Solar Physics

, Volume 249, Issue 1, pp 121–133 | Cite as

Forecast of the Decadal Average Sunspot Number

  • D. M. VolobuevEmail author
  • N. G. Makarenko


The forecast of the decadal average sunspot number (SN) becomes possible with an extension of telescopic observations based on proxy reconstructions using the tree ring radiocarbon data during the Holocene. These decadal numbers (SNRC) provide a powerful statistic to verify the forecasting methods. Complicated dynamics of long-term solar activity and noise of proxy-based reconstruction make the one-step-ahead forecast challenging for any forecasting method. Here we construct a continuous data set of SNRC which extends the group sunspot number and the international sunspot number. The known technique of nonlinear forecast, the local linear approximation, is adapted to estimate the coming SN. Both the method and the continuous data set were tested and tuned to obtain the minimum of a normalized average prediction error (E) during the last millennium using several past millennia as a training data set. E=0.58σ D is achieved to forecast the SN successive differences whose standard deviation is σ D=7.39 for the period of training. This corresponds to the correlation (r=0.97) between true and forecasted SN. This error is significantly smaller than the prediction error when the surrogate data were used for the training data set, and proves the nonlinearity in the decadal SN. The estimated coming SN is smaller than the previous one.


Solar activity Nonlinear forecast Radiocarbon 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Barnett, A.G., Wolff, R.: 2005, IEEE Trans. Signal Process. 53, 26. CrossRefMathSciNetGoogle Scholar
  2. Clilverd, M.A., Clarke, E., Ulich, T., Rishbeth, H., Jarvis, M.J.: 2006, Space Weather 4, S09005. CrossRefGoogle Scholar
  3. Farmer, J.D., Sidorowich, J.J.: 1987, Phys. Rev. Lett. 59, 845. CrossRefADSMathSciNetGoogle Scholar
  4. Hoyt, D.V., Schatten, K.H.: 1996, Solar Phys. 165, 181. CrossRefADSGoogle Scholar
  5. Kane, R.P.: 2007, Solar Phys. 243, 205. CrossRefADSGoogle Scholar
  6. Kantz, H., Schreiber, T.: 2004, Nonlinear Time Series Analysis, 2nd edn., Cambridge University Press, Cambridge, 369. zbMATHGoogle Scholar
  7. Kitchatinov, L.L., Pipin, V.V., Makarov, V.I., Tlatov, A.G.: 1999, Solar Phys. 189, 227. CrossRefADSGoogle Scholar
  8. Knobloch, E., Landsberg, A.S.: 1996, Mon. Not. Roy. Astron. Soc. 278, 294. ADSGoogle Scholar
  9. Kugiumtzis, D.: 2000, Phys. Rev. E 62, 1. CrossRefGoogle Scholar
  10. Lorenz, E.N.: 1969, J. Atmos. Sci. 26, 636. CrossRefADSGoogle Scholar
  11. Marchal, O.: 2005, Clim. Dyn. 24, 71. CrossRefGoogle Scholar
  12. Muscheler, R., Joos, F., Müller, S.A., Snowball, I.: 2005, Nature 436, E3. CrossRefGoogle Scholar
  13. Muscheler, R., Joos, F., Beer, J., Müller, S., Vonmoos, M., Snowball, I.: 2007, Quart. Sci. Rev. 26, 82. CrossRefADSGoogle Scholar
  14. Nagovitsyn, Yu.A.: 2005, Astron. Lett. 31, 557. CrossRefADSGoogle Scholar
  15. Nicolis, C.: 1998, J. Atmos. Sci. 55, 465. CrossRefADSGoogle Scholar
  16. Ogurtsov, M.G.: 2005, Solar Phys. 231, 167. CrossRefADSGoogle Scholar
  17. Ostryakov, V.M., Usoskin, I.G.: 1990, Solar Phys. 127, 405. CrossRefADSGoogle Scholar
  18. Packard, N.H., Grutchfield, J.P., Farmer, J.D., Shaw, R.S.: 1980, Phys. Rev. Lett. 45, 712. CrossRefADSGoogle Scholar
  19. Reimer, P.J., Baillie, M.G.L., Bard, E., Bayliss, A., Beck, J.W., Bertrand, C.J.H., et al.: 2004, Radiocarbon 46, 1029. Google Scholar
  20. Sello, S.: 2001, Astron. Astrophys. 377, 312. CrossRefADSGoogle Scholar
  21. Solanki, S.K., Usoskin, I.G., Kromer, B., Schüssler, M., Beer, J.: 2004, Nature 431, 1084. CrossRefADSGoogle Scholar
  22. Stuiver, M., Quay, P.D.: 1980, Science 207, 11. CrossRefADSGoogle Scholar
  23. Stuiver, M., Reimer, P.J., Bard, E., Beck, J.W., Burr, G.S., Hughen, K.A., Kromer, B., McCormac, G., van der Plicht, J., Spurk, M.: 1998, Radiocarbon 40, 1041. Google Scholar
  24. Usoskin, I.G., Kovaltsov, G.A.: 2004, Solar Phys. 224, 37. CrossRefADSGoogle Scholar
  25. Volobuev, D.: 2006, Solar Phys. 238, 421. CrossRefADSGoogle Scholar
  26. Volobuev, D.M., Nagovitsyn, Yu.A., Jungner, H., Ogurtsov, M.G., Miletsky, E.V.: 2004, In: Stepanov, A.V., Benevolenskaya, E.E., Kosivichev, A.G. (eds.) Multiwavelength Investigations of Solar Activity, IAU Symp. 223, 565. Google Scholar
  27. Weiss, N.O.: 1985, J. Stat. Phys. 39, 477. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Pulkovo ObservatorySt.-PetersburgRussia

Personalised recommendations