Solar Physics

, Volume 291, Issue 12, pp 3793–3805 | Cite as

Dependence of the Sunspot-Group Size on the Level of Solar Activity and its Influence on the Calibration of Solar Observers

  • I. G. UsoskinEmail author
  • G. A. Kovaltsov
  • T. Chatzistergos


We study the distribution of the sunspot-group size (area) and its dependence on the level of solar activity. We show that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is mainly defined by large groups. We analyze the possible influence of solar activity on the ability of a realistic observer to see and report the daily number of sunspot groups. It is shown that the relation between the number of sunspot groups as seen by different observers with different observational acuity thresholds is strongly nonlinear and cannot be approximated by the traditionally used linear scaling (\(k\)-factors). The observational acuity threshold [\(A_{\mathrm{th}}\)] is considered to quantify the quality of each observer, instead of the traditional relative \(k\)-factor. A nonlinear \(c\)-factor based on \(A_{\mathrm{th}}\) is proposed, which can be used to correct each observer to the reference conditions. The method is tested on a pair of principal solar observers, Wolf and Wolfer, and it is shown that the traditional linear correction, with the constant \(k\)-factor of 1.66 to scale Wolf to Wolfer, leads to an overestimate of solar activity around solar maxima.


Solar activity Sunspots Solar observations Solar cycle 



I.G.U. and G.A.K. acknowledge support by the Academy of Finland to the ReSoLVE Center of Excellence (project No. 272157). T.C. acknowledges the postgraduate fellowship of the International Max Planck Research School on Physical Processes in the Solar System and Beyond.

Disclosure of Potential Conflict of Interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.ReSoLVE, Space Climate GroupUniversity of OuluOuluFinland
  2. 2.Sodankylä Geophysical ObservatoryUniversity of OuluOuluFinland
  3. 3.Ioffe Physical-Technical InstituteSt. PetersburgRussia
  4. 4.Max-Planck-Institut für SonnensystemforschungGöttingenGermany

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