4.2 Quasi-periodicities and characteristic times

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Figure 19: Wavelet (Morlet basis) spectrum of the sunspot-number reconstruction shown in Figure 17View Image. Left and right-hand panels depict 2D and global wavelet spectra, respectively. Upper and lower panels correspond to period ranges of 500 – 5000 years and 80 – 500 years, respectively. Dark/light shading denotes high/low power.

In order to discuss spectral features of long-term solar-activity dynamics, we show in Figure 19View Image a wavelet spectral decomposition of the sunspot number reconstruction throughout the Holocene shown in Figure 17View Image. The left-hand panels show the conventional wavelet decomposition in the time-frequency domain, while the right-hand panels depict the global spectrum, namely, an integral over the time domain, which is comparable to a Fourier spectrum. The peak in the global spectrum at about an 80-year period corresponds to the Gleissberg periodicity, known from a simple Fourier analysis of the Δ14C series (Peristykh and Damon, 2003). The peak at an approximately 150 year period does not correspond to a persistent periodicity, but is formed by a few time intervals (mostly 6000 – 4000 BC) and can be related to another “branch” of the secular cycle, according to Ogurtsov et al. (2002). The de Vries/Suess cycle, with a period of about 210 years, is prominent in the global spectrum, but it is intermittent and tends to become strong with around 2400 clustering time (Usoskin and Kovaltsov, 2004). Another variation with a period of around 350 years can be observed after 6000 BC. Variations with a characteristic time of 600 – 700 years are intermittent and can be hardly regarded as a typical feature of solar activity. Of special interest is the 2000 – 2400 year Hallstatt cycle (see, e.g., Vitinsky et al., 1986Jump To The Next Citation PointDamon and Sonett, 1991Vasiliev and Dergachev, 2002), which is relatively stable and mostly manifests itself as a modulation of long-term solar activity, leading to the clustering of grand minima (Usoskin et al., 2007Jump To The Next Citation Point).

On the other hand, an analysis of the occurrence of grand minima (see Section 4.3) shows no clear periodicity except for a marginal 2400 year clustering, implying that the occurrence of grand minima and maxima is not a result of long-term cyclic variability but is defined by stochastic/chaotic processes.

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