Earth’s Cryosphere, 2024, Vol. XXVIII, No. 2, p. 39-48.

CLIMATE AND CRYOSPHERE

SOLAR GEOCHRONOLOGY OF THE LATE PLEISTOCENE AND HOLOCENE

V.M. Fedorov*, D.M. Frolov

Lomonosov Moscow State University, Faculty of Geography, Leninskie Gory 1, Moscow, 119991 Russia
*Corresponding author; e-mail: fedorov.msu@mail.ru

The calculation of the Earth’s insolation with high spatial and temporal resolution made it possible to calculate solar characteristics that reflect changes in astronomical factors regulating variations in the incoming solar radiation and in the intensity of radiative heat transfer (meridional, in the ocean–continent system, and interhemispheric). In accordance with this, the astronomical theory of climate change has been modernized on the Holocene scale. Based on the synchronization of global climatic events with extremes of solar characteristics in the Holocene and Late Pleistocene, a method of solar geochronology is proposed, which makes it possible to clarify the chronology of global climatic events and explain their origin.

Keywords: astronomical theory of climate change, variations of insolation, radiative heat transfer, synchronization, solar geochronology, Late Pleistocene, Holocene.

---

Recommended citation: Fedorov V.M., Frolov D.M., 2024. Solar geochronology of the Late Pleistocene and Holocene. Earth’s Cryosphere XXVIII (2), 39–48.

---

Full text.

INTRODUCTION

The forecast of climate changes in the future and knowledge about them are largely determined by a retrospective analysis of climate changes in the past. In this regard, information about the nature and causes of changes in the solar and global climate of the Earth in the past seems relevant. Solar radiation is the main source of energy that determines the radiation and thermal balance of the Earth (of its surface and atmosphere) and the nature of hydrometeorological processes. Therefore, the study of the solar climate of the Earth in the Holocene and Late Pleistocene is important for determining the role of radiation factors in global climatic events of the recent geological past and for predicting global climate changes in the future. The main purpose of this study is to modernize and develop the astronomical theory of climate change on the scale of the Holocene and Late Pleistocene based on the analysis of the results of theoretical calculations of insolation with high spatial and temporal resolution for a period from 12 kyr in the past to 8 kyr in the future.

ASTRONOMICAL THEORY OF CLIMATE CHANGE

The astronomical theory of climate change (ATCC) was developed by the Serbian mathematician Milutin Milanković based on calculations of the Earth’s insolation [Milankovich, 1939]. The main purpose of the ATCC was to explain global climatic events (glacial epochs with the development of continental glaciations and interglacial epochs separating them) in the Pleistocene history of the Earth in connection with secular variations in incoming solar radiation determined by changes in astronomical parameters (longitude of perihelion, axial tilt, and eccentricity of the Earth’s orbit). Due to the goal set, as well as the technical capabilities of that time, the insolation was calculated with low spatial and temporal resolution.

Milankovich calculated the summer insolation for 65° N for the last 600 kyr. The insolation graph obtained by M. Milankovitch (in terms of latitudinal equivalents) was first published about a hundred years ago in 1924 in the work of W. Köppen and A. Wegener Climates of the Past. Equivalent latitudes are the latitudes at which the same amount of solar radiation is currently received during the caloric summer half-year as it was received in the past at 65° N. An increase in the equivalent latitude (Fig. 1) means a decrease in incoming radiation and vice versa (for example, solar radiation coming to the Earth at 65° N 590,000 years ago, is approximately equal to solar radiation at 72° N in 1800 AD). The minima of latitudinal equivalents in glacial epochs are marked with a black fill.

Summer insolation is of great importance in the changes of the Earth’s natural system and its components, one of which is the cryosphere. This is determined, firstly, by the fact that with an increase in summer insolation, the near-surface air temperature and the ocean surface temperature also increase (that is, it becomes warmer). The consequence of this is an increase in evaporation and in the content of water vapor in the atmosphere, which, in turn, enhances the greenhouse effect. As a result, additional heat appears, which makes another contribution to an increase in evaporation, water vapor concentration, and greenhouse effect and, again, leads to the appearance of additional heat. These processes, repeated many times, form a mechanism for accelerated warming. Secondly, an increase in precipitation results in the increasing release of latent heat due to the transition of water vapor into water and snow or ice. Thirdly, a decrease in the planetary albedo due to a reduction in the area of sea ice and glaciers and in the duration of snow cover leads to a stronger heating of large surface areas on the continents and in the oceans and, as a consequence, heating of the atmosphere. With the reduction of summer insolation, the opposite processes obviously occur.

Instead of calculating the amounts of heat for the summer and winter half-years, M. Milankovich used caloric half-years, that is, half-years of the same duration, when at a given latitude any value of daily insolation in the summer half-year is greater than any value of daily insolation in the winter half-year. The main results of his research are presented in [Milankovich, 1939]. The adoption by M. Milankovich of an equal duration of six months does not allow taking into account seasonality, which regulates the transfer of radiation heat in the ocean–continent system [Shuleikin, 1953] and interhemispheric transfer of radiation heat in the ocean–atmosphere system [Fedorov, 2021a].

The calculations made by M. Milankovich were subsequently carried out and specified by a number of authors. These calculations were based on new solutions to the theory of secular perturbations obtained for the entire Solar System [Brouwer, Van Woerkom, 1950]. The calculations used the latest data on the masses and motion of the planets taking into account second-order effects caused, for example, by long-period variations in the motion of Jupiter and Saturn [Berger, 1978; Sharaf, Budnikova, 1968; Vernekar, 1972; Monin, 1982; Bretagnon, 1982]. Jacques Laskar and colleagues have prepared a solution for orbital, precessional, and tilt variables for calculating low-frequency variations in insolation [Laskar et al., 1993]. He used the high-precision astronomical ephemerides DE-406 as a reference for testing his solutions over a short period of time. It should be noted that the authors used ephemerides DE-406 as initial astronomical data for preliminary calculations of insolation variations with high spatial and temporal resolution [Fedorov, 2018]. In [Laskar et al., 1993], insolation was calculated only for the parallel of 65° N and only for one day per year with increments of 1000 years (for a period of one million years).

Thus, the calculation of the Earth’s insolation has been repeatedly carried out in connection with the appearance of new astronomical data. The climate explanation scheme adopted by M. Milankovich has not been modernized and developed. It was based on accounting for changes in summer insolation at 65° N (Fig. 1). In the ATCC, the contribution of radiation heat transfer mechanisms associated with the uneven arrival and distribution of solar radiation across latitudes and seasons was not taken into account [Fedorov, 2019a,b; 2021a,b].

In general, the history of the ATCC is associated with a series of calculated values of secular (low-frequency) variations in the incoming solar radiation (solar climate of the Earth) due to secular variations in the elements of the Earth’s orbit (eccentricity, longitude of perihelion) and the tilt of the axis of rotation. The quantitative results of this solution (calculation of secular variations of incoming solar radiation) somewhat differ because of the differences in the initial conditions and calculation methods applied by researchers [Fedorov, 2019b]. The physical basis of the transition from solar to global climate in the ATCC is the acceptance of a direct dependence of temperature on variations in incoming summer radiation at 65° N. However, the temperature regime of the global climate is determined not only by variations in incoming radiation but also by changes in the intensity of radiation heat transfer. These changes were described in the ATCC only qualitatively (changes in seasonal and latitudinal differences due to changes in orbital characteristics) and were not taken into account in paleoclimatic reconstructions. Nevertheless, long-term temperature changes are determined by a change in the meridional heat transfer regulated by the meridional insolation gradient associated with a change in the tilt of the axis («heat engine of the first kind») [Shuleikin, 1953]. Other factors of temperature regime change are interhemispheric radiative heat transfer (regulated by the Earth’s insolation seasonality) and radiative heat transfer in the ocean–continent system (regulated by insolation seasonality – «heat engine of the second kind») [Shuleikin, 1953; Monin, Shishkov, 1979]. Therefore, the physical basis for climate modeling should be such radiation (solar) characteristics as variations in summer radiation coming to the upper boundary of the atmosphere (UBA), the meridional insolation gradient (MIG) or insolation contrast (IC), the insolation seasonality of the Earth (ISE) and hemispheres (IH). In this regard, in its current form, the ATCC, according to its physical foundations, cannot realistically reflect and explain changes in the global climate. In addition to physical reasons, the impossibility of applying astronomical climate theory to explain the Holocene climate is due to mathematical reasons – low spatial and temporal resolution in insolation calculations. The insolation was calculated by M. Milankovich [1939] for individual parallels with a time resolution of about 5000 years. His followers also calculated insolation for individual parallels with a time resolution from 5000 [Sharaf, Budnikova, 1968; Monin, 1982] to 1000 years [Berger, 1978; Vernekar, 1972; Bretagnon, 1982; Lasker et al., 1993].

Thus, there are mathematical (related to the low spatial and temporal resolution of insolation calculations) and physical (disregard for changes in the intensity of radiation heat transfer) problems that limit the possibility of applying ATCC (in its existing form) to explain global climatic events of the Holocene and, obviously, the Pleistocene.

MODERNIZATION AND DEVELOPMENT OF THE ASTRONOMICAL THEORY OF CLIMATE CHANGE ON THE HOLOCENE SCALE

The modernization of ATCC includes the calculation of insolation with high spatial and temporal resolution (solving the mathematical problem of ATCC) and the calculation of solar characteristics regulating the intensity of radiation heat transfer (meridional, in the ocean–continent system, and interhemispheric). In accordance with this, the author, together with A.A. Kostin [Fedorov, Kostin, 2020], performed calculations of insolation with high spatial and temporal resolution based on the latest astronomical ephemerides DE-441 for a period of 12 000 years in the past and 8000 years in the future (relative to 2000 AD). The initial astronomical data for calculating insolation included the declination and ecliptic longitude of the Sun, the distance from the Earth to the Sun, the difference between the course of uniformly current coordinate time (Coordinate Time – CT), and the universal corrected time (Universal Time – UT). The Earth’s surface was approximated by an ellipsoid of the Geodetic Reference System 1980 (GRS80) with half-axes lengths equal to 6 378 137 m (large) and 6 356 752 m (small). In general, the calculation algorithm can be represented by the expression:

\[ I_{nm}\left(\varphi_1,\varphi_2\right)=\int_{t_1}^{t_2}\left(\int_{\varphi_1}^{\varphi_2}{\sigma(\varphi)\left(\int_{-\pi}^{\pi}{\Lambda(t,\varphi,\alpha)}d\alpha\right)d\varphi}\right)dt\ \ \ (1) \]

where I_nm is the incoming solar radiation for the elementary n-th fragment of the m-th tropical year (J); σ is the areal multiplier (m²), with which the areal differential σ(φ) is calculated; dαdφ is the area of an infinitesimal trapezoid cell; α is the hour angle; φ₁, φ₂ are geographical latitudes expressed in radians; Λ(t, φ, α) is solar radiation at a given moment in a given place on the surface of the ellipsoid (W/m²); and t is time (s). The integration steps were: longitude 1°, latitude 1°, time 1/360 of the duration of the tropical year taking into account its changes. Changes in solar activity were not taken into account. The value of the solar constant (the average long-term value of TSI — Total Solar Irradiance) was assumed to be 1361 W/m².

As a result of calculations for the Holocene, quantitative values of summer insolation on the UBA and solar characteristics regulating the transfer of radiation heat with high spatial and temporal resolution were obtained. The climatic effects of radiation heat transfer are as follows.

The meridional transfer of radiation heat («heat engine of the first kind») is regulated by the meridional gradient of insolation (MGI) or the insolation contrast (IC) of the hemisphere. MGI and IC depend on changes in the inclination of the Earth’s rotation axis [Fedorov, 2018, 2019a]. Three climatic effects are associated with the change in the tilt of the axis. For example, during the phase of decreasing axis inclination (in the Holocene), annual insolation increases in areas below 45° latitude of each hemisphere (heat source) and decreases in areas above 45° (heat runoff area) (Fig. 2).

As a result, a decrease in temperature is expected in areas located above 45° latitude, and an increase below 45° latitude [Voeikov, 1903; Milankovich, 1939]. However, at the same time, the meridional insolation gradient and the intensity of the meridional radiation heat transfer increase, which leads to the opposite effect – an increase in temperature in the area of radiation heat sink and a smoothing of the equator–pole temperature gradient. It should also be borne in mind that the area of the heat sources (in each hemisphere) is 2.7 times larger than the area of the heat sink. In this regard, energy (heat) is transferred from a larger area to a smaller area, and the specific characteristics of energy (heat) in the areas of heat runoff  increase significantly. All this leads to warming in the phase of decreasing the tilt of the axis, primarily in the areas of heat sink (above latitude 45°). In addition, a mechanism for increasing warming is being formed [Fedorov, 2018]. Thus, M. Milankovich and A.I. Voeikov took into account the first effect associated with variations in incoming radiation, and did not take into account another, equally important climatic effect associated with a change in the axis inclination angle – changes in the intensity of meridional radiation heat transfer. In this regard, the astronomical theory has been criticized by many climatologists and paleogeographers [Brooks, 1952; Schwarzbach, 1955; Markov, 1960; Budyko, 1974; Fedorov, 2021a].

Also, we should bear in mind that fluctuations in latitude equivalents (Fig. 1) with a span of 2.6° latitude (and a period of about 41 kyr) are determined by changes in the exposure of the Earth’s surface due to changes in the axis inclination angle (displacement of the polar circles, tropics of Cancer and Capricorn). Thus, during the phase of decreasing inclination angle, the area of the regions located beyond the arctic circles is reduced by about 25.93%. On the contrary, the area of the regions located between the tropics and the corresponding arctic circles increases by 12.87%, and the area of the regions located between the tropics and the equator decreases by 9.8%. The marked areas are characterized by different annual irradiation rates [Fedorov, Frolov, 2022]. Thus, the amplitudes of changes in summer insolation in latitudinal equivalents shown in Fig. 1 include latitudinal fluctuations associated with changes in the exposure of the Earth’s surface (regulated by a change in the axis inclination angle) and related changes in the nature of irradiation at different latitudes.

The annual IC for each hemisphere is calculated as the difference between the annual insolation in the area of 0°–45° latitude (heat source) and the area of 45°–90° (heat sink) (Fig. 2). Thus, it generically (by the areas of the heat source and drain) reflects long-term changes in the annual meridional insolation gradient, which regulates the intensity of meridional heat transfer [Shuleikin, 1953]. The increase in the annual IC determines the thermal conditions of the modern Interglacial period (Holocene). The values of the annual IC in the hemispheres are approximately (up to the third decimal place) equal (Fig. 3).

At the beginning of the period of calculations, there is a decrease in the annual IC. The absolute minimum (137.738 W/m²) was observed in the Boreal period, in 7431 BC. Starting from this time (coincides with the maximum tilt of the rotation axis), the annual IC tends to increase. The maximum value of the annual IC in the considered interval is 143.227 W/m² (in 10 000 AD). Thus, the range of changes in the annual IC reaches 5.489 W/m². The annual IC in the Southern and Northern hemispheres is linearly related to the angle of inclination of the axis of rotation (R = –0.99998). On this basis, it can be assumed that the period of change in the annual IC is close to 41 000 years. Currently, the maximum rate of increase in the annual IC is being noted.

The IC calculations were performed taking into account the seasonal displacement of the heat source (0°–35°) and sink (35°–90°) regions for the winter (astronomical) half-year in the hemisphere, as well as the heat source (0°–55°) and sink (55°–90°) regions for the summer (astronomical) half-year [Fedorov, 2018]. On average, the period of change in summer IC is about 41 kyr; in winter IC, about 21 kyr. At the same time, the relationship between the summer ICs in the hemispheres is positive, whereas it is negative for winter ICs.. The correlation coefficient between the summer ICs of the Northern and Southern hemispheres is 0.902; between the winter ICs, –0.973. The summer IC in the Northern and Southern hemispheres is closely related to the angle of inclination of the axis, R = –0.973 and –0.977, respectively, and with the annual IC. The correlation coefficient for the Northern Hemisphere is 0.972, for the Southern hemisphere – 0.978. The climatic consequence of an increase in the annual IC is a gradual increase in temperature in the areas of heat sink and a decrease in the equator–pole temperature gradient.

The interhemispheric transfer of radiation heat is regulated by the Earth’s insolation seasonality (ISE), which is determined by the ratio of precession cycles and perihelion longitude. The interhemispheric transfer of radiation heat to the UBA was calculated as follows. Calculated: (1) the difference between summer II in the Southern hemisphere and winter II in the Northern Hemisphere and (2) the difference between summer II in the Northern Hemisphere and winter II in the Southern Hemisphere. By subtracting these differences, a function was obtained that reflects the total annual transfer of radiation heat from one hemisphere to another. At the same time, in the case of subtracting difference 2 from difference 1, positive values correspond to the predominance of annual transfer from the Southern summer hemisphere to the Northern winter hemisphere, and negative values correspond, on the contrary, to the predominance of transfer from the Northern summer hemisphere to the Southern winter hemisphere. The mechanism of interhemispheric heat exchange in the atmosphere is realized through the partially displaced Hadley circulation cell of the winter hemisphere into the summer hemisphere. The transfer of radiation heat (by air and water masses) from the summer hemisphere to the winter hemisphere changes over time due to the difference in summer and winter insolation in the hemispheres (Fig. 4).

Figure 4 presents the energy transfer from 1 m² of the hemisphere surface. To estimate the transfer for the hemispheres, multiply the obtained values by the area of the hemisphere (2.550328025 × 10¹⁴ m²). For an absolute maximum in 976, this value will be 1.9232⋅× 10¹⁵ W, which is comparable to the value of annual MGI and meridional energy transfer in the ocean–atmosphere system [Fedorov, 2019a]. Due to the interhemispheric transfer, which is determined by the angular ratio of the line of apsides and the line of nodes, one winter hemisphere receives more or less radiation heat per year than the other winter hemisphere. Seasonal temperature differences in the hemispheres are smoothed out. The period of oscillation of the ISE is, on average, about 21 kyr.

The transfer of radiation heat in the ocean–continent system is regulated by the IC of the hemisphere, which is also determined by the ratio of the precession cycle and the cycle of longitude of perihelion (Fig. 5). The IC of the hemisphere is calculated as the difference between summer and winter insolation (RI, W/m²) in the hemisphere [Monin, Shishkov, 1979]. Long-term changes in the intensity of this heat exchange are associated with seasonal changes in the areas of heat source and heat sink. When seasonal differences in insolation are smoothed out, the intensity of heat exchange in the ocean–continent system decreases and vice versa.

At the maximum IS, the global climate is likely to acquire a more continental character (with sharp seasonal differences), at lows – more marine (with smoothed seasonal differences).

The noted mechanisms of heat transfer (radiation heat transfer) are determined by the uneven intake and distribution of solar radiation by seasons and latitudes. This is regulated by the astronomical characteristics of the Earth’s orbital motion (the ratio of the apside line, determined by the motion of the perihelion, and the node line, determined by the precession of the vernal equinox) and the angle of inclination of the Earth’s rotation axis.

The noted mechanisms of radiation heat transfer act simultaneously. However, the intensity of each of them is determined by a change in its regulating insolation characteristics associated with the orbital motion of the Earth and the tilt of its axis of rotation. These heat transfer mechanisms linking long-term changes in the solar and global climate were not taken into account in the ATCC when explaining changes in the paleoclimate. Thus, the use by M. Milankovich and some of his followers [Brouwer, Van Woerkom, 1950; Sharaf, Budnikova, 1968; Monin, 1982] of caloric half-years of equal duration excludes the possibility of accounting for interhemispheric heat exchange and heat exchange in the ocean–continent system. Currently, the difference in the duration of the summer and winter half-year in the hemispheres is about 7.5 days. The period of IC fluctuations in the hemispheres is, on average, close to 21 kyr.

Thus, low spatial and temporal resolution (a mathematical problem) and failure to take into account the mechanisms of radiation heat transfer (a physical problem) are the reasons limiting the application of astronomical climate theory in its current form, both for modeling paleoclimate and for explaining climate changes in the Holocene. The modernization of the ATCC on the Holocene scale, based on calculations of insolation with high spatial and temporal resolution with due account for the mechanisms of radiation heat transfer creates opportunities to clarify the chronology and explain the causes of changes in the Earth’s global climate and global climatic events in the Holocene and Late Pleistocene [Fedorov, 2021a]. The ATCC, modernized for the Holocene, may also be the key to explaining changes in the global climate of the Earth in the Pleistocene. However. one should take into account conditions of the natural system at the moment of the onset of extremes of solar characteristics, as well as the influence of factors other than radiation, such as tectonics, changing the outlines of continents and oceans, their geographical location and elevation; changes in solar activity, atmospheric composition, the speed of axial rotation of the Earth; etc.

Currently, the climatic stratigraphic model/scheme of the Pleistocene (MIS) is being adjusted according to Milankovich’s ATCC [Lisiecki, Raymo, 2005]. MIS (Marine Isotope Stage) is an orbitally tuned stratigraphic model (LR04) (oxygen-isotope curve) based on globally averaged data from oxygen-isotope analysis (δ¹⁸Q) of benthic foraminifera over 57 columns. The results of this analysis were adjusted according to the insolation at 65° N on June 21 [Lisiecki, Raymo, 2005]. The calculations noted above were used for tuning [Laskar et al., 1993]. That is, the adjustment of the isotope curve for the Earth is carried out along one of 180 parallels and one of 365 days a year. At the same time, it is known that irradiation varies both in space (by latitudes – Fig. 2) and time (by days and seasons of the year). Such an adjustment of the isotopic curve of the Earth does not seem to be physically justified. Since the change in the temperature regime of the global climate is determined by both variations in the incoming summer radiation (in the hemisphere) and changes in the intensity of radiative heat transfer adjusted only by variations of the summer insolation calculated for one day (June 21) at one parallel (65° N), the MIS stratigraphy does not realistically reflect changes in the temperature of the hemisphere and the Earth determined by the combined effect of changes in the irradiation of the hemispheres and the Earth as a whole, and changes in the intensity of radiation heat transfer (meridional, in the ocean–continent system, interhemispheric). As a result, the widespread climatic stratigraphic model/scheme of the MIS is at least inaccurate. In addition, the MIS scheme does not explain the reasons for the climate changes presented in it. Unlike the MIS scheme, solar geochronology allows one to determine not only the time of a climatic event in the hemisphere or for the Earth (by synchronization with the extreme of the solar characteristic/factor) but also its cause (by the climatic effect of the solar characteristic). Solar instrumentation allows us to obtain a more complete and detailed characterization of radiation conditions in the Late Pleistocene and Holocene, with the change of which the state of the natural environment (and climate – as a generalized characteristic of this state) changes.

It should also be noted that summer insolation in the hemispheres varies asynchronously (Fig. 6). Summer insolation was calculated by the authors as the intensity of irradiation of the entire hemisphere for the summer astronomical half-year.

The minimum of summer II in the Northern Hemisphere corresponds to the maximum of summer insolation in the Southern Hemisphere and vice versa. The IS also changes asynchronously in both hemispheres. The synchronicity of the development of events in the hemispheres, noted by many researchers on the basis of isotope analysis of ice cores from Antarctica and Greenland [Petit et al., 1999; Veres et al., 2013], in the case of the reality of this effect, can only be defined as the response of the Southern hemisphere to global climatic events occurring and taking place in the Northern Hemisphere. The response is probably realized through the mechanism of interhemispheric transport in the atmosphere and the Wallace Broecker “ocean conveyor” [Broecker, 1991].

SOLAR GEOCHRONOLOGY OF THE HOLOCENE AND LATE PLEISTOCENE

The principle of explaining global climatic events proposed by the authors is based on their synchronization with extreme values of solar characteristics (both incoming summer radiation calculated for the hemisphere and radiation heat transfer) reflecting the influence of astronomical factors on the solar and global climate of the Earth. In the Late Pleistocene–Holocene history of the Earth, eight climatic events are considered and explained by radiation factors (table 1), most of which had a global distribution. The lower boundary of the Holocene is drawn at the beginning of intense warming, which occurred around 11 700 years ago [Head, 2019; Walker et al., 2019]. The beginning of the Late Pleistocene (Valdai) glaciation dates back to the time of 71 kyr BP (Interdepartmental Stratigraphic Committee of Russia, 2008, 2011). The chronology of other climatic events in the Holocene and Late Pleistocene presented in the table is derived from classical works [Markov, 1968; Markov et al., 1965; Quaternary Period in the USA, 1968; Monin, Shishkov, 1979; Velichko, 2012].

Table 1. Solar geochronology of the Holocene and Late Pleistocene.

The chronology of extremes for the Holocene is derived from the results of calculations of solar characteristics. The chronology of extremes for the Late Pleistocene is presented according to the periods of solar characteristics calculated for the Holocene based on the assumption of equal duration of the branches of growth and decline in the cycle of solar characteristics.

The most important geochronological reference point in the studied interval is the cycle of climatic precession – the cycle of changes in summer II in the Northern Hemisphere (Fig. 7). According to the results of the analysis, in the interval from 12 000 kyr in the past to 8000 kyr in the future, its duration (along the branch of recession) is determined at 22 100 years. This cycle is linearly (0.999) related to the IS cycle of the Northern Hemisphere. Thus, summer II and IC in the hemisphere change synchronously; so, their climatic effects are manifested together. It follows from the superimposition of effects that the maximum of summer II and IC corresponds mainly to a warm and dry (more continental) global climate, the minimum is cold and humid (more marine).

In the Northern Hemisphere, the absolute maximum of summer II (440.012 W/m²) is noted at the beginning of Preboreal, in 9442 BC. The absolute minimum (417.600 W/m²) is fixed in 1605 AD. The duration of the II decline branch in the Northern Hemisphere in the Holocene is 11 047 years (according to the values of absolute extremes). The span of variation is estimated at 22.406 W/m², and the period at equilibrium of the branches is about 22 100 years. According to the Stefan–Boltzmann formula (L = σT⁴), the extreme values of summer insolation correspond to a temperature of 296.68 K (23.68°C) for the maximum and 292.83 K (19.83°C) for the minimum. The temperature range is 3.85 degrees. If we take into account the unequal albedo for the extremes (less at the maximum, more at the minimum), then the difference will increase. Also, temperature differences in extreme periods are likely to increase due to the mechanisms increasing warming (at maximum) and cooling (at minimum). The cycle of change in summer II is determined by the angular ratio of the apside line (aphelion – perihelion) and the node line (equinox points). Recall that the nodes or points of the equinox are the points of intersection of the Earth’s orbit with the plane of the ecliptic. The longitude of the perihelion is the angle between the point of the vernal equinox and the perihelion of the Earth’s orbit, the apex of which is placed in the center of the Sun. When the perihelion coincides with the point of the summer solstice, the maximum of summer II is observed in the Northern Hemisphere and the minimum – in the Southern Hemisphere. Winter II at this time reaches a maximum in the Southern Hemisphere and a minimum in the Northern Hemisphere. When aphelion coincides with the summer solstice point, a minimum II is observed in the Northern Hemisphere in summer, and a maximum – in the Southern Hemisphere (vice versa in winter). The maxima and minima of summer II in the hemisphere (in the cycle of climatic precession) are repeated, on average, after about 11 kyr and manifest themselves asymmetrically in the hemispheres. The extremes of the climatic precession cycle are represented in seven global climatic events of the Holocene and Late Pleistocene (table). In the Holocene, for example, the maximum of summer II in the Northern Hemisphere is synchronized with the beginning of the active phase of glacial degradation in Europe and North America, that is, with the transition from the cold Pleistocene to the warm Holocene epoch, and minimum, with the Little Ice Age. As summer II in the Northern and Southern hemispheres changes asynchronously, we suppose that the Northern Hemisphere was the main area of occurrence of the noted events. . In the Southern Hemisphere, they could manifest themselves as responses to interhemispheric heat transfer in the ocean and atmosphere.

Taking into account the found period of climatic precession, it is possible to approximately determine the dates of extreme values of summer II in the Northern Hemisphere in the Late Pleistocene. The maxima took place 33.3 and 52.2 kyr BP. The Bryansk interval (Dunaevsky, Paudorf, Stilfried B, Denekamp) ~25–29 kyr BP and the Brerup interstadial (~53-55/59 kyr BP) were synchronized with the maxima of summer II in the Northern Hemisphere in the Late Pleistocene. The minima of summer II in the Northern Hemisphere in the Late Pleistocene were observed 22.5 and 44.4 kyr BP. The maximum spread of the last glaciation (LGM, Bologovskaya, Brandenburg stages) about 20 kyr BP, the Shestikhinsky cold spell about 47–49 kyr BP, and the beginning of the Valdai glacial epoc about 70 kyr BP were synchronized with the minima of summer II in the Northern Hemisphere.

The period of climatic precession for the Late Pleistocene was specified by ephemerides calculated by J. Laskar (according to the longitude of perihelion). The duration of this cycle varies markedly, therefore, the table highlights in italics the updated dates of extremes of climatic precession according to J. Laskar [Laskar et al., 2011; http://vo.imcce.fr/insola/earth/online/earth/earth.html, 2024]. According to J. Laskar, for an interval of 10 million years (ephemerides cover the period from 5 million years into the past to 5 million years into the future), it turned out that the duration of the cycle of climatic precession varies widely (from 10 to 33 kyr), averaging 21 585 years. In total, 464 complete cycles are allocated over an interval of about 10 million years. Of these, only 200 have a duration of 21 and 22 kyr.

The medieval optimum of the Holocene (800–1100 AD) is synchronized with the maximum of the winter IC in the Northern Hemisphere (and the maximum of the ISE, interhemispheric transfer of radiation heat from the Southern Hemisphere to the Northern Hemisphere). The Amersfoort event (64 kyr BP) in Europe and the Sent-Pierre event ~64–65 kyr BP in North America were also synchronized with the maximum of the winter IC in the Northern Hemisphere (63.5 kyr BP).

Also, according to J. Laskar, the duration of the cycle of changes in the angle of the rotation axis inclination, which regulates the fluctuation of the annual and summer IC, was analyzed. There are 242 complete cycles in the interval of 10 million years. Their duration varies from 33 to 52 kyr, only averaging 40 967 years. Currently, using Lascar ephemerides, the authors perform calculations of solar characteristics with high spatial resolution for a period from 3 million years in the past to 100 kyr in the future to construct a solar geochronological scheme of the Pleistocene based on the dynamics of the external energy (radiation) signal determined by astronomical factors.

As follows from the table, in the seven noted global climatic events of the Holocene and Late Pleistocene, the extremes of summer II calculated for the Northern Hemisphere are presented (the radiation factor taken into account by the ATCC for irradiation at 65° N). In addition, radiation heat transfer factors — IS, ISE, and IC (radiation factors not considered in the ATCC) influenced these global climatic events. Thus, modernization and development of the ATCC makes it possible to take into account both variations in the incoming radiation and changes in the intensity of radiation heat transfer. That is, the modernized ATCC represents a more advanced toolkit for geochronology, climatic stratigraphy, and explanation of the causes of global climatic events of the Holocene and Late Pleistocene.

CONCLUSION

The basis of solar geochronology of the Holocene and Late Pleistocene is the synchronization of global climatic events and extreme values of solar characteristics reflecting variations in summer radiation entering the hemisphere and changes in the intensity of radiative heat transfer (meridional – «heat engine of the first kind», in the ocean–atmosphere system – «heat engine of the second kind,» and interhemispheric heat exchange). Variations in solar characteristics reflect the influence of astronomical factors on the nature of the Earth’s irradiation, its solar and global climate. Given the fact that solar radiation is the main source of heat on Earth, the synchronization of global climatic events and extremes of solar characteristics can be considered as a result of causal relationships between them. This makes it possible to clarify the chronology of global climatic events in the Holocene and Late Pleistocene and to identify solar (radiation) characteristics/factors as a possible cause of such events. Based on the extremes of solar characteristics calculated for the future, a forecast of global climate events is possible. For example, in approximately 9–10 kyr, the extremes (maxima) of three solar characteristics in the Northern Hemisphere (summer II, IS, and annual IC) are expected to overlap, which may result in significant warming of the global climate.

 ACKNOWLEDGMENTS

This study was carried out in accordance with the state assignment of the Faculty of Geography of Lomonosov Moscow State University, projects «Paleogeographic Reconstructions of Natural Geosystems and Forecasting Their Changes» (121051100135-0) and «Hazard and Risk of Natural Processes and Phenomena» (121051300175-4).

References

Bretagnon P., 1991. Theorie du movement de l’ensemble des planetes. Solution VSOP82. Astron. Asrtrophys. 114, 278–288.

Broecker W.S., 1991. The great ocean conveyor. Oceanography 4 (2), 79–89.

Brooks С., 1952. Climates of the Past (Translated from: Brooks C.E.P., Climate through the Ages, ed. 2, London, 1950). Moscow, Inostran. Literatura, 358 p. (in Russian)

Brouwer D., Van Woerkom A.J.J., 1950. The secular variation of the orbital elements of the principal planets. Astronom. Pap. 13, 81–107.

Budyko M.I., 1974. Climate Changes. Leningrad, Gidrometeoizdat, 280 p. (in Russian)

Fedorov V.M., 2018. Insolation of the Earth and Modern Climate Change. Moscow, Fizmatlit, 232 p. (in Russian)

Fedorov V.M., 2019a. The problem of meridional heat transfer in the astronomical theory of climate. Geofizich. Protsessy Biosfera 18 (3), 117–128. DOI: 10.21455/GPB 2019.3-8 (in Russian)

Fedorov V.M., 2019b. Earth’s insolation variation and its incorporation into physical and mathematical climate models. Usp. Fizich, Nauk 189 (1), 33–46. DOI: 10.3367/UFNr.2017.12.038267. (in Russian)

Fedorov V.M., 2021a. Astronomical theory of climate: issues of modernization and development. Gidrometeorolog. Ekolog. 64, 435–465. DOI: 10.33933/2713-3001-2021-64-435-465 (in Russian)

Fedorov V.M., 2021b. Holocene paradox in the astronomical theory of climate and problems of orbital tuning. Geofiz. Prots. Biosfera 20 (1), 95–104. DOI: 10.21455/GPB2021.1-9 (in Russian)

Fedorov V.M., Frolov D.M., 2022. Change in the irradiation of the Earth in the phase of decreasing the inclination of its axis of rotation. Geofiz. Prots. Biosfera 21 (3), 75–84. DOI: 10.21455/GPB 2022.4-59 (in Russian)

Fedorov V.M., Kostin A.A., 2020. The calculation of the Earth`s insolation for the 3000 BC–2999 AD. In: Chaplina T.O. (Ed.),  Processes in GeoMedia. Vol. I. Springer Geology. Springer, Cham. DOI: 10.1007/978-3-030-38177-6_20

Imbrie J., Imbrie K.P., 1988. Mysteries of the Ice Ages. (Translated from: Imbrie J., Imbrie K.P. Ice Ages. Solving the Mystery. Harvard Univ. Press, Cambridge, 1986) Moscow, Progress, 264 p. (in Russian)

Head M.J., 2019. Formal subdivision of the Quaternary System/Period: Present status and future directions. Quat. Int. 500, 32–51. DOI: 10.1016/j.quaint.2019.05.018

Laskar J., Joutel F, Boudin F., 1993. Orbital, pretreatment and insolation for the Earth from –20 Myr to +10 Myr. Astron. Astrophys. 287, 522–533.

Laskar J., Fienga A., Gastineau M,. Manche H., 2011. La2010: A new orbital solution for the long-term motion of the Earth. Astron. Astrophys. 5, A89. DOI: 10.1051/0004-6361/201116836

Lisiecki L.E., Raymo M.E., 2005. A Pliocene-Pleistocene stack of 57 globally distributed benthic δ¹⁸O records. Paleoceanography 20, PA1003, 1–17. DOI: 10.1029/2004PA001071

Markov K.K., 1960. Paleogeography. Moscow, Izd. Mosk. Gos. Univ., 268 p. (in Russian)

Markov K.K., 1968. Pleistocene. Moscow, Vysshaya Shkola, 304 p. (in Russian)

Markov K.K., Lazukov G.I., Nikolaev V.A., 1965. Quaternary Period. Vol. 1. Moscow, Izd. Mosk. Gos. Univ., 372 p. (in Russian)

Milankovich M., 1939. Mathematical Climatology and Astronomical Theory of Climate Fluctuations. Moscow, GONTI, 208 p. (in Russian)

Monin A.S., 1982. Introduction to the Theory of Climate. Leningrad, Gidrometeoizdat, 246 p. (in Russian)

Monin A.S., Shishkov Yu.A., 1979. History of the Climate. Leningrad, Gidrometeoizdat, 408 p. (in Russian)

Petit J.R. Jouzel J. Raynaud D. et al., 1999. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399, 429–437.

Markov K.K. (Ed.), 1968. Quaternary Period in the USA. Vol. 1. Moscow, Mir, 696 p.

Sharaf Sh.G., Budnikova N.A., 1968. Fluctuations in the Earth’s solar irradiation caused by secular changes in the elements of the Earth’s orbit. Dokl. Akad. Nauk SSSR 182 (2), 291–293. (in Russian)

Shwartsbach M., 1955. Climates of the Past. Introduction to Paleoclimatology (Translated from: Shwarzbach M., 1950. Das Klima der Vorzeit. Eine Einfuhrung in die Palaoklimatologie. Stuttgart). Moscow, Izd. Inostr. Literatury, 144 p. (in Russian)

Shuleikin V.V., 1955. Physics of the Sea. Moscow, Izd. Akad. Nauk SSSR, 990 p. (in Russian)

Velichko A.A., 2012. Evolutionary Geography: Problems and Solutions. Moscow, GEOS, 562 p. (in Russian)

Veres D., Bazin L., Landais A. et al., 2013. The Antarctic ice core chronology (AICC2012): an optimized multi-parameter and multi-site dating approach for the last 120 thousand years. Clim. Past 9 (4), 1733–1748. DOI: 10.5194/cp-9-1733-2013

Vernekar A., 1972. Long-period global variations of incoming solar radiation. Ser. Meteorological Monographs. Am. Meteorol. Soc. 12 (34), 128p.

Voeikov A.I., 1903. Meteorology. St. Petersburg, Izd. kartograf. A. Ilyina, 737 p. (in Russian)

Walker M., Head MJ, Lowe J. et al., 2019. Subdividing the Holocene Series/Epoch: formalization of stages/ages and subseries/subepochs, and designation of GSSPs and auxiliary stratotypes. J. Quat. Sci. 34 (3), 173–186. DOI: 10.1002/jqs.3097.

Received July 26, 2023
Revised January 22, 2024
Accepted February 5, 2024
Translated by S. Sokolov