The study demonstrates the synchronicity of the positive and negative phases of summer irradiation of the Northern Hemisphere in the precession cycle with periods of global climate warming and cooling for the Late Pleistocene and Holocene. The cold phase 50–41.5 ka BP corresponds to the Shestikhinsky cooling in Eastern Europe and the development of glaciation in North America. The warm phase 41–30 ka BP accounts for climate warming in Europe (Bryansk interstadial, Paudorf, Gotwei warming) and in North America (Plum Point Interstadial). The period of maximum development of glaciation in Europe and North America is synchronized with the cold phase 29.5–17.5 ka BP. The warm phase 17–5.5 ka BP is associated with the transition from the cold Pleistocene to the relatively warm Holocene. The Little Ice Age falls on the cold phase 5 ka BP – 5000 CE. It is expected that warming of the climate with respect to the present will correspond to the Warm Epoch 5000–13 000 CE. Changes in solar radiation arriving in the first astronomical half of the year in 5° latitude zones were determined for all astronomical months of the tropical year for climatic precession extrema. This makes it possible to compare spatiotemporal changes in Earth’s solar climate during years of climate precession extrema.

The paper presents the results of the analysis of changes in Earth’s solar climate over the period from 1900 to 2100. It has been determined that the annual meridional gradient of irradiation intensity from 1900 to 2100 and latitudinal differences in the Earth irradiation intensity increase. A relative increase in winter irradiation intensity for the hemispheres is observed in the regions where extratropical cyclones develop, which may contribute to the activation of cyclonic processes in the atmosphere in the winter half-year. In the Northern Hemisphere, seasonal differences in the irradiation intensity increase during the period of interest, whereas in the Southern Hemisphere they smooth out. Meridional contrasts in irradiation in the summer half-year increase in the Southern and Northern hemispheres; in the winter half-year in the Northern Hemisphere, meridional contrasts in irradiation decrease; in the Southern Hemisphere, they increase. Insolation seasonality increases slightly in the Northern Hemisphere and increases in the Southern Hemisphere. The transfer of radiative heat from the summer Southern Hemisphere to the winter Northern Hemisphere prevails. There is, however, a tendency for it to decrease.

The distribution of the calculated values of the specific irradiation of the Earth and its surroundings from the Earth’s surface to the lower mesosphere is analyzed. The change of incoming transit radiation along three axes of space and time is considered. It was determined that in the annual course of transit irradiation in the polar regions at all altitude levels, two long periods of complete shading (associated with solstices) and two short periods of full illumination (associated with equinoxes) are synchronously observed for the hemispheres. In the latitudinal distribution of annual transit irradiation at all altitude levels in the latitudinal zone of 65°–70° and near it, a maximum is noted in each hemisphere, and a minimum in the equatorial region. For the time interval from 3000 B.C.E. until 2999 A.D. in each hemisphere there are areas of increase, decrease and zero values of transit irradiation. In general, for this time interval there is an increase in transit irradiation of the polar regions of the hemispheres (semi-surfaces of ellipsoids) at all altitude levels and a slight decrease in irradiation to areas located approximately between the polar circles. The result of this is an increase in the transit irradiation of half-surfaces and surfaces of ellipsoids in the space surrounding the Earth.

The synchronicity between the extreme values of summer insolation in the northern hemisphere and the global climatic events of the Holocene is found. The transition from the cold Pleistocene to the warm Holocene epoch is synchronized with the summer irradiation maximum. The Little Ice Age is synchronized with the minimum of summer irradiation in the northern hemisphere. For the Holocene and Late Pleistocene, the leading role of climatic precession in changes in the global climate of the Earth has been determined. Accounting for variations in solar activity made it possible to detail the structure of the minimum irradiation of the northern hemisphere during the Little Ice Age. The necessity and possibility of simultaneously taking variations in incoming radiation of different physical nature associated with changes in the Earth’s orbital motion and changes in the activity of the Sun into account are shown in the reconstruction and forecasting of global climatic events.

The problems associated with the failure to take into account periodic long-term and interannual changes in incoming solar radiation by latitudes and seasons, as well as long-term changes in the intensity of radiative heat transfer in the parameterization of the radiation block of physical and mathematical climate models, are shown. Existing problems with the radiation block parameterization limit the possibilities of modeling climate and forecasting its changes. To solve the problems, a review of Earth's insolation data with different time resolutions available for parameterization is presented.

Studies of the spatial and temporal features of the annual irradiation of the Earth and its surroundings were carried out, based on an analysis of the results of theoretical calculations of insolation. Using the tropical year 2022 as an example, it is shown that the incident and incoming transit exposures are characterized by an asynchronous change in the annual course and an asymmetric change in the latitudinal distribution. It is determined that the ratio of transit exposure to incident radiation increases with height. In the annual course of the incoming transit radiation in the polar regions (synchronously for the hemispheres) for all altitude levels from the upper troposphere to the lower mesosphere (from 10 to 60 km), there are two long periods of complete obscuration associated with solstices and two short periods of full illumination associated with equinoxes.

On the basis of calculations of the Earth’s insolation, the changes in the annual meridional insolation gradient from 3000 BCE to 2999 CE were determined. Changes in the meridional insolation gradient are associated with a change in the angle of inclination of the Earth’s rotation axis. A regression model was used to show that the trends in changes in surface air temperature and sea surface temperature (the temperature regime of the global climate) are determined by 69.3–84.1

Features of the change in the specific irradiation energy and irradiation intensity in the latitudinal zones of the Earth during the phase of decreasing axial tilt (in the interval from 3000 BC to 2999 AD) have been determined. Variations in the annual specific irradiation energy and irradiation intensity are similar in character, which reflects the increase in latitudinal contrast in the annual irradiation of the Earth. The specific irradiation energy decreases in the summer half-years and increases in the winter half-years (seasonal differences are smoothed out). The irradiation intensity exhibits a more complex pattern, in which seasonal differences in the Northern Hemisphere are smoothed out more noticeably than in the Southern Hemisphere. In the phase of decreasing angle of inclination, the area of the regions located beyond the polar circles decreases by approximately 25.93%, the regions between the tropics and the polar circles increases by 12.87%, and the regions between the tropics and the equator decreases by 9.80%.

Orbital tuning is a technology for adjusting the time scale of a geological or climate record to achieve maximum synchronization with the cycles of orbital motion (insolation) presented in astronomical climate theory. The procedure for coordinating climatic events with orbital insolation cycles seems natural due to the fact that solar radiation is the main source of energy for hydrometeorological, biochemical, soil biological and other processes that determine the state and dynamics of the natural system of the Earth. The climate is a generalized characteristic of the state of the natural system. A paradox was found in the change in insolation and temperature in the Holocene. Based on the analysis of the causes of the Holocene paradox, it is shown that the technologies of orbital adjustment relative to the calculations of insolation performed in the astronomical climate theory are premature. The main problem of orbital alignment is to accept the direct dependence of temperature on insolation and not take into account the influence of insolation-related heat transfer mechanisms on the Earthʼs temperature regime. It is shown that, with correct calculated insolation data, the climatic–stratigraphic scale of the astronomical theory of climate is not complete or objective without taking into account the temperature changes caused by the mechanisms of heat transfer.

On the basis of calculations of insolation and insolation characteristics, taking into account changes in solar activity, the causes of global climatic events in the late Holocene have been determined. The main reasons for the Little Ice Age (LIA) are the long and deep minimum of summer insolation and insolation seasonality (IS) in the Northern Hemisphere. The values of the minimums are fixed in the range of approximately 1400–1750. The depth of the minimum over the past 5000 years, taking into account the change in solar activity, is about 8.0 W/m 2 for summer insolation and about 13.3 W/m 2 for IS in the Northern Hemisphere. The medieval climatic optimum is associated with the winter maximum of insolation contrast (IC) in the Northern Hemisphere, reflecting an increase in the meridional heat transfer in the winter half of the year from the equatorial region to the polar regions, as well as with a maximum of interhemispheric heat transfer. The increase in winter IC at maximum (1118) relative to 3000 BC is 28.4 W/m 2 . The difference between the hemispheric radiative heat transfer at the maximums (881, 940, and 976) increases by 5.0 W/m 2 relative to 3000 BC. Thus, global events of the late Holocene are associated with extremes of insolation characteristics (incoming radiation, IC, and IS of the Earth), but the temporal structure of the extrema themselves is determined by variations in solar activity. It follows from the above that, when reconstructing and predicting global climatic events, it is important to take into account not only variations in the incoming radiation, but also the associated changes in insolation characteristics (IC and IS of the Earth), reflecting the mechanisms of heat transfer. The IC regulates the meridional transfer of radiation heat; its cause is a change in the tilt of the axis and precession. The IS of the Earth determines the intensity of interhemispheric heat transfer. The noted characteristics of insolation, reflecting not only variations in the arrival of solar radiation, but also variations in the mechanisms of heat transfer, are not taken into account in the general astronomical theory of climate. Taking these indicators into account will help obtain more complete information about climate changes in past eras and will allow the more accurate forecasting of the future climate.