Advertisement

Solar Physics

, Volume 281, Issue 2, pp 847–862 | Cite as

A Bayesian Analysis of the Correlations Among Sunspot Cycles

  • Y. Yu
  • D. A. van Dyk
  • V. L. Kashyap
  • C. A. Young
Article

Abstract

Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and we conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97±15, to occur in January – February 2014 ± six months.

Keywords

Solar Activity Posterior Distribution Markov Chain Monte Carlo Sunspot Number Sunspot Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported by CXC NASA contract NAS 8-39073 (VLK) and NSF grants DMS 04-06085 and DMS 09-07522 (DvD, YY).

References

  1. Benestad, R.E.: 2005, Geophys. Res. Lett. 32, L15714. ADSCrossRefGoogle Scholar
  2. Bonev, B.P., Penev, K.M., Sello, S.: 2003, Astrophys. J. Lett. 605, L81. ADSCrossRefGoogle Scholar
  3. Charbonneau, P.: 2007, Adv. Space Res. 39, 11 1661. CrossRefGoogle Scholar
  4. Charbonneau, P., Dikpati, M.: 2000, Astrophys. J. 543, 1027. ADSCrossRefGoogle Scholar
  5. Choudhuri, A.R.: 1992, Astron. Astrophys. 253, 277. ADSMATHGoogle Scholar
  6. Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Phys. Rev. Lett. 98, 131103. ADSCrossRefGoogle Scholar
  7. Dikpati, M., Gilman, P.A.: 2006, Astrophys. J. 649, 498. ADSCrossRefGoogle Scholar
  8. Dikpati, M., de Toma, G., Gilman, P.A.: 2006, Geophys. Res. Lett. 33, L05102. CrossRefGoogle Scholar
  9. Esch, D.N., Connors, A., Karovska, M., van Dyk, D.A.: 2004, Astrophys. J. 610, 1213. ADSCrossRefGoogle Scholar
  10. Gelfand, A.E., Smith, A.F.M.: 1990, J. Am. Stat. Assoc. 85, 398. MathSciNetMATHCrossRefGoogle Scholar
  11. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: 2004, Bayesian Data Analysis, 2nd edn., CRC Press, London. MATHGoogle Scholar
  12. Geman, S., Geman, D.: 1984, IEEE Trans. Pattern Anal. Mach. Intell. 6, 721 – 741. MATHCrossRefGoogle Scholar
  13. Gil-Alana, L.A.: 2009, Solar Phys. 257, 371, ADS: 2009SoPh..257..371G, doi: 10.1007/s11207-009-9390-1. ADSCrossRefGoogle Scholar
  14. Hastings, W.K.: 1970, Biometrika 57, 97 – 109. MATHCrossRefGoogle Scholar
  15. Hathaway, D., Wilson, R.M.: 2006, Geophys. Res. Lett. 33, L18101. ADSCrossRefGoogle Scholar
  16. Hathaway, D., Wilson, R.M., Reichmann, D.J.: 1994, Solar Phys. 151, 177, ADS: 1994SoPh..151..177H, doi: 10.1007/BF00654090. ADSCrossRefGoogle Scholar
  17. Hathaway, D., Wilson, R.M., Reichmann, E.J.: 2002, Solar Phys. 211, 357, ADS: 2002SoPh..211..357H, doi: 10.1023/A:1022425402664. ADSCrossRefGoogle Scholar
  18. Hill, F., Howe, R., Komm, R., Hernández, I.G., Kholikov, S., Leibacher, J.: 2010, In: Brummell, N.H., Brun, A.S., Miesch, M.S., Ponty, Y. (eds.) Astrophysical Dynamics: From Stars to Galaxies, Proc. IAU Symp. 271, Cambridge University Press, Cambridge, 15. Google Scholar
  19. Hudson, H.: 2007, Astrophys. J. Lett. 663, L45. ADSCrossRefGoogle Scholar
  20. Kakad, B.: 2011, Solar Phys. 270, 393, ADS: 2011SoPh..270..393K, doi: 10.1007/s11207-011-9726-5. ADSCrossRefGoogle Scholar
  21. Kane, R.P.: 2001, Solar Phys. 202, 395, ADS: 2001SoPh..202..395K, doi: 10.1023/A:1012211803591. ADSCrossRefGoogle Scholar
  22. Kane, R.P.: 2008, Solar Phys. 248, 203, ADS: 2008SoPh..248..203K, doi: 10.1007/s11207-008-9125-8. ADSCrossRefGoogle Scholar
  23. Kendall, M.: 1975, Rank Correlation Methods, Griffin, London. MATHGoogle Scholar
  24. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: 1953, J. Chem. Phys. 21, 1087 – 1092. ADSCrossRefGoogle Scholar
  25. Noble, P.L., Wheatland, M.S.: 2012, Solar Phys. 276, 363, ADS: 2012SoPh..276..363N, doi: 10.1007/s11207-011-9884-5. ADSCrossRefGoogle Scholar
  26. Park, T., van Dyk, D.A., Siemiginowska, A.: 2008, Astrophys. J. 688, 807. ADSCrossRefGoogle Scholar
  27. Pesnell, W.D.: 2008, Solar Phys. 252, 209, ADS: 2008SoPh..252..209P, doi: 10.1007/s11207-008-9252-2. ADSCrossRefGoogle Scholar
  28. Ramesh, K.B., Lakshmi, N.B.: 2012, Solar Phys. 276, 395, ADS: 2012SoPh..276..395R, doi: 10.1007/s11207-011-9866-7. ADSCrossRefGoogle Scholar
  29. Sabarinath, A., Anilkumar, A.K.: 2008, Solar Phys. 250, 183, ADS: 2008SoPh..250..183S, doi: 10.1007/s11207-008-9209-5. ADSCrossRefGoogle Scholar
  30. Schüssler, M.: 2007, Astron. Nachr. 328, 1087. ADSMATHCrossRefGoogle Scholar
  31. Solanki, S.K., Usoskin, I.G., Kromer, B., Schüssler, M., Beer, J.: 2004, Nature 431, 1084. ADSCrossRefGoogle Scholar
  32. Svalgaard, L.: 2010, arXiv:1008.4832.
  33. Usoskin, I.G., Solanki, S.K., Kovaltsov, G.A.: 2007, Astron. Astrophys. 471, 301. ADSCrossRefGoogle Scholar
  34. van Dyk, D.A., Connors, A., Kashyap, V.L., Siemiginowska, A.: 2001, Astrophys. J. 548, 224. ADSCrossRefGoogle Scholar
  35. Vaquero, J.M., Trigo, R.M.: 2008, Solar Phys. 250, 199, ADS: 2008SoPh..250..199V, doi: 10.1007/s11207-008-9211-y. ADSCrossRefGoogle Scholar
  36. Volobuev, D.M.: 2009, Solar Phys. 258, 319, ADS: 2009SoPh..258..319V, doi: 10.1007/s11207-009-9429-3. ADSCrossRefGoogle Scholar
  37. Waldmeier, M.: 1935, Astron. Mitt. Eidgenöss. Sternwarte Zür. 14, 105. ADSGoogle Scholar
  38. Waldmeier, M.: 1939, Astron. Mitt. Eidgenöss. Sternwarte Zür. 14, 470. ADSGoogle Scholar
  39. Waldmeier, M.: 1971, Astron. Mitt. Eidgenöss. Sternwarte Zür. 304, 10. ADSGoogle Scholar
  40. Watari, S.: 2009, Space Weather 6, S12003. ADSCrossRefGoogle Scholar
  41. Wolf, R.: 1852, Viertel. Nat. Ges. Bern 245, 179. Google Scholar
  42. Xu, T., Wu, J., Wu, Z.-S., Li, Q.: 2008, Chin. J. Astron. Astrophys. 8, 337. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Y. Yu
    • 1
  • D. A. van Dyk
    • 2
  • V. L. Kashyap
    • 3
  • C. A. Young
    • 4
  1. 1.University of CaliforniaIrvineUSA
  2. 2.Imperial College LondonLondonUK
  3. 3.Harvard-Smithsonian Center for AstrophysicsCambridgeUSA
  4. 4.ADNET Systems Inc.NASA/GSFCGreenbeltUSA

Personalised recommendations