Surveys in Geophysics

, Volume 36, Issue 6, pp 773–801 | Cite as

Global and Regional Gravity Field Determination from GOCE Kinematic Orbit by Means of Spherical Radial Basis Functions

  • Blažej BuchaEmail author
  • Aleš Bezděk
  • Josef Sebera
  • Juraj Janák


We present global and regional gravity field models to degree 130 based on the GOCE kinematic orbit from the period 01 November 2009 to 11 January 2010. The gravity field models are parameterized in terms of the Shannon and Kaula's spherical radial basis functions. The relation between the unknown expansion coefficients and the kinematic orbit of the satellite is established by the acceleration approach. We show that our global GOCE-only solutions free from prior information can compete with unconstrained spherical harmonic models in terms of accuracy. Furthermore, we utilize our low-degree global GOCE-based models to introduce prior information into the least-squares adjustment. This procedure substantially improves the zonal and near-zonal spherical harmonic coefficients, which are usually degraded due to the polar gap problem. As an unwanted side effect, low-pass filtering of the geopotential may occur, but this can be adjusted by the spectral content of the prior information. We show that the regional enhancement of the global solutions reduces noise in the final model between degrees 70 and 130 by ~10 % in terms of RMS error. In general, our Shannon-based solutions systematically outperform the Kaula-based ones. To validate our results, we use the EIGEN-6S model, which is superior to the solutions from kinematic orbits at least by one order of magnitude. Both the global and the regional models satisfy the GOCE-only strategy.


Spherical radial basis functions Spherical harmonics  Geopotential GOCE Polar gap Regularization 



The authors acknowledge ESA for GOCE mission data and ICGEM for the access to the global gravity field models. We thank Oliver Baur for providing us with the global gravity field models from GOCE kinematic orbits (Baur et al. 2014). Two anonymous reviewers are gratefully acknowledged for their helpful reviews. Blažej Bucha and Juraj Janák were supported by the Projects APVV-0072-11 and VEGA 1/0954/15. Aleš Bezděk and Josef Sebera were supported by the Projects GA 13-36843S and RVO: 67985815. Some of the computations were performed on the computational resources kindly provided by the Department of Mathematics and Descriptive Geometry, Slovak University of Technology in Bratislava. The maps were produced using the Generic Mapping Tools (Wessel and Smith 1998).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Blažej Bucha
    • 1
    Email author
  • Aleš Bezděk
    • 2
  • Josef Sebera
    • 2
    • 3
  • Juraj Janák
    • 1
  1. 1.Department of Theoretical Geodesy, Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislavaSlovak Republic
  2. 2.Astronomical InstituteCzech Academy of SciencesOndřejovCzech Republic
  3. 3.Research Institute of Geodesy, Cartography and TopographyZdibyCzech Republic

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