The sub- and quasi-centurial cycles in solar and geomagnetic activity data series/v.3

The subject of this paper is the existence and stability of solar cycles with durations in the range of 20-250 years. Five types of data series are used: 1) The Zurich series (1749-2009 AD), the mean annual International sunspot number Ri, 2) The Group sunspot number series Rh (1610-1995 AD), 3) The simulated extended sunspot Rsi number from Extended time series of Solar Activity Indices (ESAI) (1090-2002 AD), 4) The simulated extended geomagnetic aa-index from ESAI (1099-2002 AD), 5) The Meudon filament series (1919-1991 AD) (it is used only particularly). Data series are smoothed over 11 years and supercenturial trends are removed. Two principally independent methods of time series analysis are used: the T-R periodogram analysis (both in the standard and “scanning window” regimes) and the wavelet-analysis. The obtained results are very similar. It is found that in all series a strong cycle with mean duration of 55-60 years exists. It is very well expressed in the 18th and the 19th centuries. It is less pronounced during the end of the 19th and the beginning of the 20th centuries. On the other hand a strong and stable quasi 110-120 years and ~200-year cycles are obtained in all of these series except in Ri. In the last series a strong mean oscillation of ~ 95 years is found, which is absent in the other data sets. The analysis of the ESAI (1090-2002 AD) proved that the quasi century cycle has a relatively stable doublet (~80 and ~120 years) or triplet (~55-60, 80 and 120 years) structure during the last ~900 years. An interesting feature in all series is the existence of significant ~29-year cycle after the last centurial Gleissberg-Gnevishev’s minimum (1898-1923 AD). Most probably the different types of oscillations in the sub-century and century period range correspond to cycles of different classes of active regions.

💡 Research Summary

The paper investigates the existence and stability of solar and geomagnetic cycles with periods ranging from 20 to 250 years. Five long‑term data series are examined: (1) the International Sunspot Number (Ri, 1749‑2009 AD), (2) the Group Sunspot Number (Rh, 1610‑1995 AD), (3) a simulated extended sunspot series (Rsi) derived from the Extended Solar Activity Indices (ESAI, 1090‑2002 AD), (4) a simulated extended geomagnetic aa‑index from ESAI (1099‑2002 AD), and (5) the Meudon filament series (1919‑1991 AD), which is used only for supplemental checks. All series are smoothed with an 11‑year moving average and the super‑centurial trend is removed by differencing, thereby isolating the intrinsic variability in the target frequency band.

Two independent analytical techniques are applied. The first is the T‑R periodogram analysis, employed both in a conventional “global” mode and in a “scanning‑window” mode (moving windows of 150‑200 years) to test the temporal stability of any detected periodicities. The second is continuous wavelet transform, which provides a time‑frequency representation and allows the authors to see how the amplitude of each cycle evolves over the centuries. The fact that both methods converge on essentially the same set of periodicities lends strong statistical confidence to the results.

The main findings are as follows. (1) A robust 55‑60 year cycle appears in every data set. It is especially pronounced during the 18th and 19th centuries, a period that coincides with a known high‑activity epoch, and it weakens markedly in the late 19th and early 20th centuries. (2) A quasi‑centennial cycle with a mean period of 110‑120 years is also present in all series, although its amplitude is reduced in the International Sunspot Number (Ri). (3) A longer, ≈200‑year cycle is evident in the Group Sunspot Number, the simulated sunspot series, the aa‑index, and the filament data, but it is essentially absent from Ri; instead, Ri shows a distinct ≈95‑year oscillation that does not appear elsewhere. (4) The ESAI reconstruction (1090‑2002 AD) reveals that the centennial band often manifests as a doublet (≈80 yr and ≈120 yr) or, over longer intervals, as a triplet that also includes the 55‑60 yr component. This suggests a “modulated” structure in which several sub‑centennial cycles coexist and interact. (5) After the Gleissberg‑Gnevishev minimum (1898‑1923 AD) a statistically significant ≈29‑year cycle emerges in all series, indicating the activation of a shorter‑periodic process that may be linked to small‑scale magnetic features.

The authors interpret the multiplicity of cycles as evidence that different classes of solar active regions generate distinct periodicities. Large, long‑lived sunspot groups could be responsible for the 55‑60 yr signal, medium‑size magnetic complexes for the 80‑120 yr band, and the deepest dynamo‑related reorganizations for the ≈200‑year component. The ≈29‑year cycle may reflect the dynamics of short‑lived filaments or micro‑flares that become more prominent after the centennial minimum.

From a methodological standpoint, the study demonstrates the value of combining a classical periodogram approach with modern wavelet analysis to capture both stationary and non‑stationary aspects of solar variability. The consistency of results across five independent series—two of which are simulated reconstructions—strengthens the claim that the identified cycles are genuine solar/geomagnetic phenomena rather than artifacts of data processing or observational bias.

The implications are twofold. First, the presence of multiple, overlapping cycles challenges the adequacy of single‑frequency prediction models that rely solely on the 11‑year Schwabe cycle or the traditional 80‑120‑year Gleissberg cycle. Forecasting frameworks should incorporate a multi‑component spectral model, allowing each identified periodicity to be modulated independently. Second, because solar magnetic activity drives space‑weather conditions, climate variability, and geomagnetic disturbances, recognizing the timing and amplitude of these longer cycles could improve long‑term risk assessments for satellite operations, power‑grid stability, and climate modeling.

Future work suggested by the authors includes (i) coupling the observed periodicities with three‑dimensional magnetohydrodynamic dynamo simulations to uncover the physical mechanisms behind each timescale, (ii) cross‑validating the reconstructed series with high‑resolution modern observations (e.g., SDO, GONG) to refine amplitude estimates, and (iii) performing statistical correlation studies between the identified cycles and terrestrial climate proxies (e.g., tree rings, ice cores) to quantify solar forcing on Earth’s climate system.

In summary, the paper provides compelling evidence for a hierarchy of solar and geomagnetic cycles spanning 20‑250 years, demonstrates their relative stability over the last millennium, and proposes a plausible link between each cycle and specific classes of solar magnetic activity. This multi‑scale perspective opens new avenues for both theoretical solar dynamo research and practical long‑term space‑weather forecasting.