1 INTRODUCTION

Solar-activity (SA) variation results in modulations of intensity of galactic cosmic rays (GCRs) during their propagation in the heliosphere. When GCR particles enter the Earth’s atmosphere, they produce cosmogenic isotopes that contain information on the GCR intensity in the Earth-centered orbit, which allows the use of data on cosmogenic isotopes for the study of SA during past centuries and millennia. The content of cosmogenic isotopes in natural archives is also influenced by the Earth’s time-varying magnetic field, which prevents charged particles from penetrating the Earth’s atmosphere. Below, the focus is on one of these cosmogenic isotopes, the carbon isotope 14С (radiocarbon). Note that the Earth’s climate changes cause radiocarbon redistribution among natural reservoirs, which also influences the radiocarbon concentration.

The world ocean temperature and the polar glacial caps play fundamental roles in changes of the Earth’s climatic system (e.g., Dergachev, 2019). Polar ice cores are excellent archives of the Earth’s climatic history over the past few hundred thousand years.

Over the past two decades, a method has been successfully developed to detect changes in the air temperature and the ocean mean temperature based on the use of the element and isotope ratios of argon and nitrogen and heavy noble gases (krypton and xenon) contained inside the atmospheric air bubbles captured in the ice cores, which are preserved over long time periods (Schwander, 1989). Recent achievements in the development of equipment to measure the content of these isotopes have improved the accuracy of the assessment of temperature variation. This makes it possible to determine the temperature changes in the Greenland ice with a high resolution, which, in turn, enhances our insight into climate fluctuations of the past.

The purpose of this paper is to consider the efficiency of the use of temperature reconstructions obtained from the measurement of the content of an argon isotope (40Ar) in the layers of the Greenland ice sheet as a source of information on global temperature variation in order to reconstruct past SA based on radiocarbon data. Figure 1a shows data on the relative 14С content (∆14C) in the Earth’s atmosphere starting from the second millennium B.C. (Reimer et al., 2013). During this time span, the ∆14C content reaches its absolute minimum in the middle of the first millennium A.D. There are several maxima and minima; the most significant of them are the maxima of 1860, 1365, 725, and 340 B.C. and the minima of 695, 785, and 1055 A.D. (Oort minima of SA), 1330 A.D. (Wolf minimum of SA), 1530 A.D. (Spörer minimum of SA), and 1710 A.D. (Maunder minimum of SA). While the last two minima have recently been actively studied, the more ancient minima of SA are poorly studied. It is known that the ∆14C parameter describes the deviation of the concentration ratio for 14С and 12С from the standard value. We study the climatic-parameter variation staring from the second millennium B.C.

Fig. 1.
figure 1

(a) Change in Δ14C (Reimer et al., 2013); (b) change in the СО2 concentration in the Earth’s atmosphere (Monnin et al., 2001); (c) anomalies of the global temperature (Marcott et al., 2013); and (d) reconstruction of the temperature in Greenland (Kobashi et al., 2011).

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2 VARIATION IN THE EARTH’S CLIMATE, THE 14С CONTENT IN THE EARTH’S ATMOSPHERE, AND THE HELIOSPHERE MODULATION POTENTIAL SINCE THE SECOND MILLENNIUM B.C.

Figure 1b presents the variation in the СО2 concentration in the Earth’s atmosphere (Monnin et al., 2001). Up to the early 13th century A.D., it is possible to see a tendency toward increased concentration; however, with the onset of the Little Ice Age (LIA), the increase in the СО2 concentration is replaced by a decrease. The LIA is distinctly displayed in the temperature reconstructions. Figures 1b and 1c present the reconstructions of anomalies (i.e., deviations from mean value for 1961–1990) of the global temperature (Marcott et al., 2013) and Greenland temperature (Kobashi et al., 2011) (the solid line shows the averaging for 100 years), respectively. The last temperature reconstruction is obtained based on the 40Ar content in the annual ice layers for the last 4000 years. These data also present the LIA period and the subsequent temperature growth.

However, there are also considerable differences between these temperature reconstructions. Thus, the minima of approximately 1700 and 750 B.C., as well as the long cold periods about 500 B.C. and 200 A.D. and 500 A.D. are clearly visible in the temperature reconstruction (Kobashi et al., 2011).

We consider the SA variation from the late second millennium B.C. For this purpose, we calculate the rate of production of the 14С cosmogenic isotope Q(t) under the impact of GCR particles. The method used to calculate Q(t) with allowance for climate change was described in detail by Kudryavtsev et al. (2016). The value of Q(t) is calculated based on the five-reservoir model. A feature of this method is that it takes into account the dependence of the rate of radiocarbon transition from the higher layer of the ocean to the atmosphere under the impact of the global temperature variation, which is a consequence of the temperature dependence of the carbon dioxide solubility in water and causes changes in the carbon dioxide flux from the ocean (Takahashi et al., 1993). Since fluctuations of 14С concentration in natural reservoirs occur around the equilibrium values, the radiocarbon content in natural reservoirs is considered equilibrial at the initial time moment (2000 B.C.), as in the work by Kudryavtsev et al., (2019). In our calculations, we use the Greenland temperatures averaged over 100 years (Kobashi et al., 2011) and proceed from the premise that the Greenland temperature variation are representative of the global temperature variation. In order to identify the rate of radiocarbon transition from the higher layer of the ocean to the atmosphere, we, like Kudryavtsev et al. (2016), use the following expression:

$${{\lambda }_{{mOa}}} = \left( {1 + k\left( {T - {{T}_{0}}} \right)} \right)\lambda _{{mOa}}^{0},$$

where k is the temperature coefficient; T is the Greenland temperature (Kobashi et al., 2011) averaged over 100 years; T0 is the mean temperature T for the period of 1961–1990, and \(\lambda _{{mOa}}^{0}\) is the rate of the radiocarbon ocean-to-atmosphere transition at T = T0.

The use of the temperature data from Kobashi et al. (2011) on the temperature of annual ice layers at their formation (Fig. 1d) causes some discrepancies in the calculation procedure. Kudryavtsev et al. (2016) used the reconstructions of the ground-level air temperature, and the temperature coefficient k connected the variation in λmOа with these temperature variations. Koudriavtsev et al. (2014) showed that these coefficient values were 0.05–0.1 K–1 during the LIA period, and the global temperature changed by up to 0.7 K (Esper et al., 2002). Thus, the rate of radiocarbon transition from the higher ocean layer to the atmosphere changed by 3.5% to 7%. In this paper, we use the variation in the ice-layer temperature instead of the air-temperature variation. According to Fig. 1d, the ice-layer temperature variation exceeds by several times the air-temperature variation. Therefore, the temperature coefficient should be lower now. Thus, for example, when k = 0.02 K–1 and the ice temperature varies, the change in λmOа does not exceed 5%, which is shown by the solid curve in Fig. 1d.

Figure 2a presents the results of Q(t) reconstruction based on the radiocarbon data (Reimer et al., 2013). It follows from the figure that the use of the temperature variation in Greenland as the global temperature variation leads to an increase in the rate of 14С production at certain times, e.g., in 750 and 500 B.C., about 200 A.D., and during the Oort (≈1050 A.D.), Wolf (≈1300 A.D.), Spörer (≈1400–1510 A.D.), and Maunder (≈1645–1700 A.D.) SA minima.

Fig. 2.
figure 2

(a) Reconstructions of the rate of production of the 14С cosmogenic isotope Q(t) for two values of the temperature coefficient k; (b) change in the Earth’s magnetic dipole moment (Knudsen et al., 2008); and (c) reconstruction of the heliosphere modulation potential. The letters O, W, S, and M indicate the Oort, Wolf, Spörer, and Maunder SA minima.

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Next, we consider the variation in the heliosphere modulation potential φ(t), which we calculate based on the Q(t) reconstruction. It is known that the variation in φ(t) shows the SA variation (an increase in SA leads to an increase, and a slowdown leads to a decrease in φ(t)). The method to find φ(t) takes into account the geomagnetic field variation; it is well known and has been stated in detail (e.g., Kovaltsov et al., 2012; Poluianov et al., 2016). In our calculations, we use the values of the Earth’s magnetic dipole moment presented by Knudsen et al. (2008) (Fig. 2b). Figure 2c presents the results of φ(t) reconstruction.

3 CONCLUSIONS

The reconstructed time dependence of φ(t) displays all of the SA minima mentioned above: the Oort (≈1050 A.D.), Wolf (≈1300 A.D.), Spörer (≈1400–1510 A.D.), and Maunder (≈1645–1700 A.D.) minima (e.g., Usoskin et al., 2007). The depth of the reconstructed SA minima varies depending on the temperature coefficient: if the reconstructed value of φ(t) at k = 0 K–1 during the Oort minimum fell to 80 MV, then it can almost vanish at k = 0.02 K–1, which also takes place during the Spörer and Maunder minima. A similar situation occurs during the Wolf minimum. The minima that occurred about 750 and 500 B.C. may be the next in depth, and their duration can reach several hundred years and exceed the duration of the subsequent global SA minima, so their cooling effect on the Earth’s climate can be expected. Note that, according to Borisenkov and Pasetskii (1988), the cold sub-Atlantic period occurred during 900–300 B.C. The Spörer minimum that preceded the LIA was apparently the next in width.

However, there are also time spans in which φ(t) varies in antiphase at k = 0 K–1 and k = 0.02 K–1. These intervals include the periods 535–415 B.C., 125–260 A.D., 635–730 A.D., and 770–900 A.D. This may indicate that the Δ14C peaks of 535 B.C. and 140 A.D., 695 A.D., and 785 A.D. presented in the figure are the results of high-energy solar flares or GCR outbursts rather than GCR modulation by the interplanetary magnetic field. Here, it should be noted that Miyake et al. (2017) concluded that the event of 775 A.D. was the result of a high-energy solar flare.

Hence, the use of temperature reconstructions obtained based on measurements of the content of stable isotopes in glaciers of polar zones can provide interesting and important results for research on past SA and its relationship to the changes in the Earth’s climate.