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


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).


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



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.


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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

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