Investigations And Analyses Of Characteristics Of Long-term Solar Activity

We Summarize the theoretical studies of long-term solar activity on sunspot cycle, extended cycle, the prediction of solar activity and the asymmetric distribution of solar activity on the hemisphere and present the results of our studies on the long-term solar activity. The main results are as followings:1. The wavelet technique is used to analyze the periodicities of the monthly average solar flux at 2800 MHz, sunspot numbers, and sunspot areas. Our results show: (1) the existence of the different candidates of the periodicity in three data above. Almost all the curves of three global wavelet spectra exhibit the same periodicities of 10.69 years, 5.11 years, and around 155 days, and the more prominent periodicity of monthly average sunspot numbers, sunspot areas, and solar flux at 2800 MHz is the same: around 10.69 years. (2) the wavelet spectrum provides continuous temporal evolution of the entire rang of periods and gives detailed information on the time localization of frequency component. (3)the temporal evolution of wavelet powers corresponding to a few selected periods of 155.5 days, 5.11 years, and 10.69 years in sunspot numbers, sunspot areas, and radio flux at 2800 MHz reveals that the wavelet powers for shorter-period oscillations in sunspot numbers, sunspot areas, and radio flux at 2800 MHz evolve rapidly compared to that of long-period oscillations. As period increases, the temporal evolution of the period becomes more and more prominent and less rapid. Wavelet powers of Rsn, Rsa and Rsf in both the periods 155.5 days and 5.11 years are very similar, having almost same fluctuations with peaks of wavelet powers appearing almost at same times.2. We use a same four-parameter function as Hathaway et al.(1994) proposed to describe the temporal behavior of both the monthly averages of sunspot areas and the smoothed monthly averages of sunspot areas in cycles 12-22. Our study clearly showsthat the parameter b appears to be unrelated to the other parameters, and little changes from cycle to cycle, thus can be taken a simple value for all cycles, and the parameter a and c are strongly correlated. Then, the cycle shapes of sunspot areas can be adequately described by using a simple function with only two free parameters. But the two-parameter function used to describe the temporal behavior of the monthly averages of sunspot areas is obviously different from that used to describe the smoothed monthly averages of sunspot areas, namely, different series data of sunspot areas were used to give difference values of the parameter b and different relationship between the parameters a and c. As a cycle progresses, with the use of a two-parameter function the amplitude parameter a and the starting time to can be better determined within 4-4.5 years following the start of the cycle into its cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 5-10 years of the cycle. The values of a and to determined with the use of the smoothed monthly averages can be well determined about one year earlier than the values of a and to determined with the use of the monthly averages of sunspot areas determined, but the smoothed monthly averages need 6 months of observations more to obtain a 13-month average. Error analyses show that the smoothed monthly averages of sunspot areas are more suitable to be employed in the approach at the maximum time and at the descending period of a cycle, but at the early period of a cycle, the monthly averages are more suitable. The solar activity in the remaining and forthcoming years of cycle 23 is predicted in this paper.3. The monthly averages of sunspot areas in solar cycles 12 to 22 are employed to analyze their statistical characteristics. The comparison of the monthly averages of sunspot areas and the monthly averages of sunspot numbers is given. Our results show that the maximum times of sunspot numbers and the maximum times of sunspot areas are n...