Solar Physics

, Volume 291, Issue 9–10, pp 2685–2708 | Cite as

A New Calibrated Sunspot Group Series Since 1749: Statistics of Active Day Fractions

  • I. G. UsoskinEmail author
  • G. A. Kovaltsov
  • M. Lockwood
  • K. Mursula
  • M. Owens
  • S. K. Solanki
Sunspot Number Recalibration


Although sunspot-number series have existed since the mid-nineteenth century, they are still the subject of intense debate, with the largest uncertainty being related to the “calibration” of the visual acuity of individual observers in the past. A daisy-chain regression method is usually applied to inter-calibrate the observers, which may lead to significant bias and error accumulation. Here we present a novel method for calibrating the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900 – 1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [\(S_{\mathrm{S}}\)] defined such that the observer is assumed to miss all of the groups with an area smaller than \(S_{\mathrm{S}}\) and report all the groups larger than \(S_{\mathrm{S}}\). Next, using a Monte-Carlo method, we construct a correction matrix for each observer from the reference data set. The correction matrices are significantly non-linear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot-group records reported by the observers for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series is provided as supplementary material in electronic form and displays secular minima around 1800 (Dalton Minimum) and 1900 (Gleissberg Minimum), as well as the Modern Grand Maximum of activity in the second half of the twentieth century. The uniqueness of the grand maximum is confirmed for the last 250 years. We show that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the eighteenth and nineteenth centuries in some reconstructions.


Solar activity Sunspots Solar observations Solar cycle 



We are thankful to Rainer Arlt for the revised data of Staudacher. Contributions from I. Usoskin, K. Musrsula, and G. Kovaltsov were done in the framework of the ReSoLVE Centre of Excellence (Academy of Finland, project no. 272157). Work at the University of Reading is supported by the UK Science and Technology Facilities Council under consolidated grant number ST/M000885/1. G. Kovaltsov acknowledges partial support from Programme No. 7 of the Presidium RAS. This work was partly supported by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interests.

Supplementary material

11207_2015_838_MOESM1_ESM.xls (228 kb)
Number of sunspot group, monthly series for the period 1749 through 1899. (XLS 228 kB)


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • I. G. Usoskin
    • 1
    • 2
    Email author
  • G. A. Kovaltsov
    • 1
    • 3
  • M. Lockwood
    • 4
  • K. Mursula
    • 1
  • M. Owens
    • 4
  • S. K. Solanki
    • 5
    • 6
  1. 1.ReSoLVE, Space Physics GroupUniversity of OuluOuluFinland
  2. 2.Sodankylä Geophysical ObservatoryUniversity of OuluOuluFinland
  3. 3.Ioffe Physical-Technical InstituteSt. PetersburgRussia
  4. 4.Department of MeteorologyUniversity of ReadingReadingUK
  5. 5.Max-Planck Institute for Solar System ResearchGöttingenGermany
  6. 6.School of Space ResearchKyung Hee UniversityYonginKorea

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