Solar Physics

, 292:34 | Cite as

The Effect of Sunspot Weighting

  • Leif SvalgaardEmail author
  • Marco Cagnotti
  • Sergio Cortesi
Sunspot Number Recalibration


Although W. Brunner began to weight sunspot counts (from 1926), using a method whereby larger spots were counted more than once, he compensated for the weighting by not counting enough smaller spots in order to maintain the same reduction factor (0.6) as was used by his predecessor A. Wolfer to reduce the count to R. Wolf’s original scale, so that the weighting did not have any effect on the scale of the sunspot number. In 1947, M. Waldmeier formalized the weighting (on a scale from 1 to 5) of the sunspot count made at Zurich and its auxiliary station Locarno. This explicit counting method, when followed, inflates the relative sunspot number over that which corresponds to the scale set by Wolfer (and matched by Brunner). Recounting some 60,000 sunspots on drawings from the reference station Locarno shows that the number of sunspots reported was “over counted” by \({\approx}\,44~\%\) on average, leading to an inflation (measured by an effective weight factor) in excess of 1.2 for high solar activity. In a double-blind parallel counting by the Locarno observer M. Cagnotti, we determined that Svalgaard’s count closely matches that of Cagnotti, allowing us to determine from direct observation the daily weight factor for spots since 2003 (and sporadically before). The effective total inflation turns out to have two sources: a major one (15 – 18 %) caused by weighting of spots, and a minor source (4 – 5 %) caused by the introduction of the Zürich classification of sunspot groups which increases the group count by 7 – 8 % and the relative sunspot number by about half that. We find that a simple empirical equation (depending on the activity level) fits the observed factors well, and use that fit to estimate the weighting inflation factor for each month back to the introduction of effective inflation in 1947 and thus to be able to correct for the over-counts and to reduce sunspot counting to the Wolfer method in use from 1894 onwards.


Sunspot weighting Waldmeier sunspot weight factor Correcting the Sunspot Number Locarno sunspot drawings 



We have benefited from participation in the four Sunspot Number Workshops ( ) and from discussions with the team at the WDC/SILSO. Sunspot data was supplied by WDC/SILSO, Royal Observatory of Belgium. We acknowledge with pleasure the use of drawings from Specola Solare Ticinese, Locarno ( ). This study includes data from the synoptic program at the 150-Foot Solar Tower of the Mt. Wilson Observatory ( ). The Mt. Wilson 150-Foot Solar Tower is operated by UCLA, with funding from NASA, ONR and NSF, under agreement with the Mt. Wilson Institute. We thank a reviewer for prompting us to re-examine the contribution of William Brunner. LS thanks Stanford University for support.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


  1. Balmaceda, L.A., Solanki, S.K., Krivova, N.A., Foster, S.: 2009, A homogeneous database of sunspot areas covering more than 130 years. J. Geophys. Res. 114, A07104.  DOI. ADSCrossRefGoogle Scholar
  2. Beck, R.: 1984, Zum Problem der Gruppeneinteilung von Sonnenflecken. In: Sonne – Mitteilungsblatt der Amateursonnenbeobachter 8, 64 ( [downloaded on 13 August 2016]. Google Scholar
  3. Brunner, W.: 1936, Zürich observatory. Terr. Magn. Atmos. Electr. 41(2), 210.  DOI. CrossRefGoogle Scholar
  4. Brunner, W.: 1945, Tabellen und Kurven zur Darstellung der Häufigkeit der Sonnenflecken in den Jahren 1749 – 1944. Astron. Mitt. Eidgenöss. Sternwarte Zür. 145, 135. Google Scholar
  5. 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
  6. Cortesi, S., Cagnotti, M., Bianda, M., Ramelli, R., Manna, A.: 2016, Sunspot observations and counting at specola solar ticinese in locarno since 1957. Solar Phys. 291, 3075.  DOI. ADSCrossRefGoogle Scholar
  7. Friedli, T.K.: 2009, Die Wolfsche Reihe der Sonnenfleckenrelativzahlen. In: Verbesserte Likelihood Ratio Tests zur Homogenitätsprüfung in struturelle Zustandsraummodellen, Südwestdeutcher Verlag für Hochschulschriften, Saarbrücken. Google Scholar
  8. Kopecký, M., Kuklin, G.V., Růžičková-Topolová, B.: 1980, On the relative inhomogeneity of long-term series of sunspot indices. Bull. Astron. Inst. Czechoslov. 31, 267. ADSGoogle Scholar
  9. 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. Space Phys. 119, 5172.  DOI. ADSCrossRefGoogle Scholar
  10. Ostrow, S.M., PoKempner, M.: 1952, The difference in the relationship between ionospheric critical frequencies and sunspot number for different sunspot cycles. J. Geophys. Res. 57(4), 473.  DOI. ADSCrossRefGoogle Scholar
  11. Pavai, V.S., Arlt, R., Dasi-Espuig, M., Krivova, N.A., Solanki, S.K.: 2015, Sunspot areas and tilt angles for solar cycles 7 – 10. Astron. Astrophys. 584, A73.  DOI. CrossRefGoogle Scholar
  12. Svalgaard, L.: 2007, Calibrating the Sunspot Number using “the Magnetic Needle”. CAWSES Newsletter 4(1). - Sunspots.pdf [downloaded on 13 August 2016].
  13. Svalgaard, L.: 2010, Updating the historical sunspot record. In: Cranmer, S.R., Hoeksema, J.T., Kohl, J.L. (eds.) SOHO-23: Understanding a Peculiar Solar Minimum, Astron. Soc. Pacific, San Francisco CS-428, 297. Google Scholar
  14. Svalgaard, L.: 2012, How well do we know the sunspot number? In: Mandrini, C.H., Webb, D.F. (eds.) Comparative Magnetic Minima: Characterizing Quiet Times in the Sun and Stars, Proc. IAU Sympos. 286, Cambridge University Press, Cambridge, 15.  DOI. Google Scholar
  15. Svalgaard, L.: 2014. [downloaded on 13 August 2016].
  16. Svalgaard, L.: 2016, Reconstruction of Solar Extreme Ultraviolet Flux 1740 – 2015. Solar Phys. 291.  DOI.
  17. Svalgaard, L.: 2017, A Recount of Sunspot Groups on Staudach’s Drawings. Solar Phys. 292, 4.  DOI. ADSCrossRefGoogle Scholar
  18. Svalgaard, L., Schatten, K.H.: 2016, Reconstruction of the Sunspot Group Number: The Backbone Method. Solar Phys. 291.  DOI.
  19. Waldmeier, M.: 1938, Chromosphärische Eruptionen. I. Zeit. Astrophys. 16, 276. ADSGoogle Scholar
  20. Waldmeier, M.: 1948, 100 Jahre Sonnenfleckenstatistik. Astron. Mitt. Eidgenöss. Sternwarte Zür. 152, 1. Google Scholar
  21. Waldmeier, M.: 1961, The Sunspot-Activity in the Years 1610 – 1960, Schulthess & Co., Swiss Federal Observatory, Zürich. Google Scholar
  22. Waldmeier, M.: 1968, Die Beziehung zwischen der Sonnenflecken-relativzahl und der Gruppenzahl. Astr. Mitteil. Eidgn. Sternw. Zürich 285, 1. Google Scholar
  23. Waldmeier, M.: 1978, Solar activity 1964 – 1976 (cycle no. 20). Astr. Mitteil. Eidgn. Sternw. Zürich 368, 1. ADSGoogle Scholar
  24. Wolf, R.: 1856, Beobachtungen der Sonnenflecken in den Jahren 1849 – 1855, Mittheil. über die Sonnenflecken I, 3. Google Scholar
  25. Wolfer, A.: 1907, Die Häufigkeit und heliographische Verteilung der Sonnenflecken im Jahre 1906. Astron. Mitt. Eidgenöss. Sternwarte Zür. XCVIII, 10, 251. Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Specula Solare TicineseLocarnoSwitzerland

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