Evolutional characteristics of longterm solar activity are usually shown with the sunspot relative number and the Butterfly Diagram of sunspot groups' distribution in the latitude. In this paper the both are studied, and the latter in especial. Solar activity indicators do not occur evenly on the solar disk, many types of solar phenomena exhibit some north-south asymmetric distributions. Study on this aspect is one of the main research tasks of solar physics since about the 1970s, and it is found that the N-S asymmetric distribution of solar activity does indeed exist, although the existence of the west-east asymmetric distribution has not yet confirmed up to now. Solar activity indicators are not uniformly distributed in the longitude. The data of the X-ray flare events of Imp ≥ M1.0 during the interval of the year 1987 to 1992 corresponding to the maximum period of the 22~(nd) solar cycle have been investigated to study the N-S and W-E asymmetries. During that period it has been shown the existence of a real N-S asymmetry. The W-E asymmetry during that period is not significant, but a non-uniform flare distribution in the longitude has been evidenced. It is also found that the degree of N-S asymmetry is not a function of the intensity of the studied events. The other work done on this aspect is the attempt to clarify whether the southern dominance of solar activity really exists in solar cycle 21. 20 solar-activity phenomena are collected to investigate solar activity in solar cycle 21, and the results obtained show that we can hardly say that either the south dominance of solar activity or the north dominance exists for solar cycle 21. A briefly investigation of the research situation of longterm solar activity has been given, and an analysis on the characteristics of the solar cycles described by sunspot areas has been also given here. It is found that a single function containing only two parameters can be used to represent the temporal behavior of the sunspot cycles 12 to 22, this result is very useful in predictions of longterm solar activity. The Butterfly Diagram has been detailed studied to show or to discover some characteristics of longterm solar activity, to quantitatively reproduce some existed rules and effects on longterm solar activity. At the end of this dissertation, we summarize both the prediction methods and the prediction results of longterm solar activity. The prediction cases given for solar cycles 21 to 23 indicate that the precursor methods are obviously more successful than other methods. The Moscow Neutron Monitor Pressure-Corrected Values have been used to do a prediction of the maximum sunspot relative number for solar cycle 23, and here we predict that the maximum sunspot relative number is about 151.1 (in terms of smoothed monthly mean). The investigations of predictions of the maximum sunspot relative number show that the maximum is probably about 162.3 in terms of smoothed monthly mean.
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