Nature Unbound IV – The 2400-year Bray cycle. Part B

by Javier

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.

Conclusions

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.

Acknowledgements

I thank Andy May for reading the manuscript and improving its English.

References [link]

Moderation note:  As with all guest posts, keep your comments civil and relevant

112 responses to “Nature Unbound IV – The 2400-year Bray cycle. Part B

  1. Even if the 2400-yr Bray cycle is not a property of long-term solar activity it still is something we must reckon with and especially if changes in atmospheric CO2 levels have nothing to do with it– that’s how science works.

    • Are you competing with Javier’s first paragraph ?

      Not much follows from two non sequiturs laid end to end.

      • No one was around to count sunspots 11,000 years ago. If cosmogenic isotope production is related to solar activity which in turn is related to sunspots, which taken together are related to historical instances of global warming and cooling corresponding to a ~2400-year solar cycle, we should be skeptical of the science of AGW as a complete explanation of climate change.

  2. Harry Twinotter

    Considering the sun is heading into it’s minimum after a fairly average solar maximum (for the 20th and 21st centuries anyway), let’s see how the global mean temperature responds.

    I am betting it will continue to go up regardless of what the sun is doing.

    • That may not be the best given the facts– as it turns out, “the modern Grand maximum (which occurred during solar cycles 19–23, i.e., 1950-2009),” says Ilya Usoskin, “was a rare or even unique event, in both magnitude and duration, in the past three millennia.” [Usoskin et al., Evidence for distinct modes of solar activity, A&A 562 (2014)]

      • Usoskin’s opinion on a modern grand maximum is very controversial. While 20th century solar activity is clearly above Holocene average, it does not appear highly unusual after the revised sunspot series, that is supported by the great majority of solar experts.

    • Harry,

      Global temperatures have not increased for the 21st century except for the El Niño 2014-2016 warming that it is now being corrected (2001-2013 = flat). Without a contribution from long-term above average solar activity, global temperatures are likely to rise at a reduced rate, if at all.

      The important point is that if solar forcing has been underestimated, which is easy because it has been considered a very small factor by IPCC, then the dangers of global warming have been greatly overestimated.

      • And I guess all bets are off in the event of a Grand Minimum, which is always a definite possibility even if not a certain prediction.

        The issue is that no one knows when the new Grand Minimum occurs and no one really knows what would happen then. I call such extended minima of suppressed solar activity Grand Minima, since the Maunder Minimum (lasting from 1645 till about 1700 or 1712) is only one of those. Later minima, such as the Dalton Minimum (ca. 1800 AD) and modern (ca. 1900 AD) ones were not really Grand Minima, in neither depth or duration. ~Usoskin

      • Harry Twinotter

        Javier.

        You seem pretty sure of yourself.

      • No Harry,

        I just defend my interpretation of the evidence. I am prepared to change my position if the evidence demands it.

        I change my position quite often when the evidence available to me changes. Three years ago I believed solar variability had little effect on climate, due in part to Leif Svalgaard skeptic arguments. I used to say that the LIA was just one off, and N=1 doesn’t make a statistic case. However one day I decided to check what the available evidence showed, and saw that essentially all SGM and cluster of SGM display a clear cooling and climatic deterioriation with important changes in precipitation. The climatic evidence doesn’t support Leif Svalgaard position, and thus I changed mine. Since then more evidence available to me reinforces my position.

        Since I am not a climate scientist, and I have no strong position on the causes of global warming, I don’t care on the way we satisfy our energetic needs as long as it is technologically and economically sound, I have no skin in this game.

        I am prepared to change my position on anything. I don’t believe the CO2 warming alarmism simply because it is not supported by the evidence. In particular since there has not been significant warming for the entire 21st century, discounting meteorological causes like El Niño. If warming had continued at the same rate as in the 1980-90’s I’d be in the opposite side. As a scientist I am wedded to evidence, not theory.

    • Harry

      I did a study of CET set against volcanism and sunspots

      I am not convinced by either factor, other than there is some sunspot correlation wth some years of some of the intermittent little ice age

      Tonyb

      • Harry Twinotter

        climatereason.

        Who cares – not global.

      • Harry

        There are many fine scientists plus the UK and Dutch met offices that say that CET is a good (but not perfect) proxy for global and certainly NH temperatures. I have cited these sources many times here.

        Lets assume they do have some global resonance as science believes. What would be your reaction?
        tonyb

    • Harry, I certainly won’t take you up on your bet. The data fiddlers are almost certain to come up with a higher figure regardless of what temperatures actually do.

      • Harry Twinotter

        Forrest Gardener.

        Conspiracy Theory.

      • No Harry. No conspiracy.

        Merely continuation of the motivated decision making so evident in everything the data fiddlers have done so far. That combined with not wanting to be denounced for rocking the gravy boat are more than adequate to explain what is happening.

        Unless of course you know of a conspiracy and have details to share?

      • afonzarelli

        (just because you’re paranoid doesn’t mean they aren’t out to get you)…

      • An oldy but a goldy with much to offer for the likes of those having more than one otter.

  3. Pingback: Nature Unbound IV – The 2400-year Bray cycle. Part B – Enjeux énergies et environnement

  4. “The third objection is that for the past four decades solar activity and global temperatures have been going in opposite directions.”

    Straw man argument…
    Higher solar activity correlates with warming, lower activity with cooling.

    (graph courtesy of javier)

    • Higher solar activity correlates with warming, lower activity with cooling.

      Obviously I agree ;-)
      But we are unable to determine what part of the warming has a solar cause. To me the evidence suggests that neither CO2, nor the sun, can account for all the warming. It is probably a combination plus perhaps some other factors, like lower than average volcanic activity, and a long term climate reorganization after the LIA (internal centennial variability).

      • afonzarelli

        “Obviously, I agree ;-)”

        Obviously, you agree! Where do you think i stole the idea from? (not to mention the graph… ☺)

      • we are unable to determine what part of the warming has a solar cause

        That’s the kind of honesty climate science sorely needs. There’s always a very human temptation to look at any highly complex phenomenon and prefer an explanation that is simple, elegant and wrong.

    • Except your solar series is WRONG.

      One of the hazards of javier cut and paste science .. you know where you cut and paste old charts that use deprecated data.. is that you cant update them.

      Rules.
      if you read something where a guy takes a chart from an old paper, you
      can be pretty sure he never checked the data for himself. he never
      checked that they plotted the data correctly. he never checked if the
      data had been improved.
      These are basic QC checks. If your goal is supporting what you believe
      ( religion) you will never check sources. You will just “trust” your sources
      and republish what you believe. If you are a scientist you always probe
      the sources you rely on.. you doubt them as a methodological step.
      IS that data correct? has it been updated? can I rely on it?

      If you see no evidence of the researcher going to sources, going to
      primary sources and checking the lines of actual evidence, going
      to the actual data, then they really havent made a case. They have
      merely collected pictures. Pictures that may not even accurately
      reflect the data.
      There is a reason why journals don’t allow you to merely cut and paste
      figures from other papers. one is style, the other is they expect you
      to actually check the data you rely on.

      IF you see a paper on solar that does not use the latest sunspot series,
      THROW IT IN THE TRASH. basically all the “science” on solar cycles
      needs to be redone. It should be easy to recompile all this science.
      right? I mean these guys should just be able to re run their code
      and determine if the new series changes their conclusions or not.
      Thats QC 101.

      IF, that is, they kept their code.

      • Except your solar series is WRONG.

        So you say, without showing evidence, as usual. That’s an opinion and we all know the value of your opinions.

        IF you see a paper on solar that does not use the latest sunspot series, THROW IT IN THE TRASH.

        Again an opinion. The correction to the sunspot series only affects the sunspot series that is 400 years old. It does not affect the cosmogenic record on which the Bray solar cycle is based. And the Bray solar cycle is present in every solar activity reconstruction of the Holocene even the ones from the 80’s no matter how incorrect they were, because it is based in the position of grand solar minima that have always been correctly identified (even named) in the cosmogenic record. That’s why the Bray (aka Hallstatt) cycle was identified in the late 60’s and 50 years later continues to be identified and studied. Let’s see what’s left from BEST reconstruction just ten years from now.

        So another big FAIL from Steven. Is this the best you can do?

      • afonzarelli

        Javier, is mosh talking about your little graph there that i presented? It’s dated 2008, but presumably that refers to the temperature reconstructions. The solar data is the most updated “svalgaard approved” solar data, right? It sure looks just like any of the newest solar series that we’ve seen. (IOW, is mosh just wandering off the reservation AGAIN?)

  5. Straw man argument…
    Higher solar activity correlates with warming, lower activity with cooling.

    During the most recent ten thousand years, solar input to the NH above 60 degrees decreased almost 40 watts per square meter and the solar input to the SH below 60 degrees increased by that same amount and ice core records show both hemispheres kept cycling in the same bounds.
    That straw man argument is that both hemispheres are self regulating.
    Warmer causes oceans to thaw and promote enough more snowfall.
    Colder causes oceans to freeze and promote enough less snowfall.

  6. During the most recent ten thousand years, solar input to the NH above 60 degrees decreased almost 40 watts per square meter and the solar input to the SH below 60 degrees increased by that same amount and ice core records show both hemispheres kept cycling in the same bounds.

    A common bias is to consider geographic hemispheres instead of climatic hemispheres. The climatic equator is the Inter Convergence Tropical Zone that does not have a fixed position. During the year climatic hemispheres contract and expand with their inverted seasons. For the past 10,000 years they also have been changing their respective sizes according to Milankovitch changes in insolation. Those climatic hemisphere changes account for a great deal of temperature buffering. Internal climate teleconnections account for the rest.

    None of those changes have much to do with solar variability changes, that are superimposed on them.

    • You wrote; “A common bias is to consider geographic hemispheres instead of climatic hemispheres.”

      I don’t do that, I understand the boundaries vary around the globe and vary from time to time.

      The oceans that circulate in the NH provide moisture for Greenland ice cores. The oceans that circulate in the SH provide moisture for Antarctic ice cores. It does not matter where the boundaries are between the hemispheres. It matters that each system is self correcting and that each system stays in same bounds in cycles that are not in phase with each other.

      • For me, the NH is the NH circulation cycles, the SH is the SH circulation cycles, I don’t even need to know where the boundaries are because they are not really well known and they change all the time. Each hemisphere records its history in its own respective ice cores.

      • Pope’s
        The Antarctic ice core data records CO2 data from both hemispheres.

        This is evident in current sample data, and the seasonal trend.

    • Natural cycles that manmade CO2 did not and cannot cause!

  7. Pingback: Nature Unbound IV – The 2400-year Bray cycle. Part B – I Didn't Ask To Be a Blog

  8. As a signal processing guy, my reaction is that that’s not how you detect cycles.

    You design a filter that gives a detection with such and so a false alarm rate with such and so failure to detect rate.

    By eye, cycles are everywhere. By detector, they’re not.

    So that’s how a signal detection guy would peer review it.

    • Aye, and if you start breaking it down by region or by other metric, then you need to be careful about cherry-picking / p-hacking.

      If you look at five times as many regions, then the odds of one of them showing the cycle you’re looking for goes up quite a bit. So test for statistical significance, and make sure you’re careful about how you do it.

      • I trust that journals, editors, and referees have done their job at evaluating all those papers, because otherwise after 40 years a lot of articles would be denouncing the finding. And quite the contrary the number of articles on solar cycles keeps increasing with time.

        After 40 years of being wrong the number of wrong articles keep increasing with time. They are getting more and more desperate to accomplish anything before their manmade global warming scam gets shuts down.

      • They are getting more and more desperate to accomplish anything before their manmade global warming scam gets shuts down.

        Except that we are talking about the existence of a very long solar variability cycle that is not precisely a popular or consensus hypothesis, and nobody is making money with that. Quite the contrary it is not easy to build a successful scientific career on the effect of solar variability on climate. And yet many of the papers presented in the article’s bibliography have been published in very good journals where we can be quite sure that due to their controversial nature they must have been scrutinized.

    • that’s not how you detect cycles.

      I am not detecting this cycle. The Bray (aka Hallstatt) solar cycle has been peer reviewed literally hundreds of times. For example:

      Vasiliev, S. S., & Dergachev, V. A. (2002). The~ 2400-year cycle in atmospheric radiocarbon concentration: bispectrum of 14 C data over the last 8000 years. In Annales Geophysicae (Vol. 20, No. 1, pp. 115-120).
      https://hal.archives-ouvertes.fr/docs/00/31/69/27/PDF/angeo-20-115-2002.pdf

      They detect the cycle by power spectrum, time-spectrum and bispectrum analyses of the long-term series of the radiocarbon concentrations, and find that a principle feature of the time series is the long period of ∼ 2400 years.

      • That’s an awfully smooth power spectrum. Is it by any chance from a squared discrete fourier transform of all the data, made smooth for the plot by evaluation at frequencies that do not appear in the discrete fourier transform?

        That is, would the actual discrete fourier transform over the plotted frequency range consist of ~40 points?

        In which case, the falloff near 0 is likely to be from detrending and the low peak from a general appearance of low frequency energy.

        Fourier transforms are extremely noisy beasts; smoothed either by doing lots of short fourier transforms, and squaring them and adding them, which is correct (it will be smooth if the process has a smooth spectrum) but costs you low frequency analysis since those frequences are then gone; or by interpolating with frequencies not in the fourier transform at all, which is not significant analysis-wise.

        So, do you know how many degrees of freedom are in the plot?

        Not actually as an attack but as a sample of how a signal processing guy is skeptical.

      • a sample of how a signal processing guy is skeptical.

        I am fine with skepticism. I have provided a link to the paper where you can try to find the details that you are interested into.

        If you are not satisfied with that, you can write Vassily Dergachev at:
        v.dergachev (at) mail.ioffe.ru
        It is very likely he will provide answers for your doubts.

        If still not convinced I can provide citations for dozens of articles that report on the ~ 2400 year cycle in cosmogenic records since the 1980’s. You can repeat the procedure for those works whose researchers are still active.

        I trust that journals, editors, and referees have done their job at evaluating all those papers, because otherwise after 40 years a lot of articles would be denouncing the finding. And quite the contrary the number of articles on solar cycles keeps increasing with time.

      • Well you know it’s a different field. Climate science has its own signal processing standards.

        Signal processing knows the statistics of its noise and goes by type I and type II error probabilities instead.

        That leads it to doubt climate science’s science, though.

        It doesn’t look like an empirical power spectrum. (For a stationary gaussian random process, the power at any frequency is independent of the power at the adjacent frequency, and negative exponentially distributed, which is incredibly noisy. That independence is the whole point of spectral analysis; otherwise it’s just a coordinate transformation of the data.)

      • I should add that I don’t think you can do better. I just think that climate science doesn’t know what it thinks it knows.

        You don’t have enough data to do anything with frequencies that low, beyond remarking that through the aeons there have been huge swings.

        So lots of low frequency energy. That ought to be enough to say that predictions from CO2 are idle as well.

    • Geoff Sherrington

      If you are seeing pictorial signals by eye, it is OK to proceed to formal analysis, but first you have to be sure that no other factors give similar pictures, or if some do they can be explained – quantitatively if you proceed to numerical analysis.
      Going digital can be an open door to adoption of suspect methods that so often grace these pages. Quality scientists keep to the straight and narrow.
      That said, I am not so impressed by these glimpses of that Javier is kindly giving us. They might look good to researchers in his field and others but my eyes were calibrated on harder data. Geoff

      • This is a very incomplete list of articles where a formal numerical analysis of the cosmogenic record has been carried out, identifying the Bray (aka Hallstatt) cycle:

        Damon, P. E., & Sonett, C. P. (1991). Solar and terrestrial components of the atmospheric C-14 variation spectrum. In The Sun in Time (pp. 360-388).

        Dergachev, V. A., Raspopov, O. M., & Vasiliev, S. S. (2000). Long-term variability of solar activity during the Holocene. In The Solar Cycle and Terrestrial Climate, Solar and Space weather (Vol. 463, p. 489).

        Hood, L. L., & Jirikowic, J. L. (1990). A probable approx. 2400 year solar quasi-cycle in atmospheric delta C-14. In NASA Conference Publication (Vol. 3086).

        Kern, A. K., et al. “Strong evidence for the influence of solar cycles on a Late Miocene lake system revealed by biotic and abiotic proxies.” Palaeogeography, palaeoclimatology, palaeoecology 329 (2012): 124-136.

        McCracken, K. G., & Beer, J. (2008). The 2300 year Modulation in the Galactic Cosmic Radiation. In Proceedings of the 30th International Cosmic Ray Conference (Vol. 1, pp. 3-11).

        McCracken, K. G., et al. “A phenomenological study of the cosmic ray variations over the past 9400 years, and their implications regarding solar activity and the solar dynamo.” Solar Physics 286.2 (2013): 609-627.

        McCracken, K., Beer, J., Steinhilber, F., & Abreu, J. (2013). The heliosphere in time. Space Science Reviews, 176(1-4), 59-71.

        Stuiver, M., & Braziunas, T. F. (1993). Sun, ocean, climate and atmospheric 14CO2: an evaluation of causal and spectral relationships. The Holocene, 3(4), 289-305.

        Suess, H. E. (1980). The radiocarbon record in tree rings of the last 8000 years. Radiocarbon, 22(2), 200-209.

        Usoskin, I. G., Gallet, Y., Lopes, F., Kovaltsov, G. A., & Hulot, G. (2016). Solar activity during the Holocene: the Hallstatt cycle and its consequence for grand minima and maxima. Astronomy & Astrophysics, 587, A150.

        Vasiliev, S. S., & Dergachev, V. A. (2002). The~ 2400-year cycle in atmospheric radiocarbon concentration: bispectrum of 14 C data over the last 8000 years. In Annales Geophysicae (Vol. 20, No. 1, pp. 115-120).

        There is no point in me repeating what so many researchers have done multiple times for the past 40 years.

      • Geoff Sherrington

        Javier,
        My apologies for not writing clearly.
        I enjoy your essays here. There is a lot of work and deduction behind them and they cover interpretations that are not seen so often by the casual science reader. So, no criticism of your work was intended. My words above were more in response to rhhardin. Simply, I sought to express that the signal:noise that you show in your diagrams is weaker than I’ve been used to in another area of earth science. I wish it was better. In time, with more measurements, it might be.
        I also sought to caution others against being too enthusiastic in adopting mathematical/statistical methods that have often been used poorly in climate work as many past examples on Dr Curry’s blog have shown.
        Thank you for the list of references. I had already read some of them. Corporately, we used to interact with Ken McCracken in the 70s and 80s.
        I look forward to further of your essays. Geoff

    • rhhardin:

      Indeed “climate science” has its own signal processing standards, which often bear little resemblance to those in competent signal analysis. One need only look at the raw “periodogram” of the sunspot data presented in Javier’s July 18 comment in Part A of this article to recognize the lack of comprehension of the basics of analyzing random-signal data.

      The Vasiliev et al. analysis of radiocarbon series, however, is somewhat of a pleasant exception. Done by physicists at a prestigious institute, it utilizes the (bivariate) autocorrelation function of the data. Truncating that function at a reasonable effective length before applying the DFT is what gives smoothness to the power density, via the width of the spectral window. It only lacks confidence intervals to constitute an entirely credible analysis.

  9. “When the oceans cool they absorb more CO2, and for a constant rate of production the 14C/12C ratio increases.”

    While discriminating far less strongly than photosynthesis, there is significant fractionation of heavy isotopes in both absorption and evaporation from the ocean surface. Discrimination against 13C is about 2 per mil in absorption and 10 per mil in evaporation. Discrimination against 14C should be somewhat stronger.

    The heavier isotopes are always “left behind”. In the case of absorption, the heavier are left in the atmosphere and in the case of evaporation they are left in the ocean.

    The net effect is very significant concentration (8 per mil for 13C) of heavy isotopes in the ocean during warming regimes when evaporation exceeds absorption; and modest concentration in the atmosphere during cooling regimes when absorption exceeds evaporation.

    • That’s an interesting observation, thanks. I suppose that means the equilibration time for 14C should be longer that for 12C.

  10. Pingback: Surprisingly Good Technical Series on Climate | Musings from the Chiefio

  11. “It can be expected that the low of ~ 2095 AD should barely be noticeable.”

    I regard that as irresponsible to make such an assertion on the basis of an unreliable millennial cycle that you don’t know the origin of.
    What can be expected is a solar minimum from the 2090’s that will cause a negative NAO regime for more solar cycles than the Maunder Minimum did. My model directly plots the duration of every solar minima without need for offbeat modulations. For example it readily plots the Wolf-Sporer-Maunder Triplet from around 810 BC, which starts right on one of your Eddy cycle maximums.
    http://www.geo.arizona.edu/palynology/geos462/holobib.html

    • I regard that as irresponsible to make such an assertion on the basis of an unreliable millennial cycle that you don’t know the origin of.

      Well, nobody knows the origin of any solar cycle. Even the origin of the 11-year Schwabe cycle is under intense debate.

      But if you have followed the article you should have seen in figure 58 that the 208-year de Vries cycle is modulated by the higher ~ 2400 year periodicity. This is described in several articles as indicated.

      It is possible to see that the modulation of the 208-year cycle has already caused more solar activity in its last low. If past is prologue the next 208-year low ~ 2,095 AD should have more activity, not less, than the previous.

      For example it readily plots the Wolf-Sporer-Maunder Triplet from around 810 BC, which starts right on one of your Eddy cycle maximums.

      810 BC is 2760 BP. If you have been following the article, that is a low (B2) of the Bray cycle, the main Holocene cycle.

      • Ulric Lyons

        That certainly is problem where you have a low in Bray and a high in Eddy at the same time. It is your view that your next Eddy maximum at 2100 will make the ‘low of ~ 2095 AD barely noticeable’ that concerns me. Your next Bray maximum isn’t until much later, if there is such a thing.

      • That certainly is problem where you have a low in Bray and a high in Eddy at the same time.

        This has happened several times in the past. A low in any of the long cycles (Bray or Eddy) increases the chances of a solar grand minimum, and at least one is likely to result. I haven’t been able to find a clear climatic signature at times of cycle highs, thus I consider the lows to be determinant for climate change.

        However you still don’t understand what I said. It is not the Eddy maximum at 2100 that will make the low at ~ 2095 barely noticeable. What will make the de Vries low at ~ 2095 barely noticeable is that it is 600 years after the 1350-1550 B1 Bray low.

        Perhaps you will see it more clearly in this model of solar activity for the past 3000 years that I made a year ago. It was posted in the article: Periodicities in solar variability and climate change: A simple model


        Figure 6. Adjustment of the solar variability model (red curve) to the sunspots groups number for the past 400 years and the solar activity reconstructed by Steinhilber et al., 2012, for the past 3000 years. The ~ 1000-year Eddy cycle is shown as a pink sinusoidal curve. The ~ 2500-year Bray cycle is shown as a yellow sinusoidal curve with the active phase as solid line and the inactive as dashed line. The ~ 208-year de Vries cycle is shown as red filled circles during the active phase, and as red empty circles during the inactive phase. The ~ 87-year Gleissberg cycle is shown in blue. Grand solar minima are named in black, warm periods in red and cold periods in blue. Known colder periods from temperature reconstructions are highlighted in turquoise. A quiet Sun mode during grand solar minima has been proposed by several authors and shown as a black dashed line.

        The position for all the de Vries lows for the past 3000 years is indicated. And we have already entered the inactive phase of the Bray cycle (yellow dashed curve) that is characterized by inconspicuous de Vries lows (empty circles).

        If you have a reason to be concerned is because your model is probably wrong if it expects a strong minimum towards the end of the century. Past data suggest the de Vries cycle is no longer very active. It is unlikely that a solar grand minimum takes place within the next 300-400 years. And these are really good news.

      • Ulric Lyons

        “However you still don’t understand what I said. It is not the Eddy maximum at 2100 that will make the low at ~ 2095 barely noticeable. What will make the de Vries low at ~ 2095 barely noticeable is that it is 600 years after the 1350-1550 B1 Bray low.”

        I was going by what you wrote in the post:
        “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.”
        I was also going by what you said here on your last post:
        https://judithcurry.com/2017/07/11/nature-unbound-iv-the-2400-year-bray-cycle-part-a/#comment-854015

        But if you are saying that Bray dominates over Eddy, then that would a be an issue for the Antique LIA starting around 380 AD, as your Bray is very high then.

        “I haven’t been able to find a clear climatic signature at times of cycle highs, thus I consider the lows to be determinant for climate change.”

        Then why claim there will be one at 2100 AD?

        “The position for all the de Vries lows for the past 3000 years is indicated.”

        995 BC to 1885 AD divided by 13 is 221.5 years. That won’t work.

        “If you have a reason to be concerned is because your model is probably wrong if it expects a strong minimum towards the end of the century.”

        It reveals the astronomical mechanism of solar minima, and it renders any cycle based approach obsolete as it shows exactly where each minimum starts, and its duration.

      • I was going by what you wrote in the post

        What I have been writing all along is that the de Vries cycle is modulated by the Bray cycle, not by the Eddy cycle. Both the Bray and Eddy cycles have been going up for the past 400 years.

        But if you are saying that Bray dominates over Eddy

        I haven’t said that. The evidence supports that these two cycles are independent of each other. A low in any of them can cause a solar grand minimum.

        Then why claim there will be one at 2100 AD?

        If a high is defined as the mid-point between two lows, and might be characterized by higher solar activity, and a climate optimum, even if the climate signal in proxy records is not clearly recognizable.

        995 BC to 1885 AD divided by 13 is 221.5 years. That won’t work.

        140 year drift in 3000 years is not too bad, considering that solar cycles are everything but precise.

        It reveals the astronomical mechanism of solar minima, and it renders any cycle based approach obsolete as it shows exactly where each minimum starts, and its duration.

        Get it published then so experts can take a look at it.

      • Ulric Lyons

        “What I have been writing all along is that the de Vries cycle is modulated by the Bray cycle, not by the Eddy cycle.”

        Not so, you wrote in your last post:
        “It shouldn’t be difficult to greatly improve Steinhilber & Beer 2013 forecast, as they predict a low for 2100, when it corresponds to a high in the millennial cycle (1100 AD Medieval Warming Period -> 2100 AD Modern Warming Period).”

        Nothing about Bray there.

        “If a high is defined as the mid-point between two lows, and might be characterized by higher solar activity, and a climate optimum, even if the climate signal in proxy records is not clearly recognizable.”

        If? Might be? You also said that you “haven’t been able to find a clear climatic signature at times of cycle highs” Now you are suggesting that solar highs may not even have a clearly recognisable climate signal.

        “140 year drift in 3000 years is not too bad, considering that solar cycles are everything but precise.”

        175 years adrift, and that is bad as you have it labelled as 208 years, but have placed them at 221.5 year intervals. It’s not de Vries at that pitch. Your Bray cycle on that chart is only 2300 years too. It’s sloppy work, not ‘drift’.

        “Get it published then so experts can take a look at it.”

        Get the astronomy application and take a look for yourself.

      • you wrote in your last post

        I am not willing to get into a “I said, you said” type of debate. I only care about what the evidence shows.

        The evidence shows that the 980 year Eddy cycle is going up and close to a high that should take place ~ 2100 AD.
        I am not the only one seeing this. Read:
        Scafetta, N. (2012). Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter–Saturn tidal frequencies plus the 11-year solar dynamo cycle. Journal of Atmospheric and Solar-Terrestrial Physics, 80, 296-311.
        https://arxiv.org/pdf/1203.4143

        He sees with his model the same I see with past evidence:

        The evidence also shows that the 2475-year Bray cycle is going up and due to its known and published modulation of the 210-year de Vries cycle, the de Vries lows are becoming less conspicuous, not more.

        Due to all above, whoever expects a solar grand minimum, or lower than present solar activity for the next 200 years, is very likely to be wrong. The sun is favorable to the present optimum lasting a few centuries more.

      • So we won’t know why you contradicted yourself about Eddy, OK then. From what I gather of your Bray, the early Antique Little Ice Age starting in fact from around 354 AD, should not even exist, nor should the super minimum from around 1117 AD in the MWP. OK then.

      • Modern solar activity reconstructions, like that of Steinhilber et al., 2012 do not show unusually low solar activity at 354 AD or 1117 AD. Why do you think those cold periods should be due to low solar activity?

      • Ulric Lyons

        Scafetta is pseudo harmonics employing cycles that don’t exist such as his mean of orbital and synodic periods that he creates his 115 and 130 yr periods with. How these behave as wave functions and drive beat harmonics of that length is pure voodoo. Which brings me to a major criticism I have of your work. It’s fair enough to note a periodicity in major cold events, but there isn’t really any basis for assuming Bray or Eddy are sinusoidal, and that their effect is in a sinusoidal manner.

        “Steinhilber et al., 2012 do not show unusually low solar activity at 354 AD or 1117 AD. Why do you think those cold periods should be due to low solar activity?”

        Steinhilber 2012 gives the wrong signal for the latter solar minimum in what is called Sporer, from 1550 for a few decades. It’s not reliable. From 354 AD and from 1117 AD were long duration solar minima according to my model, both longer than it makes Maunder.

      • there isn’t really any basis for assuming Bray or Eddy are sinusoidal

        You are correct. It is just a way of representing it. The climate evidence suggests a cumulative effect takes place above or below a threshold value of solar activity.

        From 354 AD and from 1117 AD were long duration solar minima according to my model

        Can you confirm this with any published solar reconstruction?

      • I could give you a list of solar minimum start dates and approximate duration that it plots for the last 6700 years, but you would still need to visually inspect the progression to actually confirm them. Alcyone Ephemeris do a free demo download. I gave the basic rules on your last post. The sunspot cycle maximum dates in this list is a great help in getting acquainted with the break points into and out of each solar minima. The exact break point into each minima is not always clear, such as the unusually late start to Dalton, but it is apparent that the progression is intrinsic to the ordering of sunspot cycle maxima, and to the occurrence and duration of solar minima. Take a look, it’s very intriguing.

      • It is unlikely that a solar grand minimum takes place within the next 300-400 years. And these are really good news.

        :) I like my neighborhood without the mile-high glaciers.

  12. Pingback: Nature Unbound IV – The 2400-year Bray cycle. Part B | privateclientweb

  13. Javier, the solar proxy data you have used looks old (INTCAL98).

    Your source Kern et al 2012 is based on the Solanki record which is now outdated and I can’t find any reference to IntCal13? Figure 57 is not looking legit.

    There are many changes in the radiocarbon record over the past few revisions, we need to test your data before moving forward.

    • No, Geoff. I have used IntCal13, that is linked in the legend of figure 57:
      http://www.radiocarbon.org/IntCal13%20files/intcal13.pdf
      Go download the pdf and check the dates with those given by me in the text. Check also the figures in the pdf for the lows of the Bray cycle. Anybody can do that and reproduce that figure.

      The Bray cycle is defined in IntCal13. It doesn’t matter if you use Solanki’s 2004 solar activity reconstruction, or any other one more to your taste. The position of the grand solar minima that define the Bray cycle is not going to change significantly, as they are a feature of every solar activity reconstruction since Eddy’s times, when the minima were given their names.

      A Bray cycle of 2400-2500 years is a conspicuous feature of the 14C calibration curve that has been very carefully reconstructed by hundreds of researchers over more than six decades. There is no way around it, because there is nothing to interpret. The people getting interesting about signal analysis are plain wrong because the evidence is there for anybody to see it, and everybody that has done a proper signal analysis on the data has come with the same result. The cycle is in the 14C and 10Be data.

  14. No Javier you are incorrect. You have not used the IntCal13 record for fig 57. Show us the Kern et al 2012 paper that depicts this record.

    And you are also highly mistaken when stating the old Solanki 2004 record is the same as IntCal13, I pointed this out in your part A article but once again it went through to the keeper.

    The revisions of the radiocarbon data are VASTLY different. The whole basis of your part B is based on old data, there was a 340 year anomaly occurring in the German Dendrochronology record between 3200BC-2600BC at IntCal04 that has now been revised and carried forward with further revisions in IntCal13.

    I covered some of the anomalies in a article on my blog.

    http://www.landscheidt.info/?q=node/323

    As stated several times there does seem to be a quasi Bray type cycle in the solar proxy record varying between 2100 & 2500 years, but trying to claim there is a rigid 2450 year cycle does not cut it. The most up to date data shows a solid 4627 year cycle for clusters of grand minima indispersed with another weaker cluster occurring at 2100 and 2500 intervals depending which side of the 4627 year cycle you are viewing.

    • Geoff,

      No Javier you are incorrect. You have not used the IntCal13 record for fig 57.

      Do not accuse me of lying. The calibration curve is IntCal13, as stated.
      Here you have a blow up of the 2000-3400 BC (3900-5400 BP) period of my figure that you comment about, compared with IntCal13 (marked with a red ellipse). You can see that all your German trees are at the exact same position.

      I did not expect that you would be convinced no matter how irrefutable the evidence. You are too invested on your hypothesis. This is the same problem with global warming. Many people think that when there is no warming, or when scientific articles demonstrating that IPCC assumptions are incorrect are published the whole thing will just die. Most climate scientists are too invested to recant. They won’t accept any amount of contrary evidence.

      • “This is the same problem with global warming. Many people think that when there is no warming, or when scientific articles demonstrating that IPCC assumptions are incorrect are published the whole thing will just die. Most climate scientists are too invested to recant. They won’t accept any amount of contrary evidence.”

        I’m very sympathetic to this but climate science has its own rules.

        Jokingly I said that physics is a social arrangement unified by a common set of equations and climate science is a social arrangement united by a common set of predictions.

        You can’t fix it without the field itself disappearing, leaving only bits of this or that showing up as isolated publications in the JGR, when there is physics to apply, but it won’t be called climate science.

        Anyway disputing climate science’s preferred predictions using climate science rules isn’t going to get anywhere. What a signal processing guy sees as flaky results on either side doesn’t matter. What matters is the prediction.

        It would be amusing to send all climate science papers to be peer reviewed by signal processing guys. Everything concluded about long term data would disappear.

      • What matters is the prediction.

        Not even. Failed predictions, like 0.2-0.3°C/decade warming in the 21st century, are erased. A posteriori, ad hoc, explanations are given making it impossible to falsify the hypothesis due to failed predictions, and the data is adjusted to continue showing warming when there isn’t.
        Hard core, highly invested scientists will continue to defend dangerous global warming regardless of evidence and predictions, while lowly invested scientists will abandon the hypothesis, and it will slowly stop being a hot topic.

        During the late 1990’s we were nearly all convinced that the warming was essentially anthropogenic. A lot of skeptics are so because they have changed their opinion.

      • I think Iowahawk, a witty blogger who happens to do statistics for whatever his job is, disposed of the hockey stick instantly with a spreadsheet.

        There’s a lot of expertise out there that climate science peer review needs.

  15. Javier,

    Not accusing you of lying, just prove to us that your fig. 57 is IntCal13.

    Show us in the referenced paper (Kern et al 2012) that the IntCal13 record is being used.

    • just prove to us that your fig. 57 is IntCal13.

      I just did. The calibration curve in figure 57 is IntCal13. The comparison I showed proves it:


      Right-click on the graph to see a larger version. It is the same thing.

      The solar activity curve in figure 57 is the one displayed in Kern et al., 2012 (figure 8) based on Solanki’s data:
      Kern, A. K., et al. “Strong evidence for the influence of solar cycles on a Late Miocene lake system revealed by biotic and abiotic proxies.” Palaeogeography, palaeoclimatology, palaeoecology 329 (2012): 124-136.
      http://www.sciencedirect.com/science/article/pii/S003101821200096X

      Figure 57 is a composite of two different things and both support the same interpretation. Your attempt to defend that I have not used IntCal13 when I did is both insulting and pitiful. You have no credit left with me.

      • Your fig 57 does not appear in your referenced data source, and nor does your source refer to IntCal13 in any respect. Not surprising as your source is published a year before IntCal13.

        Your source is IntCal 98 as I suggested, and way out of date…you have wasted our time. Your data is busted.

        Hopefully Judith will abandon part C ?

      • My figure 57 is mine. I did it. I put IntCal13 in it, and I put solar activity reconstruction from Kern et al., 2012 in it. I have linked the sources I used for the figure:
        IntCal13: http://www.radiocarbon.org/IntCal13%20files/intcal13.pdf
        Kern et al., 2012: http://www.sciencedirect.com/science/article/pii/S003101821200096X
        Anybody can check it as the evidence used for the figure is available (IntCal13 and Solanski’s reconstruction used by Kern et al. can be downloaded), and anybody can reproduce it. What I have done is reproducible.

        you have wasted our time.

        No, you have wasted your time pursuing the wrong hypothesis. Your reaction of accusing me of lying is unacceptable. I have nothing further to say to you.

      • The truth is slowly coming out, you made it up yourself.

        You have no expertise in presenting a radiocarbon record of your own. There is no way you can combine IntCal98 with IntCal13, the records are completely different.

        You have presented to us bogus data.

      • You are becoming obnoxious. I made the figure from published, peer-reviewed data. I didn’t made it up. The data is not bogus. The data is published and available to anybody.

        You are trying to raise an issue that doesn’t exist, to hide the fact that IntCal13 is incompatible with your hypothesis. The bumps in IntCal13 coincide with the lows of the 2475-year Bray cycle. There is no way to deny that because anybody can download IntCal13 from the official page and check it in 5 minutes by himself.
        http://www.radiocarbon.org/IntCal13%20files/intcal13.pdf

        The way I have done figure 57 is irrelevant. IntCal13 supports the 2475-year Bray cycle. Therefore you are wrong. Your false accusations are not improving your position.

      • Yes you made it up. You presented IntCal98 values and labelled it as IntCal13.

        To illustatrate the differences (again) look at the grand minima cluster centre of IntCal98 at around 5450 BP (correct?)

        Now look at the same cluster on IntCal13 and you can see it has shifted by about 400 years to 5000 BP (correct?)

        The records are completely different.

        The error was picked up in IntCal04 as shown.

        Your fig 57 shows the same clustering as IntCal98 and is not a representation of the current data set. The new data backs up my paper that is still unchallenged but unfortunately discredits your attempts to claim a rigid 2450 year cluster cycle over the Holocene.

      • Steven Mosher

        Geoff.

        If you check through Javier sources you will find that they contradict him on occasion or claim different numbers for this 2200…oh wait 2300..
        Err 2400
        ER 2475 year cycle.

        It’s a load.

  16. The very existence of the Grand Maximum is not questioned by others I think… This indicates that even in the “corrected” sunspot series the Grand Maximum is observed as a period of clustering of several consecutive high cycles, even though the height of the cycles is not unique. ~Usoskin

    • I see the admission by Usoskin that the height of the cycles is not unique, as an admission that his former position that the modern grand maximum represents a period of unusual activity not seen in thousands of years was incorrect.

      Extraordinary claims, like those that the present situation is highly unusual within a multi-millennial time scale, require extraordinary evidence. So far only the amount of CO2 in the atmosphere has passed that test. Neither temperatures, nor solar activity have enough evidence to claim they are extraordinary.

      • Surely, even if not a unique event over the past 11 millennia, the fact that the Grand Maximum over last half of the 20th century, “is rare but not unique on the time scale of the Holocene,” still is of significance. “Several similar Grand Maxima (about 20) took place over the last 11 millennia,” says Usoskin, “thus one per about 500 years. Therefore, the Grand Maximum in the 20th century is not a unique event but a rare event.”

      • thus one per about 500 years.

        That is a lot more like it. Clearly solar activity during the 20th century has been highest for the past 500 years.

      • afonzarelli

        If as usoskin says, grand maxima are rare events, should we expect to see back to back grand maxima in the 20th and 21st centuries?

      • Afonzarelli,

        Unlike Grand Minima, that in most cases have always been clearly identified, and named, Grand Maxima suffer from problems of definition and identification, compounded by the use of different solar activity reconstructions that differ most precisely on this issue.

        This is a table from two articles where the identification of grand solar maxima and minima is attempted, Usoskin et al., 2007, and Inceoglu et al., 2015, both in Astronomy & Astrophysics.

        They cover different periods, as Inceoglu starts in 6600 BC and ends in 1650 AD, thus avoiding the issue of the modern maximum. I have highlighted the coincidences, and it is clear that there are not that many.

        Back to back solar maxima do exist in both tables.

        In principle I would expect that solar activity during the 21st century should not be very different from solar activity during the 20th. However it is not clear that we have correctly identified all the periodicities that matter, some periodicities display variable behavior, and there are solar changes not easily attributable to periodicities, so I would consider it a working hypothesis, and not a prediction.

        What is clear to me is that there is little basis in past solar behavior to predict a 21st century grand solar minimum, so I am really surprised so many people are predicting one even in published articles. Perhaps it can be attributed to our natural catastrophic inclination. We are always expecting a catastrophe and very surprised it hasn’t arrived yet. Global warming also fits that category.

      • What about the, clustering of several consecutive high cycles, referred to above by Usoskin? “The Modern Maximum reached a double peak once in the 1950s and again during the 1990s.” (see wiki)

      • “In principle I would expect that solar activity during the 21st century should not be very different from solar activity during the 20th.”

        We have returned to 19th century levels with SC24, and with another weak cycle to follow. The 20th century did not include a solar minimum.

        Inceoglu 2015 has no Grand Maximum in the MWP?

      • The 20th century did not include a solar minimum.

        You seem to forget the Gleissberg Minimum, that was named by McCracken and defined as 1879-1914. SC14 had lower activity than SC24, and SC16 after this minimum is similar. So far the 20th century has a period with lower solar activity than anything we have seen in the 21st.

        You can see some info about this minimum in this power point from Tom Woods:
        http://lasp.colorado.edu/sorce/news/2011ScienceMeeting/docs/presentations/6k_Woods_SolarCycle_and_Summary.pdf
        It is also reflected in several publications.

        Inceoglu et al., 2015 match the 10Be record from GRIP to the 14C record from IntCal13. Since GRIP goes only to ~ 1670 they stopped their analysis there.

      • Fair enough SC24 second peak did go higher than SC14. So the early 20th century had the tail end of a minimum, but the 21st century will see more low cycles than the 20th.

      • but the 21st century will see more low cycles than the 20th.

        Or not. The future is unknown.

      • Ulric Lyons

        If that is your belief then you should not be asserting that there will be no GSM for the next few hundred years. This minimum is certain to continue into SC25, on that basis 21st century activity would be slightly lower than the 20th. Though I am also seeing another minimum starting from the 2090’s.

      • Ulric,
        I really have a problem with you attributing things to me that I have not said.
        You say:
        “you should not be asserting that there will be no GSM for the next few hundred years.”
        While what I have said just above is:
        “I would consider it a working hypothesis, and not a prediction.”
        This has happened several times as you try to fight strawman arguments.
        So I am going to ask you please that you quote my exact words. That is if you want an answer from me.

        Remember that the sun is variable and so far unpredictable. All we have are hypotheses. Those that make nearby predictions like the one from David Archibald, can quickly be shown wrong. The ones that only make distant predictions, like yours and mine, can only be judged on how well they explain the past and will remain untested long after we have passed away.

        The advantage of my approach is that I arrive to solar variability not from the cosmogenic data, or some astronomical model, but from the climate side. So I already know the periods I am studying had undergone important climate change, and thus if they present relevant solar activity variability, the match is already established. This approach has been used for example by Michael Magny, that arrived to solar variability from his climatic studies. It is very powerful as he has demonstrated with his studies on Central Europe precipitation and lake levels during the Holocene.

      • Ulric Lyons

        You said:
        “It can be expected that the low of ~ 2095 AD should barely be noticeable.”
        and later said:
        “It is unlikely that a solar grand minimum takes place within the next 300-400 years. And these are really good news.”
        and:
        “If you have a reason to be concerned is because your model is probably wrong if it expects a strong minimum towards the end of the century.”
        and:
        “whoever expects a solar grand minimum, or lower than present solar activity for the next 200 years, is very likely to be wrong.”
        and you more recently said:
        “I would consider it a working hypothesis, and not a prediction.”

        That’s a change of tune I suppose.

        “The advantage of my approach is that I arrive to solar variability not from the cosmogenic data, or some astronomical model, but from the climate side. So I already know the periods I am studying had undergone important climate change, and thus if they present relevant solar activity variability, the match is already established”

        Well I correlate past climate data to the astronomical model to verify solar minima and grand solar minima. I don’t do it blind and just imagine it was cold.

      • Again you seem to be quite selective. I have also said:
        “it is not clear that we have correctly identified all the periodicities that matter, some periodicities display variable behavior, and there are solar changes not easily attributable to periodicities”

        Long solar cycles (200-2500 years) are not favorable to produce a deep minimum in the next few centuries. I disagree with those like you that predict a deep minimum in the 21st century based on cycles. I think you are incorrectly interpreting the evidence to identify the relevant periodicities and their amplitudes.

        But unlike you I understand that our knowledge of solar variability is tremendously poor, and therefore our predictions have very low confidence. My main point is that a deep minimum in the 21st century cannot be predicted based on solar cycles, not that a deep minimum cannot take place. Nobody knows what the solar activity is going to be in the future.

      • “I disagree with those like you that predict a deep minimum in the 21st century based on cycles.”

        You are basing your outlook on cycles, I am not. The long minimum starts very late this century, and so is mostly in the 22nd century. Long ones can tend to go deeper yes.

        “I think you are incorrectly interpreting the evidence to identify the relevant periodicities and their amplitudes.”

        The model plots solar minima and grand solar minima where they actually occur. A regular cycle or periodicity can never do that, as they are not regular. I haven’t even mentioned amplitude, that is cycle talk. I reckon you are doing what you say you think I am doing.

        “But unlike you I understand that our knowledge of solar variability is tremendously poor, and therefore our predictions have very low confidence.”

        Standard solar science cannot predict any further ahead than the next cycle, that is well known. Though standard solar science is caught in a similar false paradigm of internal variability that climate science is.

        “My main point is that a deep minimum in the 21st century cannot be predicted based on solar cycles, not that a deep minimum cannot take place.”

        With hindcasts that don’t miss a beat however out of time, of course they can be forecast.

      • You are basing your outlook on an astronomical cycle, which is even worse because to date nobody has been able to demonstrate that the movements of the planets can affect solar activity (or climate) at all.

        As you look for astronomical coincidences with what for most scientists are unconnected phenomena (planetary conjunctions and solar activity), the distinction between what you do and astrology appears blurred to me.

      • “As you look for astronomical coincidences with what for most scientists are unconnected phenomena (planetary conjunctions and solar activity), the distinction between what you do and astrology appears blurred to me.”

        Says the person that cited Scafetta, hard to get lower than that. The progression that I have identified without doubt orders each sunspot maximum, and it orders the occurrence of solar minima and determines their duration. And it naturally offers the best clues to the nature of the mechanisms. You would have a much harder time proving your case to most scientists as its mostly speculation rather than observation.

        “to date nobody has been able to demonstrate that the movements of the planets can affect solar activity (or climate) at all.”

        In fact Kepler first found his fame doing such by making predictions at the scale of weather. I have been developing long range solar based weekly scale NAO/AO forecasts since 2008, with a huge quantity of rule based hindcasts through CET.

      • Says the person that cited Scafetta, hard to get lower than that.

        Do you think citing somebody means sharing all his views? I’ve got some news for you. As a scientist I cite articles that show evidence or support an argument I am making. If you only cite articles that agree with your views you must use very few citations.

        You would have a much harder time proving your case to most scientists as its mostly speculation rather than observation.

        Again you don’t understand. I don’t need to convince anybody or prove any case because I don’t do original research on climate. I am just connecting the dots from published evidence. The ones that do the research and make a case are the original climate scientists that did the research.

        You are unlikely to get your model published, much less accepted. The evidence I present has already been published and it is being cited. That is a significant difference.

      • Ulric Lyons

        “As a scientist I cite articles that show evidence or support an argument I am making.”

        The argument that you were last making was that Bray and not Eddy would weaken de Vries etc through the following centuries, so Scafetta’s ‘pseudo beat astrology’ was off point.

        “I am just connecting the dots from published evidence.”

        Yes with an imaginary sine wave that reduces the ‘centennial cycle’ except when it doesn’t. There are periodic and quasi-periodic events, but there are no long term sinusoidal cycles in solar activity levels. It’s pure fantasy.

      • “Sunspot Reconstruction for Past 11,000 Years (blue) With Recent Measured Sunspot (red)”

      • That hockey stick is also wrong. There is a real hockey stick in 14C records that comes from the atomic bomb, but that is not solar activity.

  17. Time is needed to even figure out the current solar situation.

  18. http://hockeyschtick.blogspot.com/2010/01/climate-modeling-ocean-oscillations.html

    This has a 96 % correlation to global temperatures which gets very little focus in contrast to the bogus CO2 global warming claims.

  19. Ok. Let’s do this one by one. Some people don’t appear to distinguish between IntCal13, a calibration curve, and solar activity reconstructions. Solar activity reconstructions include several assumptions about the relationship between cosmogenic isotopes production and deposition rates, and solar activity. The IntCal13 calibration curve is not related to climate or solar activity, and is based on the amount of 14C found at each tree ring (or speleothem growth) with the goal of being able to date ancient biological materials.

    Big deviations from linearity in the IntCal13 calibration curve are not too common. A subset of them displays an interesting regularity:

    B1: 500 BP

    B2: 2,700 BP

    B3: 5,250 BP

    B5: 10,200 BP

    B6: 12,650 BP

    Now that you have seen them, let’s see those distances:
    B6 – B5: 2,450 years
    B6 – B3: 7,400/3: 2467 years
    B6 – B2: 9,950/4: 2487 years
    B6 – B1: 12,150/5: 2430 years
    B5 – B3: 4950/2: 2475 years
    B5 – B2: 7,500/3: 2500 years
    B5 – B1: 9,700/4: 2425 years
    B3 – B2: 2550 years
    B3 – B1: 4750/2: 2375 years
    B2 – B1: 2200 years

    This regularity is quite good for a solar cycle, a lot better than for the non-controversial Schwabe cycle. It defines a 2400-2500 year cycle, not 2300. The missing B4 causes a problem and is one of the reasons numerical analyses sometimes produce shorter cycles, as they tend to pick lows at 7,300 and 8,200 BP that don’t belong to this periodicity. Few signal analyses can correctly work with missing periods at the same time other similar periodicities are present. But we know between 1640-1700 AD several Schwabe cycles were undetectable in sunspots, so we should not be surprised B4 is missing. The article above deals with this problem.

    Whoever wants to propose a different (shorter) Bray (aka Hallstatt) cycle will have to correctly identify its lows. Good luck with that. Picking the Maunder lower at 300 BP instead of the 500 BP low would only make the cycle longer, not shorter.

  20. Trying to decipher clusters of solar grand minima from a calibration curve is ludicrous. The main purpose of the calibration curve is to allow for geomagnetic changes in earth over time.

    Leave the proxy reconstructions to the experts, instead of trying to do it yourself.

    • Another criticism is the width of your so called windows B1-B6. The window size looks to be around 180 years which is not nearly enough to cover a cluster of solar grand minima. A time span of around 500-600 years would be more accurate and not allow the cherry picking of single grand minima to suit your needs.

      Overall this study is far from convincing and would fail any reasonable test of peer review.

    • Trying to decipher clusters of solar grand minima from a calibration curve is ludicrous.

      You are not acquainted with the relevant bibliography on an issue you claim to be an expert.

      “Aims. This study aims to improve our understanding of the occurrence and origin of grand solar maxima and minima. Methods. We first investigate the statistics of peaks and dips simultaneously occurring in the solar modulation potentials reconstructed using the Greenland Ice Core Project (GRIP) 10Be and IntCal13 14C records for the overlapping time period spanning between ∼1650 AD to 6600 BC. Based on the distribution of these events, we propose a method to identify grand minima and maxima periods.”

      Inceoglu, Fadil, et al. “Grand solar minima and maxima deduced from 10Be and 14C: magnetic dynamo configuration and polarity reversal.” Astronomy & Astrophysics 577 (2015): A20.
      https://www.aanda.org/articles/aa/full_html/2015/05/aa24212-14/aa24212-14.html

  21. Great reading, Javier. Thanks for sharing this.

  22. Seems to me the good news is we aren’t due for another Maunder minimum for another 1000 years or so.

  23. “I would expect significant cooling and climate change from reduced solar activity around 2600 AD when the next low in the ~ 1000-year Eddy cycle is expected.”
    http://euanmearns.com/periodicities-in-solar-variability-and-climate-change-a-simple-model/

    Strange, that is only 200-250 years after the next peak of your Bray cycle. Or even less going by your chart as it shows Bray minimums at 775 BC and 1475 AD, which is only 2250 years.

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