基于奇异谱分析研究太阳黑子长期行为的周期性及其预报

发布时间：2018-07-10 09:04

本文选题：太阳黑子 + 奇异谱分析　；参考：《重庆大学》2015年硕士论文

【摘要】：奇异谱分析(Singular Spectrum Analysis——SSA)作为一个处理时间序列的重要的工具,应用于太阳黑子活动的时间序列中。前人研究发现,太阳活动具有一定的周期性和复杂性。本文通过对太阳Wolf黑子数时间序列的奇异谱分析,来讨论和分析太阳活动的周期性和趋势性,并结合最大熵法对太阳黑子活动做出预报。对于短的、充满噪音的、非线性的时间序列的周期性分析,奇异谱分析(SSA)是一种有效恰当的方法。本文采用奇异谱分析,得到了太阳Wolf月平均黑子数和每日黑子数的不同阶的主成分。这些不同阶的主成分代表了太阳活动的不同的长期规律,而各阶主成分的和则构成了太阳黑子活动的总体特征。为了进一步确定SSA的每一阶主成分所代表的周期性,再对每一阶主成分的重构成分(Reconstruction Components——RC)进行小波变换。月平均黑子数的结果显示,在前20阶显著成分中,最显著的周期仍然是准11年周期和一个重要的趋势,周期性质大约107年。同时,也显示有丰富的中期周期性,比如8.1年、5.3年、5.1年、4.2年和3.9年——与磁场周期相关的周期、3.7年和3.5年——Rieger型周期。更高阶的主成分似乎被噪音掩盖。因此,我们进一步分析了更短时间尺度的22活动周和23活动周的每日黑子数。结果显示,在这两个活动周的前8阶主成分中,最显著的还是准11年周期以及太阳自转周期约27天。另外,22活动周中,还出现165天的Rieger型周期;23活动周中,出现135天的周期,被认为是27天的5倍谐波。结合以上SSA的分析结果,我们应用最大熵法对太阳活动进行了预报。结果表明,24活动周将在2019年达到极小期,而25活动周将在2024年达到极大期。所以,以黑子数表征的太阳活动长期行为,具有丰富的周期性。奇异谱分析的结果与前人的结果是一致的。同时也表明,太阳活动中的一些周期之间的可能关系,即很多周期可能是太阳自转周期的几倍谐波。但也存在另外一些不同的周期和趋势,它们的起源和相互关系都还需要进一步的研究。
[Abstract]:As an important tool to deal with time series, singular Spectrum Analysis (SSA) is applied to the time series of sunspot activities. Previous studies have found that solar activity has a certain periodicity and complexity. In this paper, the periodicity and tendency of solar activity are discussed and analyzed by the singular spectrum analysis of the time series of solar Wolf sunspot number, and the maximum entropy method is used to predict the sunspot activity. Singular spectral analysis (SSA) is an effective and appropriate method for the periodic analysis of short, noisy and nonlinear time series. In this paper, by using singular spectral analysis, the principal components of the monthly mean sunspot numbers and daily sunspot numbers of the solar Wolf are obtained. These principal components of different order represent different long-term laws of solar activity, and the sum of principal components of each order constitutes the general characteristics of sunspot activity. In order to further determine the periodicity represented by each order principal component of SSA, the reconstruction components (RC) of each order principal component are transformed by wavelet transform. The results of the monthly mean sunspot number show that the most significant period of the first 20 significant components is still a quasi-11-year period and an important trend with a periodic property of about 107 years. At the same time, there are abundant medium-term periodicity, such as 8.1 years, 5.3 years, 5.1 years, 4.2 years and 3.9 years, which are related to the period of magnetic field, 3.7 years and 3.5 years of Rieger-type cycles. Higher-order principal components seem to be obscured by noise. Therefore, we further analyze the daily sunspot numbers of 22 and 23 activity cycles in shorter time scales. The results show that among the first eight principal components of the two cycles, the quasi-11-year period and the solar rotation period are about 27 days. In addition, 165 days of Rieger cycle and 135 days of cycle appear in the activity week of Yi-22, which is considered to be 5 times of that of 27 days. The maximum entropy method is used to predict the solar activity based on the above results of SSA. The results show that the activity week of Yi-24 will reach the minimum period in 2019 and the activity week of 25 will reach the maximum period in 2024. Therefore, the long-term behavior of solar activity represented by sunspot number is rich in periodicity. The results of singular spectrum analysis are in agreement with those of the predecessors. At the same time, it also shows the possible relationship between some periods in solar activity, that is, many periods may be several times harmonics of the solar rotation period. But there are also some different cycles and trends whose origins and interrelationships need further study.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P182.41

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