**5. TSI variations and terrestrial temperature**

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

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.

*Solar System Planets and Exoplanets*

**4.3 Imbalance of the TSI depositions in the two millennia**

same for each year for both centuries, as currently assumed.

**Figure 14.**

**46**

Since there is a shift of the minimum point of the TSI annual variations (**Figure 13**) from 21 June (M1) to 15 July (end of M2), this indicates a possible imbalance between the annual TSI input and output in M2 (1600–2600). From the daily magnitudes of TSI shown in **Figures 11** and **12**, it is possible to count the total annual amount of TSI emitted by the Sun towards the Earth in each year of the both millennia. If this amount does not change from year to year, then TSI is, indeed, the

However, the real annual magnitudes of TSI deposited to the Earth during the

two millennia are shown in **Figure 14** calculated for the two cases: (a) added together the averaged monthly TSI magnitudes (left plot) calculated for the S-E distances shown in **Figure 13** when only 12 magnitudes per year (for 12 months);

*The total annual TSI variations (W=m*<sup>2</sup>*) in the millennia M1 and M2 derived by summation of the mean*

*monthly (top) and daily TSI magnitudes (bottom). Axis X shows the years of the millennia.*

1.Solar irradiance *S* variations at Earth owing to 11 year cycle is about 0.1% of the average magnitude of TSI *S* (1366 W*m*<sup>2</sup> accepted in this study) increasing by 1.4 W*m*<sup>2</sup> during maxima and decreasing during minima [33, 54]. The terrestrial temperature variations during 11 year cycle are negligible.

However, these are rather rough estimations. Further investigation of the level

Note, this proposed prediction of the baseline temperature variations does not explain further temperature fluctuations above the baseline temperature which can well be caused by either anthropogenic or other terrestrial activities not considered

Although in the next 33 years the Sun is entering a period of the reduced solar activity, the modern grand solar minimum, which can be called a 'mini ice age', similar to Maunder Minimum. The GSMs are caused by significantly reduced solar magnetic field imposed by the disruptive interference of two magnetic waves generated by the double dynamo in the solar interior [10]. The first modern GSM1 occurs in 2020–2053 [10, 60] and the second modern GSM2 will happen in 2370–

Because the solar irradiance and terrestrial temperature already increased since the MM owing to the SIM effects discussed in section 5.1, the terrestrial temperature during the first modern GSM1 is expected to drop by about 1.0C to become just

The temperature decrease during the second modern GSM (2375–2415) can be estimated calculated as follows. The current temperature increase in 2020 is by 1.5<sup>∘</sup>

C higher than in 1700. After each of the modern

which should increase by 2375 by another 1.5<sup>∘</sup> C (=3 x 0.5C [35]) giving the total increase since 1700 by 3.0<sup>∘</sup> C. The temperature decrease caused by a reduction of solar magnetic field and solar activity during the GSM2 would lead to a reduction of temperature by about 1.0<sup>∘</sup> C. This will produce the total temperature during

GSMs, solar activity is expected to return to normal 11 year cycles as shown in

In this chapter the investigation of Sun-Earth distances from the ephemeris by VSOP87 [47] and JPL ephemeris [48] is presented. The Sun is found shifting in millennia M1 and M2 along the direction of the minor axis towards the spring equinox that leads to a significant reduction of S-E distances in January–June by about 0.005 au in M1 and up to 0.011 au in M2, which are followed by the asymmetric increases in the second half of the year (July–December). However, the S-E distance increases and decreases are not identical as expected from elliptic orbit. These S-E distances are found affected not only by the Earth revolution about the focus of the ellipse, but also by the Sun's motion about the barycentre caused by the gravitational effects of other planets (Jupiter, Saturn, Neptune and Uranus), or solar inertial motion (SIM). This shift of the position of the Sun with respect to the barycentre has been recognised as the solar inertial motion - SIM [25, 27, 30]. The resulting S-E distances are defined by the superposition of these two motion: Earth revolution and SIM. The similar inertial motion effects are often observed in other stars, which have planetary systems, leading to the wobbling star effect that is used

C,

of conversion of solar radiation into the atmospheric heating and radiation of terrestrial atmosphere using radiative transfer simulations are required. This can provide more accurate numbers for the terrestrial temperature variations caused by the increase of solar irradiance owing to solar activity and SIM, in general, and their

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

fluctuations in the hemispheres, in particular.

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

(1.5–1.0=) 0.5<sup>∘</sup> C higher than that in 1700.

the GSM2 of (3.0–1.0=) 2.0<sup>∘</sup>

to trace possible exoplanets [50, 51].

**5.2 Effects of upcoming grand solar minimum (2020–2053)**

on this paper.

2415 [10, 60].

**Figure 1** [10].

**6. Conclusions**

**49**

2. Solar irradiance *S* variations at Earth owing to GSM is about 2.5–3 *W=m*2, or 0.22 % of *S* [31, 37, 55] as shown in **Figure 2** (left plot). These estimations are also supported by conclusions by other authors [55, 56] showing sometimes up to 0.4% contributions of active regions into the solar radiance intensity *I*⊙.

The terrestrial temperature curve presented in **Figure 2** (right plot) shown a reduction during MM of the average terrestrial temperature by about 1<sup>∘</sup> .0C [36, 57, 58], e.g. the decrease of TSI by 0.11% secures a decrease of the terrestrial temperature by approximately 0<sup>∘</sup> .5C. Let us use this simple estimation until we carry out more precise model simulations.

#### **5.1 Expected effects of the TSI increase by SIM on the terrestrial temperature**

The terrestrial temperature is found increasing since Maunder minimum as shown in **Figure 4**, bottom plot derived by Akasofu [35] that is close to the plot presented in the NASA and IPCC report *https* : *==www:ipcc:ch=sr*15*=*. At the same time the solar activity of 11 years, and thus, solar irradiance caused by it in the past four solar cycles was decreasing.

Now we established that there is an additional effect leading to the increase of solar irradiance in the millennium M2 (1600–2600) because of the changing Sun-Earth distances imposed by the solar inertial motion (SIM) owing to gravitational effects from Jupiter, Saturn, Neptune and Uranus. The overall increase of solar irradiance for M2 is shown in **Figure 14** to reach about 20–25 *W=m*<sup>2</sup> for the whole planet, which can be assumed to split evenly to each hemisphere with 10–12 *W=m*2.

Although, the conversion of this extra solar radiation into the terrestrial temperature is a complex process involving exchanges between the deposited solar radiation to different hemispheres, ocean and atmospheric radiative transfer [59]. In fact, using line-by-line radiation transfer (LBL-RT) calculations under different cloudiness conditions, ground temperatures, and humidity models for radiative transfer of UV solar radiation by atmospheric molecules including *CO*2, Hardy [59] has shown that even a smaller increase of solar radiation by 5 *W=m*<sup>2</sup> leads to a noticeable (60%) increase of the terrestrial temperature defined by the Sun and only 40% defined by the *CO*<sup>2</sup> emission. The further increase of solar irradiance owing to the millennial TSI misbalance derived here in section 4.3 from the ephemeris of the Sun-Earth distances would definitely lead to a further contribution (possibly, above 80%) of the Sun's radiation into the observed terrestrial temperature growth.

Although, in the current study we do not carry out radiative transfer simulations, and thus, can only roughly estimate possible variations of the average terrestrial temperature using the observed curves similar to those measured [35, 45] (**Figure 4**, bottom plot). The baseline temperature was shown to increase, or to recover from 'little ice age' after Maunder minimum, in the past three centuries (black straight line in [19, 35]). Since the TSI increase by up to 25 *W=m*<sup>2</sup> for two hemispheres, or 12.5 *W=m*<sup>2</sup> per hemisphere is expected until, at last, 2500, then using the link between the solar irradiance and terrestrial temperature derived from **Figure 2**, the increase in the baseline terrestrial temperature from 1700 can be expected by about 4*:*0<sup>∘</sup> C in 2500, or by 2*:*0<sup>∘</sup> C in 2100 and by 1*:*5<sup>∘</sup> C in 2020.

However, these are rather rough estimations. Further investigation of the level of conversion of solar radiation into the atmospheric heating and radiation of terrestrial atmosphere using radiative transfer simulations are required. This can provide more accurate numbers for the terrestrial temperature variations caused by the increase of solar irradiance owing to solar activity and SIM, in general, and their fluctuations in the hemispheres, in particular.

Note, this proposed prediction of the baseline temperature variations does not explain further temperature fluctuations above the baseline temperature which can well be caused by either anthropogenic or other terrestrial activities not considered on this paper.
