Journal of Geodesy

, Volume 83, Issue 7, pp 659–678 | Cite as

Preprocessing of gravity gradients at the GOCE high-level processing facility

  • Johannes BoumanEmail author
  • Sietse Rispens
  • Thomas Gruber
  • Radboud Koop
  • Ernst Schrama
  • Pieter Visser
  • Carl Christian Tscherning
  • Martin Veicherts
Open Access
Original Article


One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10−3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10−2 level with this method.


GOCE High-level processing facility Gravity gradients Preprocessing Calibration 



This study was performed in the framework of the European Space Agency project (No. 18308/04/NL/MM): GOCE High-level Processing Facility.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. Abrikosov O, Jarecki F, Müller J, Petrovic S, Schwintzer P (2006) The impact of temporal gravity variations on GOCE gravity field recovery. In: Flury J, Rummel R, Reigber C, Rothacher M, Boedecker G, Schreiber U (eds) Observation of the Earh system from space. Springer, Heidelberg, pp 255–269CrossRefGoogle Scholar
  2. Albertella A, Migliaccio F, Sansò F, Tscherning C (2000) The space-wise approach—overall scientific data strategy. In: Sünkel H (ed) From Eötvös to mGal, Final report. ESA/ESTEC contract no. 13392/98/NL/GDGoogle Scholar
  3. Arabelos D, Tscherning C (1998) Calibration of satellite gradiometer data aided by ground gravity data. J Geod 72: 617–625CrossRefGoogle Scholar
  4. Bouman J (2004) Quick-look outlier detection for GOCE gravity gradients. Newton’s Bull 2: 78–87Google Scholar
  5. Bouman J, Koop R (2003a) Calibration of GOCE SGG data combining terrestrial gravity data and global gravity field models. In: Tziavos I (ed) Gravity and geoid 2002; 3rd meeting of the IGGC Ziti editions, pp 275–280Google Scholar
  6. Bouman J, Koop R (2003b) Error assessment of GOCE SGG data using along track interpolation. Adv Geosci 1: 27–32CrossRefGoogle Scholar
  7. 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
  8. Bouman J, Kern M, Koop R, Pail R, Haagmans R, Preimesberger T (2005) Comparison of outlier detection algorithms for GOCE gravity gradients. In: Jekeli C, Bastos L, Fernandes J (eds) Gravity, geoid and space missions, vol 129, International Association of Geodesy Symposia. Springer, Heidelberg, pp 83–88Google Scholar
  9. 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
  10. Catastini G, Cesare S, Sanctis SD, Dumontel M, Parisch M, Sechi G (2007) Predictions of the GOCE in-flight performances with the end-to-end system simulator. In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  11. Cesare S (2005) Performance requirements and budgets for the gradiometric mission. Issue 3 GO-TN-AI-0027, Alenia Spazio, TurinGoogle Scholar
  12. Cesare S, Catastini G (2005) Gradiometer on-orbit calibration procedure analysis. Issue 3 GO-TN-AI-0069, Alenia Spazio, TurinGoogle Scholar
  13. Cesare S, Sechi G (2005) Gradiometer ground processing algorithms documentation. Issue 6 GO-TN-AI-0067, Alenia Spazio, TurinGoogle Scholar
  14. Dobslaw H, Thomas M (2007) Simulation and observation of global ocean mass anomalies. J Geophys Res 112:(C05040). doi: 10.1029/2006JC004035
  15. Drijfhout S, Heinze C, Latif M, Maier-Reimer E (1996) Mean circulation and internal variability in an ocean primitive equation model. J Phys Oceanogr 26: 559–580CrossRefGoogle Scholar
  16. ECMWF (2007). IFS documentation. CY31r1 operational implementation, Part 1–7.
  17. 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
  18. Eshagh M, Sjöberg L (2008) Topographic and atmospheric efects of GOCE gradiometric data in a local north-oriented frame: a case study in Fennoscandia and Iran. Studia Geophysica et Geodaetica (accepted)Google Scholar
  19. Farrell W (1972) Deformation of the earth by surface loads. Rev Geophys Space Phys 10: 761–797CrossRefGoogle Scholar
  20. Flechtner F (2007) AOD1B product description document for product release 01 to 04. Document GRACE, issue 3.1, pp 327–750Google Scholar
  21. Foerste C, Schmidt R, Stubenvoll R, Flechtner F, Meyer U, Koenig R, Neumayer H, Biancale R, Lemoine J-M, 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
  22. González J, Canales A, Acarreta J, López-Hazas E, de Candia D, Salzo S, Floberghagen R (2007) The GOCE calibration and monitoring facility (CMF). In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  23. Gruber T, Rummel R (2006) Concept and capability of GOCE. In: Proceedings of the GOCINA workshop, vol 25. Cahiers du Centre Europeen de Geodynamique et de Seismologie, pp 31–37Google Scholar
  24. Gruber T, Rummel R, Abrikosov O, van Hees R (2007a) GOCE level 2 product data handbook. GO-MA-HPF-GS-0110, issue 3.3Google Scholar
  25. Gruber T, Rummel R, Koop R (2007b) How to use GOCE level 2 products. In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  26. Hoaglin D, Mosteller F, Tukey J (1983) Understanding robust and exploratory data analysis. Wiley, New YorkGoogle Scholar
  27. IERS Conventions (2004) IERS technical note no. 32. Technical report, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main. Available at
  28. Jarecki F, Müller J (2007) GOCE gradiometer validation in satellite track cross-overs. In: Kilicoglu A, Forsberg R (eds) Gravity field of the Earth, vol 73. of Harita Dergisi. Harita Genel Komutanligi, Ankara. Proceedings of the 1st international symposium of the gravity field service, pp 223–228Google Scholar
  29. Jarecki F, Wolf K, Denker H, Müller J (2006) Quality assessment of GOCE gradients. In: Flury J, Rummel R, Reigber C, Rothacher M, Boedecker G, Schreiber U (eds) Observation of the Earh System from Space. Springer, Heidelberg, pp 271–285CrossRefGoogle Scholar
  30. Kern M, Preimesberger T, Allesch M, Pail R, Bouman J, Koop R (2005) Outlier detection algorithms and their performance in GOCE gravity field processing. J Geod 78: 509–519CrossRefGoogle Scholar
  31. Koop R, Bouman J, Schrama E, Visser P (2002) Calibration and error assessment of GOCE data. In: Ádám J, Schwarz K-P (eds) Vistas for geodesy in the new millenium, vol 125, International Association of Geodesy Symposia. Springer, Heidelberg, pp 167–174Google Scholar
  32. Koop R, Gruber T, Rummel R (2007) The status of the GOCE high-level processing facility. In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  33. Lambeck K (1988) Geophysical geodesy, the slow deformations of the earth. Clarendon Press, OxfordGoogle Scholar
  34. Lemoine F, Kenyon S, Factor J, Trimmer R, Pavlis N, Chinn D, Cox C, Klosko S, Luthcke S, Torrence M, Wang Y, Williamson R, Pavlis E, Rapp R, Olson T (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. TP 1998-206861, NASA Goddard Space Flight CenterGoogle Scholar
  35. Li Y (2001) 3-D inversion of gravity gradiometer data. Electrical and magnetic studies, Department Geophysics, Colorado School of MinesGoogle Scholar
  36. Migliaccio F, Reguzzoni M, Sansò F (2004) Space-wise approach to satellite gravity field determination in the presence of coloured noise. J Geod 78: 304–313CrossRefGoogle Scholar
  37. Moritz H (1980) Advanced physical geodesy. Wichmann, KarlsruheGoogle Scholar
  38. Overhauser A (1968) Analytic definition of curves and surfaces by parabolic blending. Techn. report no. SL68-40, Scientific Research Staff Publication, Ford Motor Company, DetroitGoogle Scholar
  39. Pail R (2004) GOCE quick-look gravity field analysis: treatment of gravity gradients defined in the gradiometer reference frame. In: Proceedings of the 2nd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 8–10 March 2004, ESA SP-569Google Scholar
  40. Pail R (2005) A parametric study on the impact of satellite attitude errors on GOCE gravity field recovery. J Geod 79: 231–241CrossRefGoogle Scholar
  41. Pail R, Plank G (2004) Gravity field processing strategy. Stud Geophys Geod 48: 289–309CrossRefGoogle Scholar
  42. Pawlowski B (1998) Gravity gradiometry in resource exploration. Leading Edge 17: 51–52CrossRefGoogle Scholar
  43. Rowlands D, Marshall J, McCarthy J, Moore D, Pavlis D, Rowton S, Luthcke S, Tsaoussi L (1995) Geodyn ii system description. Contractor report vols 1–5. Hughes STX Corp., Greenbelt, MDGoogle Scholar
  44. Schmidt R, Schwintzer P, Flechtner F, Reigber C, Gütner A, Döll P, Ramillien G, Cazenave A, Petrovic S, Jochmann H, Wünsch J (2006) GRACE observations of changes in continental water storage. Glob Planet Change 50: 112–126CrossRefGoogle Scholar
  45. Schrama E (1995) Gravity Research Missions reviewed in the light of the indirect ocean tide potential. In: Rapp R, Cazenave A, Nerem R (eds) Global gravity field and its temporal variations, vol 116, International Association of Geodesy Symposia. Springer, Heidelberg, pp 131–140Google Scholar
  46. Schrama E, Ray R (1994) A preliminary tidal analysis of Topex/Poseidon altimetry. J Geophys Res 99(C12): 24799–24808CrossRefGoogle Scholar
  47. Standish E (1998) JPL planetary and lunar ephemerides DE405/LE405. Technical report JPL IOM 312.F - 98 - 047, JPL Pasadena CAGoogle Scholar
  48. 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(8): 467–478. doi: 10.1007/s00190-005-0480-z CrossRefGoogle Scholar
  49. Teunissen P (2000) Testing theory; an introduction. Delft University Press, DelftGoogle Scholar
  50. Thomas M (2002) Ocean induced variations of the Earth’s rotation—results from a simultaneous model of global circulation and tides. Ph.D. thesis, University of Hamburg, GermanyGoogle Scholar
  51. Tscherning C (1976) Covariance expressions for second and lower order derivatives of the anomalous potential. Report no. 225, Department of Geodetic Science and Surveying, Ohio State UniversityGoogle Scholar
  52. Tscherning C (1993) Computation of covariances of derivatives of the anomalous gravity potential in a rotated reference frame. Manusc Geod 8(3): 115–123Google Scholar
  53. Tscherning C, Veicherts M, Arabelos D (2006) Calibration of GOCE gravity gradient data using smooth ground gravity. In: Proceedings of the GOCINA workshop, vol 25. Cahiers du Centre Europeen de Geodynamique et de Seismologie, pp 63–67Google Scholar
  54. Velicogna I, Wahr J (2006) Measurements of time-variable gravity snow mass loss in Antarctica. Science 311: 1754–1756CrossRefGoogle Scholar
  55. 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
  56. Visser P, van den IJssel J (2000) GPS-based precise orbit determination of the very low Earth orbiting gravity mission GOCE. J Geod 74(7/8): 590–602CrossRefGoogle Scholar
  57. 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
  58. Visser P, van den IJssel J, van Helleputte T, Bock H, Jaeggi A, Beutler G, Hugentobler U, Svehla D (2007) Rapid and precise orbit determination for the GOCE Satellite. In: Proceedings of the 3rd international GOCE user workshop. ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP-627Google Scholar
  59. Wolff J, Maier-Reiner E, Legutke S (1996) The Hamburg ocean primitive equation model hope. Technical report no. 13, DKRZ, HamburgGoogle Scholar
  60. Yunck T, Bertiger W, Wu S, Bar-Sever Y, Christensen E, Haines B, Lichten S, Muellerschoen R, Vigue Y, Willis P (1994) First assessment of GPS-based reduced dynamic orbit determination on TOPEX/Poseidon. Geophys Res Lett 21(7): 541–544CrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Johannes Bouman
    • 1
    • 2
    • 3
    Email author
  • Sietse Rispens
    • 1
  • Thomas Gruber
    • 4
  • Radboud Koop
    • 5
  • Ernst Schrama
    • 2
  • Pieter Visser
    • 2
  • Carl Christian Tscherning
    • 6
  • Martin Veicherts
    • 6
  1. 1.SRON Netherlands Institute for Space ResearchUtrechtThe Netherlands
  2. 2.Delft Institute of Earth Observation and Space Systems (DEOS)Faculty of Aerospace Engineering, Delft University of TechnologyDelftThe Netherlands
  3. 3.Deutsches Geodätisches Forschungsinstitut (DGFI)MunichGermany
  4. 4.Institut für Astronomische und Physikalische Geodäsie (IAPG)Technische Universität MünchenMunichGermany
  5. 5.DelftThe Netherlands
  6. 6.Niels Bohr InstituteUniversity of CopenhagenCopenhagenDenmark

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