Abstract
We analyse the series of the Wolf sunspot number in the frequency domain to determine the dimension of the solar cycle system by using the properties of its strange attractor and to study the stability in time of this dimensionality and of the main quasiperiodicities. The two classical methods of time series analysis, Fourier harmonic and Blackman-Tukey spectral analysis, have been applied first to the series of the annual Wolf sunspot numbers to determine its overall character. To detect stationarity, periodic regression based upon the three most statistically significant quasi-periods and especially a moving form of the maximum entropy spectrum analysis (mesa) have been used. Both analyses show a splitting of the 11-year cycle before 1800, when a ± 55-year cycle is dominant, and a single 11-year and + 100-year peak after 1800. Moreover, these quasi-periods are very sensitive to the time interval over which the analysis is carried out. The reason is that the sunspot numbers constitute a widely non-stationary process, which therefore implies that Fourier techniques are not useful to predict solar activity and must be used as fitting procedure only. The minimum cross-entropy method serves to improve the maximum entropy spectrum. With a good a priori estimate and data containing a low noise level, this method allows the detection of very close peaks and the refinement of the main frequencies; it does not split nor introduce artificial peaks. The Thomson model was also applied for its superior bias control, its excellent leakage resistance and a better statistical information. The same methods were then used to study the 22-year magnetic cycle, which is formed by taking into account the change in polarity of the succeeding 11 -year cycle. The moving form of mesa confirms the 22-year cycle to be highly stable in contrast to the instability in the period of the 11-year sunspot series. This suggests the importance of working with the more invariant 22-year magnetic series to explain the complex, non-stationary behaviour of the sunspot series and of the solar—terrestrial interactions. Finally, we tried to see if the system generated by the sunspot data was allowing the existence of an attractor and tried to determine the minimum number of variables necessary to describe this system. It is shown that the dimension of the attractor is highly unstable varying from 2.21 to 4.95 in a quasi-cyclic way.
Reference14 articles.
1. Bloomfield P. 1976 Fourier analysis of time series: an introduction. New York: Wiley.
2. THE RELATIONSHIP BETWEEN MAXIMUM ENTROPY SPECTRA AND MAXIMUM LIKELIHOOD SPECTRA
3. Long term periodicities in the sunspot cycle
4. Climate and the changing sun
5. Jenkins G. & Watts D. 1968 Spectral analysis and its applications. San Francisco: Holden-Day.
Cited by
56 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献