Skip to main content
Log in

The Amplitude of Sunspot Minimum as a Favorable Precursor for the Prediction of the Amplitude of the Next Solar Maximum and the Limit of the Waldmeier Effect

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

The linear relationship between the maximum amplitudes (R max) of sunspot cycles and preceding minima (R min) is one of the precursor methods used to predict the amplitude of the upcoming solar cycle. In the recent past this method has been subjected to severe criticism. In this communication we show that this simple method is reliable and can profitably be used for prediction purposes. With the 13-month smoothed R min of 1.8 at the beginning, it is predicted that the R max of the ongoing cycle will be around 85±17, suggesting that Cycle 24 may be of moderate strength. Based on a second-order polynomial dependence between the rise time (T R) and R max, it is predicted that Cycle 24 will reach its smoothed maximum amplitude during the third quarter of the year 2013. An important finding of this paper is that the rise time cycle amplitude relation reaches a minimum at about 3 to 3.5 years, corresponding to a cycle amplitude of about 160. The Waldmeier effect breaks down at this point and T R increases further with increasing R max. This feature, we believe, may put a constraint on the flux transport dynamo models and lead to more accurate physical principles-based predictions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahluwalia, H.S.: 2000, Solar cycle 23 prediction update. Adv. Space Res. 26, 187 – 192.

    Article  MathSciNet  ADS  Google Scholar 

  • Ahluwalia, H.S., Ygbuhay, R.C.: 2010, Current forecast for sunspot cycle 24 parameters. In: AIP conf. Proc. 12th Solar Wind Conf., 671 – 674. doi: 10.1063/1.3395956 .

    Google Scholar 

  • Brajša, R., Wöhl, H., Hanslmeier, A., Verbanac, G., Ruždjak, D., Cliver, E., Svalgaard, L., Roth, M.: 2009, On solar cycle predictions and reconstructions. Astron. Astrophys. 496, 855 – 861.

    Article  ADS  Google Scholar 

  • Brown, G.M.: 1976, What determines sunspot maximum. Mon. Not. Roy. Astron. Soc. 174, 185 – 189.

    ADS  Google Scholar 

  • Cameron, R., Schüssler, M.: 2008, A robust correlation between growth rate and amplitude of solar cycles: consequences for prediction methods. Astrophys. J. 685, 1291 – 1296.

    Article  ADS  Google Scholar 

  • Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Predicting solar cycle 24 with a solar dynamo model. Phys. Rev. Lett. 98, 131103.

    Article  ADS  Google Scholar 

  • Dikpati, M., Gilman, P.A.: 2006, Simulating and predicting solar cycles using a flux-transport dynamo. Astrophys. J. 649, 498 – 514.

    Article  ADS  Google Scholar 

  • Dikpati, M., Gilman, P.A., de Toma, G.: 2008, The Waldmeier effect: an artifact of the definition of Wolf sunspot number? Astrophys. J. 673, 99 – 101.

    Article  ADS  Google Scholar 

  • Du, Z.: 2011, The relationship between prediction accuracy and correlation coefficient. Solar Phys. 270, 407 – 416.

    Article  ADS  Google Scholar 

  • Du, Z.L., Wang, H.N.: 2010, Does a low solar cycle minimum hint at a weak upcoming cycle? Res. Astron. Astrophys. 10, 950 – 955.

    Article  ADS  Google Scholar 

  • Du, Z., Wang, H., Zhang, L.: 2009a, Correlation function analysis between sunspot cycle amplitudes and rise times. Solar Phys. 255, 179 – 185.

    Article  ADS  Google Scholar 

  • Du, Z.L., Li, R., Wang, H.N.: 2009b, The predictive power of Ohl’s precursor method. Astron. J. 138, 1998 – 2001.

    Article  ADS  Google Scholar 

  • Harvey, K.L., White, O.R.: 1999, What is solar cycle minimum? J. Geophys. Res. 104, 19759 – 19764.

    Article  ADS  Google Scholar 

  • Hathaway, D.H.: 2010, The solar cycle. Living Rev. Solar Phys. 7, 1 – 65.

    ADS  Google Scholar 

  • Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, The shape of the sunspot cycle. Solar Phys. 151, 177 – 190.

    Article  ADS  Google Scholar 

  • Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 2002, Group sunspot numbers: sunspot cycle characteristics. Solar Phys. 211, 357 – 370.

    Article  ADS  Google Scholar 

  • Javaraiah, J.: 2007, North-south asymmetry in solar activity: predicting the amplitude of the next solar cycle. Mon. Not. Roy. Astron. Soc. 377, 34 – 38.

    Article  ADS  Google Scholar 

  • Kakad, B.: 2011, A new method for prediction of peak sunspot number and ascent time of the solar cycle. Solar Phys. 270, 393 – 406.

    Article  ADS  Google Scholar 

  • Kane, R.P.: 1997, A preliminary estimate of the size of the coming solar cycle 23, based on Ohl’s precursor method. Geophys. Res. Lett. 24, 1899 – 1902.

    Article  ADS  Google Scholar 

  • Karak, B.B., Choudhuri, A.R.: 2010, The Waldmeier effect in sunspot cycles. In: Hasan, S.S., Rutten, R.J. (eds.) Magnetic Coupling Between the Interior and Atmosphere of the Sun, 402 – 404. doi: 10.1007/978-3-642-02859-5-40 .

    Chapter  Google Scholar 

  • Karak, B.B., Choudhuri, A.R.: 2011, The Waldmeier effect and the flux transport solar dynamo. Mon. Not. Roy. Astron. Soc. 410, 1503 – 1512.

    ADS  Google Scholar 

  • Kennedy, J.B., Neville, A.M.: 1964, Basic Statistical Methods for Engineers and Scientists, Dun-Donnelley, New York, 180.

    Google Scholar 

  • Lantos, P.: 2000, Prediction of the maximum amplitude of solar cycles using the ascending inflexion point. Solar Phys. 196, 221 – 225.

    Article  ADS  Google Scholar 

  • McKinnon, J.A.: 1987, Sunspot numbers, 1610 – 1985: based on “The sunspot activity in the years 1610 – 1960, by Prof. M. Waldmeier”, Report UAG, 0579-7144; 95. World Data Center A for Solar-Terrestrial Physics, Boulder, Colorado.

  • Pesnell, W.D.: 2008, Predictions of solar cycle 24. Solar Phys. 252, 209 – 220.

    Article  ADS  Google Scholar 

  • Petrovay, K.: 2010, Solar cycle prediction. Living Rev. Solar Phys. 1, 6 – 59.

    ADS  Google Scholar 

  • Ramesh, K.B.: 2000, Dependence of SSN M on SSN m – a reconsideration for predicting the amplitude of a sunspot cycle. Solar Phys. 197, 421 – 424.

    Article  ADS  Google Scholar 

  • Schatten, K.: 2005, Fair space weather for solar cycle 24. Geophys. Res. Lett. 32, 21106. doi: 10.1029/2005GL024363 .

    Article  ADS  Google Scholar 

  • Schatten, K.H., Scherrer, P.H., Svalgaard, L., Wilcox, J.M.: 1978, Using dynamo theory to predict the sunspot number during solar cycle 21. Geophys. Res. Lett. 5, 411 – 414.

    Article  ADS  Google Scholar 

  • Solanki, S.K., Krivova, N.A., Schüssler, M., Fligge, M.: 2002, Search for a relationship between solar cycle amplitude and length. Astron. Astrophys. 396, 1029 – 1035.

    Article  ADS  Google Scholar 

  • Svalgaard, L., Cliver, E.W., Kamide, Y.: 2005, Sunspot cycle 24: smallest cycle in 100 years? Geophys. Res. Lett. 32, 01104. doi: 10.1029/2005GL021664 .

    Article  Google Scholar 

  • Waldmeier, M.: 1935, Neue Eigenschaften der Sonnenfleckenkurve. Astron. Mitt. 14, 105 – 130.

    ADS  Google Scholar 

  • Wang, Y.M., Sheeley, N.R.J.: 2009, Understanding the geomagnetic precursor of the solar cycle. Astrophys. J. 694, 11 – 15.

    Article  ADS  Google Scholar 

  • Wilson, R.M., Hathaway, D.H., Reichmann, E.J.: 1998, An estimate for the size of cycle 23 based on near minimum conditions. J. Geophys. Res. 103, 6595 – 6603.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. B. Ramesh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramesh, K.B., Lakshmi, N.B. The Amplitude of Sunspot Minimum as a Favorable Precursor for the Prediction of the Amplitude of the Next Solar Maximum and the Limit of the Waldmeier Effect. Sol Phys 276, 395–406 (2012). https://doi.org/10.1007/s11207-011-9866-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-011-9866-7

Keywords

Navigation