Solar Cycle Signal in Climate and Artificial Neural Networks Forecasting

Abstract

Natural climate variability is partially attributed to solar radiative forcing. The purpose of this study is to contribute to a better understanding of the influence of solar variability on the Earth’s climate system. The object of this work is the estimation of the variation of multiple climatic parameters (temperature, zonal wind, relative and specific humidity, sensible and latent surface heat flux, cloud cover and precipitable water) in response to solar cycle forcing. An additional goal is to estimate the response of the climate system’s parameters to short-term solar variability in multiple forecasting horizons and to evaluate the behavior of the climate system in shorter time scales. The solar cycle is represented by the 10.7 cm solar flux, a measurement collected by terrestrial radio telescopes, and is provided by NOAA/NCEI/STP, whereas the climatic data are provided by the NCEP/NCAR reanalysis 1 project. The adopted methodology includes the development of a linear regression statistical model in order to calculate the climatic parameters’ feedback to the 11-year solar cycle on a monthly scale. Artificial Neural Networks (ANNs) have been employed to forecast the solar indicator time series for up to 6 months in advance. The climate system’s response is further forecasted using the ANN’s estimated values and the regression equations. The results show that the variation of the climatic parameters can be partially attributed to solar variability. The solar-induced variation of each of the selected parameters, averaged globally, was of an order of magnitude of 10⁻¹–10⁻³, and the corresponding correlation coefficients (Pearson’s r) were relatively low (−0.5–0.5). Statistically significant areas with relatively high solar cycle signals were found at multiple pressure levels and geographical areas, which can be attributed to various mechanisms.

1. Introduction

The Sun is the major source of energy for the Earth’s climate system. The Earth receives approximately 340 W/m² of solar irradiance globally averaged over the Earth’s sphere, according to the 2013 Intergovernmental Panel on Climate Change (IPCC) assessment [1]. Solar energy output varies according to processes occurring on the Sun, which subsequently leads to variations in Earth’s climate system. Solar energy variability, reportedly, has various periodicities. The solar activity variation under study is the 11-year solar cycle. The 11-year solar cycle is directly related to the Sun’s magnetic 22-year cycle and can be explained by the solar dynamo model [2,3]. As the solar cycle progresses, there are time periods where the solar activity reaches the maximum and minimum levels (also called the solar maximum and minimum; S_max, S_min). The differences between solar maximum and minimum activity result in a variation of approximately 0.1% in Total Solar Irradiance (TSI) and up to several percent ($~ 6\%$) in the UV part of Solar Spectral Irradiance (SSI), which induce variations in climatic parameters [4].

The solar proxy that is used in this study is the 10.7 cm solar flux (F10.7). The F10.7 is the intensity of the disc-integrated solar radio emissions centered at 2800 MHz (wavelength of 10.7 cm). These solar flux density measurements are made using a passive remote sensing system, which is composed of two small radio telescopes, also called the flux monitors [5]. Data values are corrected for variations in the Earth–Sun distance. The F10.7 index is measured in solar flux units (sfu), where 1 sfu is 10⁻²² W/m² Hz. F10.7 ranges between 50 and 300 sfu. This measure of solar activity has some advantages over the sunspot number and area indices, such as it is more objective, and measurements can be taken in any weather conditions [3]. F10.7 correlates highly with the number of sunspots (0.940) and the core–wing ratio of the Mg II line (0.956) [6], which is often taken as an index of solar UV variability [4].

The fact that F10.7 can sufficiently express the variability in solar UV radiation is highly important, as it has been reported that stratospheric ozone correlates positively with solar UV variability [7]. In a relevant study, the authors state that the increase in the UV radiation that reaches the stratosphere enhances the photodissociation of molecular oxygen, thus resulting in increased ozone production.

The study and investigation of the Earth’s climate are of interest to various scientific fields [8,9,10,11]. Many studies have dealt with the connection between solar energy output and atmospheric parameters. The most discussed topic is the solar cycle-induced variation of the ozone [12,13,14,15]. Since the relationship of ozone concentrations with the temperature is known [16], the solar cycle can produce variations in Earth’s stratospheric temperatures through ozone [17]. Similar results can be obtained from other studies that research the connection of the solar cycle with stratospheric–mesospheric ozone and temperatures [18,19]. The results signify that, although solar UV radiation impacts the thermal structure and composition of the middle atmosphere, the exact details of the responses are not well established. Regarding the surface of the Earth, it has been found that regional sea surface pressure is negatively influenced by solar activity during the winter west phase of Quasi-Biennial Oscillation (QBO), and regional surface air temperature correlates positively with the F10.7 solar flux [20]. A study on the connection between solar activity variations and the global water cycle [21], using Solar Modulation Potential (SMP) as a solar activity index (high SMP values are inversely correlated with high solar activity), showed that there is a negative correlation between SMP and the global evaporation rate. Moreover, based on the calculations of a relatively recent study, the global surface temperature is said to increase by 4.7%, the global sea level will increase by 0.67% and the global sea-ice extent will decrease about 5.3% due to TSI variations in the next 10 years [22]. A possible link between the Sunspot Number (SN) and the summer monsoon rainfall has been also studied. Results showed that in the west QBO phase, the link is much stronger than in the east QBO phase, although both phases exhibit rather low correlation coefficients [23]. Another study found significant variations in both tropospheric and sea surface temperatures due to solar activity variations, and an assessment of the possible physical processes was also provided [24]. Lastly, there are studies about the increase in cloud cover in solar minimum conditions due to the weakening of the solar magnetic field, which allows for more cosmic radiation to enter the solar system and, subsequently, Earth [25]. On the contrary, some studies report statistically insignificant correlations or no relation whatsoever between solar activity and other variables, which shows the complexity and ambiguity of the subject. For example, a study on the relationship between the Sunspot Number and surface solar irradiance in Madrid showed that, after applying corrections for seasonal variations and volcanic eruptions, as well as outlier data, non-significant correlations are observed [26]. Another study on the relationship between Galactic Cosmic Rays (GCRs) and atmospheric aerosol particle formation found no correlation between all the quantities related to aerosol formation and the cosmic ray-induced ionization intensity. The study concluded that GCRs seems to play a negligible role in the formation of atmospheric aerosol and, by extension, in the relevant climate effects regarding cloud cover and other closely connected climatic parameters [27].

Based on the above studies, it is clear that the search for the solar cycle’s effects on Earth’s climate is a relatively recent research field, and both the mechanisms and the exact magnitude of the impact are not fully assessed. In fact, the IPCC report [1] states that the confidence level regarding the impact of solar forcing on the terrestrial climate is medium. The confidence level depends on both strong evidence and agreement among different studies on the subject. However, global mean radiating forcing, which corresponds to solar forcing, is about 0.05 (to 0.10) W/m². This number is quite small when compared to the global mean radiative forcing produced by the well-mixed greenhouse gases (2.83 W/m²); nevertheless, solar radiative forcing is partially linked to natural climate variability and, thus, it is important to fully understand this topic. It should be mentioned that there is uncertainty regarding the calculation of solar forcing that depends on the TSI estimates and, thus, caution should be taken with regards to the exact influence of the Sun’s variability, for instance on temperature trends [28].

In the present work, we used data that cover five full solar cycles (5 S_max–6 S_min), and we used multiple climatic parameters on a global scale in order to produce a more holistic view of the solar cycle’s effect on the Earth’s climate system. Our focus is to identify the solar signal at the Earth’s surface, troposphere and lower stratosphere, as relevant data are more abundant in these areas. The aim is, first, to estimate the quantitative difference in the climatic parameters between solar maximum and solar minimum conditions, and then, to assess the climatic parameters’ future responses due to predicted solar flux variations. The solar flux variations are predicted with the help of ANNs. The use of ANNs can contribute to predicting the solar energy flux and, based on the established relationship of the solar cycle with the climatic parameters, it can possibly lead to a successful prediction of the solar variation’s impacts on the terrestrial climate. Our methodology extends the use of the already established linear regression equations from identifying the effect of solar forcing on multiple climatic parameters to high-quality estimates of this effect on short and medium scales.

2. Materials and Methods

Remote sensing systems are useful for obtaining a vast variety of data. As it is presented in more detail in this section, both the solar proxy and the climatic parameters that were used contain data collected by remote sensing systems.

The solar proxy that was used in this research study is the solar flux 10.7 cm (F10.7). Figure 1 shows the time evolution of the F10.7 from 1948 to 2015. The data are provided by the National Oceanic and Atmospheric Administration/National Centers for Environmental Information/Solar-Terrestrial Physics program (NOAA/NCEI/STP) and the National Research Council of Canada (NRCC) and National Resources Canada (NRC; Space Weather Canada, Solar Monitoring Program, Ottawa and Penticton, Canada). The F10.7 time series consists of monthly averages from January 1948 to February 2015.

The climatic data that were used in this paper are provided by the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis 1 project [29]. The data of this project are produced by using assimilation methods on data collected from various sources (land surface, ship, rawinsonde, pibal, aircraft, satellite and more). The climatic parameters that were selected for this study are temperature, zonal wind, relative and specific humidity, latent and sensible surface heat flux, cloud cover and precipitable water. All climatic data are also provided as monthly averages from January 1948 to February 2015. A report of the spatial coverage/characteristics of the climatic data is presented.

• Temperature (°C) and zonal wind (m/s) data are given in a global geographical grid with a resolution of 2.5° × 2.5° (144 longitude × 73 latitude points). The vertical dimension consists of 17 pressure levels (1000–10 hPa).
• Relative (%) and specific humidity (g/Kg) data are also given in a global geographical grid with a resolution of 2.5° × 2.5° (144 longitude × 73 latitude points). The vertical dimension consists of 8 pressure levels (1000–300 hPa).
• Latent and sensible surface heat flux (W/m²) data are provided in a Gaussian T62 global grid (192 longitude × 94 latitude points). The data refer to the Earth’s surface.
• Cloud cover (%) data are provided in a Gaussian T62 global grid (192 longitude × 94 latitude points). The atmosphere is considered to be a single layer, meaning that the cloud cover information over the entire atmospheric column is concentrated in one layer.
• Precipitable water (Kg/m²) data are provided in a global geographical grid with a resolution of 2.5° × 2.5° (144 longitude × 73 latitude points). As in the cloud cover data, the atmosphere is considered to be a single layer.

Linking the sensible and latent surface heat fluxes with surface skin temperature and the evaporation rate, respectively, is useful for the interpretation of the results. The sensible heat flux is parameterized as:

$$F_{Hs}=C_H\times \left|V\right|\times \left(T_S-T_{air}\right)$$

(1)

where:

• $F_{Hs}$: Sensible heat flux;
• $C_H$: Bulk transfer coefficient for heat (dimensionless);
• $\left|V\right|:$ Wind speed;
• $T_S-T_{air}$: Difference between air and surface skin temperature.

To convert from kinematic to dynamic heat flux (W/m²), $F_{Hs}$ must be multiplied by air density times the specific heat constant pressure (ρ$\times$c_p). The above are derived from Wallace and Hobbs [30].

In order for latent heat flux to be parameterized, the moisture flux should be addressed first:

$$F_{water}=C_E\times \left|V\right|\times \left[q_s\left(T_s\right)-q_{air}\right]$$

(2)

where:

• $F_{water}$: Moisture flux;
• $C_E$: Bulk transfer coefficient for moisture (dimensionless);
• $\left|V\right|$: Wind speed;
• $q_s$: Specific humidity near surface (due to Clausius–Clapeyron equation,$q_s=q_{saturation}$ near surface);
• $T_s$: Surface skin temperature;
• $q_{air}$: Specific humidity of ambient air.

Then, latent heat flux is parameterized as:

$$F_{water}=\gamma \times F_{Es}=\frac{{\rho }_{liq}}{{\rho }_{air}}\times E$$

(3)

where:

• $\gamma =\frac{C_P}{L_v}=0.4 \frac{{\mathrm{g}}_{\mathrm{water} \mathrm{vapor}}}{{\mathrm{Kg}}_{\mathrm{air}} \times \mathrm{Kelvin}}$, the psychrometric constant;
• $F_{Es}$: Latent heat flux;
• ${\rho }_{liq}:$ Density of pure liquid water;
• ${\rho }_{air}:$ Density of air;
• $E:$ Evaporation rate (mm/day).

Again, to convert from kinematic to dynamic heat flux (W/m²), $F_{Es}$ must be multiplied by air density times the specific heat constant pressure (ρ × c_p) [30].

Initially, the climatic data have been pre-processed with the following steps:

• For temperature, zonal wind and humidity data, the zonal averages have been computed, and the results will be presented in pressure level–latitude axes. This is not necessary for the rest of the parameters, which will be presented in latitude–longitude axes.
• The 1980–2010 climatology have been removed from all time series, according to the World Meteorological Organization (WMO) guidelines, to allow comparison between different data forms on a consistent basis [31].
• A moving average filter has been applied to all time series in order to exclude some periodicities (e.g., seasonality).
• The linear trend has been removed from all time series, due to the fact that the linear regression results can be altered by trends [32], which can be attributed to different causes other than the solar cycle, e.g., an increase in temperature data due to the greenhouse gases increase, etc.

The applied methodology includes the development of a statistical linear regression model, which calculates the dependency of the climatic parameters on the solar activity variation for every point of the global data grid. The dependency is expressed by the regression coefficients (a, b) and, by using the linear regression equation, Equation (4), the climatic parameter values can be estimated for every point in the data grid and for every month.

$$\widehat{y}=a\times \text{F10.7}+b$$

(4)

where:

• $\widehat{y}$: Estimated values of each climatic parameter
• F10.7: Solar proxy data
• a, b: Regression coefficients

Subsequently, the estimated values of the climatic parameters in each of the solar maxima and minima are isolated and averaged respectively, thus producing the mean climatic parameter values in the solar maximum and minimum years (5 ${\widehat{y}}_{Smax}$ and 6 ${\widehat{y}}_{Smin}$; there are five solar maxima and six solar minima in the F10.7 data). Afterwards, the average values of the climatic parameters in solar maximum and minimum conditions ($\overline{{\widehat{y}}_{Smax}}$ and $\overline{{\widehat{y}}_{Smin}}$, respectively) are calculated.

$$\overline{{\widehat{y}}_{Smax}}=\frac{\sum {\widehat{y}}_{Smax}}{5}$$

(5)

$$\overline{{\widehat{y}}_{Smin}}=\frac{\sum {\widehat{y}}_{Smin}}{6}$$

(6)

Finally, the numerical differences in the values of the climatic parameters between solar maximum and minimum conditions are produced. This is the quantity that is presented and discussed in the Results and Discussion sections.

$$\overline{{\widehat{y}}_{Smax}}-\overline{{\widehat{y}}_{Smin}}={\widehat{y}}_{Diffs}$$

(7)

The second objective of this work is to forecast the solar flux time series, and, via the aforementioned regression equations and coefficients, to estimate the response of the climatic system. For the first part we developed and trained an Artificial Neural Network (ANN), and the models are used for forecasting the solar indicator for up to six months in advance. Specifically, we used the Feed Forward Neural Network (FFNN) architecture, and the networks were trained using the Backpropagation Learning Algorithm (BP algorithm) based on the Levenberg Marquardt Algorithm [33,34,35,36,37,38,39]. The main characteristic of the FFNN is that the information is spread in one direction (forward) to the neurons of the next hidden layer. According to the BP algorithm, synaptic weights change with each iteration so as to minimize the mean square error between the inputs (d_k) and outputs (y_k) for k examples of the ANN. In other words, the backpropagation algorithm calculates the gradient of the loss function (J—Equation (8)) with respect to the weights of the network for a single input–output example.

$$J=\frac{1}{2}{\displaystyle \sum }_k{e}_k^2$$

(8)

where:

$$e_k=d_k-y_k$$

(9)

The BP algorithm adapts the synaptic weights (W) so as the loss function becomes minimized between 2 adjacent time steps (t and t+1):

$$J\left(W_{t+1}\right)<J\left(W_t\right)$$

(10)

The weights are adapted until the gradients of the J function are zero, that is, the weights stay the same in every iteration:

$$\nabla J\left(w\right)=0$$

(11)

In order to counter the known local minima problem, we applied the BP algorithm multiple times with different starting conditions. Additionally, to avoid overfitting, we used the early stopping method, which stops the BP algorithm when it detects an increase in the validation error (J_val—Equation (12)):

$$J_{val}=\frac{1}{\left|I_{val}\right|} {\displaystyle \sum }_{i ϵI_{val}}\Vert d^{\left(i\right)}-y^{\left(i\right)}{\Vert }^2$$

(12)

The solar cycle indicator time series were initially divided into training, validation and test sets, following the 70/15/15 percent rule.

The optimum ANN architecture was selected based on minimizing the Mean Absolute Error (MAE) of the validation set. ANNs with 1 to 50 hidden layer neurons were tested in order to find the minimum number of hidden layer neurons for which the ANN exhibits satisfactory generalization ability. Furthermore, each of the 50 ANNs was initiated with 25 random initial conditions, and the optimum ANN is the network that is associated with the minimum MAE for the validation test.

After the selection of the ANN with the optimum architecture, we can predict the solar flux time series for six-month forecasting horizons. The two forecasting periods were from January 2019 to June 2019 and from March 2020 to August 2020.

Then, based on the regression coefficients of the previous step, each of the climatic parameter’s values (${\widehat{y}}_{Forecasted})$ for each time range can be estimated again:

$${\widehat{y}}_{Forecasted}=a\times x_{Forecasted}+b$$

(13)

The climatic parameter’s response to the variation of the solar flux in the selected time periods can be calculated by subtracting from the forecasted climatic parameter’s values their initial values (at January 2019 and March 2020, respectively). The results should indicate how the climate system behaves in response to short-term variations in the solar flux. The implementation of the FFNN forecasts is performed using the MATLAB Deep Learning toolbox.

3. Results

The following Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 show the differences in each climatic parameter’s estimated values between solar maximum and minimum conditions (${\widehat{y}}_{Diffs}$). In all figures, positive values mean that the variable under consideration has larger values in solar maximum conditions compared to solar minimum conditions. The corresponding correlation coefficients between the solar flux time series and each of the climatic parameters falls between −0.5 and 0.5, and the respective figures exhibit similar spatial patterns with Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9. Due to space limitations, they are not presented in this study. An assessment of the possible mechanisms that link solar cycle forcing to the variations in the selected climatic parameters will be presented in the discussion section. In Section 3.7,

Table 1. Spatial distribution of the largest responses of the climatic parameters to the solar cycle.

Parameter	Largest Responses
	Positive Responses	Negative Responses
Temperature	70–90°S/10 hPa 80–90°N/10 hPa 20°S–20°N/100 hPa	85–90°S/850–1000 hPa
Zonal wind	10°S–10°N/100 hPa 0°/20 hPa 15–25°S/10 hPa 30–35°N/10 hPa 75°S/250 hPa 52.5°S/300 hPa	60–65°S/10 hPa 30°S/200 hPa
Relative humidity	15°S–15°N/300 hPa 85°–90°N/700 hPa	87.5°–90°S/500 hPa 65–55°S/300 hPa 65–80°N/300 hPa 30–40°S/850 hPa 35–40°N/850 hPa 5°S–5°N/600–700 hPa
Specific humidity	0°–45°S/1000 hPa 40°S, 10°S, 20°N/1000 hPa 15°S–15°N/400 hPa 85°–90°S/925–1000 hPa 85°–90°N/700 hPa	5°S–5°N/600 hPa 40°Ν/850 hPa 30°S/850 hPa
Surface latent heat flux	West Pacific Ocean Indian Ocean North and South Atlantic Ocean Polar regions	South Pacific Ocean Indian Ocean Central Pacific Ocean Atlantic Ocean (Subtropics)
Surface sensible heat flux	Western South America Central Africa Eastern Australia High latitudes (>60°) of the Northen Hemisphere	Eastern and southern Africa Southern South America Western North America Indonesia Throughout Asia Oceanic regions of the northern and southern Pacific Ocean North of Japan
Cloud cover	North and South America Southern Africa West Pacific Ocean Oceanic region west of Australia South of Australia Antarctica Arctic	South of Australia Antarctica Eastern Asia Saudi Arabia South of South America Southern Pacific Ocean
Precipitable water content	India East Africa South Africa Indian Ocean Southern South America Pacific Ocean	Indonesia North Africa Northern and eastern South America

summarizes the spatial distribution of the largest positive and negative responses of the climatic parameters to the solar cycle.

3.1. Impact on Temperature

Figure 2 shows the numerical difference between solar maximum and solar minimum conditions for temperature (°C) over the period of study. It is evident that the largest positive response, which means that the temperature is greater in solar maximum than in solar minimum conditions, is located in the Antarctic stratosphere (70–90°S/10 hPa) with a difference of $1.6–$1.9 °C. There are more areas of positive response in the Arctic stratosphere (80–90°N/10 hPa) and in the tropical tropopause (20°S–20°N/100 hPa), with ranges of 0.8–1 and 0.5–0.7 °C, respectively. The largest area of negative response is located in the Antarctic troposphere (85–90°S/850–1000 hPa) and the range difference is −0.4–−0.1 °C. All the reported areas of highest differences between solar maximum and solar minimum conditions are statistically significant at the 99.9% level. Similar results regarding the positive responses can be obtained from older studies [10]. Specifically, the positive response regions at 70–90°S/10 hPa, 20°S–20°N/100 hPa and 80–90°N/10 hPa can be associated with areas in similar locations in the reported study, although they have different magnitudes and spatial distribution. Nevertheless, in the study conducted by Crooks and Gray [17], there are two areas of positive response near 50° in the lower troposphere on either side of the equator which cannot be identified in our research. Similarly, the large negative response region at 85–90°S /850–1000 hPa in our study cannot be identified in the study by Crooks and Gray [17].

3.2. Impact on Zonal Wind

Figure 3 shows the difference in the zonal wind speed (m/s) between solar maximum and solar minimum conditions over the study’s period of time. Positive values show that the wind speed is greater at the solar maximum than the solar minimum. The largest positive response areas are located in the equator near the tropopause region (10°S–10°N/100 hPa), and in the equatorial stratosphere (0°/20 hPa, although this region is not statistically significant in the 99.9% level) with a difference of $~$1 m/s. Smaller positive response areas of $~$0.75–0.9 m/s difference are located in the stratosphere in lower-mid latitudes (15–25°S/10 hPa; 30–35°N/10 hPa). Additionally, an area of large negative response of −1.8–−1.9 m/s is located near the Antarctic stratosphere (60–65°S/10 hPa). Other areas of statistically significant positive/negative responses are located at 75°S/250 hPa (0.35), 52.5°S/300 hPa (0.44) and 30°S/200 hPa (−0.76). Similar results are found in other studies [4,17], although the areas of positive/negative responses have differences in magnitudes and their corresponding spatial distribution. In more detail, areas with similar variations in other studies are (a) the equatorial tropopause–troposphere, (b) a small negative response region located at 30°S/200 hPa, (c) a small positive response at 52.5°S/300 hPa, (d) a large negative response around 60–65°S/10 hPa and, lastly, (e) a large positive response around 30–35°N/10 hPa, which can be possibly linked to an area of positive response at 40–45°N/10 hPa in other studies. The negative response area at 15–30°N/10–1000 hPa identified in Gray et al. [4] was not identified in this study.

3.3. Impact on Humidity

The next figures show the impact of the solar cycle on relative and specific humidity. Changes in tropospheric relative humidity (Figure 4) are presented first.

There are two areas of large positive response (greater relative humidity during the solar maximum) which are located in the tropical upper troposphere (1–1.7% at 15°S–15°N/300 hPa) and the Arctic region (1.5–1.8% at 85–90°N/700 hPa). The negative responses (lower relative humidity during the solar maximum) are located at 87.5–90°S/500 hPa (−2.5–−1.5%), 65–55°S/300 hPa (−1.3–−1%), 65–80°N/300 hPa (−1.2–−1%), 30–40°S/850 hPa (−0.9–−0.7%), 35−40°N/850 hPa (−0.35–−0.25) and at 5°S–5°N/600–700 hPa (−0.4–−0.7%).

In Figure 5, which shows the differences in specific humidity between solar maximum and solar minimum conditions, the largest area of positive response is located near the surface in the Southern Hemisphere. This area of positive response extends from the equator to the mid-southern latitudes (0–45°S/1000 hPa), where a difference of approximately 0.06$–$0.08 g/kg is observed. Around 40°S and 10° S, as well as 20°N, at 1000 hPa (where regions with smaller positive responses are located), the areas of positive response are observed to extend vertically. More areas of positive response are located in the tropical upper troposphere (15°S–15°N/400 hPa), with a difference of approximately 0.02–0.03 g/kg, and the Arctic and Antarctic regions (85–90°S/925–1000 hPa and 85–90°N/700 hPa), with differences around 0.02–0.03 g/kg. The largest negative responses (which are not statistically significant) are located in the equatorial troposphere region (5°S–5°N/600 hPa) and in two smaller areas at 40°Ν/850 hPa and 30°S/850 hPa, where differences of approximately −0.02 g/kg are observed. The results regarding specific humidity show that there might be a higher water content during the solar maximum in the southern tropical and subtropical regions (0–45°S) near the surface, and in the tropical upper troposphere (which coincides with the increase in relative humidity).

3.4. Impact on Surface Heat Fluxes

The impact of the solar cycle on surface heat fluxes is assessed for sensible and latent heat flux.

As Equation (1) states, an important driver of sensible heat flux changes is the difference between air and surface skin temperature. Therefore, if a difference in sensible heat flux due to solar forcing is observed, it is an indication that the surface skin temperature might have changed.

Figure 6 shows the differences in surface sensible heat flux between solar maximum and solar minimum conditions. Areas of positive and negative responses can be observed scattered around the globe.

Relatively large positive differences (>5 W/m²) can be seen in western South America, central Africa and eastern Australia, as well as in high latitudes (above 60°) mainly in the Northern Hemisphere. Relatively large negative differences (−10–−5 W/m²) can be seen in eastern and southern Africa, southern South America, western North America, Indonesia and throughout Asia, as well as in the oceanic regions of the northern and southern Pacific (south of South America and Australia) and north of Japan. Relatively small differences (−5–5 W/m²), but mostly positive, can be observed throughout the rest of the world.

As Equation (3) states, an important driver of latent heat flux changes is the evaporation rate. Therefore, if a difference in latent heat flux due to solar forcing is observed, it is an indication that the evaporation rate might have changed.

In Figure 7, which shows the differences in surface latent heat flux between solar maximum and solar minimum conditions, there are several areas of relatively large positive and negative responses scattered around the globe.

It is clear that the tropical and the subtropical oceanic regions (the West Pacific Ocean, Indian Ocean and North and South Atlantic Ocean) are dominated by areas of relatively large positive responses (5$–$10 W/m²), whereas higher latitudes are mostly covered by either large negative (−10–−5 W/m² in the South Pacific Ocean and Indian Ocean) or relatively small negative or positive responses (−5–5 W/m²). There are a few exceptions for this general distribution pattern, such as a few areas of large negative response in the tropics (Central Pacific Ocean) and the subtropics (Atlantic Ocean), and a few areas of large positive response in very high latitudes (near the polar regions). The results show an increase in the surface latent heat flux in tropical and subtropical oceanic regions, which could be linked to an increase in the evaporation rate in the same regions.

3.5. Impact on Cloud Cover

Figure 8 shows the differences in cloud cover (%) between solar maximum and solar minimum conditions. Areas of relatively large positive response (2–5%) are located mostly in a zone which ranges from 45°S to 45°N (North and South America, southern Africa, a region on the West Pacific Ocean and the oceanic region west of Australia). The equator displays mostly negative differences, either large (−5–−2%) or small (−2–0%). An exception to this distribution is a region of large positive response south of Australia, near Antarctica, as well as an area of large positive response in the Arctic. A region of large negative response is located west of the previously reported region of large positive response (south of Australia). More large negative differences can be found close to Antarctica, eastern Asia, Saudi Arabia, south of South America and in the southern Pacific. Relatively small differences (−2–2%), but mostly positive, can be observed throughout the rest of the world. The results indicate that there is an increase in cloud cover in subtropical regions, and a decrease in cloud cover over the equator during the solar maximum.

3.6. Impact on Precipitable Water

Figure 9 shows the differences in precipitable water content (Kg/m²) between solar maximum and solar minimum conditions. All regions with large positive (1–1.5 Kg/m²) and negative (−1.5–−1 Kg/m²) responses are located in a latitudinal range from 30°S to 30°N. Specifically, large positive response areas are located in India (1.5 Kg/m²), the east Africa region (1 Kg/m²), the south Africa region (0.7 Kg/m²), the Indian Ocean (0.8 Kg/m²), southern South America (0.9 Kg/m²) and multiple regions in the Pacific Ocean (close to 1 Kg/m²). Large negative response regions are located in Indonesia (−1 Kg/m²), north Africa (−0.9 Kg/m²) and northern and eastern South America (−1 Kg/m²; −0.8 Kg/m²). Smaller (−1–1 Kg/m²) statistically significant regions with positive and negative responses can be observed throughout the world. Figure 9 could indicate that there is an overall increase in the precipitable water content in tropical and subtropical zones between solar maximum and solar minimum conditions, with some exceptions of smaller (in absolute value) negative responses in specific regions. When we compare the results to other studies, some similarities and differences can be found. In a study by Meehl et al. [40], there is a large area of positive response in southern Africa and the Indian ocean, which might be linked to the positive responses in the same areas in our study, although with different spatial distribution characteristics and magnitudes. Moreover, positive responses are found in the southwest and central-northwest Pacific Ocean, which can be linked to the large area of positive responses in the Pacific Ocean in our study. Lastly, in the same study [40], there is a large area of negative response in northern Australia, which can be linked to an area of negative response close to Indonesia in Figure 9. The main differences between the two studies are a positive response in India, which cannot be identified in the study of Meehl et al. [40], and a negative response in the Central Pacific, which cannot be identified in our study. Perhaps the differences between the two studies can be attributed to the different measurement unit (the figure in Meehl et al. [40] is expressed in mm/day, whereas Figure 9 is expressed in Kg/m²), or to the fact that only the winter months were taken under consideration in the study by Meehl et al. [40] compared to our study, where data from all months were used.

3.7. Summary of Largest Responses

The table below (Table 1) contains the spatial distributions of the largest positive and negative differences of each of the climatic parameters between solar maximum and solar minimum conditions. As we have already mentioned, positive differences mean that larger values are observed during the solar maximum, whereas negative responses mean the opposite.

3.8. ANN Solar Flux Forecasting and Climatic System’s Variation

As previously explained in the methodology section, an ANN was developed and trained for modelling and forecasting the solar flux time series for six monthly steps. In Figure 10, the architecture of the examined ANNs is presented, and in this work the most efficient ANN had a single hidden layer with 27 neurons. Figure 11 shows the comparison between the observed solar flux values and the values estimated by the ANN for each data set (training, validation and test data sets). We trained the ANN by using 800 samples of 12-value input (1 year) and six-value output groups. After the selection of the ANN, we forecasted the solar flux time series in two forecasting periods (January 2019–June 2019; March 2020–August 2020).

Then, after the forecast of the solar flux timeseries, we can use the regression equation and coefficients to estimate the climatic parameter’s values in the same time range as the forecast horizons. We subtract the final state from the initial state, thus calculating the variation of each climatic parameter in the two 6-month time ranges. The climatic parameter’s variations in these time ranges are expected to be minimal, as the solar flux changes slightly. Figure 12 contains the relevant figures.

4. Discussion

Regarding temperature (Figure 2), the areas of positive response can be linked to a few known processes. Primarily, the temperature’s positive response in the stratosphere is probably due to the absorption of UV radiation by ozone. Radiation absorption by stratospheric ozone is more prevalent in the region of 240–320 nm, where the solar cycle variations reach 4% [4]. Furthermore, stratospheric ozone concentrations are shown to correlate positively with the solar cycle [18]. This is mostly due to the enhancing of the photolysis rates during the solar maximum which leads to increased ozone production. As stated in other studies [41,42], ozone is produced and destroyed by the following photochemical reactions, known as the Chapman cycle (Equations (14)–(17)):

$${\mathrm{O}}_2+hv\to \mathrm{O}+\mathrm{O} (\lambda < 242 \mathrm{nm})$$

(14)

$$\mathrm{O}+{\mathrm{O}}_2+M\to {\mathrm{O}}_3+M$$

(15)

$${\mathrm{O}}_3+hv\to {\mathrm{O}}_2+\mathrm{O} \left({}_{}{}^{1}D\right) (240 \mathrm{nm} < \lambda < 320 \mathrm{nm})$$

(16)

$$\mathrm{O}({}_{}{}^{1}D)+M \to \mathrm{O}+M$$

(17)

where Μ is any inert molecule that can absorb energy from the reaction and dissipate it as heat and λ is the wavelength in which the reaction takes place. The Chapman cycle is enhanced when the UV radiation (hv) is increased. However, in addition to Equations (14)–(17), there are more chemical reactions that lead to the destruction of stratospheric ozone (e.g., catalytic destruction), as well as other factors and mechanisms that can further affect stratospheric temperature.

As for the zonal wind parameter, the responses can be attributed to a few possible natural mechanisms, too. One of the mechanisms involves the interaction between planetary waves and the mean circulation flow, which can be possibly linked to the response areas in the equatorial and midlatitude stratosphere. These interactions are said to cause positive responses in the mesosphere, which can propagate downwards in the stratosphere [43]. The large response in the equatorial tropopause–troposphere can be possibly attributed to the enhanced Walker circulation, which is part of the “bottom-up” mechanism and will be discussed below.

The variations of zonal wind, relative and specific humidity, latent and sensible heat fluxes, cloud cover and precipitable water between solar minimum and solar maximum phases can be partially attributed to the “bottom-up” mechanism described in Gray et al. [4] and Meehl et al. [40]. According to this mechanism, increased solar radiation during the solar maximum results in increased radiation absorption by subtropical oceanic regions, resulting in increased surface temperature (which is linked to the sensible heat flux), increased evaporation (linked to latent heat flux), and increased water vapor content in the atmosphere (linked to relative and specific humidity). The increased water vapor converges to the precipitation zones, which then enhances: a) cloud cover; b) the climatological precipitation maximum, and c) the associated upward vertical motions, resulting in stronger trade winds and more vigorous Hadley and Walker circulations. The strengthened circulation results in a stronger downward air motion in subtropical areas and a reduction of cloud cover, thus increasing solar forcing at the surface and creating positive feedback.

Comparing our findings to the “bottom-up” mechanism, the latent heat flux results agree with the mechanism, as there is an overall latent heat flux increase in the subtropics, as well as the relative and specific humidity results, which indicate increased humidity in the precipitation zones. The results for the precipitable water content partially support the reported mechanism, as overall increased precipitation is observed in the tropics. Finally, the strengthened Walker circulation can be possibly seen in the zonal wind differences, where an increase in zonal wind speed in the troposphere near the equator is observed. On the other hand, the results on surface sensible heat flux do not support the reported mechanism, as no strong evidence of increased sensible heat flux in the subtropical areas is observed. The same goes for the cloud cover results where, while increased cloud cover in the equatorial region and decreased cloud cover in the subtropics is expected, the opposite is observed. It should be noted that an additional mechanism has been proposed called the “top-down” mechanism, which states that the solar heating of the stratosphere during solar maximum conditions indirectly influences the troposphere through dynamical coupling, and could lead to strengthened tropical convection and poleward shifting of the Intertropical Convergence Zone (ITCZ) and South Pacific Convergence Zone (SPCZ) [4,40,44]. This additional physical mechanism could induce variations in some of the parameters presented in this study.

5. Conclusions

The results show that the variation of the climatic parameters can be partially attributed to the solar cycle. The solar-induced variation of each of the selected parameters, averaged globally, was of an order of magnitude of 10⁻¹–10⁻³, and the corresponding correlation coefficients (Pearson’s r) were relatively low (−0.5–0.5). Statistically significant areas (>95%) with relatively high solar cycle signals were found in multiple pressure levels and geographical areas, which can be attributed to multiple possible mechanisms.

One of the mechanisms involves the increase in stratospheric ozone concentrations because of the higher UV output by the Sun, and the increase of stratospheric temperature due to the increased stratospheric ozone concentrations. Moreover, statistically significant responses are observed in the subtropical zonal wind, and the explanation possibly involves the interaction of planetary waves with the mean circulation flow. Finally, the results in the remaining climatic parameters can be partially attributed to the ‘’ bottom-up’’ mechanism. The results of this work contribute towards the understanding of the effects of the solar cycle on the terrestrial climate, as it provides more information about the variation of multiple climatic parameters between solar maximum and solar minimum conditions from long-term climatic and solar data sets. Our study also helps to achieve a more holistic view on the subject, as we use multiple climatic parameters which are interconnected.

To conclude, it should be noted that it is difficult to identify a clear solar cycle signal in the climatic parameters’ variations due to the climate system’s complexity, and thus advanced machine learning techniques could be useful in order to obtain a more accurate understanding of this complex research field.