Periods Analysis And Prediction Of The Sunspot Long-term Behavior By SSA

For nonlinear time series analysis, Singular Spectrum Analysis(SSA) is an important tool and applied to study long-term behavior of solar sunspot. It has been found that the long-term behavior of solar activity has periodicity and complexity.Basing on Wolf sunspot number, we investigate the periodicity and tendency of solar activity by using SSA and forecast solar activity by Maximum Entropy Method(MEM)in the present work.For periodicity of short, noised, nonlinear time series, SSA is an effective and suitable method. Used SSA, we obtain the principle components(PCs) of different order of Wolf monthly and daily sunspot number. The PC of each order presents a different long-term regularity and sum of every-order PC shows global characteristic of solar sunspot activity. In order to determine periodicity of every-order PC, wavelet transform is adopted to analyze Reconstruction Component(RC) of each-order PC.The results of monthly sunspot number show that the most prominent period is about 11 years and an important trend is about 107 years periodicity,for the first 20 order RC, respectively. Furthermore, they display rich mid-range periodicity, such as 8.1years, 5.3,5.1 years, 4.2 years and 3.9 years – correlative with magnetic period, 3.7years and 3.5 years – Rieger type period. The higher-order RCs seemingly are covered by noise. Therefore, the shorter time-scale data, daily sunspot number of cycle 22 and cycle 23 is adopted to study shorter periodicity, respectively. We find that the first-8-order RC of these two cycles display the most prominent two periods, about 11 years and 27 days – Carrington rotational period. The cycle 22 has a Rieger type period, about165 days. The cycle 23 has 135-day period. We think it is a 5 multiple harmonic of 27 days. Combining the SSA results, we forecast solar activity by MEM. We find sunspot activity of cycle 24 will reach its minimum in 2019 and cycle 25 will reach its maximum in 2024.Therefore, the solar long-term behavior of sunspot number has rich periodicity.The results obtained by SSA are identical with the previous studies. They show that some relationship between the different periods, namely some periods are multiple harmonic of 27 days. There are else different periods and trends, however. Their originand relationship will be studied in the future.