Journal of Geodesy

, Volume 89, Issue 9, pp 857–871 | Cite as

Second-degree Stokes coefficients from multi-satellite SLR

  • Mathis BloßfeldEmail author
  • Horst Müller
  • Michael Gerstl
  • Vojtěch Štefka
  • Johannes Bouman
  • Franziska Göttl
  • Martin Horwath
Original Article


The long wavelength part of the Earth’s gravity field can be determined, with varying accuracy, from satellite laser ranging (SLR). In this study, we investigate the combination of up to ten geodetic SLR satellites using iterative variance component estimation. SLR observations to different satellites are combined in order to identify the impact of each satellite on the estimated Stokes coefficients. The combination of satellite-specific weekly or monthly arcs allows to reduce parameter correlations of the single-satellite solutions and leads to alternative estimates of the second-degree Stokes coefficients. This alternative time series might be helpful for assessing the uncertainty in the impact of the low-degree Stokes coefficients on geophysical investigations. In order to validate the obtained time series of second-degree Stokes coefficients, a comparison with the SLR RL05 time series of the Center of Space Research (CSR) is done. This investigation shows that all time series are comparable to the CSR time series. The precision of the weekly/monthly \(C_{21}\) and \(S_{21}\) coefficients is analyzed by comparing mass-related equatorial excitation functions \(\chi ^{\text {mass}}_{1,2}\) with geophysical model results and reduced geodetic excitation functions. In case of \(\chi ^{\text {mass}}_{1}\), the annual amplitude and phase of the DGFI solution agrees better with three of four geophysical model combinations than other time series. In case of \(\chi ^{\text {mass}}_{2}\), all time series agree very well to each other. The impact of \(C_{20}\) on the ice mass trend estimates for Antarctica are compared based on CSR GRACE RL05 solutions, in which different monthly \(C_{20}\) time series are used for replacing. We found differences in the long-term Antarctic ice loss of \(12.3\) Gt/year between the GRACE solutions induced by the different \(C_{20}\) SLR time series of CSR and DGFI, which is about 13 % of the total ice loss of Antarctica. This result shows that Antarctic ice mass loss quantifications must be carefully interpreted.


Multi-satellite SLR Stokes coefficients C20 Lageos Equatorial excitation functions Antarctic ice mass loss 



The authors want to thank the International Laser Ranging Service (Pearlman et al. 2002, ILRS) for providing the observations to the satellites. The work contributes to the research group ’Space-Time Reference Systems for Monitoring Global Change and for Precise Navigation’ (FOR 1503) of the German Research Foundation (DFG). The authors also want to thank the three anonymous reviewers and the associate editor who helped to improve the quality of the manuscript.

Supplementary material

190_2015_819_MOESM1_ESM.pdf (9.2 mb)
Supplementary material 1 (pdf 9435 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Mathis Bloßfeld
    • 1
    Email author
  • Horst Müller
    • 1
  • Michael Gerstl
    • 1
  • Vojtěch Štefka
    • 2
  • Johannes Bouman
    • 1
  • Franziska Göttl
    • 1
  • Martin Horwath
    • 3
  1. 1.Deutsches Geodätisches Forschungsinstitut (DGFI)MunichGermany
  2. 2.Astronomical InstituteAcademy of Sciences of the Czech RepublicPragueCzech
  3. 3.Institut für Planetare GeodäsieTechnische Universität DresdenDresdenGermany

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