by Javier
Summary: Holocene climate has been affected in different periods by several centennial to millennial solar cycles. The ~ 1000-year Eddy solar cycle seems to have dominated Holocene climate variability between 11,500-4,000 years BP, and in the last two millennia, where it defines the Roman, Medieval, and Modern warm periods. The ~ 208-year de Vries solar cycle displays strong modulation by the ~ 2400-year Bray solar cycle, both in its cosmogenic isotope signature and in its climatic effects. The Centennial, and Pentadecadal solar cycles are observable in the last 400-year sunspot record, and they are responsible for the present extended solar minimum that started in 2008.
Introduction
In a recent review of Holocene climate variability (Part A, and Part B) it was shown that Milankovitch forcing was likely the primary driving force behind the general climate evolution from the Holocene Climatic Optimum to the Neoglacial period, for the past 12,000 years. Additionally, the ~ 2400-year Bray climate cycle (Part A), of solar origin (Part B and Part C), appears responsible for the main climatic subdivisions of the Holocene, and the climatic pessima that separate them, such as the Little Ice Age. Additional periodic climate variability in the centennial to millennial range is produced by the 1500-year oceanic cycle, and by several solar activity periodicities that, according to numerous authors, correlate well with climate variability.
The study of solar cycles and their climatic effect is hampered by a very short observational record (~ 400 years), an inadequate understanding of the physical causes that might produce centennial to millennial changes in solar activity, and an inadequate knowledge of how such changes produce their climatic effect. Despite this lack of a solid theoretical framework, paleoclimatologists keep publishing article after article where they report correations between solar proxy periodicities and climate proxy periodicities, and the observational evidence is now so abundant as to obviate the lack of a theory or well defined mechanism.
The millennial Eddy solar cycle
Every frequency analysis of Holocene solar activity reconstructions shows a strong peak at ~ 1000 year (figure 62 A & C, Darby et al., 2012; Kern et al., 2012). Wavelet analysis shows the ~ 1000-year periodicity having a strong signal between 11,500 and 4,000 yr BP, and between 2,000 and 0 yr BP, but a very low signal between 4,000 and 2,000 yr BP (figure 79; Ma 2007; Kern et al., 2012). The average duration of the ~ 1000-year cycle can be calculated from the grand solar minimum at 11,115 yr BP to the one at 1,265 yr BP (dates from Usoskin et al., 2016) for ten periods at 985 years, a span in very good agreement with the calculated 970 years from frequency analysis (Kern et al., 2012) and the calculated 983.4 years from astronomical cycles (Scafetta, 2012).
Figure 79. The 980-year Eddy cycle in solar activity reconstructions. a) Solar sunspot number reconstruction from cosmogenic 10Be and 14C isotopes. A regularly spaced 980-year periodicity is shown as arches above. The Eddy lows that correspond to this periodicity (orange bars) are numbered from most recent. Grand solar minima that correspond to these lows are indicated with boxes with their names. W/S/M correspond to the Wolff, Spörer, and Maunder minima. Source: A.K. Kern et al., 2012. Palaeo. 329–330, 124–136. b) Wavelet analysis of the sunspot number reconstruction, with the Eddy periodicity indicated by a continuous line, and the Bray periodicity by a dashed line. c) Scale-averaged wavelet power for the 800-1200 years band (Eddy periodicity, continuous line, left scale), and the 1700-2800 years band (Bray periodicity, dashed line, right scale). Notice that the Bray periodicity is continuous over the entire Holocene, while the Eddy periodicity is very strong in the early Holocene and very weak in the mid-to-late Holocene. Source: L.H. Ma. 2007. Solar Phys. 245, 411-414.
The 980-year solar cycle, despite its shorter period and variable amplitude compared to the Bray solar cycle, seems to have dominated Holocene climate variability between 11,500 yr BP and 4,000 yr BP. Several authors have noticed this solar forcing dominance during the early Holocene (figure 41; Debret et al., 2007; Simonneau et al., 2014). The Bond series of North Atlantic drift-ice record reflects a clear ~ 1000-year periodicity during the first 6,500 years of the Holocene that correlates with the 980-year Eddy solar cycle (figures 48 & 80; Debret et al., 2007).
Figure 80. The 980-year Eddy cycle correspondence to Bond events. a) Solar sunspot number reconstruction from cosmogenic 10Be and 14C isotopes. A regularly spaced 980-year periodicity is shown as arches above. The Eddy lows that correspond to this periodicity (orange bars) are numbered from most recent. Source: A.K. Kern et al., 2012. Palaeo. 329–330, 124–136. b) Holocene record of North Atlantic iceberg activity determined by the presence of drift-ice petrological tracers. Source: G. Bond et al., 2001. Science 294, 2130-2136. The correspondence is very clear for the periods when the Eddy cycle has high power.
The 1000-year periodicity displays very low power in solar activity wavelet analysis during several millennia (figures 79 & 81; Ma 2007; Kern et al., 2012; Steinhilber et al., 2013). When the amplitude of the 1000-year solar signal is adjusted by its wavelet power (figure 81), a high correlation between North Atlantic iceberg activity and the 980-year Eddy solar cycle corresponds to the periods when the 1000-year solar signal is high, while the correlation is low at periods of weak 1000-year solar signal, strengthening the relationship between climatic Bond events and solar activity, that has been acknowledged by multiple authors, starting with Gerald Bond himself (Bond et al., 2001). The unusually long Roman Warm Period (2500-1600 BP; Wang et al., 2012) coincided with the final part of this interval of low Eddy solar cycle activity, while known warm and cold periods have faithfully followed the since strengthened 980-year Eddy solar cycle (figure 81).
Figure 81. North Atlantic iceberg activity and the Eddy solar cycle. Blue curve, inferred iceberg activity in the North Atlantic (inverted) from petrological tracers. Source: G. Bond et al., 2001. Science 294, 2130-2136. Black curve, a 1000-year frequency cycle representing solar activity for that periodicity, whose amplitude reflects the relative power (colored bar) of that frequency in a solar activity reconstruction wavelet analysis. Source of wavelet analysis: F. Steinhilber & J. Beer. 2013. J. Geophys. Res. 118, 1861-1867. Periods of higher correlation between both curves correspond to periods of high signal amplitude, and a period of lower correlation corresponds to a period of lower signal amplitude. The last three warm periods (orange bars) and 2 cold periods (blue bars) are indicated. RWP, Roman Warm Period. DACD, Dark Ages Cold Period. MWP, Medieval Warm Period. LIA, Little Ice Age. MGW, Modern Global Warming.
The 980-year solar cycle was named the Eddy cycle by Abreu et al. (2010), and its lows have been numbered here, from more recent, as E1, E2, … (figure 79). The climatic effect of the Eddy cycle should manifest in the two periods when solar activity was most affected by this millennial periodicity. In the most recent period, we observe a millennial separation between warm periods: Modern Global Warming (present), Medieval Warm Period (~ 1100 AD), Roman Warm Period (~ 100 AD); and between cold periods: Little Ice Age (~ 1650 AD; E1), and Dark Ages Cold Period (~ 650 AD; E2). During the early Holocene, the lows of the Eddy cycle coincide with prominent climate change episodes defining a clear millennial periodicity (figure 82; Marchitto et al., 2010). E12 (11,250 BP) coincides with a particularly humid phase in northwestern and central Europe towards the end of the Preboreal oscillation (van der Plicht et al., 2004; Magny et al., 2007). E11 (10,300 BP) coincided with the first cold, humid event, of the Boreal phase (Björck et al., 2001; Magny et al., 2004b), while E9 (9,300 BP) matches the second Boreal event (Rasmussen et al., 2007; Magny et al., 2004b). E8 (8,300 BP) coincided with the outbreak of Lake Agassiz, and researchers are trying to differentiate the relative climatic contribution to the 8.2 kyr event from the solar minimum and the proglacial lake outbreak (Rohling & Pälike, 2005). E7 (7,300 BP) coincides with the last cold, humid phase of the sixth millennium BC (Berger et al., 2016). E6 (6,300 BP) is less well established in the literature, although clearly identified as a dry event in Oman caves speleothems (Fleitmann et al., 2007). E5 (5,200 BP) has been well described worldwide as an abrupt cold event (figure 44; Thompson et al., 2006).
Figure 82. Millennial climate change periodicity. Climatic and solar proxy records, spanning the early Holocene, 250-year smoothed and 1800-year high-pass filtered. Records are Soledad Basin G. bulloides Mg/Ca (SST temperature proxy, blue), tree-ring–derived 14C production rate (solar activity proxy, gold), ice core 10Be flux (solar activity proxy, gray), Dongge Cave (southern China) stalagmite δ18O (Asian monsoon proxy, light blue), Hoti Cave (Oman) stalagmite δ18O (Indian monsoon proxy, green), and North Atlantic stack of IRD petrologic tracers (North Atlantic iceberg activity proxy, red). Source: T.M. Marchitto et al. 2010. Science, 330, 1378-1381.
The identification of the Eddy cycle lows, as well as the Bray cycle lows (figure 64), allows an examination of grand solar minima (GSM) distribution according to the two main solar cycles of the Holocene. Usoskin (2017) gives a conservative list of 25 GSM that were identified in previous studies by different researchers for the past 11,500 years. There is a notable coincidence. Since the Eddy cycle is so close to one thousand years, all the lows of the cycle take place at ~ X,300 yr BP, with X being every millennia of the Holocene. We can observe in the list of GSM that 15 of them take place at ~ X,300 ± 80 yr BP (figure 83 a; Usoskin, 2017). Those GSM are assigned to the Eddy cycle given the good temporal coincidence (figure 83 b). Next, we have 9 GSM that coincide with the lows of the 2,475-year Bray cycle, and in fact define it (figure 83 b). Two of these GSM, at 10,165 and 5,275 years BP, also coincide with the Eddy cycle, as both cycles tend to coincide in phase when two Bray cycles (4,950 years), and five Eddy cycles (4,900 years) have passed.
Figure 83. Grand solar minima of the Holocene. a) Conservative list with approximate dates (in -BC/AD and BP) of grand minima in reconstructed solar activity. The name refers in some cases to a GSM cluster (cl.). The cycle states if the GSM shows a temporal coincidence with a low from the Bray (B), or Eddy (E) cycle. References: 1-listed in Usoskin et al. (2007); 2-listed in Inceoglu et al. (2015); 3-listed in Usoskin et al. (2016). Source: I.G. Usoskin, 2017. Living Rev. Sol. Phys. 14, 3. b) Sunspot based solar activity reconstruction from the radiocarbon record showing the disposition of the GSM associated with the Bray (blue) and Eddy (orange) cycle lows. Source of solar reconstruction: A.K. Kern et al. 2012. Palaeo. 329-330, 124-136.
Of the 25 GSM identified by Usoskin (2017) during the Holocene, only three are not located close to the lows of the Eddy or Bray cycles. The Oort (920 BP), Noach (4805 BP), and an unnamed GSM at 8995 BP, that could be considered part of the Boreal 2 cluster. Since 88% GSM occur during an Eddy or Bray low, it is unlikely that the next GSM will take place before ~ 2600 AD, when the next Eddy cycle low is expected.
The 208-year de Vries solar cycle
As previously described (see The 2400-year Bray Cycle), the de Vries solar cycle is strongly modulated by the Bray solar cycle. For about a millennium centered in each Bray cycle low, the de Vries cycle reduces solar activity every ~ 208 years, and when a cluster of GSM takes place, it establishes the average spacing between them (figure 61). Outside these windows centered in the Bray cycle lows, the de Vries periodicity has very low power in wavelet analysis indicating it has little effect on solar activity (figure 58). The climatic effect of the de Vries cycle matches its solar (cosmogenic isotope) signature.
In 1984, Charles Sonett and Hans Suess proposed that the 208-year cycle seen in solar activity proxies could be related to ~ 200-year periodicity changes in tree-rings width. This finding has been confirmed for tree-rings, which reflect changes in temperature or precipitation, in several regions of the planet. Anchukaitis et al. (2017) have constructed a tree-ring multi-proxy (54 series), extra-tropical Northern Hemisphere, warm season (MJJA), temperature record spanning 1,200 years (750-1988 AD). The record shows high and stable coherence and consistent phasing with solar irradiance estimates at bi-centennial time scales (194-222-year periods), the ~ 208-year de Vries solar cycle frequency (figure 84; Anchukaitis et al., 2017).
Figure 84. Bi-centennial solar influence on Northern Hemisphere summer temperatures from tree-rings. a) Left scale: Reconstructed Northern Hemisphere mean MJJA temperature anomaly time series (black line), smoothed with a 30-year Gaussian filter. Right scale: Solar forcing relative to the period 1976-2006 CE, with the pink shaded region showing the range of the forcing reconstructions compiled by Schmidt et al. (2012), Geosci. Model Dev. 5, 185-191. b) Wavelet coherence between the Northern Hemisphere mean MJJA temperature anomaly time series and solar forcing variability from Vieira and Solanki (2010), Astron. Astrophy. 509, A100. Arrows indicate the phase of the relationship where coherence >0.65. In-phase signals point directly to the right of the plot. A continuous in phase coherence between tree-ring temperatures and solar activity is seen at the de Vries periodicity. Source: K.J. Anchukaitis et al., 2017. Quat. Sci. Rev. 163, 1-22.
The modulation of the de Vries cycle by the Bray cycle is also apparent in the climatic data. Breitenmoser et al. (2012) analyzed the ~ 200-year periodicity during the past two millennia using seventeen near worldwide distributed tree chronologies, and found significant periodicities in the 208-year frequency band, corresponding to the DeVries cycle of solar activity, indicating a solar contribution in the temperature and precipitation series. The result continued being significant after the removal of the volcanic signal, and was most prominent in records from Asia and Europe (figure 85; Breitenmoser et al., 2012). When the 180-230 years band-pass filtered variability was compared with that of solar variability, highlighting the de Vries cycle, it can be seen that as the de Vries signal increases after about 800 AD due to its modulation by the Bray cycle, the climatic signals start to synchronize with the solar signal and in some cases also increase their amplitude (figure 85). This synchronization means that after 800 AD the geographical region is responding to solar forcing, changing the climate according to the 208-year solar periodicity.
Figure 85. Climate response to the De Vries solar cycle in tree-ring chronologies over the past 2000 years. Band-pass filtered total solar irradiation (dotted red line) and tree-ring-derived climate data series in the range of periods 180–230 years for (a) Asia, and (b) Europe. The values in the brackets describe the variability in the band-pass filtered time series in relation to the corresponding unfiltered data series for the displayed time intervals. The synchronization, and in some cases amplitude, of the climatic signal correlates with the strength of the solar signal, indicating that the modulation of the de Vries cycle by the Bray cycle extends to its climatic effect. Source: P. Breitenmoser et al., 2012. Palaeo. 313-314, 127–139.
Phase relationships between hemispheric and global climate reconstructions from tree-rings and the solar irradiance time series indicate a lag of ~ 10 years (range, 5-20 years), with solar changes leading temperature anomalies, consistent with both climate modeling and other climate and solar variability studies (Eichler et al., 2009; Breitenmoser et al., 2012; Anchukaitis et al., 2017).
Other studies link the 208-year de Vries cycle to climate change, including Central Asian ice-cores (Eichler et al., 2009), Asian (Duan et al., 2014) and South American (Novello et al., 2016) monsoon-record speleothems, Mesoamerican lake-sediment cores as drought proxies (Hodell et al., 2001), and Alpine glaciers (Nussbaumer et al., 2011). The climatic effect of the de Vries solar cycle is thus well established.
The 88-year Gleissberg solar cycle
Despite the popularity of the Gleissberg solar cycle in the literature I have not been able to unambiguously identify this cycle as important for solar-climate effects. This is due to the Gleissberg cycle being different things for different researchers.
In 1944, Wolfgang Gleissberg, working at the University of Istanbul observatory, described a long solar cycle that could only be revealed by applying what he called a “secular smoothing” (a trapezoidal 1-2-2-2-1 filter) to a numerical sequence formed by the maximum sunspot values of the known 11-year solar cycles. According to him this numerical procedure revealed “a long cycle which produces systematic changes of the features of the 11-year cycle and which includes seven 11-year cycles, or 77.7 years.” The cycle thus described is not apparent in the sunspot record, and cannot be produced from it by frequency analysis.
As originally described, the Gleissberg cycle is unacceptable by modern scientific standards (and I would dare to say inexistent), and due to it the term Gleissberg cycle means different things to different authors. For some authors it is a frequency peak of ~ 88 years that appears in frequency analysis of the cosmogenic record (McCracken et al., 2013b; Knudsen et al., 2011; figure 86). Other researchers have found that applying the trapezoidal filter of Gleissberg separately to dates of solar cycle minima and maxima from sunspot records then merging them, one also obtains an ~ 80-year time domain periodicity (Peristykh & Damon, 2003). They interpret this result as confirmation of the cycle, that would simultaneously regulate the 11-year cycle amplitude and period. Yet the biggest group of researchers just call any periodicity between 50 and 150 years the Gleissberg cycle, often giving the name simultaneously to two different bands. Joan Feynman, sister of the famous physicist, has studied the centennial solar cycle under the Gleissberg flag of convenience (Feynman & Ruzmaikin, 2014).
Figure 86. The ~ 88-year Gleissberg cycle during the Holocene. a) Lomb-Scargle spectrogram on 14C solar activity reconstruction data grouped in 2000-yr windows, showing the distribution of spectral power for the 50-125 year range. b) The spectral power distribution calculated for a 2000-yr window centered at 2,225 BP. c) The spectral power distribution of a 2000-yr window centered at 4,525 BP, showing the Gleissberg cycle (~ 88 yr) as the most dominant feature in this frequency range for the 3,500-6,500 BP period. The result is reproduced using a 10Be solar activity reconstruction. Source: M.F. Knudsen et al. 2011. The Holocene 22, 5, 597-602. Supplementary material.
Of interest to us here is only the ~ 88-year periodicity present in cosmogenic records that we can also call the Gleissberg cycle, if only to avoid further confusion. The problem is that wavelet analysis shows that this periodicity was only apparent between 6,500 and 3,500 BP (figure 86). This explains why the cycle cannot be detected in the sunspot record. Whether it is a real cycle subject to a very long modulation, or a temporal pseudo-periodicity that emerged from the unknown interactions that generate long term solar variability, cannot be determined. It is also very unlikely that we will be able to determine if it played a significant role in the climate of the period. As the evidence indicates this periodicity is not currently relevant, we will not consider it further.
Other solar periodicities
By now it should be obvious that solar cycles are pseudocycles or periodicities that display a relatively high level of period and amplitude variability. Some of the cycles, like the ~ 2400-year Bray and the ~ 1000-year Eddy cycle, appear to be featured in records several million years old (Kern et al., 2012). The ~ 208-year de Vries cycle has been detected in ice-cores for at least the past 50,000 years (Raspopov et al., 2008b). Other periodicities however, like the 88-year Gleissberg cycle, have only been found for a few millennia.
Frequency analysis of 14C and 10Be display other clear peaks at 52, 104, 130, 150, 350, 515, and 705 years (McCracken et al., 2013b). Some of them could be harmonics of longer cycles. 6,000 and 9,500-year solar cycles have also been proposed (Xapsos & Burke, 2009; Sánchez-Sesma, 2015).
Is the Sun subject to over a dozen different cycles? Or are some of them simply artifacts and not solar variability cycles? Instead of assuming every peak in a frequency analysis constitutes sufficient evidence for the existence of a cycle, I only consider those where abundant evidence exists in the scientific literature that solar cycles match the climate evidence precisely. They are the Bray, Eddy, and de Vries cycles. Of interest are also the periodicities recognizable in the sunspot record, the Schwabe (11-year), Pentadecadal, and Centennial (Feynman) cycles. These last two might be simply harmonics of the de Vries cycle, but as they are currently observable, they may be useful to interpret the past, as well as project future solar activity.
It is worth noting, however, that multiple harmonic constituents in complex astronomical phenomena are a reality. Until the advent of computers, tides were predicted by complex “brass brain” machines. The first of these was built by Lord Kelvin in 1873. After identifying the spectral harmonic components from a long tidal data series at a specific port, machines that could handle up to 40 tidal constituents would produce a year of tidal predictions for that port in a few hours (Parker, 2011).
The Centennial (Feynman) and Pentadecadal solar cycles.
In 1862 Rudolf Wolf, after completing the first continuous record of sunspot numbers, “concluded from the sunspot observations available at that time that high and low maxima did not follow one another at random: a succession of two or three strong maxima seemed to alternate with a succession of two or three weak maxima”. That observation lead to the suggestion of the existence of a long cycle, or secular variation, the length of which was estimated at that time to be equal to 55 years (Peristykh & Damon, 2003). Thus, the Pentadecadal solar cycle is the oldest discovered secular variation of the sun.
Although the Pentadecadal solar cycle displays low power and is statistically non-significant in the sunspot record, it is very prominent in the 10Be record from the one year resolution Dye 3 ice core for the period 1420-1992 AD (McCracken et al., 2013a; figure 87).
Figure 87. Solar activity spectra during the last centuries. Fourier spectra of a) the 1610-2010 sunspot number and b) the annual 10Be data from Dye 3 ice core for the interval 1420-1992. Period in years. Main periodicities names have been added. Source: K.G. McCracken et al. 2013a. Solar Phys. 286, 609–627.
The Pentadecadal cycle should be responsible for the decrease in solar activity at Solar Cycle 20 (SC20) between 1965 and 1976 (figure 89, red arrows). This periodicity is interesting in that it could be related to the pentadecadal variability described in sea level pressure and temperatures in the North Pacific (Minobe 2000). Besides having the same length, the pentadecadal solar change that took place at SC20 was shortly followed by the well-known and studied Pacific climate shift that took place in 1976 (Miller et al., 1994). However, their relation at this time is speculative.
The Centennial solar cycle appears as a peak of ~ 104 years in cosmogenic isotopes frequency analysis, and as a decrease in maximum and minimum sunspot numbers at the beginning of each century since there have been telescopic sunspot observations. Despite this precedent, most solar physicists were expecting SC24 to have a slightly lower level of activity than SC23 and were surprised by the depth and duration of the 2008 minimum and the subsequent low activity of SC24. Of the 54 SC24 predictions published or submitted to the SC24 Prediction Panel in six general categories, spectral analysis predictions (figure 88 a, light blue; Pesnell, 2008) based on Fourier, wavelet, or autoregressive-based forecasts, outperformed all other categories, predicting below average SC24 activity (figure 88 b). In this real test, the use of long periodicities found in solar activity records, for which we have no explanation, fared better than methods based on our clearly inadequate understanding of solar physics. A subcategory based on polar fields produced a better prediction, but it can only predict the next cycle when it is close to the minimum, while spectral methods can predict multiple cycles in advance.
Figure 88. Solar Cycle 24 prediction. Solar Cycle 24 corresponds to a low in the Centennial solar cycle. a) 54 Cycle 24 predictions ordered by increasing predicted maximum, and color coded by categories as indicated in the key. The final maximum value is indicated by the red arrow. Source: W.D. Pesnell. 2008. Solar Phys. 252, 209-220. b) Solar Cycle 24 Panel consensus high (red curve) and low (orange curve) predictions, with the final sunspot number being lower than both. Source: NOAA. c) Average sunspot number prediction by a low-frequency modulation model (dotted curve) based on frequency analysis from sunspot and cosmogenic isotope records, compared to the average sunspot number since 1750 (continuous curve). Despite a low bias, the model predicted the current centennial minimum for cycles 24 and 25. Source: M.A. Clilverd et al. 2006. Space Weather 4, S09005.
Of the spectral predictions, the one published (Clilverd et al., 2006) used a low-frequency modulation model that has some clear inadequacies, like including the Gleissberg 88-year cycle that is no longer observable, assigning an extremely low amplitude to the 208-year de Vries cycle, and not including the modulation by the ~ 2400-year Bray cycle that we have discussed previously. However, since it included the 104-year Centennial periodicity, it predicted very low activity for SC24 (figure 88 c). Indeed, SC24 turned out to be the least active cycle in 100 years. With its faults corrected the model would have predicted accurately slightly more activity for SC24 than for SC14 (in 1904), instead of less. Importantly, the model also predicted in 2006 that SC25 will again be a below average cycle of similar amplitude to SC24. As we approach the 2019-2020 solar minimum the polar field method appears to confirm that SC25 will again be a below average solar cycle. A new prolonged solar minimum, like the Gleissberg minimum of 1879-1914, is being established by the Centennial cycle, and should last at least until around 2032. There is a petition to name this extended minimum as the Eddy solar minimum.
The Centennial cycle has been studied mainly by Joan Feynman. She started studying the Gleissberg cycle and realized the Centennial cycle was different, naming it Centennial Gleissberg Cycle, or CGC. To avoid confusion, the name Feynman cycle appears more appropriate. Feynman and Ruzmaikin (2014) have showed that this periodicity is observable on the Sun, in the solar wind, at the Earth, and throughout the Heliosphere. It is supported by the very weak solar wind at the SC23-24 transition, the weakest observed in the space age. Feynman cycle lows (extended minima) are characterized by very low annual sunspot numbers (less than 3, figure 89 a, black arrows and blue asterisks), and a slight increase in the duration of the 11-year cycle (figure 89 d).
Figure 89. The Feynman (Centennial) solar cycle. a) The annual sunspot number (SSN) record in 1700–2012 (grey curve, left scale). Black arrows and blue asterisks denote times when the annual sunspot number was less than 3, indicating the Feynman minima. Added to the original figure, the annual average aa index in 1868-2012 (dark green curve, right scale), and the position of the additional Pentadecadal cycle minima (red arrows). b) Wavelet spectrum of SSN. Solid lines mark the 11-year and 100-year periods. c) The integral spectrum obtained by averaging over the time axis. The dashed line shows the significance of this spectrum at the 1σ level. Red labeling added. d) The detailed wavelet spectrum in the 5.2-17.4-year period region. A slight increase in the duration of the Schwabe cycle is observed associated to the Feynman cycle lows, particularly ~ 1800 AD. e) The time series of the 80-110-year band. Source: J. Feynman & A. Ruzmaikin. 2014. J. Geophys. Res. Space Physics, 119, 6027–6041.
The Feynman cycle is the only long periodicity whose lows have been observed with modern instrumentation. The aa (antipodal amplitude) index that started in 1868 and measures the disturbance of the Earth’s magnetic field by solar wind, clearly displays the last full period of the Feynman cycle, with its lowest values in 1901 and 2009 (figure 89 a). In the Sun, surface differential rotation changes on a centennial time scale coincide with the observed phase change between the toroidal and poloidal magnetic field components and the time dependence of the dipole and quadrupole components of the poloidal magnetic field (Feynman & Ruzmaikin, 2014). Solar dynamo models still have to accommodate these centennial variations in the Sun.
Previous Feynman lows are associated with colder periods at the early decades of each of the past three centuries. The present extended minimum is associated with an unexpected hiatus in global warming that has yet to be adequately explained.
Conclusions
1) The ~ 1000-year Eddy solar cycle seems to have dominated Holocene climate variability between 11,500-4,000 years BP and in the last two millennia, where it defines the Roman, Medieval, and Modern warm periods.
2) The ~ 208-year de Vries solar cycle displays strong modulation by the ~ 2400-year Bray solar cycle, both in its cosmogenic isotope signature and in its climatic effects.
3) The ~ 88-year Gleissberg solar cycle is ill-defined in the literature and hasn’t manifested itself for the past 3,500 years.
4) Besides the ~ 11-year Schwabe solar cycle, the Centennial (Feynman), and Pentadecadal solar cycles are observable in the sunspot record. The ~ 100-year Feynman solar cycle is responsible for the present extended solar minimum.
5) In all cases a decadal or longer decrease in solar activity is associated with a decrease in temperatures and a change in precipitation patterns. A 10-year delay between solar changes and climatic changes is observed in some studies.
References [Bibliography]
Acknowledgements
I thank Andy May for reading the manuscript and improving its English.
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