Solar Physics

, 293:69 | Cite as

A Test of the Active-Day Fraction Method of Sunspot Group Number Calibration: Dependence on the Level of Solar Activity

  • T. Willamo
  • I. G. Usoskin
  • G. A. Kovaltsov


The method of active-day fraction (ADF) was proposed recently to calibrate different solar observers to standard observational conditions. The result of the calibration may depend on the overall level of solar activity during the observational period. This dependency is studied quantitatively using data of the Royal Greenwich Observatory by formally calibrating synthetic pseudo-observers to the full reference dataset. It is shown that the sunspot group number is precisely estimated by the ADF method for periods of moderate activity, may be slightly underestimated by 0.5 – 1.5 groups (\({\leq}\,10\%\)) for strong and very strong activity, and is strongly overestimated by up to 2.5 groups (\({\leq}\,30\%\)) for weak-to-moderate activity. The ADF method becomes inapplicable for the periods of grand minima of activity. In general, the ADF method tends to overestimate the overall level of activity and to reduce the long-term trends.


Solar activity Sunspots Solar observations Solar cycle 



We are grateful for fruitful discussions with Frédéric Clette, Ed Cliver, Greg Kopp, Laure Lefévre, Andrés Mũnoz-Jaramillo, Alexei Pevtsov, Leif Svalggard, and José Vaquero. VarSITI/SCOSTEP is acknowledged for an opportunity to discuss this material during the 2nd VarSITI General Symposium (Irkutsk, 2017). This work was carried out in the framework of the ReSoLVE Centre of Excellence (Academy of Finland, project no. 272157).

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


  1. Chatzistergos, T., Usoskin, I.G., Kovaltsov, G.A., Krivova, N.A., Solanki, S.K.: 2017, New reconstruction of the sunspot group numbers since 1739 using direct calibration and “backbone” methods. Astron. Astrophys. 602, A69. DOI. ADS. ADSCrossRefGoogle Scholar
  2. Clette, F., Lefèvre, L.: 2016, The new sunspot number: Assembling all corrections. Solar Phys. 291, 2629. DOI. ADS. ADSCrossRefGoogle Scholar
  3. Clette, F., Svalgaard, L., Vaquero, J.M., Cliver, E.W.: 2014, Revisiting the sunspot number: A 400-year perspective on the solar cycle. Space Sci. Rev. 186, 35. DOI. ADSCrossRefGoogle Scholar
  4. Lockwood, M., Owens, M.J., Barnard, L.: 2014, Centennial variations in sunspot number, open solar flux, and streamer belt width: 1. Correction of the sunspot number record since 1874. J. Geophys. Res. 119, 5172. DOI. ADS. CrossRefGoogle Scholar
  5. Svalgaard, L., Schatten, K.H.: 2016, Reconstruction of the sunspot group number: The backbone method. Solar Phys. 291, 2653. DOI. ADS. ADSCrossRefGoogle Scholar
  6. Svalgaard, L., Schatten, K.H.: 2017, Assessment of the failure of active days fraction method of sunspot group number reconstructions. ArXiv e-prints. arXiv. ADS.
  7. Usoskin, I.G.: 2017, A history of solar activity over millennia. Living Rev. Solar Phys. 14, 3. DOI. ADSCrossRefGoogle Scholar
  8. Usoskin, I.G., Kovaltsov, G.A., Lockwood, M., Mursula, K., Owens, M., Solanki, S.K.: 2016, A new calibrated sunspot group series since 1749: Statistics of active day fractions. Solar Phys. 291, 2685. DOI. ADS. ADSCrossRefGoogle Scholar
  9. Willamo, T., Usoskin, I.G., Kovaltsov, G.A.: 2017, Updated sunspot group number reconstruction for 1749 – 1996 using the active day fraction method. Astron. Astrophys. 601, A109. DOI. ADS. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of HelsinkiHelsinkiFinland
  2. 2.Space Climate Research UnitUniversity of OuluOuluFinland
  3. 3.Sodankylä Geophysical ObservatoryUniversity of OuluOuluFinland
  4. 4.Ioffe Physical-Technical InstituteSt. PetersburgRussia

Personalised recommendations