Journal of Geodesy

, Volume 91, Issue 7, pp 839–848 | Cite as

Joint analysis of celestial pole offset and free core nutation series

  • Zinovy Malkin
Original Article


Three combined celestial pole offset (CPO) series computed at the Paris Observatory (C04), the United States Naval Observatory (USNO), and the International VLBI Service for Geodesy and Astrometry (IVS), as well as six free core nutation (FCN) models, were compared from different perspectives, such as stochastic and systematic differences, and FCN amplitude and phase variations. The differences between the C04 and IVS CPO series were mostly stochastic, whereas a low-frequency bias at the level of several tens of \(\upmu \)as was found between the C04 and USNO CPO series. The stochastic differences between the C04 and USNO series became considerably smaller when computed at the IVS epochs, which can indicate possible problems with the interpolation of the IVS data at the midnight epochs during the computation of the C04 and USNO series. The comparison of the FCN series showed that the series computed with similar window widths of 1.1–1.2 years were close to one another at a level of 10–20 \(\upmu \)as, whereas the differences between these series and the series computed with a larger window width of 4 and 7 years reached 100 \(\upmu \)as. The dependence of the FCN model on the underlying CPO series was investigated. The RMS differences between the FCN models derived from the C04, USNO, and IVS CPO series were at a level of approximately 15 \(\upmu \)as, which was considerably smaller than the differences among the CPO series. The analysis of the differences between the IVS, C04, and USNO CPO series suggested that the IVS series would be preferable for both precession-nutation and FCN-related studies.


Earth orientation parameters (EOP) Celestial pole offset (CPO) Free core nutation (FCN) Very long baseline interferometry (VLBI) International VLBI Service for Geodesy and Astrometry (IVS) International Earth Rotation and Reference Systems Service (IERS) 



The author is grateful to Santiago Belda for providing their latest FCN models for this research. Three anonymous reviewers are sincerely acknowledged for their constructive criticism and useful suggestions. Most results of this work are heavily based on the VLBI observations coordinated by the IVS (Schuh and Behrend 2012, Nothnagel et al. 2015). This work was partially supported by the Russian Government Program of Competitive Growth of Kazan Federal University.


  1. Belda S, Ferrándiz JM, Heinkelmann R, Nilsson T, Schuh H (2016) Testing a new free core nutation empirical model. J Geodyn 94:59–67. doi: 10.1016/j.jog.2016.02.002
  2. Bizouard C, Gambis D (2009) The combined solution c04 for earth orientation parameters consistent with international terrestrial reference frame 2005. In: Drewes H (ed) Geodetic reference frames, IAG symposia, vol 134. Springer, Berlin, pp 265–270. doi: 10.1007/978-3-642-00860-3_41
  3. Böckmann S, Artz T, Nothnagel A, Tesmer V (2010) International VLBI service for geodesy and astrometry: earth orientation parameter combination methodology and quality of the combined products. J Geophys Res (Solid Earth) 115:B04404. doi: 10.1029/2009JB006465
  4. Capitaine N, Wallace PT, Chapront J (2003) Expressions for IAU 2000 precession quantities. A&A 412:567–586. doi: 10.1051/0004-6361:20031539
  5. Capitaine N, Wallace PT, Chapront J (2005) Improvement of the IAU 2000 precession model. A&A 432:355–367. doi: 10.1051/0004-6361:20041908
  6. Capitaine N, Mathews PM, Dehant V, Wallace PT, Lambert S (2008) Comparisons of precession–nutation models. In: Behrend D, Finkelstein A (eds) Measuring the future, proceedings of the fifth IVS, pp 221–230Google Scholar
  7. Capitaine N, Mathews PM, Dehant V, Wallace PT, Lambert SB (2009) On the IAU 2000/2006 precession nutation and comparison with other models and VLBI observations. Celest Mech Dyn Astr 103:179–190. doi: 10.1007/s10569-008-9179-9
  8. Dehant V, Mathews PM (2015) Precession. In: Nutation and wobble of the earth. Cambridge University Press, CambridgeGoogle Scholar
  9. Dick WR, Thaller D (eds) (2015) IERS annual report 2014. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  10. Galleani L, Tavella P (2009) The dynamic allan variance. IEEE Trans UFFC 56(3):450–464. doi: 10.1109/TUFFC.2009.1064
  11. Gattano G, Lambert S, Bizouard C (2015) Comparison of VLBI nutation time series. In: Haas R, Colomer F (eds) Proceedings of the 22nd European VLBI group for geodesy and astronomy working meeting, 18–21 May 2015, Ponta Delegata, Azores, pp 205–209Google Scholar
  12. Herring TA, Mathews PM, Buffett BA (2002) Modeling of nutation–precession: very long baseline interferometry results. J Geophys Res 107:2069. doi: 10.1029/2001JB000165
  13. Krásná H, Böhm J, Schuh H (2013) Free core nutation observed by VLBI. A&A 555:A29. doi: 10.1051/0004-6361/201321585
  14. Lambert SB, Dehant V (2007) The Earth’s core parameters as seen by the VLBI. A&A 469:777–781. doi: 10.1051/0004-6361:20077392
  15. Lambert SB (2016) Empirical modeling of the Earth’s free core nutation. http://www.syrteobspmfr/lambert/fcn/notice_fcnpdf
  16. Malkin ZM (2007) Empiric models of the Earth’s free core nutation. Sol Syst Res 41:492–497. doi: 10.1134/S0038094607060044
  17. Malkin ZM (2011a) Study of astronomical and geodetic series using the Allan variance. Kinemat Phys Celes Bod 27:42–49. doi: 10.3103/S0884591311010053
  18. Malkin ZM (2014) On the accuracy of the theory of precession and nutation. Astron Rep 58:415–425. doi: 10.1134/S1063772914060043
  19. Malkin Z (2002) A comparison of the VLBI nutation series with model. In: IERS technical note 29. In: Implementation of the new IAU resolutions, pp 107–108Google Scholar
  20. Malkin Z (2003) A comparative analysis of the VLBI nutation series. In: Capitaine N (ed) Proc. Journées 2001 Systèmes de référence spatio-temporels, Brussels, Belgium, September 24–26, pp 34–39Google Scholar
  21. Malkin Z (2004) Comparison of VLBI nutation series with the IAU2000A model. In: Finkelstein A, Capitaine N (eds) Proc. Journées 2003 Systèmes de Référence Spatio-temporels, St. Petersburg, Russia, Sep 22–25, pp 24–31Google Scholar
  22. Malkin Z (2011b) The impact of celestial pole offset modelling on VLBI UT1 intensive results. J Geod 85:617–622. doi: 10.1007/s00190-011-0468-9
  23. Malkin Z (2012) Celestial pole offsets: from initial analysis to end user. In: Behrend D, Baver KD (eds) International VLBI service for geodesy and astrometry 2012 general meeting proceedings, pp 375–379Google Scholar
  24. Malkin Z (2013) Free core nutation and geomagnetic jerks. J Geod 72:53–58. doi: 10.1016/j.jog.2013.06.001
  25. Mathews PM, Herring TA, Buffett BA (2002) Modeling of nutation and precession: new nutation series for nonrigid Earth and insights into the Earth’s interior. J Geophys Res 107:2068. doi: 10.1029/2001JB000390
  26. Nothnagel A, International VLBI Service for Geodesy and Astrometry (IVS) (2015) The IVS data input to ITRF2014. International VLBI Service for Geodesy and Astrometry, GFZ Data Services. doi: 10.5880/GFZ.1.1.2015.002
  27. Petit G, Luzum B (eds) (2010) IERS conventions (2010). IERS technical note no. 36, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  28. Schuh H, Behrend D (2012) VLBI: a fascinating technique for geodesy and astrometry. J Geodyn 61:68–80. doi: 10.1016/j.jog.2012.07.007
  29. Vondrák J, Ron C (2008) VLBI observations of nutation, its geophysical excitations and determination of some Earth model parameters. In: Capitaine N (ed) Journées Systèmes de Référence Spatio-temporels 2007, p 95Google Scholar
  30. Vondrák J, Ron C (2009) Stability of period and quality factor of free core nutation. Acta Geodyn Geomater 6:217–224Google Scholar
  31. Wooden W, Luzum B, Stamatakos N (2010) Current status and future directions of the IERS RS/PC predictions of UT1. Highlights Astron 15:218–218. doi: 10.1017/S1743921310008872
  32. Zharov VE (2005) Model of the free core nutation for improvement of the Earth nutation series. In: Capitaine N (ed) Journées 2002-systèmes de référence spatio-temporels, pp 106–109Google Scholar
  33. Zhou Y, Zhu Q, Salstein DA, Xu X, Shi S, Liao X (2016) Estimation of the free core nutation period by the sliding-window complex least-squares fit method. Adv Space Res 57(10):2136–2140. doi: 10.1016/j.asr.2016.03.028

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Pulkovo ObservatorySt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Kazan Federal UniversityKazanRussia

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