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A nonlinear solar cycle model with potential for forecasting on a decadal time scale

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Abstract

This paper describes a novel non-linear oscillator model of the sunspot cycle which accurately reproduces several of the observed qualitative and quantitative characteristics of the real cycle including the long term amplitude modulation pattern. The model accounts for 96% of cycle peak height variance over the period 1859 to 1980. The aim of this work is to assess the potential of such models for forecasting solar activity on decadal and possibly longer time scales. Longer term forecasts may have practical economic significance because of the growing evidence for relationships between solar cycle variations and terrestrial weather and climatic variations (Bandeen and Moran, 1975; Currie, 1980; Williams, 1981). The model predicts that cycle 22 will have an annual mean peak amplitude in the range 25 to 45, the lowest peak activity for 260 yr.

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References

  • Akaike, H.: 1978, The Statistician 27, 217.

    Google Scholar 

  • Andronov, A., Witt, A., and Khaikin, C.: 1966, The Theory of Oscillators, Pergamon Press, Oxford.

    Google Scholar 

  • ASRRG: 1977, Ancient Sunspot Records Research Group, Chinese Astron. 1, 347.

  • Bandeen, W. R. and Moran, S. P.: 1975, ‘Possible Relationships between Solar Activity and Meteorological Phenomena’, NASA Publ. SP-366.

  • Box, G. E. P. and Jenkins, G. M.: 1970, Time Series Analysis, Forecasting and Control, Holden Day.

  • Brown, G. M.: 1974, Nature 251, 592.

    Google Scholar 

  • Brown, G. M.: 1976, Monthly Notices Roy. Astron. Soc. 174, 185.

    Google Scholar 

  • Brown, G. M.: 1981, Solar Phys. 74, 125.

    Google Scholar 

  • Cohen, T. J. and Lintz, P. R.: 1974, Nature 250, 398.

    Google Scholar 

  • Cole, T. W.: 1973, Solar Phys. 30, 103.

    Google Scholar 

  • Courtillot, V. and Le Moüel, J. L.: 1976, J. Geophys. Res. 81, 2441.

    Google Scholar 

  • Currie, R. G.: 1980, Geophys. J. Roy. Astron. Soc. 61, 131.

    Google Scholar 

  • Dickie, R. H.: 1978, Nature 276, 676.

    Google Scholar 

  • Eddy, J. A.: 1977, Science 198, 824.

    Google Scholar 

  • Granger, C. W. J. and Anderson, A. P.: 1978, An Introduction to Bilinear Time Series Models, Vandenhoech and Ruprecht.

  • Gurney, W., Blythe, S., and Nisbet, R.: 1980, Nature 287, 17.

    Google Scholar 

  • Hill, J. R.: 1977, Nature 266, 151.

    Google Scholar 

  • Kopecký, M.: 1980, Bull. Astron. Inst. Czech. 31, 1.

    Google Scholar 

  • Kopecký, M.: 1983, Bull. Astron. Inst. Czech. 34, 23.

    Google Scholar 

  • Livshits, M. A., Valchuck, T., and Feldstein, Y.: 1979, Nature 278, 241.

    Google Scholar 

  • May, R. M.: 1976, Nature 261, 459.

    Google Scholar 

  • Moffat, H. K.: 1980, Nature 285, 16.

    Google Scholar 

  • Moore, D. M., Toomre, J., Knoblock, E., and Weiss, N. O.: 1983, Nature 303, 663.

    Google Scholar 

  • Morris, M. J.: 1977, J. Roy. Stat. Soc. A140, 437.

    Google Scholar 

  • Oerlemans, J.: 1980, Nature 287, 430.

    Google Scholar 

  • Ramaswamy, G.: 1977, Nature 265, 713.

    Google Scholar 

  • Schuster, A.: 1906, Roy. Soc. Proc. A206, 69.

    Google Scholar 

  • Stuiver, M. and Quay, P. D.: 1980, Science 207, 11.

    Google Scholar 

  • Tong, H. and Lim, K. S.: 1979, Department of Mathematics UMIST, Technical Report No. 117.

  • Waldmeir, M.: 1961, Sunspot Activity in the Years 1610–1690, Schulthess and Co., Zürich.

    Google Scholar 

  • Wilcox, J. M.: 1976, Science 192, 745.

    Google Scholar 

  • Williams, G. E.: 1981, Nature 291, 624.

    Google Scholar 

  • Wilson, O. C., Vaughan, A. H., and Michalas, D.: 1981, Scientific Am. 244, 104.

    Google Scholar 

  • Yoshimura, H.: 1980, Astrophys. J. 235, 625.

    Google Scholar 

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Gregg, D.P. A nonlinear solar cycle model with potential for forecasting on a decadal time scale. Sol Phys 90, 185–194 (1984). https://doi.org/10.1007/BF00153794

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