*Solar System Planets and Exoplanets*

atmosphere is heated by the Sun than in July–December when the atmospheric cooling occurs (see **Figures 11** and **12**, right column). This is more evident in the annual variations of the monthly averaged TSI magnitudes (**Figure 13**) revealing a steady increase of the solar irradiance input in millennia M1 and, especially, in M2 during spring-summers and decrease during autumn-winters in the Northern hemisphere in each century caused by the variations of S-E distances shown in

*The annual variations of TSI magnitudes (W=m*<sup>2</sup>*) in millennia M1 (600–1600) (left) and iM2 (1700–*

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600*

Because of a reduction of the S–E distances in the first half of a year caused by SIM, the TSI deposition from years 1700 to 2600 is increased by about 11 *W=m*<sup>2</sup> (0.95%) in February–March (and decreased by the close amount in August–September), by 15 *W=m*<sup>2</sup> (1.2%) in April–May (decreased in October–November) and by 7–8 *W=m*<sup>2</sup> (0.5%) in June–July (decreased in December–January) (see **Figures 11** and **12**). These TSI variations can naturally explain a wide variety of the measured TSI magnitudes in the earlier space observations of 1370 *W=m*<sup>2</sup> (Shirley et al. 1990), 1971 *W=m*<sup>2</sup> (Wolff & Hickey 1987), or 1972 *W=m*<sup>2</sup> (Lee III et al. 1995) if they are measured during May–June or July–August. The numbers of TSI variations during a first half of a year can be added to produce more than 2.7% of solar irradiance increase in M2 because of the S-E distance decrease by SIM that is comparable with the estimations up to 3.5% hinted in the retracted paper [19]. *This amount* of the extra solar radiation input into the terrestrial atmosphere and ocean

The variations of solar irradiance averaged for every month in a year are plotted

for both millennia in **Figure 13**, showing that the minimum of the mean solar irradiance is shifting in M2 towards 15 July, thus, securing the extra heating of Northern atmospheres in the summer months of second half of June and half of July in this millennium M2. These shifts of the largest S-E distances aphelion from 21 June to 15 July (local aphelion) in M2 can also explain why the baseline solar magnetic field is an ascending phase of Hallstatt's current cycle, with a maximum of the northern polarity at 2600 before the longest distance becomes shifting back to June in the next few millennia. As shown in [19] (see **Figure 3**) there have been about 60 super-grand (Hallstatt's) cycles over the past 120,000 year. This means such the millennial changes of the TSI on Earth are regular patterns, which will continue to appear in the current Hallstatt's cycle shown in **Figure 4**, top plot [19]. Based on the location of Earth on its orbit, these solar irradiance inputs has to be

divided between the hemispheres depending on which one of them is turned towards the Sun. This means that, because of the Earth axis tilt of 23.5<sup>∘</sup> from the vertical to the ecliptics, in the millennium M1 (600–1600) the input of solar

**Figure 9** discussed above.

*2600) (right). Axis X shows months of a year.*

*DOI: http://dx.doi.org/10.5772/intechopen.96450*

**Figure 13.**

**45**

*has not been yet considered in the current climate models.*

#### **Figure 12.**

*Variations of the daily solar irradiance (W=m*<sup>2</sup>*) in July–December of three sample years in the millennium M1 (600–1600) (left) and M2 (1600–2600) (right). Left column: Blue - 600, red 1100 and green 1600; right column: Blue - 1700, red - 2020 and grey - 2600. X-axis shows days of the months.*

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

**Figure 13.**

*The annual variations of TSI magnitudes (W=m*<sup>2</sup>*) in millennia M1 (600–1600) (left) and iM2 (1700– 2600) (right). Axis X shows months of a year.*

atmosphere is heated by the Sun than in July–December when the atmospheric cooling occurs (see **Figures 11** and **12**, right column). This is more evident in the annual variations of the monthly averaged TSI magnitudes (**Figure 13**) revealing a steady increase of the solar irradiance input in millennia M1 and, especially, in M2 during spring-summers and decrease during autumn-winters in the Northern hemisphere in each century caused by the variations of S-E distances shown in **Figure 9** discussed above.

Because of a reduction of the S–E distances in the first half of a year caused by SIM, the TSI deposition from years 1700 to 2600 is increased by about 11 *W=m*<sup>2</sup> (0.95%) in February–March (and decreased by the close amount in August–September), by 15 *W=m*<sup>2</sup> (1.2%) in April–May (decreased in October–November) and by 7–8 *W=m*<sup>2</sup> (0.5%) in June–July (decreased in December–January) (see **Figures 11** and **12**). These TSI variations can naturally explain a wide variety of the measured TSI magnitudes in the earlier space observations of 1370 *W=m*<sup>2</sup> (Shirley et al. 1990), 1971 *W=m*<sup>2</sup> (Wolff & Hickey 1987), or 1972 *W=m*<sup>2</sup> (Lee III et al. 1995) if they are measured during May–June or July–August. The numbers of TSI variations during a first half of a year can be added to produce more than 2.7% of solar irradiance increase in M2 because of the S-E distance decrease by SIM that is comparable with the estimations up to 3.5% hinted in the retracted paper [19]. *This amount* of the extra solar radiation input into the terrestrial atmosphere and ocean *has not been yet considered in the current climate models.*

The variations of solar irradiance averaged for every month in a year are plotted for both millennia in **Figure 13**, showing that the minimum of the mean solar irradiance is shifting in M2 towards 15 July, thus, securing the extra heating of Northern atmospheres in the summer months of second half of June and half of July in this millennium M2. These shifts of the largest S-E distances aphelion from 21 June to 15 July (local aphelion) in M2 can also explain why the baseline solar magnetic field is an ascending phase of Hallstatt's current cycle, with a maximum of the northern polarity at 2600 before the longest distance becomes shifting back to June in the next few millennia. As shown in [19] (see **Figure 3**) there have been about 60 super-grand (Hallstatt's) cycles over the past 120,000 year. This means such the millennial changes of the TSI on Earth are regular patterns, which will continue to appear in the current Hallstatt's cycle shown in **Figure 4**, top plot [19].

Based on the location of Earth on its orbit, these solar irradiance inputs has to be divided between the hemispheres depending on which one of them is turned towards the Sun. This means that, because of the Earth axis tilt of 23.5<sup>∘</sup> from the vertical to the ecliptics, in the millennium M1 (600–1600) the input of solar

**Figure 12.**

*Solar System Planets and Exoplanets*

**44**

*Variations of the daily solar irradiance (W=m*<sup>2</sup>*) in July–December of three sample years in the millennium M1 (600–1600) (left) and M2 (1600–2600) (right). Left column: Blue - 600, red 1100 and green 1600; right*

*column: Blue - 1700, red - 2020 and grey - 2600. X-axis shows days of the months.*

radiation in the Northern hemisphere was slowly increasing from January until 21 June not only because of the elliptic Earth orbit but also because of the Sun's shift from the focus of this ellipse in the minor axis direction towards the spring equinox and become reducing from 21 June through the whole July. While in M2 (1600– 2600) during the months June – July the input of solar irradiance to the Northern hemisphere will be higher than in the elliptic orbit. This means that in M2 the increase of the solar input in February–July must be ahead of its decrease in August– January. This would happen also because, according to Kepler's second law, the Earth moves slower at the parts of the orbit in June–July–August than in December– January, thus, passing quicker through the positions with a reduced radiation in December than with the increased one in June–July.

(b) added together the daily TSI magnitudes (right plot) taken from **Figures 11** and **12** associated with the daily magnitudes of TSI (for 366 days for the leap

show the increase of TSI by about 1–1.3 *W=m*<sup>2</sup> in 2020 compared to 1700

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600*

These two plots clearly demonstrate that the monthly TSI variations (case a)

(**Figure 14**, left plot). This TSI increase found from the S-E distance ephemeris is close to the magnitude of 1–1.5 *W=m*<sup>2</sup> reported from the current TSI observations [34]. However, the annual TSI magnitudes, calculated from the daily S-E distances (case b) reveal a much larger annual increase of the total solar irradiance by about 20–25 *W=m*<sup>2</sup> (> 1.8%) in M2 (by 2500) than in millennium M1 (**Figure 14**, right plot). This analysis gives the indication of the averaged TSI increase in M2 could be 2.5–2.8 *W=m*<sup>2</sup> per century, or (0.18–0.20)%, comparing to the TSI in 1700. This is the very important hidden solar irradiance input in millennium M2 (1600–2600) caused by the SIM effects, which was significantly underestimated if only the averaged monthly TSI magnitudes are used (**Figure 14**, compare left and right plots). The essential issue is how much of this extra solar radiation is distributed between the hemispheres owing to the Earth tilt, its position on the orbit or the level

Our study of the S-E distance variations shows that at the start of any year, in January, the Earth is turned to the Sun with its southern hemisphere, meaning that any decrease and increase of solar radiation during this time is mostly absorbed by the parts in Southern hemisphere. When the Earth's orbiting approaching March, the distribution of solar irradiance between the hemispheres becomes nearly even, while in April–June the main part of the solar radiation input is shifted towards the Northern hemisphere, having its maximum theoretically (by Kepler's law) on 21 June, while in reality, shifted to 5 July in 2020 and to 16 July in 2500. Hence, in M2 the Northern hemisphere should get the extra solar radiation not only in the first six months of a year but also in the 25 days from 21 June by approaching the local aphelion on 16 July, which is not compensated later by its expected cooling because

By comparing the mean-by-time and mean-by-arc S-E distances for an elliptic orbit (see Appendices B and C) based on the calculated shifts of aphelion and perihelion [49] with the real S-E distances derived from the ephemeris one can conclude that the ephemeris of the S-E distances have to reflect the Sun shifts in SIM, in addition to the Earth revolution about the ellipse focus. Therefore, the solar radiation deposition in the millennium M2 is expected to be essentially higher than in in millennium M1 and different from the standard seasonal changes because of the uneven shifts of Sun-Earth distances on the orbit owing to SIM. This extra TSI amount caused by SIM (from the variations of a distance *d* in formula (2) will undoubtedly add to the magnitude of solar irradiance coming from the solar activity itself (or the parameter *I*<sup>⊙</sup> in formula (2)) shown in **Figure 4** (bottom plot, blue lines) leading to the overall solar irradiance increase that, in turn, can account for a large amount of the terrestrial temperature increase shown by the red curves in **Figure 4** (bottom plot). This extra solar forcing caused by SIM needs to be taken

Let us try to evaluate how these variations of solar irradiance can affect terrestrial temperature from the general similarity approach. The TSI variations caused by the solar activity in normal cycles of 11 years and during grand solar minima

years used).

of exposure to solar radiation [42, 49].

*DOI: http://dx.doi.org/10.5772/intechopen.96450*

of a shift of the local perihelion to 16 January.

into account in any climate models.

**47**

**5. TSI variations and terrestrial temperature**

(similar to Maunder Minimum) can be described as follows.
