Advertisement

Journal of Geodesy

, Volume 88, Issue 4, pp 319–333 | Cite as

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

  • Moritz Rexer
  • Christian Hirt
  • Roland Pail
  • Sten Claessens
Original Article

Abstract

In March 2013, the fourth generation of European Space Agency’s (ESA) global gravity field models, DIR4 (Bruinsma et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010b) and TIM4 (Migliaccio et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010), generated from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity observation satellite was released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with Gravity Recovery and Climate Experiment (GRACE) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude (\(h=250\) km) show both fourth generation models to improve significantly w.r.t. their predecessors. Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors, TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manusrcipta Geodaetica 20:379–385, 1995).

Keywords

GOCE Global gravity field model DIR TIM Spherical harmonic analysis Coefficient transformation method Meissl scheme 

Notes

Acknowledgments

This study was supported by the Australian Research Council (Grant DD12044/100) and through funding from Curtin University’s Office of Research and Development. We would like to thank Thomas Gruber for suggesting evaluations in accordance with the Meissl scheme. We thank Will Featherstone for providing the Australian gravity grids. We highly acknowledge the efforts of ESA and the HPF team for providing GOCE products in a very convenient and timely manner.

References

  1. Abdalla A, Fashir H, Ali A, Fairhead D (2012) Validation of recent GOCE/GRACE geopotential models over Khartoum state—Sudan. J Geod Sci 2:88–97. doi: 10.2478/v10156-011-0035-6 Google Scholar
  2. Andersen O, Knudsen P, Berry P (2009) The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J Geod 84:191–199. doi: 10.1007/s00190-009-0355-9 CrossRefGoogle Scholar
  3. Badura T (2006) Gravity field analysis from satellite orbit information applying the energy integral approach. PhD thesis, Graz University of TechnologyGoogle Scholar
  4. Bouman J, Fuchs M (2012) GOCE gravity gradients versus global gravity field models. Geophys J Int 189:846–850. doi: 10.1111/j.1365-246X.2012.05428.x CrossRefGoogle Scholar
  5. Bruinsma S, Lemoine J, Biancale R, Valès N (2010a) CNES/GRGS 10-day gravity field models (release 2) and their evaluation. Adv Space Res 45(4):587–601. doi: 10.1016/j.asr.2009.10.012 CrossRefGoogle Scholar
  6. Bruinsma S, Marty J, Balmino G, Biancale R, Förste C, Abrikosov O, Neumayer H (2010b) GOCE gravity field recovery by means of the direct numerical method. In: Lacoste-Francis H (ed) Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686Google Scholar
  7. Chen J, Wilson C (2010) Assessment of degree-2 zonal gravitational changes from GRACE, earth rotation, climate models, and satellite laser ranging. In: Mertikas S (ed) Gravity, geoid and earth observation, vol 135. Springer, Berlin, pp 669–676. doi: 10.1007/978-3-642-10634-7_88
  8. Claessens S (2006) Solutions to ellipsoidal boundary value problems for gravity field modelling. PhD thesis, Curtin University of TechnologyGoogle Scholar
  9. Claessens S, Featherstone W, Anjasmar I, Filmer M (2009) Is Australian data really validating EGM2008, or is EGM2008 just in/validating Australian data? In: Newton’s Bulletin Issue no 4, international association of geodesy and international gravity field service, pp 207–251Google Scholar
  10. Dahle C, Flechtner F, Gruber C, Knig D, Knig R, Michalak G, Neumayer K (2013) GFZ GRACE level-2 processing standards document for level-2 product release 0005: revised edition. GeoForschungsZentrum, PotsdamGoogle Scholar
  11. Driscoll J, Healy D (1994) Computing Fourier transforms and convolutions on the 2-sphere. Adv Appl Math 15(2):202–250. doi: 10.1006/aama.1994.1008 CrossRefGoogle Scholar
  12. ESA (1999) Gravity field and steady-state ocean circulation mission. Report for the mission selection of the four candidate earth explorer missions (ESA SP-1233(1)), European Space AgencyGoogle Scholar
  13. Featherstone W, Kirby J (2000) The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data. Geophys Int 141:204–212CrossRefGoogle Scholar
  14. Featherstone W, Kirby J, Hirt C, Filmer M, Claessens S, Brown N, Hu G, Johnston G (2010) The AUSGeoid model of the Australian height datum. J Geod 85(3):133–150CrossRefGoogle Scholar
  15. Forsberg R, Kenyon S (2004) Gravity and geoid in the Arctic region—the Northern polar gap now filled. In: Proceedings of the 2nd GOCE User, Workshop, March 2004, EsrinGoogle Scholar
  16. Gerlach C, Šprlák M, Bentel K, Pettersen B (2013) Observation, validation, modeling—historical lines and recent results in Norwegian gravity field research. Kart og Plan 73(2):128–150Google Scholar
  17. Gruber T, Visser P, Ackermann C, Hosse M (2011) Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons. J Geod 85(11):845–860. doi: 10.1007/s00190-011-0486-7 CrossRefGoogle Scholar
  18. Gruber T, Rummel R, HPF-Team (2013) The 4th realease of GOCE gravity field models—overview and performance. In: Presentation at EGU general assembly 2013. http://www.iapg.bv.tum.de/mediadb/5533197/5533198/20130411_EGU_Gruber_GOCE.pdf
  19. Guimarães G, Matos A, Blitzkow D (2012) An evaluation of recent GOCE geopotential models in Brazil. J Geod Sci 2:144–155. doi: 10.2478/v10156-011-0033-8 Google Scholar
  20. Hashemi Farahani H, Ditmar P, Klees R, Liu X, Zhao Q, Guo J (2013) Validation of static gravity field models using GRACE K-band ranging and GOCE gradiometry data. Geophys J Int 194:751–771. doi: 10.1093/gji/ggt149 CrossRefGoogle Scholar
  21. Hirt C, Gruber T, Featherstone W (2011) Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights. J Geod 85:723–740CrossRefGoogle Scholar
  22. Hirt C, Kuhn M, Featherstone W, Göttl F (2012) Topographic/isostatic evaluation of new-generation GOCE gravity field models. J Geophys Res Solid Earth 117:B05407. doi: 10.1029/2011JB008878
  23. Holmes S, Pavlis N (2008) EGM harmonic synthesis software. National Geospatial-Intelligence Agency. http://earth-info.nga.mil/GandG/wgs84/gravitymod/new_egm/new_egm.html
  24. HPF (2013a) Datasheet GO\_CONS\_GCF\_2 \_DIR\_R4. GFZ, GRGS, published at ICGEMGoogle Scholar
  25. HPF (2013b) Datasheet GO\_CONS\_GFC\_2 \_TIM\_R4. Graz University of Technology, University of Bonn, TU Mnchen, published at ICGEMGoogle Scholar
  26. Ihde J, Wilmes H, Müller J, Denker H, Voigt C, Hosse M (2010) Validation of satellite gravity field models by regional terrestrial data sets. In: Flechtner F, Gruber T, Gntner A, Mandea M, Rothacher M, Schne T, Wickert J (eds) System earth via geodetic-geophysical space techniques. Springer, Berlin, pp 277–296. doi: 10.1007/978-3-642-10228-8_22
  27. Janák J, Pitoňák M (2011) Comparison and testing of GOCE global gravity models in Central Europe. J Geod Sci 1:333–347Google Scholar
  28. Jekeli C (1988) The exact transformation between ellipsoidal and spherical harmonic expansions. Manuscripta Geodaetica 13(2):106–113Google Scholar
  29. Kaula W (1966) Theory of satellite geodesy. Blaisdel, WalthamGoogle Scholar
  30. Lavallée D, Moore P, Clarke P, Petrie E, van Dam T, King M (2010) J2: an evaluation of new estimates from GPS, GRACE, and load models compared to SLR. Geophys Res Lett 37. doi: 10.1029/2010GL045229
  31. Mayer-Gürr T, Eicker A, Ilk KH (2006) Gravity field recovery from GRACE-SST data of short arcs. In: Flury J, Rummel R, Reigber C, Rothacher M, Boedecker G, Schreiber U (eds) Observation of the earth system from space. Springer, Berlin, pp 131–148CrossRefGoogle Scholar
  32. Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010
  33. Metzler B, Pail R (2005) GOCE data processing: the spherical cap regularization approach. Studia Geophysica et Geodaetica 49(4):441–462. doi: 10.1007/s11200-005-0021-5 CrossRefGoogle Scholar
  34. Migliaccio F, Reguzzoni M, Sanso F, Tscherning C, Veicherts M (2010), GOCE data analysis: the space-wise method approach and the first space-wise gravity field model. In: Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686Google Scholar
  35. Moritz H (2000) Geodetic reference system 1980. J Geod 74(1):128–162CrossRefGoogle Scholar
  36. Pail R, Goiginger H, Mayrhofer R, Schuh WD, Brockmann JM et al (2010) GOCE gravity field model derived from orbit and gradiometry data applying the Time-Wise Method. In: Lacoste-Francis H (ed) Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686Google Scholar
  37. 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, Sanso F, Tscherning CC (2011a) First GOCE gravity field models derived by three different approaches. J Geod 85(11):819–843. doi: 10.1007/s00190-011-0467-x (special issue: “GOCE—the Gravity and Steady-state Ocean Circulation Explorer”)Google Scholar
  38. Pail R, Goiginger H, Schuh W, Höck E, Brockmann J, Fecher T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D, Gruber T (2011b) Combination of GOCE data with complementary gravity field information (GOCO). In: Proceedings of 4th international GOCE user workshop, Munich, 31st March 2011, ESA SP-696, NoordwijkGoogle Scholar
  39. Pail R, Fecher T, Murböck M, Rexer M, Stetter M, Gruber T, Stummer C (2012) Impact of GOCE L1b data reprocessing on GOCE-only and combined gravity field models. In: Studia Geophysica et Geodaetica. Springer, Berlin. doi: 10.1007/s11200-012-1149-8
  40. Pavlis N, Holmes S, Kenyon S, Factor J (2012) The developement and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res 117. doi: 10.1029/2011JB008916
  41. Rummel R, van Gelderen M (1995) Meissl scheme—spectral characteristics of physical geodesy. Manusrcipta Geodaetica 20:379– 385Google Scholar
  42. Sneeuw N, van Gelderen M (1997) The polar gap. In: Geodetic boundary value problems in view of the one centimeter geoid. Lecture Notes in Earth Science, vol 65, pp 559–568Google Scholar
  43. Šprlák M, Gerlach C, Omang O, Pettersen B (2011) Comparison of GOCE derived satellite global gravity models with EGM2008, the OCTAS geoid and terrestrial gravity data: case study for Norway. In: Proceedings of the 4th international GOCE user workshop, Munich, 31st March 2011, ESA SP-696, NoordwijkGoogle Scholar
  44. Šprlák M, Gerlach C, Pettersen B (2012) Validation of GOCE global gravity field models using terrestrial gravity data in Norway. J Geod Sci 2(2):134–143Google Scholar
  45. Stummer C, Pail R, Fecher T (2011) Alternative method for angular rate determination within the GOCE gradiometer processing. J Geod 85(9):585–596CrossRefGoogle Scholar
  46. Stummer C, Siemes C, Pail R, Frommknecht B, Floberghagen R (2012) Upgrade of the GOCE Level 1b gradiometer processor. Adv Space Res 49(4):739–752CrossRefGoogle Scholar
  47. Szücz E (2012) Validation of GOCE time-wise gravity field models using GPS-levelling, gravity, vertical deflections and gravity gradients in Hungary. Civil Eng 56(1):3–11Google Scholar
  48. Tapley B, Reigber C (2001) The grace mission: status and future plans. In: AGU fall, meeting abstracts, vol 1Google Scholar
  49. Tapley B, Schutz B, Eanes R, Ries J, Watkins M (1993) LAGEOS laser ranging contributions to geodynamics, geodesy, and orbital dynamics. Geodyn Ser 24:147–173Google Scholar
  50. Torge W (2001) Geodesy, 3rd edn. Walter de Gruyter, BerlinGoogle Scholar
  51. Tscherning C, Arabelos D (2011) Gravity anomaly and gradient recovery from GOCE gradient data using LSC and comparisons with known ground data. In: Proceedings 4th International GOCE user workshop, Munich, 31st March 2011, ESA SP-696, NoordwijkGoogle Scholar
  52. Voigt C, Denker H (2011) Validation of goce gravity field models by astrogeodetic vertical deflections in germany. In: Proceedings of the 4th international GOCE user workshop, SP-696, ESA/ESTEC, The Netherrlands, vol 4Google Scholar
  53. Voigt C, Rülke A, Denker H, Ihde J, Liebsch G (2010) Validation of goce products by terrestrial data sets in Germany. In: Observation of the system earth from space, vol 17. Geotechnolgien, PotsdamGoogle Scholar
  54. Wang Y (1989) Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution, Poisson’s integral and terrain-correction—numerical comparison and computations. 4, Department of Geodetic Science and Surveying, Ohio State UniversityGoogle Scholar
  55. Zwally H, Schutz B, Abdalati W, Abshire J, Bentley C, Brenner A, Bufton J et al (2002) ICESat’s laser measurement of polar ice, atmosphere, ocean, and land. J Geodyn 34:404–445Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Moritz Rexer
    • 1
    • 2
  • Christian Hirt
    • 1
  • Roland Pail
    • 2
  • Sten Claessens
    • 1
  1. 1.Western Australian Centre for GeodesyCurtin University of TechnologyPerthAustralia
  2. 2.Institute for Astronomical and Physical GeodesyTechnische Universität MünchenMunichGermany

Personalised recommendations