Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arabelos D, Tscherning CC (1998) Calibration of satellite gradiometer data aided by ground gravity data. J Geod 72: 617–625
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)
Bouman J (2004) Quick-look outlier detection for GOCE gravity gradients. Newton’s Bull 2: 78–87
Bouman J (2007) Alternative method for rotation to TRF. GO-TN-HPF-GS-0193, issue 1.0
Bouman J, Koop R (2003) Error assessment of GOCE SGG data using along track interpolation. Adv Geosci 1: 27–32
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: 124–137
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-627
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: 659–678
Bouman J, Lamarre D, Rispens S, Stummer C (2010) Assessment and improvement of GOCE Level 1b data. J Geod, GOCE special issue (submitted)
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)
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
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-03426
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: 18–25
Frommknecht B, Lamarre D, Bigazzi A, Meloni M, Floberghagen R (2011) GOCE level 1b data processing. J Geod, GOCE special issue (submitted)
Fuchs MJ, Bouman J (2011) Rotation of GOCE gravitational gradients to local frames. Geophys J Int (submitted)
Gruber T, Rummel R, Abrikosov O, van Hees R (2007) GOCE level 2 product data handbook. GO-MA-HPF-GS-0110, issue 3.3
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 51–83
IERS (2008) International Earth Rotation Service. http://www.iers.org/. Last accessed 1 july 2008
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-627
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
Mayer-Gürr T, Kurtenbach E, Eicker A, ITG-Grace2010 (2010) http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010. Last accessed 15 April 2010
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, Norway
Migliaccio F, Reguzzoni M, Sansò F (2004) Space-wise approach to satellite gravity determination in the presence of coloured noise. J Geod 78: 304–313
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–I69
Müller J (2003) GOCE gradients in various reference frames and their accuracies. Adv Geosci 1: 33–38
Pail R, Plank G (2004) Gravity field processing strategy. Stud Geophys Geod 48: 289–309
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
Pavlis DE, Poulouse S, McCarthy JJ (2006) GEODYN operations manual, Contract report. SGT Inc., Greenbelt, MD
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, Austria
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): 1558–1566
Standish EM, Newhall XX, Williams JG, Folkner WF (1995) JPL Planetary and Lunar Ephemerides, DE403/LE403, JPL IOM 314. 10–127
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): 89–98
Visser P (2007) GOCE Gradiometer Validation by GPS. Adv. Space Res. 39(10): 1630–1637. doi:10.1016/j.asr.2006.09.014
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bouman, J., Fiorot, S., Fuchs, M. et al. GOCE gravitational gradients along the orbit. J Geod 85, 791–805 (2011). https://doi.org/10.1007/s00190-011-0464-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-011-0464-0