Scholar
  4. Bouman J (2007) Alternative method for rotation to TRF. GO-TN-HPF-GS-0193, issue 1.0Google Scholar
  5. Bouman J, Koop R (2003) Error assessment of GOCE SGG data using along track interpolation. Adv Geosci 1: 27–32CrossRefGoogle Scholar
  6. Bouman J, Koop R, Tscherning C, Visser P (2004) Calibration of GOCE SGG data using high–low SST, terrestrial gravity data, and global gravity field models. J Geod 78: 124–137CrossRefGoogle Scholar
  7. Bouman J, Rispens S, Koop R (2007) GOCE gravity gradients for use in earth sciences. In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  8. Bouman J, Rispens S, Gruber T, Koop R, Schrama E, Visser P, Tscherning C, Veicherts M (2009) Preprocessing of gravity gradients at the GOCE high-level processing facility. J Geod 83: 659–678CrossRefGoogle Scholar
  9. Bouman J, Lamarre D, Rispens S, Stummer C (2010) Assessment and improvement of GOCE Level 1b data. J Geod, GOCE special issue (submitted)Google Scholar
  10. ESA (1999) Gravity field and steady-state ocean circulation mission. Reports for mission selection; the four candidate earth explorer core missions. ESA SP-1233(1)Google Scholar
  11. Förste C, Schmidt R, Stubenvoll R, Flechtner F, Meyer U, Koenig R, Neumayer H, Biancale R, Lemoine JM, Bruinsma S, Loyer S, Barthelmes F, Esselborn S (2007) The GeoForschungsZentrum Potsdam/Groupe de Recherche de Géodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C. J Geod. doi: 10.1007/s00190-007-0183-8
  12. Förste C, Flechtner F, Schmidt R, Stubenvoll R, Rothacher M, Kusche J, Neumayer H, Biancale R, Lemoine JM, Barthelmes F, Bruinsma S, Koenig R, Meyer U (2008) EIGEN-GL05C—a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. Geophys Res Abstr 10, EGU2008-A-03426, SRef-ID:1607-7962/gra/EGU2008-A-03426Google Scholar
  13. Förste C, Stubenvoll R, König R, Raimondo JC, Flechtner F, Barthelmes F, Kusche J, Dahle C, Neumayer H, Biancale R, Lemoine JM, Bruinsma S (2010) Evaluation of EGM2008 by comparison with other recent global gravity field models. Newton’s Bull 4: 18–25Google Scholar
  14. Frommknecht B, Lamarre D, Bigazzi A, Meloni M, Floberghagen R (2011) GOCE level 1b data processing. J Geod, GOCE special issue (submitted)Google Scholar
  15. Fuchs MJ, Bouman J (2011) Rotation of GOCE gravitational gradients to local frames. Geophys J Int (submitted)Google Scholar
  16. Gruber T, Rummel R, Abrikosov O, van Hees R (2007) GOCE level 2 product data handbook. GO-MA-HPF-GS-0110, issue 3.3Google Scholar
  17. Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform, In: Proceedings of the IEEE 66, vol 66(1), pp 51–83Google Scholar
  18. IERS (2008) International Earth Rotation Service. Last accessed 1 july 2008
  19. Koop R, Gruber T, Rummel R (2006) The status of the GOCE high-level processing facility, in 3rd GOCE User Workshop, 6–8 November 2006, Frascati, Italy, pp 199–205, ESA SP-627Google Scholar
  20. Lyard F, Lefevre F, Letellier T (2006) Modelling the global ocean tides: modern insights from FES2004. Ocean Dyn 56(5–6):394–415. doi: 10.1007/s10236-006-0086-x CrossRefGoogle Scholar
  21. Mayer-Gürr T, Kurtenbach E, Eicker A, ITG-Grace2010 (2010) Last accessed 15 April 2010
  22. Mayerhofer R, Pail R, Fecher T (2010) Quick-look gravity field solution as part of the GOCE quality assessment. In: Proceedings of the ESA Living Planet Symposium, 28 June–2 July 2010, Bergen, NorwayGoogle Scholar
  23. Migliaccio F, Reguzzoni M, Sansò F (2004) Space-wise approach to satellite gravity determination in the presence of coloured noise. J Geod 78: 304–313CrossRefGoogle Scholar
  24. Mikhailov V, Pajot G, Diament M, Price A (2007) Tensor deconvolution: a method to locate equivalent sources from full tensor gravity data. Geophysics 72(5): I61–I69CrossRefGoogle Scholar
  25. Müller J (2003) GOCE gradients in various reference frames and their accuracies. Adv Geosci 1: 33–38CrossRefGoogle Scholar
  26. Pail R, Plank G (2004) Gravity field processing strategy. Stud Geophys Geod 48: 289–309CrossRefGoogle Scholar
  27. Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod, GOCE special issue. doi: 10.1007/s00190-011-0467-x
  28. Pavlis DE, Poulouse S, McCarthy JJ (2006) GEODYN operations manual, Contract report. SGT Inc., Greenbelt, MDGoogle Scholar
  29. Pavlis DE, Holmes SA, Kenyon SC, Factor JK (2008) An Earth Gravitational Model to Degree 2160: EGM2008. In: Presented at EGU General Assembly 2008, Vienna, AustriaGoogle Scholar
  30. Pedersen LB, Rasmussen TM (1990) The gradient tensor of potential field anomalies: some implications on data collection and data processing of maps. Geophysics 55(12): 1558–1566CrossRefGoogle Scholar
  31. Standish EM, Newhall XX, Williams JG, Folkner WF (1995) JPL Planetary and Lunar Ephemerides, DE403/LE403, JPL IOM 314. 10–127Google Scholar
  32. Visser P, van den IJssel J, Koop R, Klees R (2001) Exploring gravity field determination from orbit perturbations of the European Gravity Mission GOCE. J. Geod. 75(2/3): 89–98CrossRefGoogle Scholar
  33. Visser P (2007) GOCE Gradiometer Validation by GPS. Adv. Space Res. 39(10): 1630–1637. doi: 10.1016/j.asr.2006.09.014 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Johannes Bouman
    • 1
    Email author
  • Sophie Fiorot
    • 2
  • Martin Fuchs
    • 1
  • Thomas Gruber
    • 3
  • Ernst Schrama
    • 4
  • Christian Tscherning
    • 5
  • Martin Veicherts
    • 5
  • Pieter Visser
    • 4
  1. 1.Deutsches Geodätisches Forschungsinstitut (DGFI)MunichGermany
  2. 2.SRON Netherlands Institute for Space ResearchUtrechtThe Netherlands
  3. 3.Institut für Astronomische und Physikalische Geodäsie (IAPG), TU MünchenMunichGermany
  4. 4.Delft Institute of Earth Observation and Space Systems (DEOS), TU DelftDelftThe Netherlands
  5. 5.Niels Bohr InstituteUniversity of CopenhagenCopenhagenDenmark

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