In Part A, we established the existence of a ~ 2400-year climate cycle, discovered in 1968 by Roger Bray. This climate cycle correlates in period and phase with a ~ 2400-year cycle in the production of cosmogenic isotopes, that corresponds with clusters of solar grand minima at times of abrupt cooling and climate deterioration. The relationship between solar activity and cosmogenic isotope production during the past centuries confirms the ~ 2400-year solar cycle as the origin of the climate cycle.
The solar variability 2400-year cycle
Radiocarbon dating was developed by Willard Libby in 1952 based on the idea that biological carbon samples that reflected atmospheric 14C/12C proportion at the time they were alive would progressively become 14C depleted due to the isotope’s radioactive decay, and thus would provide a clock to measure elapsed time. But Libby warned that there was no guarantee that the 14C/12C ratio had been constant in time. Therefore, a considerable effort has been ongoing since the 1960s to determine the proportion of 14C in the atmosphere over past millennia. The resulting calibration curve (figure 57) is used to convert radiocarbon dates into real time dates. But the radiocarbon clock does not run at a constant speed as the real-time clock does. There are times when the radiocarbon clock runs faster and times when it runs slower, creating bumps in the calibration curve (figure 57, ovals and arrowheads). That the radiocarbon clock runs faster (Y values decrease faster in figure 57), implies that the 14C/12C ratio is deviating upwards, as samples with more 14C are more recent. This means that either 14C is being produced at a higher rate, or total CO2 is decreasing while 14C is not. Most scientists believe the first explanation contributes more to the observed changes because the proportion of 14C is so small in the atmosphere (~ 10–12) as to require very large changes in total CO2 to produce the alterations that can be explained by small increases in 14C. And we know from ice core records that CO2 changes have been relatively small during the Holocene. A carbon cycle model has been used since the late 1970s to account for the effect of CO2 variations on radiocarbon dating. Thus, the best explanation for the acceleration observed in the radiocarbon clock is that the production rate from cosmic rays in the atmosphere increased due to a decrease in the solar magnetic flux that takes place when the Sun is in a prolonged period of low activity known as a grand solar minimum (GSM). This conclusion is supported by the same variability shown by a different cosmogenic isotope, 10Be, whose deposition does not depend on the carbon cycle.
Figure 57. Radiocarbon decay and solar activity. The radiocarbon calibration curve (IntCal13) is unrelated to climate change and obtained through the efforts of hundreds of researchers over decades to provide an accurate way of measuring the time elapsed since a biological sample stopped living. The calibration curve presents periods of time in the past, when there was a noticeable deviation from linearity (ovals and arrowheads). Five of those periods (ovals) are separated by multiples of ~ 2450 years delimitating a 14C cycle. Solar activity reconstruction from cosmogenic 10Be and 14C isotopes shows that those periods correspond to periods of unusually high isotopic production interpreted as grand solar minima like the Spörer and Maunder minima. Those periods correspond precisely to the lows of the Bray climate cycle (blue bars). Source: A.K. Kern et al., 2012. Palaeo. 329–330, 124–136.
From the early 14C production data available in the late 1960s Roger Bray noticed a correspondence between climate change and radiocarbon production (Bray, 1968), thus defining both a climate cycle and a solar variability cycle. This caused him to propose that changes in solar activity were responsible for the climatic changes. The solar cycle can be clearly seen in the radiocarbon data from the ~ 2450 year spacing of higher 14C production at 12800-12650, 10300-10100, 5350-5200, 2800-2650, and 600-400 BP, corresponding to all the Bray lows in the Holocene and Younger Dryas except B4, that lacks a similarly noticeable 14C production signature (figure 57 ovals).
The Bray solar cycle was again identified by J. C. Houtermans in his PhD thesis of 1971, and has since been confirmed multiple times independently. The uncertainty regarding the position of B4, that should fall around 7.8 kyr BP, together with very low solar activity at around 8.3 and 7.3 kyr BP, plus the presence of other periods of very high 14C production between 11.5 and 9 kyr BP (figure 57 arrowheads), has caused different studies to differ in the length of the Bray solar cycle between 2200 and 2600 years depending on the methodology used. The best studies however establish the length of the Bray solar activity cycle between 2400-2500 years, and thus it is commonly referred as the ~ 2400-year cycle. In the late 1980s Sonnet and Damon despite being aware of Bray’s and Houtermans’ studies decided, against established custom, to name the cycle not by the name of its discoverer, but as Hallstattzei (later Hallstatt) for a late Bronze-early Iron cultural transition in an Austrian archeological site during the cycle’s B2 minimum, 2800 years ago. The inappropriateness of a human cultural name from a particular period for a solar cycle that has been acting for tens of thousands, and probably millions of years (Kern et al., 2012), plus the injustice of ignoring its discoverer, demand that the cycle be properly renamed as the Bray cycle.
One peculiarity of the ~ 2400-year solar cycle is that it modulates the amplitude and phase of the ~ 210-year de Vries solar cycle (Sonett, 1984; Hood & Jirikowic, 1990). The amplitude of the de Vries cycle is maximal at the lows of the Bray cycle (figure 58), and minimal at mid-time between lows, to the point of becoming imperceptible.
Figure 58. Modulation of the de Vries cycle by the Bray cycle. Sunspot activity reconstruction from 14C data (top panel) and its wavelet spectrum. Left and right-hand panels depict 2D and global wavelet spectra, respectively. Upper and lower panels correspond to period ranges of 500 – 5000 years and 80 – 500 years. Dark/light shading denotes high/low power. Source: I.G. Usoskin 2013. Living Rev. Solar Phys. 10, 1. It is known since 1984 that the ~ 208-year de Vries solar cycle is strongly modulated by the ~ 2400-year Bray solar cycle such that the amplitude of the de Vries cycle is maximal at the lows of the Bray cycle and minimal in the middle of two lows, to the point of becoming unnoticeable. Wavelet analysis of solar activity reconstructions show the 208-year power accumulating close to the lows of the Bray cycle (blue bars). The cause of this modulation is unknown, but indicates that both cycles are not independent.
This property of some of the short solar cycles, of being modulated by the long cycles can be observed in the sunspot record of the past 400 years, where we observe that both the de Vries and centennial cycle lows display progressively more activity as we get farther away from the Bray and millennial lows, becoming less conspicuous with time (figure 59). This is how solar activity has been increasing for the past 400 years, by reducing the periods of below average activity, due to this modulation.
Figure 59. Modulation of the short solar cycles during the telescope era. Sunspot group number (black curve) reconstructed back to 1610 AD. Red curve, empirical fitted function for the centennial solar cycle with a period of 103 years described by B. Tan, 2011. Astrophys. Space Sci. 332, 65-72. The centennial cycle (orange scale) presents lows of decreasing intensity at 1700, 1805 (SC5), 1910 (SC14), and 2015 (SC24), going from the millennial low at ~ 1600 AD to the millennial high at ~ 2100 AD. The pentadecadal cycle is also shown as shorter orange bars between the centennial lows. The modulation of the de Vries cycle (blue scale) can also be seen as the low of ~ 1675 AD is much lower than the low of ~ 1885 AD. It can be expected that the low of ~ 2095 AD should barely be noticeable. Thus, moving forward from the Bray low at ~ 1500 AD, we see more solar activity at each successive centennial low.
The de Vries cycle modulation by the Bray cycle allows the identification of its lows during the last glacial period, when drastic climatic changes obscured the ~ 2400-year climatic cycle, and made the cosmogenic record less reliable. Adolphi et al. (2014), isolated the 180-230-year signal containing the de Vries cycle in ∆14C production and 10Be flux data between 22 and 10 kyr BP. This signal displays the 2400-year Bray cycle modulation, allowing the identification, albeit imprecisely, of the position of Bray lows B7-B9 (figure 60) at ~ 15, 17.6, and 20.5 kyr BP. If correct, these dates support a periodicity for the Bray solar cycle between 2450-2500 years, further substantiating its close association with the climatic cycle that also appears closer to 2500 than 2400 years. The authors also propose that, during the Last Glacial Maximum, solar minima correlate with more negative δ18O values in ice (lower temperatures) and are accompanied by increased snow accumulation and sea-salt input over Central Greenland (Adolphi et al., 2014). This supports the idea that the Bray climate cycle also acts during glacial periods.
Figure 60. The Bray cycle during the last glacial maximum. a). Reconstruction of the 10Be flux using accumulation rates and ice-flow modeling from the GRIP ice core. b). 14C concentration after correction for fractionation and decay, from tree rings (pink) and Hulu Cave speleothem H82 (black). c). 14C production rate (H82 speleothem, black) and 10Be flux (orange), normalized to display only the variability in the 180–230 yr band to capture the solar de Vries cycle (208 yr). Source: F. Adolphi et al., 2014. Nature Geo. 7, 662-666. Due to the modulation of the de Vries cycle by the Bray cycle, periods of maximum de Vries variability correspond to the lows of the Bray cycle, and are spaced by ~ 2450 years. GS, Greenland stadial; GI, Greenland interstadial.
The solar-climate relationship
Given the strength of the correlation between past cycles of climate change, and cycles in the production and deposition of cosmogenic isotopes, like the Bray cycle, the solar-climate relationship is accepted in paleoclimatology as non-controversial. Sixteen of twenty-eight (57%) of the articles whose climatic evidence has been reviewed here (see part A) explicitly state that changes in solar forcing are likely to be the cause of the observed climatic changes, and only one explicitly rules them out. Then, why is the solar-climate relationship so controversial outside of the paleoclimatology field?
“The reality of the Maunder Minimum and its implications of basic solar change may be but one more defeat in our long and losing battle to keep the sun perfect, or, if not perfect, constant, and if inconstant, regular. Why we think the sun should be any of these when other stars are not is more a question for social than for physical science” (Eddy, 1976).
There are three main objections that opponents of the solar-climate theory raise, and two of them will be reviewed here, as they are pertinent to the Bray cycle. Since the close relationship between climate changes of the past and changes in the cosmogenic isotope record is undeniable, the first objection is to state that the cosmogenic record is likely to be contaminated by climate and therefore is more of a climatic record than a solar activity record. The second objection is that the sun is luckily extraordinarily constant, and therefore the small changes measured in total solar irradiation (TSI) between an 11-year maximum and minimum are of about 0.1% and produce a very small, almost undetectable, effect on climate. Since there is no indication that the changes were much bigger during the last solar grand minimum, the Maunder Minimum, we know of no mechanism to produce the observed climatic changes. The third objection is that for the past four decades solar activity and global temperatures have been going in opposite directions. We will deal with this objection more in detail in a future article, but for the time being suffice it to say that solar activity is just one of the several forcings that act on climate, and therefore one should not expect temperatures to always follow solar activity, even if the theory is correct.
That the cosmogenic isotope record is affected by climate changes has been known from the beginning. The ∆14C record is affected by changes in the carbon cycle. When the oceans cool they absorb more CO2, and for a constant rate of production the 14C/12C ratio increases. Changes in vegetation go in the opposite way as plants release CO2 during periods of cooling. On a scale of years to about one decade the faster plant response dominates, while for periods of decades to millennia the slower ocean response dominates. Solar activity reconstruction from ∆14C includes a carbon cycle model, usually a box-model, but the sea level changes associated with ice-sheets melting during deglaciation are usually considered too large to be properly modeled and thus solar activity reconstructions from ∆14C usually span only the Holocene. 10Be deposition at the poles is affected by stratospheric volcanic eruptions and precipitation rates. Volcanic SO2 and precipitation rates measured from ice cores are taken into account when reconstructing solar activity from 10Be. The generally very good level of agreement between solar activity reconstructions from ∆14C and 10Be for the Holocene indicates that any remaining contamination must act similarly over the different deposition pathways of both isotopes. This is possible as a significant cooling would increase ∆14C from enhanced CO2 uptake by the oceans, while it might increase 10Be by reducing precipitation rates. But as every climate proxy requires careful evaluation of the many factors affecting it, like sedimentation rates, or upwelling strength, to provide accurate information, the question is not if there is climate contamination in the cosmogenic record, but if the reconstructed record provides a good enough proxy for solar activity.
One test available to answer this question is to examine the reconstruction from cosmogenic isotopes over the period where we have information on solar activity from other sources that cannot be affected by climate. Comparison of the cosmogenic records over the past 400 years with the sunspot record shows a very good level of agreement (figure 61) despite this period undergoing intense climate change, from the depths of the LIA to the present global warming. Aurorae are more frequent the higher the solar activity, and using auroral historical records that extend back 1000 years, we observe that the correlation remains positive for the entire period, and that similar maxima and minima can be clearly recognized, including a period of high solar activity and frequent aurorae around 1100 AD at the time of the well-known Medieval Warm Period (Hood & Jirikowic, 1990; figure 61 b). The conclusion is that within reasonable expectations the cosmogenic record reflects solar activity and thus is a useful proxy for it.
Figure 61. Correlation between cosmogenic isotope production and solar activity. a). Solar modulation function based on 10Be (grey curve) and 14C (black curve), after low-pass filtering at a cut-off frequency of 1/20 yr-1. Source: R. Muscheler et al., 2007. Quat. Sci. Rev. 26, 82-97. b). Auroral frequency record from historic sources. Source: L.L. Hood & J.L. Jirikowic 1990. In “Climate Impact of Solar Variability” NASA Conf. Proc. 98-105. c). Sunspot number. Grey bars, grand solar minima. Orange bars, position of the de Vries lows, spaced ~ 210 years. Solar activity agrees well with cosmogenic isotopes production, indicating that they are a valid proxy for solar activity.
Since the cosmogenic record has faithfully registered the solar centennial variability for the past thousand years as determined from auroral records, and for the past 400 years as determined from sunspots numbers, Hood and Jirikowic (1990) provide another argument for the solar origin of the ~ 2400-year Bray cycle. If the Bray cycle were terrestrial in origin, the modulation that it produces on the de Vries cycle (Sonett, 1984) should not be observable on solar activity records, and the ~ 210-year cycle should appear unmodulated in solar activity phenomena, like sunspots or aurorae. However, as figure 61 shows, the modulation is clearly observable, as the lows of the de Vries cycle corresponding to the Spörer and Maunder minima (dV2 & dV3, figure 61) present less solar activity that the adjacent lows. Again, the only possible conclusion is that the modulation caused by the ~ 2400-year cycle, and the cycle itself, are also of solar origin.
Further support for the implausibility of a climatic contamination of the cosmogenic record of such magnitude that would render it inadequate to determine past solar activity comes from the study of another climate cycle. A 1500-year cycle has been identified by several researchers and does not show up in cosmogenic records during the Holocene. Kern et al. (2012) identified this cycle, as well as the Bray and millennial cycles in a Miocene lake sediment 10.5 Myr old (figure 62 b). That these cycles are so old speaks of the stability of their causes over time, despite the many changes suffered by the Earth. Within the Holocene the 1500-year cycle has been identified in an Alaskan coast record of iron deposition by drift-ice from the Kara sea (Darby et al., 2012; figure 62 d). It is clear that the 1500-year climatic cycle, has left no trace in the cosmogenic record (figure 62 a, b). It is difficult to argue that some climate cycles are greatly contaminating the cosmogenic record while others do not.
Figure 62. The 1500-year climate cycle does not correspond to a solar frequency. a). Lomb–Scargle periodogram of the Holocene sunspot activity detects known solar cycles, including the de Vries cycle (~ 208 years), millennial Eddy cycle (~ 970 years), and the Bray cycle (~ 2200 years), but not a ~ 1500-year cycle. b). Time-converted periodograms of ~ 8200 years, 10.5 million years old, Miocene climate proxy data from a Lake Pannon (Austria) 6 m. sediment core. Ostracods, magnetic susceptibility (magnetic minerals), and gamma radiation (radioactive minerals) respond to different climatic conditions. Ostracods define three main periodicities at ~ 1000, ~ 1500, and ~ 2400 years. Source: A.K. Kern et al., 2012. Palaeo 329-330, 124-136. c). Wavelet analysis of a solar activity reconstruction from 10Be and 14C, showing the power of the cycles over the length of the time series and the complete absence of a ~ 1500-year cycle in the solar record. d). Wavelet analysis of the presence of iron grains at a core off the coast of Alaska, as a proxy for drift ice from the Kara sea, displaying a ~ 1500-year periodicity. Source: D.A. Darby et al., 2012. Nat. Geo. 5, 897-900.
The 8.2 Kyr event or the 7.7 kyr event?
As reviewed in part A, there is great uncertainty between different authors regarding the position of the fourth low in the Bray cycle within a period of climatic instability that extends between 8.4 and 7.1 kyr BP (figures 52-56). We have then seen that this climatic uncertainty corresponds to an unclear signal in the cosmogenic record for the B4 low (figures 57 & 58) where multiple GSM are identified. Solar cycles are irregular by nature, with the 11-year Schwabe cycle being registered as lasting between 9 and 14 years, and showing very large differences in sunspot number amplitude (figure 59). The Bray cycle is no exception and can also last between 2300 and 2600 years, with an average of 2450-2500 years. The mid-point between B5 and B3 falls at ~ 7800 BP (figure 57). As it is important to know the climatic effect of the solar Bray lows and to identify other climate cycles that are acting during the Holocene, I shall attempt to identify B4 with more precision.
The 8.2 kyr event has been one of the largest climatic changes of the Holocene, and coincides with a sudden drop in methane levels of 100 ppb in Greenland ice cores (Kobashi et al., 2007; figure 38). It has been generally attributed to the Lake Agassiz outburst dated at 8.3 kyr BP that is believed to have caused a temporary reduction in the North Atlantic thermohaline circulation (see drop in salinity figure 53 b). However, Rohling and Pälike (2005) have showed that in many well-dated proxies there was an underlying climatic deterioration between about 8.5 and 8.0 kyr BP that was punctuated by the sharp 8.3 kyr BP proglacial lake outbreak. Rohling and Pälike (2005) attribute the broad deterioration to reduced solar activity due to the temporal coincidence with the three Sahelian solar grand minima. They recommend caution when assigning global climatic effects to the periglacial lakes outburst and the effect of the melting water on the NADW formation, due to this coincidence. The combined effect of the global cooling due to this solar low with the regional or hemispheric abrupt cooling from the Lakes Agassiz and Ojibway event is what made this period between 8.4 and 7.9 kyr BP suffer the most abrupt temperature drop of the Holocene, at least in the North Atlantic region.
A detailed study of the hydrology of the Rhone Valley of France over a 1700-year period between 8.5 and 6.8 kyr BP by Berger et al. (2016) identifies three multicentennial cold and wet phases separated by warm, drier intervals (figure 63). During the cold-humid periods the Citelle river changed to a braided fluvial style, greatly increasing the water flow and sediment discharge. This fluvial change coincides with increased hydrological activity elsewhere in Europe, lower temperatures in the Greenland ice core GISP2 and glacier advances in the Alps (Berger et al., 2016; figure 63).
Figure 63. Hydrological and climate indicators during the 8.5-6.8 kyr BP. Hydrological analysis defines seven phases at Lalo site (Rhone valley, France). Four of them correspond to periods of soil formation (pedogenesis), meandering entrenched Citelle river, and normal sediment discharge. Three periods at 8.2, 7.7, and 7.2 kyr BP show braided Citelle river flow, and enhanced flux and sediment discharges. They coincide with periods of low or decreasing temperatures in Greenland, reduced solar activity, increased hydrology elsewhere in Europe and Alps glacier advances. The blue bands correspond to colder periods in the Greenland ice sheet and alpine areas and to moister signals in western/central hydrosystems, defining the known 8.2, 7.7, and 7.2 kyr events. A, B and C letters indicate the tripartite climate division of the 7.7-7.1 period. Source: J-F. Berger et al., 2016. Quat. Sci. Rev. 136, 66-84.
The first cold/wet phase corresponds to the 8.2 kyr event and coincides with the Sahel cluster of GSM, while the second and third cold/wet phases at 7.7 and 7.2 kyr BP coincide with the Jericho cluster of GSM (figures 63 & 64). The first and third phases are separated by one millennium, and also separated by a millennium from other climatic events characterized by low solar activity at 9.2 and 6.3 kyr BP (figure 64), indicating that they are the E9 and E8 lows of the ~ 1000-year Eddy solar cycle. Thus the 7.7 kyr event is unambiguously identified as the B4 low of the Bray cycle.
Figure 64. Solar grand minima clustering at the lows of the Bray cycle. a). Holocene solar activity (sunspots) reconstruction from 14C data. Source: A.K. Kern et al., 2012. Palaeo 329-330, 124-136. Blue bars indicate the lows of the Bray cycle. Blue arcs on top display a regular 2475-year periodicity for comparison. Black boxes correspond to grand solar minima close to the lows of the Bray cycle, with their names or initials. Orange bars correspond to some of the lows of the ~ 1000-year Eddy solar cycle, with only the lows at 8.3 (E9) and 7.3 (E8) kyr BP numbered. This figure illustrates the difficulty of correctly identifying B4, a cause for the variable length assigned to the cycle by different numerical analyses. b). Probability density function (PDF) of the time of occurrence of grand minima relative to the time of occurrence of the nearest low of the Bray cycle, using the superposed epoch analysis. The times of occurrence of lows of the Bray cycle were defined by considering the average of two second singular spectrum analysis components of the sunspot number reconstruction from 14C and 10Be, and are indicated by the numbers in the figure. Source: I.G. Usoskin et al., 2016. A&A 587, A150.
3) The 2400-year climatic cycle corresponds in period and phase to a cycle in cosmogenic isotopes highlighting the coincidence of abrupt cooling climate change events with clusters of grand solar minima and prolonged periods of low solar activity.
4) The 8.2 kyr event does not belong to the Bray cycle, and resulted from the coincidence of a low in the ~ 1000-year Eddy solar cycle with the outbreak of proglacial Lake Agassiz.
I thank Andy May for reading the manuscript and improving its English.
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