Gleissberg cycle of solar activity over the last 7000 years

Long-term variations of solar activity significantly affect terrestrial phenomena. Studies have shown cyclic components in solar activity and geophysical phenomena (e.g., the Schwabe, Hale, Gleissberg, and Suess cycles, and a cycle of about 2300 years). In this paper, the wavelet technique is employed to investigate the Gleissberg cycle in solar variations during 5000 BC–1995 AD. Analysis shows time-variable characteristics in the Gleissberg solar cycle over the period; no obvious correlation between the Gleissberg and Suess cycles has been found.     

Solar magnetic and bolometric cycles recorded in sea sediments

The total carbonate and thermoluminescence (TL) profiles of the GT89-3 Ionian sea sediment core have been measured in the upper 200 cm of the core spanning the last 3100 years in order to test the presence of the Gleissberg (80–90 yr) cycle in the two different time series recorded in the same archive. Two different sampling intervals respectively of 2.5 mm and 2 mm have been chosen for the measurements in order to obtain results independent from sampling effects in the time series. We have revealed the Gleissberg cycle at 83 and 92 yr in both records.     

The Sun’s Strange Behavior: Maunder Minimum or Gleissberg Cycle?

During the last few years the Sun and solar wind have shown a behavior that was so unexpected that the phenomena was described as “the strange solar minimum”. It has been speculated that the 23/24 solar cycle minimum may have indicated the onset of a Maunder-Minimum-type Grand Minimum. Here we review what is known from 1500 years of proxy data about Maunder-type Grand Minima and the minima of the cyclic Centennial Gleissberg variations. We generate criteria that distinguish between the two types of event. Applying these criteria to the observed solar terrestrial data we conclude that the unexpected behavior began well before the solar cycle 23/24 minimum. The data do not support the Maunder Minimum conjecture. However, the behavior can be understood as a minimum of the Centennial Gleissberg Cycle that previously minimized in the beginning of the 20th century. We conclude that the Centennial Gleissberg Cycle is a persistent variation that has been present 80% of the time during the last 1500 years and should be explained by solar dynamo theory.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

Long-Period Cycles of the Sun's Activity Recorded in Direct Solar Data and Proxies

Different records of solar activity (Wolf and group sunspot number, data on cosmogenic isotopes, historic data) were analyzed by means of modern statistical methods, including one especially developed for this purpose. It was confirmed that two long-term variations in solar activity – the cycles of Gleissberg and Suess – can be distinguished at least during the last millennium. The results also show that the century-type cycle of Gleissberg has a wide frequency band with a double structure consisting of 50–80 years and 90–140 year periodicities. The structure of the Suess cycle is less complex showing a variation with a period of 170–260 years. Strong variability in Gleissberg and Suess frequency bands was found in northern hemisphere temperature multiproxy that confirms the existence of a long-term relationship between solar activity and terrestial climate.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

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

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.     

On the short term variations of solar activity during solar cycle 21

Short-term variations of the last solar activity cycle were studied by the flare and coronal indices using Gleissberg method. Systematic short-term variations are found from their course during the 21st solar activity cycle. Comparison of their autocorrelograms constructed by the new set of data obtained from the magnitude of the fluctuations showed us the existence of the phase shift between the temporal variations of the two indices.     

The Sunspot and Auroral Activity Cycle Derived from Korean Historical Records of the 11th–18th Century

Historical records of sunspots and aurorae are valuable information to examine variations of solar activity and the terrestrial climate on a long-term scale. We have collected the historical records of Korea during the 11th–18th century. Through a power-spectrum analysis of these data, we have found solar activity cycles, which coincide with the Schwabe cycle and the Gleissberg cycle on short and long-term periods, respectively.     

Evidence of Solar Variation in Tree-Ring-Based Climate Reconstructions

Analyses of the summer temperature anomalies in northern Fennoscandia for A.D. –1991 and mean annual temperature in the northern hemisphere for A.D. 1000–1990 (both reconstructed by means of dendrochronological methods) are performed using Fourier and wavelet approaches. It is revealed that the century-type (65–140 yr) periodicity is present in both series during most of the full time range. A comparison of the northern Fennoscandian temperature record with a variety of indicators of solar activity (direct measurements and proxies) shows that this century-scale periodicity most probably was forced by a centennial cycle of solar activity (Gleissberg cycle). Despite the fact that the connection between the centennial variation of global northern hemispheric temperature and that of the Sun's activity is weaker, a link between the two can also not be excluded. The results obtained give us new evidence of the reality of the solar–climate link over a record long-time scale (at least during the last millennium). Variable length of the century-long temperature periodicity may reflect the corresponding changes in the length of the Gleissberg solar cycle. The effects, which can obscure the Sun's influence on the global hemispheric climate, are discussed.     

Long-Term Variations in Solar Differential Rotation and Sunspot Activity

The solar equatorial rotation rate, determined from sunspot group data during the period 1879–2004, decreased over the last century, whereas the level of activity has increased considerably. The latitude gradient term of the solar rotation shows a significant modulation of about 79 year, which is consistent with what is expected for the existence of the Gleissberg cycle. Our analysis indicates that the level of activity will remain almost the same as the present cycle during the next few solar cycles (i.e., during the current double Hale cycle), while the length of the next double Hale cycle in sunspot activity is predicted to be longer than the current one. We find evidence for the existence of a weak linear relationship between the equatorial rotation rate and the length of sunspot cycle. Finally, we find that the length of the current cycle will be as short as that of cycle 22, indicating that the present Hale cycle may be a combination of two shorter cycles. Presently working for the Mt. Wilson Solar Archive Digitization Project at UCLA.     

A Phenomenological Study of the Cosmic Ray Variations over the Past 9400 Years, and Their Implications Regarding Solar Activity and the Solar Dynamo

Two 9400-year long ¹⁰Be data records from the Arctic and Antarctic and a ¹⁴C record of equal length were used to investigate the periodicities in the cosmic radiation incident on Earth throughout the past 9400 years. Fifteen significant periodicities between 40 and 2320 years are observed in the ¹⁰Be and ¹⁴C records, there being close agreement between the periodicities in each record. We found that the periodic variations in the galactic cosmic radiation are the primary cause for periods <?250 years, with minor contributions of terrestrial origin possible >?250 years. The spectral line for the Gleissberg (87-year) periodicity is narrow, indicating a stability of ≈?0.5 %. The 9400-year record contains 26 Grand Minima (GM) similar to the Maunder Minimum, most of which occurred as sequences of 2?–?7 GM with intervals of 800?–?1200 years in between, in which there were no GM. The intervals between the GM sequences are characterised by high values of the modulation function. Periodicities <?150 years are observed in both the GM intervals and the intervals in between. The longer-period variations such as the de Vries (208-year) cycle have high amplitudes during the GM sequences and are undetectable in between. There are three harmonically related pairs of periodicities (65 and 130 years), (75 and 150 years), and (104 and 208 years). The long periodicities at 350, 510, and 708 years closely approximate 4, 6, and 8 times the Gleissberg period (87 years). The well-established properties of cosmic-ray modulation theory and the known dependence of the heliospheric magnetic field on the solar magnetic fields lead us to speculate that the periodicities evident in the paleo-cosmic-ray record are also present in the solar magnetic fields and in the solar dynamo. The stable, narrow natures of the Gleissberg and other periodicities suggest that there is a strong “frequency control” in the solar dynamo, in strong contrast to the variable nature (8?–?15 years) of the Schwabe (11-year) solar cycle.     

Limits of predictability of solar activity

The study of a nonlinear chaotic map of 11-year cycle maxima evolution recently derived from observations is presented with the purpose of predicting the features of the long-term variability of solar activity. It is stressed that dynamical forecast is limited by the Lyapunov time and a statistical approach can be justified due to the ergodic properties of the chaotic evolution. The Gleissberg variation is described as a chaotic walk and its distribution over length is shown to be broad. The global minima are identified as laminar slots of temporal intermittency and their typical distribution over length is also given. We note that a long sunspot cycle can be used as a precursor of the global minimum and a close sequence of global minima (once in approximately 1500–2000 years) may be responsible for the climatic changes (Little Ice Ages).     

An Analysis of Solar Global Activity

This article proposes a unified observational model of solar activity based on sunspot number and the solar global activity in the rotation of the structures, both per 11-year cycle. The rotation rates show a variation of a half-century period and the same period is also associated to the sunspot amplitude variation. The global solar rotation interweaves with the observed global organisation of solar activity. An important role for this assembly is played by the Grand Cycle formed by the merging of five sunspot cycles: a forgotten discovery by R. Wolf. On the basis of these elements, the nature of the Dalton Minimum, the Maunder Minimum, the Gleissberg Cycle, and the Grand Minima are presented.     

“TOY” Dynamo to Describe the Long-Term Solar Activity Cycles

Secular variations of solar activity (Gleissberg and Suess cycles) have approximately 80 – 130 and 200 year periods. They are manifested in both observed and proxy data. Here, we show that the basic dynamic features of the Schwabe cycle (asymmetry of its growth and decay phases) and secular cycles (multi-frequency structure and irregular Grand-extremes), as well as a connection between them, can be described by parameter tuning of the electromechanical “toy” dynamo system which has been widely used to model the inversions of the geomagnetic field. An amplitude-frequency diagram for the model magnetic flux has the same shape as the directly observed and reconstructed sunspot area indices. An erratum to this article is available at .     

Nitrate Concentration in Greenland Ice: an Indicator of Changes in Fluxes of Solar and Galactic High-Energy Particles

Two sets of nitrate (NO₃ ^–) concentration data in Central Greenland ice, obtained through the GISP2 collaboration and by the University of Kansas, were analyzed statistically. The two records correlate well over time scales from a few years up to a century. They both contain quasi five-year, decadal and century-type time variations. A quasi five-year periodicity resulting from increases in the mean nitrate concentration before and after maximum sunspot number was confirmed. A tendency of solar proton events to occur more frequently during the rise/decline phases of the solar cycle may cause a quasi five-year variation. Century-type (60–110 yr) variability in nitrate outstrips the corresponding Gleissberg cycle in sunspots by 12–17 years and changes synchronously (correlates with zero phase shift) with the smoothed length of the solar Schwabe cycle. A significant correlation between century-type periodicities for nitrates in Greenland ice and northern Fennoscandian temperatures was established. The results show that despite a strong dependence on local meteorology, nitrate concentration in ice contains valuable information about global geophysical phenomena in the past.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.     

Hemispherical asymmetries in sunspot areas and auroral frequencies

One thousand and fifty-two aurorae boreales and 554 aurorae australes recorded during the nineteenth century at medium latitudes 55° N or 55° S are compared statistically with the known hemispherical asymmetry of the sums of the areas of sunspots. According to the present study, the solar hemispherical asymmetry may be accompanied by an analogous pattern of the hemispherical frequency of auroral days. For the number of auroral days in each hemisphere beyond the two auroral ovals, a remarkable degree of phase equality with the sunspot areas during the second Gleissberg cycle can be demonstrated.     

The thermoluminescence profile of a recent sea sediment core and the solar variability

The analysis of the thermoluminescence (TL) profile of the GT14 recent sea sedimentary core shows the existence of four main periodicities of 137.7, 59,12.06, and 10.8 years. Here we discuss the affinity of these waves to the known cycles of solar variability. The beats of the two high frequency components produce a modulated wavetrain with a carrier wave of 11.4 years and an amplitude modulation with period 206 years. The minima of this squared amplitude modulation fall in 1810 and 1913 A.D. and closely correspond to the periods of lowest solar activity as indicated by the sunspot series. The sum of the two low frequency waves can in turn be rewritten as a component with period 82.6 years which is amplitude modulated by a second component with period of 206 years. The 82.6-yr wave has the period commonly attributed to the Gleissberg cycle of solar activity. The maxima of the 82.6-yr wave occur in agreement with the dates of maximum solar radius as suggested by Gilliland (1981).