The Bray (Hallstatt) Cycle

Guest essay by Andy May and Javier

The evidence for a persistent irregular climate cycle with a period of 2400 ±200 years is strong. There is compelling evidence of a solar cycle of about the same length and phase; suggesting that the solar cycle might be causing the climate cycle. We will present a summary of the evidence, beginning with the original paleontological evidence, followed by the cosmogenic radionuclide (¹⁰Be or Beryllium-10 and ¹⁴C or Carbon-14) evidence. For more information, a bibliography of many papers discussing topics relevant to the Bray (Hallstatt) cycle can be found here. Only a small portion of the relevant papers are mentioned in this summary post.

In the November 16, 1968 issue of Nature, James R. Bray first proposed the idea of a 2600-year solar-driven climate cycle based primarily upon evidence of Holocene global glacier advances and retreats. We prefer to call this period the Bray Cycle after him, but the same cycle is often called the Hallstatt Cycle. In this post, we will use both names interchangeably to refer both to the climate cycle and the solar cycle. Bray only considered the maximum advance of a glacier field or a major re-advance that reached the near vicinity of the maximum. He used glacier fields in North America, Greenland, Eurasia, New Zealand and South America in the study. The glacial advances were dated using tree rings, lichenometry and radiocarbon dating. Glacial events for the last 13,700 years suggested an optimum interval of 2600 years. He used a “solar index,” based upon sunspots, sunspot cycle length and auroral records that covered the period from 700BC to the present day to show the cause might be a solar cycle. Over this period, the chi-square statistictied the glacial events to solar activity with a score of 28.6 (P<0.001).

While the use of changes in the rate of ¹⁴C production as a quantitative indicator of solar activity had not matured in 1968, Bray does mention that glacier records and ¹⁴C measurements correlate. He recognizes that ¹⁴C increases in periods of low solar activity and decreases in periods of high solar activity. Later researchers take advantage of this relationship to provide more evidence for the Bray cycle and to better estimate its length.

In 1988, Pestiaux, et al. found a strong 2500-year statistically significant cycle in the δ¹⁸O (delta-Oxygen-18, an indicator of air temperature) concentration in three deep sea cores taken in the Indian Ocean. Vasiliev and Dergachev (2002) reviewed the available evidence for a ~2400-year climate cycle and summarized (note the dates of the cold periods are all a bit later than the dates we use in this post):

“There are many data confirming the cyclical nature of the Earth’s climate. The study of the δ¹⁸O concentration in ice core (Dansgaard et al., 1984) showed a ∼2500-year climatic cycle to exist. A ∼2400-year quasiperiod was observed in the δ¹⁸O concentration of deep sea core with high sedimentation rates (Pestiaux et al., 1988). Similar periodic behaviour has been found in GRIP2 and GISP ice cores over the last 12 000 years. Glaciological time series indicate that the Holocene was punctuated by a series of ∼2500-year events (O’Brien et al., 1995). The Middle Europe oak dendroclimatology demonstrates that the Little Ice Age (1500–1800 yr. AD), the Hallstattzeit cold epoch (750–400 yr. BC) and the earlier cold epoch (3200–2800 yr. BC) are separated by 2200–2500 years (see Damon and Sonett, 1992, p. 378). The time positions of these epochs are correlated with the periods of large ¹⁴C fluctuations …”

O’Brien, et al. in the December 22, 1995 issue of Science describe their geochemical analysis of the Summit Greenland ice cores. The data demonstrates that cooler climates occur at roughly 2600-year intervals in the Holocene. The oldest of these events is the Younger Dryas period cooling event (12,800BP) and the most recent is the Little Ice Age (roughly 700BP to 130BP). We will use BP as years before 1950 in this post. O’Brien continues:

“Cold events identified in our [ice core] glacio-chemical series correspond in timing to records of worldwide Holocene glacier advances and to cold events in paleoclimate records from Europe, North America, and the Southern Hemisphere, as determined by combining glacier advance, oxygen isotope (δ¹⁸O), pollen count, tree ring width, and ice core data.”

A plethora of climatic proxy evidence supports a well-established ~2400 year climatic cycle. Even in 1995, using ¹⁴C as a climate and/or solar activity proxy was controversial. But, O’Brien continues:

“Although a Δ¹⁴C -climate link is controversial, a Holocene climate quasi-cycle of ~2500 years (close to our quasi-2600-year pattern), in phase with Δ¹⁴C variations, has been identified by a number of researchers examining glacial moraines, δ¹⁸O records from ice cores, and temperature-sensitive tree ring widths.”

Van Geel, et al. (1998) discusses the dramatic rise in ¹⁴C during the Little Ice Age (1300AD-1850AD) and during the Greek Dark Age (roughly 1100BC to 800BC). The history of these cooler periods is fairly well known, so they can provide evidence of the link between ¹⁴C concentrations and climate. Van Geel discusses techniques of matching ¹⁴C reconstructions with historical and paleontological evidence, like the moss species composition of peat bogs. He also provides archaeological, paleontological and geological evidence that climate change around 850BC occurred simultaneously in both hemispheres. To this point, the ¹⁴C and ¹⁰Be radionuclide concentrations in the Earth’s carbon cycle and in ice cores, respectively, have mostly been used in a qualitative way. It was difficult to use them to estimate solar activity or climate quantitatively due to problems in determining the computational parameters. For ¹⁴C, the problems are removing the long-term geomagnetic variation and estimating the total amount of carbon in the system at the time the ¹⁴C was created by cosmic rays. For ¹⁰Be, also created by cosmic rays, it is knowing the precipitation rate in the area where the ice core was cut and how it varies over time. Steinhilber, et al., 2012, explain it well, see Figure 1:

Figure 1 (Steinhilber, et al., 2012)

Steinhilber, et al. explain the problems:

“¹⁴C enters the global carbon cycle, and therefore fluctuations of the atmospheric ¹⁴C concentration … measured as Δ¹⁴C in tree rings are damped, smoothed, and delayed relative to the ¹⁴C production. The effect of the carbon cycle can be removed by inverse carbon cycle modeling. The resulting ¹⁴C production rate … is a better measure of the cosmic radiation, but it still contains a climate signal component due to unknown temporal changes of the carbon cycle … In contrast to ¹⁴C, aerosol-borne ¹⁰Be is removed from the atmosphere relatively fast, within a few years, and stored in natural archives such as polar ice sheets. Because of its short atmospheric residence time, ¹⁰Be directly reflects cosmic ray intensity variations with almost no attenuation and a delay of 1–2 y. Uncertainties are introduced mainly on annual time scales by atmospheric mixing processes and wet and dry deposition from the atmosphere to the ice.”

Steinhilber, et al. use ¹⁴C concentrations from tree rings and ¹⁰Be ice core records from both Greenland and Antarctica. Since both are created by cosmic rays, but suffer from different environmental effects, they use principal component analysis to extract the cosmic ray effect. They found that the first principal component explained 69% of the total variance and used it to model the total radionuclide production rate.

The Bray cycle appears to be closely tied to tight clusters of grand solar maxima and minima. The Little Ice Age Wolf, Spörer, Maunder and Dalton grand minima are the best example of a solar grand minima cluster and they fall in a Bray low. The Greek Dark Age and the Homer grand minimum also fall in a Bray low. Significant historical events that fall in Bray lows are labeled in figure 2. A more complete picture of these events can be found here. The Little Ice Age (LIA) is a well-known cold period filled with plagues and suffering due to cold, for more details see here and in Dr. Wolfgang Behringer’s excellent book. The period labelled “GDA” is the Greek Dark Ages, during this Bray low the Late Bronze Age ended and after a period of civilization collapse, the Early Iron Age started. The “Uruk” Bray low event corresponds with the expansion of the Uruk civilization and the growth of some of the world’s first cities. Near the end of the Uruk Bray low, the Middle East transitions from the Copper Age to the Early Bronze Age and cuneiform writing appears.

The earliest Bray low shown corresponds with the beginning of the “LBK” or the Linear Pottery Culture along the Danube River in Europe. This period marks the beginning of the end of the hunter-gatherer culture in Europe and the beginning of the growth of an agricultural economy. We are not certain the LBK and Uruk historical events were determined by Bray lows, we just mention them to position the lows in terms of human history. However, the more recent Greek Dark Ages and the Little Ice Age are well established colder periods with numerous historical climatic crises.

It is interesting that each Bray low corresponds to a major cultural transition. The LBK is roughly the end of the Early Neolithic in Europe, when agriculture started to spread. The Uruk period is when the Middle East transitions from the Copper Age to the Early Bronze Age. The GDA occurs as the Middle East moves from the Bronze Age to the Iron Age and the LIA occurs when humans transition from the Pre-industrial era to the Industrial era. Other cultural transitions have been identified in different parts of the world for these periods. Cooler and more difficult climates times do stimulate innovation. This evidence has led some archaeologists, like Weninger et al., 2009, or Roberts et al., 2011, to develop the theory that climate caused environmental stress is an engine to societal change, and they both point to the lows of the Bray cycle as some of the best examples.

Usoskin, et al. (2016, Astronomy and Astrophysics) performed a spectral decomposition of ¹⁴C and ¹⁰Be curves to 7,000 BC. Once the first component was removed a very strong, in phase, 2400-year cycle was uncovered in both curves as shown in Figure 2. The blue curve is ¹⁴C and the red is ¹⁰Be, the vertical scale is a computed “sunspot index number.” Solar grand maxima are shown as red stars and solar grand minima are shown as open blue circles. We have historical records establishing the grand minima after 1500BC, the earlier ones are based on a model of ¹⁴C and ¹⁰Be curves.

Figure 2 (after Usoskin, et al.)

Steinhilber, et al. found that using the first component of a principal component analysis eliminated terrestrial effects from the curves and resulted in a 2200-year cycle. Usoskin, et al. used a related but different statistical technique to remove terrestrial effects and extracted a 2400-year cycle from the data. Usoskin’s Pearson’s coefficient between the ¹⁰Be and ¹⁴C records was 0.77 which is highly significant (p<10^-5). Usoskin notes:

“This Hallstatt cycle has so far either been ascribed to climate variability (Vasiliev & Dergachev 2002) or to geomagnetic fluctuations, particularly geomagnetic pole migration (Vasiliev et al. 2012). However, the fact that the signal we found is in phase and of the same magnitude in the two cosmogenic isotope reconstruction implies that it can hardly be of climatic origin. As already pointed out, ¹⁴C and ¹⁰Be respond differently to climate changes. In particular, ¹⁴C is mostly affected by the ocean ventilation and mixing, while ¹⁰Be (in particular, its deposition in central Greenland) is mainly affected by large-scale atmospheric circulation, particularly in the North Atlantic region (Field et al.2006; Heikkila et al. 2009). … We thus conclude that the ≈2400-yr Hallstatt cycle is most likely a property of long-term solar activity.”

McCracken, et al., 2013, also looked at the ¹⁰Be data and the ¹⁴C data together and separately. He provides the figure below showing how well they match each other at about 2300 years. In this Fourier amplitude spectrum, the ¹⁰Be and ¹⁴C Bray cycle peaks only differ by 20 years. They also match the cosmic ray modulation function (“Ф”) quite well. The modulation function is described by Gleeson and Axford, 1968.

Figure 3 (McCracken, et al., 2013)

Neither the Bray cycle nor the pattern of clustered grand solar minima are perfectly timed. Both, largely vary around a 2400-year cycle by about 200 years each way. Allowing for this, the Bray cycle lows and the clustered grand solar minima do correspond with major historical cold periods as shown in figure 2. Although the ¹⁰Be and ¹⁴C records suggest a regular pattern of solar and cosmic ray intensity, the grand solar minima and maxima effects on the Earth’s climate do not depict a dominant periodic behavior. The minima and maxima appear to be modified by other climatic factors that may, in part, be chaotic. That said, there is a tendency for the grand minima to cluster in Bray lows. Usoskin has investigated this and presents a probability function of the tendency, we show this in figure 4. Grand solar minima do occur outside Bray lows, but almost half occur within 250 years of a Bray low.

Figure 4, after Usoskin, 2016

The evidence herein and in the bibliography provided, supports the existence of both a climatic cycle and cosmogenic radionuclide cycle of ~2400 ±200 years that are in phase. The lows of the cosmogenic cycle have a high probability of containing grand solar minima of the Spörer and Maunder type. There are only two possible explanations for this evidence. Either the climate variations are responsible for the changes in cosmogenic isotopes ¹⁴C and ¹⁰Be, or the solar variability is responsible for the changes in the rate of production of both isotopes and is having a strong effect on the centennial to millennial climatic variability of the planet. The latter explanation is supported by two lines of evidence. For the period of time for which we have records of solar activity, the rate of cosmogenic isotope production correlates with solar activity, as figure 5 shows. Also, the lows of the Bray cycle represent the periods of highest cosmogenic isotope production and are marked by about half of the solar grand minima on record, including the Wolf, Spörer, Maunder and Dalton minima. To claim the isotopes represent a climatic contamination is akin to a claim that the cosmogenic isotopes do not represent a solar proxy at all. Given that cosmogenic isotopes are well established as a proxy for solar activity, that claim requires strong evidence that so far does not exist.

Figure 5 (References here and here)

Summary and Conclusions

The Bray cycle was first proposed as a climate cycle driven by a solar cycle of the same length and phase by James Bray in 1968. He correlated glacial advances (representing colder periods) around the world to a sunspot index and concluded that the solar cycle and the cold periods were linked. This was the same conclusion reached, with far more data in 1990 by Hood and Jirikowic, and in 2016 by Usoskin, et al.

At each Bray cycle low, beginning with the Little Ice Age and ending with the Younger Dryas period, there are significant historical and archeological events indicating a colder climate. In addition, Usoskin has shown that grand solar minima tend to cluster in Bray cycle lows. The Bray cycle varies between 2200 and 2600 years from peak to peak, with a most common length of 2300 to 2400 years. The cycle may be much more regular than that, the variation in length could be caused by two other problems. First, our ability to date events in the past is not very accurate, errors of 100 years or more are very common. Second, existing climatic conditions going into a Bray low and the state of other cycles (for example the 1000-year Eddy cycle and the 208-year de Vries cycle) help to determine the Bray cycle effect. A Bray low during a glacial period will be different than a Bray low today. So, the fact that we cannot be precise about the Bray cycle length does not invalidate the cycle.

While the cause of the solar cycle of Bray length is currently unknown, Scafetta, et al. (2016) have suggested that the orbits of the larger planets have a repeating pattern of 2318 years that might be the cause. Proof is elusive, but this is a fascinating area of study.

The Bray cycle has been recognized in glacier advances and re-advances, ice raft data, peat bog studies, δO18 data, and in ¹⁰Be and ¹⁴C records for almost 50 years. It is supported by historical accounts from Bray lows and archeological data. There is little doubt that the cycle exists, but its exact length and its ultimate cause are unknown. However, much work is being done that should bear fruit with time.

One inescapable conclusion, from the evidence presented, is that solar variability is an important cause of climate change in the centennial to millennial time frame. Therefore, it must have contributed more to recent warming since the last Bray low ended at the end of the Little Ice Age than the IPCC suggests.

This post is in response to Willis Eschenbach’s posts entitled “Sharpening a Cyclical Shovel” and “The Cosmic Problem with Rays.” His posts were in response to our previous posts on natural climate cycles: Impact of the ~ 2400 yr solar cycle on climate and human societies, Periodicities in solar variability and climate change: A simple model, and Solar variability and the Earth’s climate.