We show in this short note that the method of singular spectrum analysis (SSA) is able to clearly extract a strong, clean, and clear component from the longest available sunspot (International Sunspot Number, ISN) time series (1700 – 2015) that cannot be an artifact of the method and that can be safely identified as the Gleissberg cycle. This is not a small component, as it accounts for 13% of the total variance of the total original signal. Almost three and a half clear Gleissberg cycles are identified in the sunspot number series. Four extended solar minima (XSM) are determined by SSA, the latest around 2000 (Cycle 23/24 minimum). Several authors have argued in favor of a double-peaked structure for the Gleissberg cycle, with one peak between 55 and 59 years and another between 88 and 97 years. We find no evidence of the former: solar activity contains an important component that has undergone clear oscillations of \(\approx90\) years over the past three centuries, with some small but systematic longer-term evolution of “instantaneous” period and amplitude. Half of the variance of solar activity on these time scales can be satisfactorily reproduced as the sum of a monotonous multi-secular increase, a \(\approx90\)-year Gleissberg cycle, and a double-peaked (\(\approx10.0\) and 11.0 years) Schwabe cycle (the sum amounts to 46% of the total variance of the signal). The Gleissberg-cycle component definitely needs to be addressed when attempting to build dynamo models of solar activity. The first SSA component offers evidence of an increasing long-term trend in sunspot numbers, which is compatible with the existence of the modern grand maximum.
Solar cycle, observations Solar cycle, models Gleissberg cycle Sunspot number Singular spectrum analysis, Schwabe cycle Secular trend
This is a preview of subscription content, log in to check access
We thank A. Shapoval for useful discussions of the SSA and principal component analysis (PCA). We thank the anonymous referee for useful remarks. This is IPGP contribution NS 3822.
Disclosure of Potential Conflicts of Interest
The authors declare that they have no conflicts of interest.
Clette, F., Svalgaard, L., Vaquero, J.M., Cliver, E.W.: 2014, Revisiting the sunspot number. Space Sci. Rev.186, 35. DOI.
Hoyt, D.V., Schatten, K.H.: 1998, Group sunspot numbers: A new solar activity reconstruction. Solar Phys.181, 491. DOI.
Kittler, J., Young, P.C.: 1973, A new approach to feature selection based on the Karhunen–Loeve expansion. Pattern Recognit.5, 335.
McCracken, K.G., Beer, J., Steinhilber, F., Abreu, J.: 2013, A phenomenological study of the cosmic ray variations over the past 9400 years, and their implications regarding solar activity and the solar dynamo. Solar Phys.286, 609. DOI.
Nagovitsyn, Yu.A.: 1997, A nonlinear mathematical model for the solar cyclicity and prospects for reconstructing the solar activity in the past. Astron. Lett.23, 742.
Nagovitsyn, Yu.A.: 2001, Solar activity during the last two millennia: Solar patrol in ancient and medieval China. Geomagn. Aeron.41, 680.
Ogurtsov, M.G., Nagovitsyn, Y.A., Kocharov, G.E., Jungner, H.: 2002, Long-period cycles of the Sun’s activity recorded in direct solar data and proxies. Solar Phys.211, 371.
Otaola, G.A., Zenteno, G.: 1983, On the existence of long term periodicities in solar activity. Solar Phys.89, 209.
Rozelot, J.P.: 1994, On the stability of the 11-year solar cycle period (and a few others). Solar Phys.149, 149.
Solanki, S.K., Usoskin, I.G., Kromer, B., Schüssler, M., Beer, J.: 2004, Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature431, 1084. DOI.
Svalgaard, L., Schatten, K.H.: 2016, Reconstruction of the sunspot group number: The backbone method. Solar Phys.291, 2653. DOI.
Usoskin, I.G., Kovaltsov, G.A., Lockwood, M., Mursula, K., Owens, M.J., Solanki, S.K.: 2016, A new calibrated sunspot group series since 1749: Statistics of active day fractions. Solar Phys.291, 2685. DOI.