4 Conclusions and discussions

In the present study we have collected values of maximum sunspot numbers of solar cycles 22 and 23 predicted by numerous workers and examined the characteristics of predictions made by various methods. A comparison is given based on predictions of the maxima of the sunspot numbers within solar cycles 21 to 23, but the prediction dates of the maxima are not included in the present work, which is also an important criterion to assess the quality of solar activity predictions. Predictions for solar cycles 21 and 22 indicate that the precursor methods are always superior to other prediction methods. If this regularity should sustain in solar cycle 23, the maximum sunspot number of cycle 23 should be around 162.3, the average of Group B for the solar cycle 23. When non-precursor methods were used, almost all of the predictions underestimate the observed maximum of solar activity for solar cycle 21. What is more significant is that the predictions severely underestimate the maximum. For solar cycle 22, however most predictions underestimate the corresponding observed value of the maximum solar activity, but a few predictions overestimate observations. The starting time of solar cycle 23 is May 1996, and more than 4 years have already passed. We infer that probably the Sun should now be very close to the maximum of the activity, although the concrete date of the maximum activity is not known at present. The monthly sunspot number of recent several months (2000 Feb. to May) ranges from 112.3 to 138.2, which resides in the middle of the two prediction averages of Group A, and they are close to the average of Group B. The observed maximum sunspot number of cycle 23 is confirmed to be much larger than the average of the first part of Group A. There is a very small probability for the maximum sunspot number to reach such a higher level of around the average 202.1 of Group B. According to the existing predictions made by non-precursor methods, the running tendency of solar activity of solar cycle 23 should either underestimate or overestimate the true maximum solar sunspot number and the ratio of overestimate-to-underestimate predictions increases to about one. This demonstrates again that precursor methods are by far more successful than other prediction methods, although at present we do not know if precursor methods completely succeed in the prediction of the maximum solar activity of cycle 23. We made good progress in making predictions of the maximum solar activity of cycles 21 to 23 with the use of precursor methods. This may be due to improvement of the quality of observational data and/or it may be attributed to the fact that precursor methods are associated with the solar dynamo theory (Brown & Simon 1986; Denkmayr 1993). As far as the accuracy of predictions is concerned, precursor methods are superior to non-precursor methods. However, precursor methods usually give a prediction just around the solar minimum within the range of a few years, while non-precursor methods can make predictions ahead of time by a few years to several decades. A method to make predictions ahead of time on a larger time scale with high accuracy remains to be developed in the future.

Acknowledgements

The authors are indebted to Dr. Woehl for his helpful comments on this paper, and Dr. Katgert for improving the English. We would like to thank the staff of Solar Spectral Research Group of Yunnan Astronomical Observatory for their support and helps. This work was supported by the National Science Fundation of China, the Chinese Academy of Sciences, the Science Fundation of Yunnan Province, and the BK21 project of the Korean Government.