GPS Solutions

, Volume 14, Issue 2, pp 165–175 | Cite as

Low-degree earth deformation from reprocessed GPS observations

  • Mathias FritscheEmail author
  • R. Dietrich
  • A. Rülke
  • M. Rothacher
  • P. Steigenberger
Original Article


Surface mass variations of low spherical harmonic degree are derived from residual displacements of continuously tracking global positioning system (GPS) sites. Reprocessed GPS observations of 14 years are adjusted to obtain surface load coefficients up to degree n max = 6 together with station positions and velocities from a rigorous parameter combination. Amplitude and phase estimates of the degree-1 annual variations are partly in good agreement with previously published results, but also show interannual differences of up to 2 mm and about 30 days, respectively. The results of this paper reveal significant impacts from different GPS observation modeling approaches on estimated degree-1 coefficients. We obtain displacements of the center of figure (CF) relative to the center of mass (CM), Δr CF–CM, that differ by about 10 mm in maximum when compared to those of the commonly used coordinate residual approach. Neglected higher-order ionospheric terms are found to induce artificial seasonal and long-term variations especially for the z-component of Δr CF–CM. Daily degree-1 estimates are examined in the frequency domain to assess alias contributions from model deficiencies with regard to satellite orbits. Finally, we directly compare our estimated low-degree surface load coefficients with recent results that involve data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission.


GPS Surface mass redistribution Terrestrial reference frame 



We thank the International GNSS Service for providing the observation data via its data centers. Our sincere thanks go to the CODE Analysis Center team for their cooperation within the reprocessing project. This research was funded by the German Research Foundation (DFG). Figures were generated with the Generic Mapping Tools (; Wessel and Smith 1991). The helpful comments of two anonymous reviewers are gratefully acknowledged.


  1. Agnew D, Larson K (2007) Finding the repeat times of the GPS constellation. GPS Solut 11:71–76. doi: 10.1007/s10291-006-0038-4 CrossRefGoogle Scholar
  2. Altamimi Z, Collilieux X, Legrand J, Garayt B, Boucher C (2007) ITRF2005: a new release of the International Terrestrial Reference Frame based on time series of station positions and earth orientation parameters. J Geophys Res 112(B09401). doi: 10.1029/2007JB004949
  3. Blewitt G (2003) Self-consistency in reference frames, geocenter definition, and surface loading of the solid earth. J Geophys Res 108(B2):2103. doi: 10.1029/2002JB002082 Google Scholar
  4. Blewitt G, Lavallée D, Clarke P, Nurutdinov K (2001) A new global mode of earth deformation: seasonal cycle detected. Science 294:2342–2345. doi: 10.1126/science.1065328 CrossRefGoogle Scholar
  5. Clarke P, Lavallée D, Blewitt G, van Dam T (2007) Basis functions for the consistent and accurate representation of surface mass loading. Geophys J Int 171(1):1–10. doi: 10.1111/j.1365-246X.2007.03493.x CrossRefGoogle Scholar
  6. Dach R, Hugentobler U, Fridez P, Meindl M (eds) (2007) Bernese GPS software Version 5.0. Astronomical Institute, University of Bern, SwitzerlandGoogle Scholar
  7. Davis JL, El’osegui P, Mitrovica JX, Tamisiea ME (2004) Climate-driven deformation of the solid earth from GRACE and GPS. Geophys Res Lett 31(L24605). doi: 10.1029/2004GL021435
  8. Dong D, Yunck T, Heflin M (2003) Origin of the International Terrestrial Reference Frame. J Geophys Res 108(B4):2200. doi: 10.1029/2002JB002035 Google Scholar
  9. Dow JM, Neilan RE, Gendt G (2005) The International GPS Service (IGS): celebrating the 10th anniversary and looking to the next decade. Adv Space Res 36(3):320–326. doi: 10.1016/j.asr.2005.05.125 CrossRefGoogle Scholar
  10. Drewes H (2007) Science rationale of the global geodetic observing system (GGOS). In: Tregoning P, Rizos C (eds) IAG symposia 130 “Dynamic planet—monitoring and understanding a dynamic planet with geodetic and oceanographic tools”, Springer, Berlin, pp 703–710, doi: 10.1007/978-3-540-49350-1_101
  11. Fliegel HF, Gallini TE (1996) Solar force modeling of block IIR global positioning system satellites. J Spacecr Rockets 33(6):863–866. doi: 10.2514/3.26851 CrossRefGoogle Scholar
  12. Fliegel HF, Gallini TE, Swift ER (1992) Global positioning system radiation force model for geodetic applications. J Geophys Res 97(B1):559–568. doi: 10.1029/91JB02564 Google Scholar
  13. Fritsche M, Dietrich R, Knöfel C, Rülke A, Vey S, Rothacher M, Steigenberger P (2005) Impact of higher-order ionospheric terms on GPS estimates. Geophys Res Lett 32(L23311). doi: 10.1029/2005GL024342
  14. Heflin M, Watkins M (1999) Geocenter estimates from the global positioning system. In: IERS analysis campaign to investigate motions of the geocenter. IERS technical note no. 25, Obs. de Paris, Paris, pp 55–70Google Scholar
  15. Hugentobler U (2005) Models in GNSS data analysis. Presentation at “Advances in GPS data processing and modelling for geodynamics” held at University College London, 9–10 November 2005 (available electronically at
  16. King MA, Watson CS, Penna NT, Clarke PJ (2008) Subdaily signals in GPS observations and their effect at semiannual and annual periods. Geophys Res Lett 35(L03302). doi: 10.1029/2007GL032252
  17. Kusche J, Schrama EJO (2005) Surface mass redistribution inversion from global GPS deformation and gravity recovery and climate experiment (GRACE) gravity data. J Geophys Res 110(B09409). doi: 10.1029/2004JB003556
  18. Lavallée DA, van Dam T, Blewitt G, Clarke PJ (2006) Geocenter motions from GPS: a unified observation model. J Geophys Res 111(B05405). doi: 10.1029/2005JB003784
  19. McCarthy DD, Petit G (eds) (2004) IERS Conventions (2003). IERS technical note no. 32, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, GermanyGoogle Scholar
  20. Penna NT, Stewart MP (2003) Aliased tidal signatures in continuous GPS height time series. Geophys Res Lett 30(23):2184. doi: 10.1029/2003GL018828 Google Scholar
  21. Penna NT, King MA, Stewart MP (2007) GPS height time series: short-period origins of spurious long-period signals. J Geophys Res 112(B02402). doi: 10.1029/2005JB004047
  22. Ray J, Altamimi Z, Collilieux X, van Dam T (2007) Anomalous harmonics in the spectra of GPS position estimates. GPS Solut 12:55–64. doi: 10.1007/s10291-007-0067-7 CrossRefGoogle Scholar
  23. Rülke A, Dietrich R, Fritsche M, Rothacher M, Steigenberger P (2008) Realization of the terrestrial reference system by a reprocessed global GPS network. J Geophys Res 113(B08403). doi: 10.1029/2007JB005231
  24. Schmidt R, Flechtner F, Meyer U, Neumayer KH, Dahle C, König R, Kusche J (2008) Hydrological signals observed by the GRACE satellites. Surv Geophys 29:319–334. doi: 10.1007/s10712-008-9033-3 CrossRefGoogle Scholar
  25. Springer TA, Beutler G, Rothacher M (1999) A new solar radiation pressure model for GPS. Adv Space Res 23(4):673–676. doi: 10.1016/S0273-1177(99)00158-1 CrossRefGoogle Scholar
  26. Steigenberger P, Rothacher M, Dietrich R, Fritsche M, Rülke A, Vey S (2006) Reprocessing of a global GPS network. J Geophys Res B05402(111). doi: 10.1029/2005JB003747
  27. Swenson S, Wahr J (2008) Estimating geocenter variations from a combination of GRACE and ocean model ouput. J Geophys Res 113(B08410). doi: 10.1029/2007JB005338
  28. Urschl C, Beutler G, Gurtner W, Hugentobler U, Stefan S (2007) Contribution of SLR tracking data to GNSS orbit determination. Adv Space Res 39(10):1515–1523. doi: 10.1016/j.asr.2007.01.038 CrossRefGoogle Scholar
  29. van Dam T, Wahr J, Lavallée D (2007) A comparison of annual vertical crustal displacements from GPS and gravity recovery and climate experiment (GRACE) over Europe. J Geophys Res 112(B03404). doi: 10.1029/2006JB004335
  30. Wessel P, Smith WHF (1991) Free software helps map and display data. Eos Trans AGU 72:441. doi: 10.1029/90EO00319 CrossRefGoogle Scholar
  31. Wu X, Argus DF, Heflin MB, Ivins ER, Webb FH (2002) Site distribution and aliasing effects in the inversion for load coefficients and geocenter motion from GPS data. Geophys Res Lett 29(24):2210. doi: 10.1029/2002GL016324 Google Scholar
  32. Wu X, Heflin MB, Ivins ER, Argus DF, Webb FH (2003) Large-scale global surface mass variations inferred from GPS measurements of load-induced deformation. Geophys Res Lett 30(14):1742. doi: 10.1029/2003GL017546 Google Scholar
  33. Wu X, Heflin MB, Ivins ER, Fukumori I (2006) Seasonal and interannual global surface mass variations from multisatellite geodetic data. J Geophys Res 111(B09401). doi: 10.1029/2005JB004100

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Mathias Fritsche
    • 1
    Email author
  • R. Dietrich
    • 1
  • A. Rülke
    • 1
  • M. Rothacher
    • 2
  • P. Steigenberger
    • 3
  1. 1.Institut für Planetare GeodäsieTechnische Universität DresdenDresdenGermany
  2. 2.Institut für Geodäsie und PhotogrammetrieEidgenössische Technische Hochschule ZürichZurichSwitzerland
  3. 3.Institut für Astronomische und Physikalische GeodäsieTechnische Universität MünchenMunichGermany

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