Solar Physics

, 292:43 | Cite as

Identification of Gleissberg Cycles and a Rising Trend in a 315-Year-Long Series of Sunspot Numbers

  • Jean-Louis Le Mouël
  • Fernand Lopes
  • Vincent Courtillot


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 



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.


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Geomagnetism and Paleomagnetism, Institut de Physique du Globe de ParisSorbonne Paris CitéParisFrance

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