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.     

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.     

Maximum and minimum temperatures at armagh observatory, 1844–1992, and the length of the sunspot cycle

The question of whether or not the Earth's climate is influenced by solar activity has received considerable attention since the mid-nineteenth century. Most investigations have adopted the sunspot number as the parameter of solar activity. Recently, however, it has been shown by Friis-Christensen and Lassen (1991) that the mean northern hemisphere temperature, from 1861–1990, follows a strikingly similar trend to thelength of the sunspot cycle, suggesting that the recent global warming could, at least in part, arise from changes in solar activity. In view of the importance of this result, we have examined a set of continuous meteorological records, maintained at Armagh Observatory since 1844, to assess, first, whether data from a single site can give meaningful information on global trends, and second, whether the data from this particular site for the period 1844–1866 can be used to extend the baseline of the comparison with solar activity. We find that both are indeed the case and that there is a strong correlation between the solar cycle length and the mean temperature at Armagh over the past 149 years.     

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).     

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.     

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.     

Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

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.     

Group Sunspot Numbers: Sunspot Cycle Characteristics

We examine the `Group' sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group sunspot numbers to Zürich (International) sunspot numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zürich numbers follow the 10.7-cm radio flux and total sunspot area measurements only slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zürich numbers. We find that the `Waldmeier Effect' – the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle – is much more apparent in the Zürich numbers. The `Amplitude–Period Effect' – the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum – is also much more apparent in the Zürich numbers. The `Amplitude–Minimum Effect' – the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zürich numbers and the Group numbers. The `Even–Odd Effect' – in which odd-numbered cycles are larger than their even-numbered precursors – is somewhat stronger in the Group numbers but with a tighter relationship in the Zürich numbers. The `Secular Trend' – the increase in cycle amplitudes since the Maunder Minimum – is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80-year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zürich numbers are slightly more useful for characterizing the on-going levels of solar activity.     

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.     

The correlation between the Calern solar diameter measurements and the solar irradiance

The objective of this paper is to present some results deduced from the analysis of (space-based) solar irradiance observations used jointly with (ground-based) solar diameter variations. The idea which is explored consists in searching a possible influence of the variability of the Sun's whole shape on the luminosity. It is shown that such an effect, albeit small, may occur. Thus, the global geometry of the Sun – which is not a perfect static ellipsoid – would have to be taken into account when attempting to model the irradiance. Our very preliminary results may help to construct empirical models that can be used, in turn to force any model of the thermal structure of the ocean and atmosphere to deduce climate variations, if any.     

Correction to: Observation of a Flare and Filament Eruption in Lyman- α $\alpha $ on 8 September 2011 by the PRoject for OnBoard Autonomy/Large Yield Radiometer (PROBA2/LYRA)

In most of the solar cycles, activity in the northern and southern hemispheres peaks at different times. One hemisphere peaks well before the other, and at least one of the hemispheric maxima frequently does not coincide with the whole sphere maximum. Prediction of the maximum of a hemisphere and the corresponding north–south asymmetry of a solar cycle may help to understand the mechanisms of the solar cycle, the solar-terrestrial relationship, and solar-activity influences on space weather. Here we analysed the sunspot-group data from the Greenwich Photoheliographic Results (GPR) during 1874?–?1976 and Debrecen Photoheliographic Data (DPD) during 1977?–?2017 and studied the cycle-to-cycle variations in the values of 13-month smoothed monthly mean sunspot-group area in the whole sphere (WSGA), northern hemisphere (NSGA), and southern hemisphere (SSGA) at the epochs of maxima of Sunspot Cycles 12?–?24 and at the epochs of maxima of WSGA, NSGA, and SSGA Cycles 12?–?24 (note that solar-cycle variation of a parameter is expressed as a cycle of that parameter). The cosine fits to the values of WSGA, NSGA, and SSGA at the maxima of sunspot, WSGA, NSGA, and SSGA Cycles 12?–?24, and to the values of the corresponding north–south asymmetry, suggest the existence of a ≈132-year periodicity in the activity of the northern hemisphere, a 54?–?66-year periodicity in the activity of the southern hemisphere, and a 50?–?66 year periodicity in the north–south asymmetry in activity at all the aforementioned epochs. By extrapolating the best-fit cosine curves we predicted the amplitudes and the corresponding north–south asymmetry of the 25th WSGA, NSGA, and SSGA cycles. We find that on average Solar Cycle 25 in sunspot-group area would be to some extent smaller than Solar Cycle 24 in sunspot-group area. However, by inputting the predicted amplitudes of the 25th WSGA, NSGA, and SSGA cycles relationship between sunspot-group area and sunspot number we find that the amplitude (\(130\pm 12\)) of Sunspot Cycle 25 would be slightly larger than that of reasonably small Sunspot Cycle 24. Still it confirms that the beginning of the upcoming Gleissberg cycle would take place around Solar Cycle 25. We also find that except at the maximum of NSGA Cycle 25 where the strength of activity in the northern hemisphere would be dominant, the strength of activity in the southern hemisphere would be dominant at the maximum epochs of the 25th sunspot, WSGA, and SSGA cycles.

     

Dynamo-based scheme for forecasting the magnitude of solar activity cycles

In this paper we present a general framework for forecasting the smoothed maximum level of solar activity in a given cycle, based on a simple understanding of the solar dynamo. This type of forecasting requires knowledge of the Sun's polar magnetic field strength at the preceeding activity minimum. Because direct measurements of this quantity are difficult to obtain, we evaluate the quality of a number of proxy indicators already used by other authors which are physically related to the Sun's polar field. We subject these indicators to a rigorous statistical analysis, and specify in detail the analysis technique for each indicator in order to simplify and systematize reanalysis for future use. We find that several of these proxies are in fact poorly correlated or uncorrelated with solar activity, and thus are of little value for predicting activity maxima.We also present a scheme in which the predictions of the individual proxies are combined via an appropriately weighted mean to produce a compound prediction. We then apply the scheme to the current cycle 22, and estimate a maximum smoothed International sunspot number of 171 ± 26, which can be expressed alternatively as a smoothed 2800 MHz radio flux (F _10.7) of 211 ± 23 × (10^–22 Wm^–2Hz^–1), or as a smoothed sunspot area of 2660 ± 430 millionths of a solar disk. Once the actual maximum for cycle 22 has been established, we will have both additional statistics for all the proxy indicators, and a clearer indication of how accurately the present scheme can predict solar activity levels.     

North-South asymmetry in sudden disappearances of solar prominences

This paper presents the results of a study of the N-S asymmetry in sudden disappearances (SD) of solar prominences during solar cycles 18–21, obtained as a part of a more extensive research on SD and reappearances during years 1931–1985 (Ballester, 1984). As can be seen, the N-S SD asymmetry curve is not in phase with the solar cycle and peaks about the time of solar minimum, the asymmetry reverses in sign during the solar maximum, being, this change of sign, coincident with the reversal of the Sun's magnetic dipole. The SD asymmetry curve can be fitted by a sinusoidal function with a period of eleven years. On the other hand, the SD asymmetry curve shows a strong coincidence with the N-S asymmetries presented by other solar activity manifestations as studied by different authors.     

Variations in the solar rotation rate derived from Ca+ K plage areas

Daily calcium plage areas for the period 1951–1981 (which include the solar cycle 19 and 20) have been used to derive the rotation period of the Sun at latitude belts 10–15 ° N, 15–20 ° N, 10–15 ° S, and 15–20 ° S and also for the entire visible solar disk. The mean rotation periods derived from 10–20 ° S and N, total active area and sunspot numbers were 27.5, 27.9, and 27.8 days (synodic), respectively. A power spectral analysis of the derived rotation rate as a function of time indicates that the rotation rate in each latitude belt varies over time scales ranging from the solar activity cycle, down to about 2 years. Variations in adjacent latitude belts are in phase, whereas those in different hemispheres are not correlated. The rotation rates derived from sunspot numbers also behave similarly though the dependence over the solar cycle are not very apparent. The total plage areas, integrated over the entire visible hemisphere of the Sun shows a dominant periodicity of 7 years in rotation rate, while the other time scales are also discernible.     

Systematic Time Delay of Hemispheric Solar Activity

Five solar-activity indices – the monthly-mean sunspot numbers from January 1945 to March 2008, the monthly-mean sunspot areas during the period of May 1874 to March 2008, the monthly numbers of sunspot groups from May 1874 to May 2008, the monthly-mean flare indices from January 1966 to December 2006, and the numbers of solar filaments per Carrington rotation in the time interval of solar rotations 876 to 1823 – have been used to show a systematic time delay between northern and southern hemispheric solar activities in a cycle. It is found that solar activity does not occur synchronously in the northern and southern hemispheres, and there is a systematic time lag or lead (phase shift) between northern and southern hemispheric solar activity in a cycle. About an eight-cycle period is inferred to exist in such phase shifts. The activity on the Sun may be governed by two different and coupled processes, not by a single process.     

Periodicities in the green corona for the sun as a star

A coronal index (CI) derived from the limb observations of the 530.3 nm emission corona (green corona) over 1964–1987 was analyzed by the Fourier transform technique (FTT) to find periodicity in this layer of solar atmosphere. As expected, two pronounced periods were indicated: the rotational, about 27 d, and the activity cycle length, 11 years. Beside these there are seen other periodicities of less significancies, namely of about 5,2.2,1 and 0.5 year. The values of these periodicities in individual cycles 20 and 21 slightly differs that could be related to different activity zone depths beneath the photosphere.     

160 minute solar variations and the 22 year cycle

Systematic measurements of the differential Doppler velocity of the Sun have been performed in Crimea from 1974 through 1988 (total 987 days, 6197 hours of observations). They confirm the presence of a long-term phase-coherent solar pulsation with a period of 160.010 min. On the other hand, the analysis of new data suggests that solar 160 min pulsation might, in frequency, have a multiplet fine structure. In particular, large changes of amplitude and phase of the pulsation over the years 1982–1986 may indicate that during the last few years we have been observing the solar 160 min oscillation of the second portion of the 22 year solar cycle.It is further noted that the beat period of the two closely spaced frequencies (periods are 160.0101 and 160.0126 min) equals 19.5 ± 1.1 year, which is in good agreement with the average length of the solar magnetic activity cycle, 20–22 years. Being verified, this unpredicted property of the pulsation can offer a novel possibility for probing the Sun's interior and perhaps for the study of the internal rotation and 11(22) year cycle of a star.     

Climate sensitivity to changes in land surface characteristics

Using a recently developed global vegetation distribution, topography, and shorelines for the Early Eocene in conjunction with the Genesis version 2.0 climate model, we investigate the influences that these new boundary conditions have on global climate. Global mean climate changes little in response to the subtle changes we made; differences in mean annual and seasonal surface temperatures over northern and southern hemispheric land, respectively, are on the order of 0.5°C. In contrast, and perhaps more importantly, continental scale climate exhibits significant responses. Increased peak elevations and topographic detail result in larger amplitude planetary 4 mm/day and decreases by 7–9 mm/day in the proto Himalayan region. Surface temperatures change by up to 18°C as a direct result of elevation modifications. Increased leaf area index (LAI), as a result of altered vegetation distributions, reduces temperatures by up to 6°C. Decreasing the size of the Mississippi embayment decreases inland precipitation by 1–2 mm/day. These climate responses to increased accuracy in boundary conditions indicate that “improved” boundary conditions may play an important role in producing modeled paleoclimates that approach the proxy data more closely.     

Prolonged minima and the 179-yr cycle of the solar inertial motion

We employ the JPL long ephemeris DE-102 to study the inertial motion of the Sun for the period A.D. 760–2100. Defining solar orbits with reference to the Sun's successive close approaches to the solar system barycenter, occurring at mean intervals of 19.86 yr, we find simple relationships linking the inertial orientation of the solar orbit and the amplitude of the precessional rotation of the orbit with the occurrence of the principal prolonged solar activity minima of the current millenium (the Wolf, Spörer, and Maunder minima). The progression of the inertial orientation parameter is controlled by the 900-yr great inequality of the motion of Jupiter and Saturn, while the precessional rotation parameter is linked with the 179-yr cycle of the solar inertial motion previously identified by Jose (1965). A new prolonged minimum of solar activity may be imminent.