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A Bayesian Analysis of the Correlations Among Sunspot Cycles

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.

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References

  1. Benestad, R.E.: 2005, Geophys. Res. Lett. 32, L15714.

  2. Bonev, B.P., Penev, K.M., Sello, S.: 2003, Astrophys. J. Lett. 605, L81.

  3. Charbonneau, P.: 2007, Adv. Space Res. 39, 11 1661.

  4. Charbonneau, P., Dikpati, M.: 2000, Astrophys. J. 543, 1027.

  5. Choudhuri, A.R.: 1992, Astron. Astrophys. 253, 277.

  6. Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Phys. Rev. Lett. 98, 131103.

  7. Dikpati, M., Gilman, P.A.: 2006, Astrophys. J. 649, 498.

  8. Dikpati, M., de Toma, G., Gilman, P.A.: 2006, Geophys. Res. Lett. 33, L05102.

  9. Esch, D.N., Connors, A., Karovska, M., van Dyk, D.A.: 2004, Astrophys. J. 610, 1213.

  10. Gelfand, A.E., Smith, A.F.M.: 1990, J. Am. Stat. Assoc. 85, 398.

  11. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: 2004, Bayesian Data Analysis, 2nd edn., CRC Press, London.

  12. Geman, S., Geman, D.: 1984, IEEE Trans. Pattern Anal. Mach. Intell. 6, 721 – 741.

  13. Gil-Alana, L.A.: 2009, Solar Phys. 257, 371, ADS:  2009SoPh..257..371G , doi: 10.1007/s11207-009-9390-1 .

  14. Hastings, W.K.: 1970, Biometrika 57, 97 – 109.

  15. Hathaway, D., Wilson, R.M.: 2006, Geophys. Res. Lett. 33, L18101.

  16. Hathaway, D., Wilson, R.M., Reichmann, D.J.: 1994, Solar Phys. 151, 177, ADS:  1994SoPh..151..177H , doi: 10.1007/BF00654090 .

  17. Hathaway, D., Wilson, R.M., Reichmann, E.J.: 2002, Solar Phys. 211, 357, ADS: 2002SoPh..211..357H , doi: 10.1023/A:1022425402664 .

  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.

  19. Hudson, H.: 2007, Astrophys. J. Lett. 663, L45.

  20. Kakad, B.: 2011, Solar Phys. 270, 393, ADS: 2011SoPh..270..393K , doi: 10.1007/s11207-011-9726-5 .

  21. Kane, R.P.: 2001, Solar Phys. 202, 395, ADS: 2001SoPh..202..395K , doi: 10.1023/A:1012211803591 .

  22. Kane, R.P.: 2008, Solar Phys. 248, 203, ADS: 2008SoPh..248..203K , doi: 10.1007/s11207-008-9125-8 .

  23. Kendall, M.: 1975, Rank Correlation Methods, Griffin, London.

  24. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: 1953, J. Chem. Phys. 21, 1087 – 1092.

  25. Noble, P.L., Wheatland, M.S.: 2012, Solar Phys. 276, 363, ADS: 2012SoPh..276..363N , doi: 10.1007/s11207-011-9884-5 .

  26. Park, T., van Dyk, D.A., Siemiginowska, A.: 2008, Astrophys. J. 688, 807.

  27. Pesnell, W.D.: 2008, Solar Phys. 252, 209, ADS:  2008SoPh..252..209P , doi: 10.1007/s11207-008-9252-2 .

  28. Ramesh, K.B., Lakshmi, N.B.: 2012, Solar Phys. 276, 395, ADS: 2012SoPh..276..395R , doi: 10.1007/s11207-011-9866-7 .

  29. Sabarinath, A., Anilkumar, A.K.: 2008, Solar Phys. 250, 183, ADS: 2008SoPh..250..183S , doi: 10.1007/s11207-008-9209-5 .

  30. Schüssler, M.: 2007, Astron. Nachr. 328, 1087.

  31. Solanki, S.K., Usoskin, I.G., Kromer, B., Schüssler, M., Beer, J.: 2004, Nature 431, 1084.

  32. Svalgaard, L.: 2010, arXiv: 1008.4832 .

  33. Usoskin, I.G., Solanki, S.K., Kovaltsov, G.A.: 2007, Astron. Astrophys. 471, 301.

  34. van Dyk, D.A., Connors, A., Kashyap, V.L., Siemiginowska, A.: 2001, Astrophys. J. 548, 224.

  35. Vaquero, J.M., Trigo, R.M.: 2008, Solar Phys. 250, 199, ADS: 2008SoPh..250..199V , doi: 10.1007/s11207-008-9211-y .

  36. Volobuev, D.M.: 2009, Solar Phys. 258, 319, ADS: 2009SoPh..258..319V , doi: 10.1007/s11207-009-9429-3 .

  37. Waldmeier, M.: 1935, Astron. Mitt. Eidgenöss. Sternwarte Zür. 14, 105.

  38. Waldmeier, M.: 1939, Astron. Mitt. Eidgenöss. Sternwarte Zür. 14, 470.

  39. Waldmeier, M.: 1971, Astron. Mitt. Eidgenöss. Sternwarte Zür. 304, 10.

  40. Watari, S.: 2009, Space Weather 6, S12003.

  41. Wolf, R.: 1852, Viertel. Nat. Ges. Bern 245, 179.

  42. Xu, T., Wu, J., Wu, Z.-S., Li, Q.: 2008, Chin. J. Astron. Astrophys. 8, 337.

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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).

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Correspondence to Y. Yu.

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Yu, Y., van Dyk, D.A., Kashyap, V.L. et al. A Bayesian Analysis of the Correlations Among Sunspot Cycles. Sol Phys 281, 847–862 (2012). https://doi.org/10.1007/s11207-012-0090-x

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Keywords

  • Solar Activity
  • Posterior Distribution
  • Markov Chain Monte Carlo
  • Sunspot Number
  • Sunspot Cycle