Trends and Interdependence of Solar Radiation and Air Temperature—A Case Study from Germany

: This study characterizes the spatiotemporal solar radiation and air temperature patterns and their dependence on the general atmospheric circulation characterized by the North Atlantic Oscillation (NAO) Index in Germany from 1991 to 2015. Germany was selected as the study area because it can be subdivided into three climatologically different regions: the North German lowlands are under the maritime inﬂuence of the North and Baltic Seas. Several low mountain ranges dominate Germany’s center. In the south, the highest low mountain ranges and the Alps govern solar radiation and air temperature differently. Solar radiation and air temperature patterns were studied in the context of the NAO index using daily values from satellite and ground measurements. The most signiﬁcant long-term solar radiation increase was observed in spring, mainly due to seasonal changes in cloud cover. Air temperature shows a noticeable increase in spring and autumn. Solar radiation and air temperature were signiﬁcantly correlated in spring and autumn, with correlation coefﬁcient values up to 0.93. In addition, a signiﬁcant dependence of solar radiation and air temperature on the NAO index was revealed, with correlation coefﬁcient values greater than 0.66. The results obtained are important not only for studies on the climate of the study area but also for photovoltaic system operators to design their systems. They need to be massively expanded to support Germany’s climate neutrality ambitions until 2045.


Introduction
Changes in atmospheric transmission due to variations in cloudiness and aerosol concentration are the main factors causing trends in incoming solar radiation on a horizontal surface (SIS) penetrating the atmosphere and finally being available at the Earth's surface for the generation of solar energy.
Due to aerosol-cloud interactions and aerosol and water vapor's indirect effects on SIS, these factors are not mutually exclusive in explaining SIS changes. In order to investigate their influence, a study was carried out on the Mediterranean area as this region is one of the maritime areas with very high relative humidity and the largest aerosol loads in the world [1]. The authors used satellite data, specifically CERES (Clouds and the Earth's Radiant Energy System) SYN1deg products. Their results show that the spatial distribution of aerosol and water vapor are closely linked to the spatial distributions of its effects on solar radiation. The air constituents cause a SIS reduction between 2.0-8.0% due to aerosol and 11.5-15.0% due to water vapor effects. The authors found the greatest effects of aerosol and water vapor on SIS in the period from July to September.
Variations in SIS also cause variations in surface air temperature (TAS). Although SIS warms the air only during the day, its variability is related to the variability of daily TAS amplitude on monthly and decadal time scales [2].
Since data records are available up to 1970, a decrease in TAS due to the reduced input of SIS was detected [3]. The authors combined the temperature data with radiation data and additional components of the hemispheric energy budget. The relationship between the change in SIS and the change in TAS was applied to the reported trends in direct solar

Materials and Methods
The analysis of the spatiotemporal SIS and TAS variability comprises the following steps: (1) Obtaining daily mean values of SIS and TAS with a horizontal resolution of 0.05 • × 0.05 • for the 25-year period 1991-2015, (2) investigating the spatiotemporal variability of both variables by means of trend analysis and analysis of their inter-and intra-annual variability, (3) correlating SIS and TAS, and (4) correlating SIS and TAS with NI. The results were converted to a 10-year period (decade) to make them comparable with results from other studies.
All steps of data preparation and analysis were performed with the Satellite Application Facility on Climate Monitoring (CM SAF) R Toolbox software [17] and the Mathworks (Natick, MA, USA) Matlab software, version 2021b.
All figures showing the results for the study area are oriented north-south and have a scale of 1 cm equals 165 km.

Data
Daily mean values from the Surface Solar Radiation Data Set-Heliosat (SARAH)-Edition 2.1 were used for SIS analysis [18]. They are available on a regular grid. The SIS data records are based on observations of the MVIRI and SEVIRI instruments on board of the first and second generations of METEOSAT satellites. Preparation and provision of SIS data were carried out by CM SAF [19]. Further details on the uncertainty of SIS are given in [20].
The daily mean TAS data records for the same period were taken from the HYRAS dataset [21], interpolated on the same grid as for SIS, and finally merged into one file containing all 25-year data records. This study [21] provides information on HYRAS data quality. Monthly NI means are available on the US National Weather Service's Climate Prediction Center website [16].

Assessment of Spatiotemporal Variability
The spatiotemporal variability and the long-term development of SIS and TAS were estimated by calculating mean values over the study period (SIS P , TAS P ) at the grid cells and the study area. Monthly averages identified the SIS (SIS M ) and TAS (TAS M ) changes over the year. The long-term change (trend) in SIS (SIS T ) and TAS (TAS T ) is quantified by multiplying the slope of the trend lines by the respective interval length. The significance of SIS T and TAS T was determined by applying the Mann-Kendall test at a confidence level of α = 0.05 [22].
In contrast to a previous study [23], the inter-annual variability (IAV) was not expressed in relative terms. To obtain absolute values that more clearly highlight the differences in magnitude between individual months and years, monthly and annual SIS IAV and TAS IAV values were calculated as the range (maximum minus minimum values) of differences in mean values.

Assessment of the Correlation between SIS and TAS
An immediate reaction of TAS to a change in SIS cannot be expected, as both natural and anthropogenic air pollution within the atmosphere lead initially to the absorption and scattering of SIS. A further reduction in SIS occurs due to the varying degree of coverage. [24]. Finally, TAS reacts to these influences. A study of the correlation between SIS and TAS can therefore only provide reasonable results for the four seasons. In addition, it should be considered that SIS values are available only for daylight hours, while TAS describes the course of air temperature over the whole day.
To find possible reasons for the relationship between SIS and TAS, data from NI were included in the correlation analysis. NI characterizes the atmospheric circulation between North America and Europe transporting air masses of different temperatures into the study area. NI is defined as the difference between the normalized winter air pressures at sea level in Lisbon and Stykkisholmur (Iceland) [25]. A positive NI is found if its contrast is higher than average due to a very low pressure over Iceland and a very high pressure over the Azores with strong westerly winds over the North Atlantic between 40 • and 60 • N. The corresponding circulation leads to mild winters and abundant rainfall over Europe to Siberia and the American East Coast, while over the Mediterranean to the Near East there is drought and relatively cold winters. With a negative NI, the pressure contrast between the Icelandic low and the Azores high is significantly reduced. This stands for weaker westerly winds and an occurrence of relatively mild and humid winters in the Mediterranean and cold and dry periods in Europe and on the American East Coast. Figure 1a shows the large-scale distribution of SIS P with decreasing values from south to north. The large-scale pattern is superimposed by regional and local patterns, which are mainly influenced by orography [20].  Despite a noticeable increase in SIS in spring, this corresponds only with a small increase in TAS. Only with a delay of almost six months could a significant increase in TAS be observed in autumn. The reasons for this are: (1) the input of radiation energy into the atmosphere occurs only during daylight hours. Only in summer is the radiation input the largest due to the long daylight hours corresponding with the greatest elevation of the sun. The TAS values used in the study, on the other hand, cover the whole day. Therefore, the high amounts of solar energy available in summer can only lead to a significant increase in TAS in autumn. (2) Although the input of solar energy controls the different processes in the atmosphere and at the Earth's surface, it does not directly affect the change in TAS.

Annual Mean Pattern and Trends
The inter-annual variability SISIAV ( Figure 2a) shows a greater variability of SIS than the long-term trend SIST. In the western parts of the study area, SISIAV exceeds 45 W/m 2 . SISIAV decreases towards the east and northeast and fluctuates there in the range of 20-35 W/m 2 . In the south, there is an area stretching west-east where SISIAV is lower than in the   Figure 1c). Their total change SIS T is 2.4 W/m 2 /10 yr. This result fits well with trends based on surface measurements in Central Europe reported in another study [26]. The relative standard deviation of SIS A equals 3.9%, corresponding to an absolute value of 4.9 W/m 2 . This matches with the findings of [27] who found a SIS A variation with a relative standard deviation of 4-6% in most parts of Central Europe. A study of the spatiotemporal SIS variability over the Eastern Mediterranean in 1983-2013, using data records of SIS from the same source as used in this study, found a positive (brightening) and statistically significant SIS T at the confidence level α = 95% with 2 ± 0.05 W/m 2 /10 yr, with on-and offshore being almost equal [28].
The long-term change in TAS annual mean values (TAS A ) is significantly positive ( Figure 1d) with a total change in TAS T of 0.32 K/10 yr. A total change in TAS of 0.25 K/10 yr based on a 65-year data record was found in [5]. The relative standard deviation of the annual mean values of TAS equals 6.3%, corresponding to an absolute value of 0.57 • C.
The mean decadal changes of seasonal SIS and TAS and SIS A and TAS A values are summarized in Table 1. The annual and seasonal values for spring to autumn for ∆SIS represent more than 80% of all grid cells. Only 10% of the grid cells show a significant trend in winter. In contrast, the seasonal and annual trends of ∆TAS are only significant in autumn and to a lesser extent also for the year. Parallel to the positive trend of TAS in autumn, SIS also shows a similar trend. Only in winter does TAS not show any trend. In a study using the same SIS data records and the same period as the present study, but applied to the region of Piedmont (Northwest Italy), SIS showed an increase of about +2.5%/10 yr for annual averages, with the strongest trend in autumn (+4%/10 yr) [29]. Only in winter was a negative but non-significant trend found. A study of the spring period for the area of Germany using a 65-year TAS record (1951-2015) revealed an increase of 1.6 K for the whole period, or 0.30 K/10 yr [5]. This trend value is well in line with the corresponding spring value found in this study (Table 1).
Despite a noticeable increase in SIS in spring, this corresponds only with a small increase in TAS. Only with a delay of almost six months could a significant increase in TAS be observed in autumn. The reasons for this are: (1) the input of radiation energy into the atmosphere occurs only during daylight hours. Only in summer is the radiation input the largest due to the long daylight hours corresponding with the greatest elevation of the sun.
The TAS values used in the study, on the other hand, cover the whole day. Therefore, the high amounts of solar energy available in summer can only lead to a significant increase in TAS in autumn. (2) Although the input of solar energy controls the different processes in the atmosphere and at the Earth's surface, it does not directly affect the change in TAS.
The inter-annual variability SIS IAV (Figure 2a) shows a greater variability of SIS than the long-term trend SIS T . In the western parts of the study area, SIS IAV exceeds 45 W/m 2 . SIS IAV decreases towards the east and northeast and fluctuates there in the range of 20-35 W/m 2 . In the south, there is an area stretching west-east where SIS IAV is lower than in the surrounding areas. Here, in the Danube basin, SIS IAV is noticeably reduced compared to the surrounding areas. Near the northern coasts, the annual SIS variability is lowest, with SIS IAV values usually fluctuating in the range of 17-25 W/m 2 . The mean and standard deviation of SIS IAV is 34 ± 5 W/m 2 . The inter-annual variability of TASIAV (Figure 2b) also shows a greater variability of TAS than the long-term trend TAST. The mean spatial pattern of TASIAV is roughly divided into two parts: In the south and southwest of Germany, TASIAV is between 2 and 3 K, and in the north and northeast it is up to 5 K. The heat islands of the cities (Berlin, Halle/Leipzig, Dresden, Chemnitz, Hamburg, and Bremen) are clearly visible with values of 5 K. This confirms the findings of a previous study [5] mentioned above.

Trends and Inter-Annual Variability
Different methods of generating electricity require knowledge of the long-term trend of incoming solar energy. For this purpose, the long-term SIS values (SIST) were calculated The inter-annual variability of TAS IAV (Figure 2b) also shows a greater variability of TAS than the long-term trend TAS T . The mean spatial pattern of TAS IAV is roughly divided into two parts: In the south and southwest of Germany, TAS IAV is between 2 and 3 K, and in the north and northeast it is up to 5 K. The heat islands of the cities (Berlin, Halle/Leipzig, Dresden, Chemnitz, Hamburg, and Bremen) are clearly visible with values of 5 K. This confirms the findings of a previous study [5] mentioned above.

Trends and Inter-Annual Variability
Different methods of generating electricity require knowledge of the long-term trend of incoming solar energy. For this purpose, the long-term SIS values (SIS T ) were calculated for each grid cell and month for the study period. As a result, Figure 3a shows the monthly frequency distributions of the trends in violin plots. The width of each individual violin is a measure of the frequency of the respective monthly trend. The upward and downward peaks of the violins indicate the extreme values of the monthly trends. The median values of the trends are given as numerical values at the respective black dots.
Meteorology 2022, 2, FOR PEER REVIEW 7 of Germany [5]. The phenomenon of TAS increase in late summer and early autumn has already been reported earlier [30]. The month with the most pronounced trends in SIS and TAS is April (Figure 4). The most significant increase of SIST up to 15 W/m 2 /10 yr can be seen in Northwestern Germany as well as in Bavaria. The negative trend of cloud fractional cover (CFCT) in April of −4.1%/10 yr favors this development, further details on CFCT can be found in Figure 6 and are given in the corresponding text in [20]. From Eastern to Southwestern Germany, an area with a value of SIST around 5 W/m 2 /10 yr is discernible. Again, this behavior can be explained by the variability in CFC.
Regarding TAST in April, Germany is divided into two parts: In the northern part there is hardly any trend (<0.5 K/10 yr), while the southern part of Germany shows values up to 1.2 K/10 yr. This is in line with a previous study [5] that found an average trend of TAS in Northern Germany of 0.30 K/10 yr and for Southern Germany of 0.28 K/10 yr for a 65-year period .
This underlines the well-known fact that there has been a significant increase in TAS, especially in the last decade of the study period analyzed by [5]. An increase in TAS can be expected when the NI is positive [31]. In almost all years, the NI values are positive in April. The spatial distribution of the SIS variability in the individual months shows a pronounced annual cycle. Here it should be mentioned briefly that SIS IAV shows a much wider range of variation in all months than SIS T .
The violin plots for TAS T shown in Figure 3b were calculated using the same method as those violin plots of SIS T shown in Figure 3a. The long-term monthly grid cell values of the TAS T trend also show conspicuous values in two periods of the year (Figure 3b). April shows a noticeable long-term mean increase of TAS T = 0.8 K/10 yr. From August to December, TAS T values increase continuously up to 1.0 K/10 yr. For April, another study found similar TAS trend values of 0.5 K/10 yr for the north and 0.2 K/10 yr for the south of Germany [5]. The phenomenon of TAS increase in late summer and early autumn has already been reported earlier [30].
The month with the most pronounced trends in SIS and TAS is April (Figure 4). The most significant increase of SIS T up to 15 W/m 2 /10 yr can be seen in Northwestern Germany as well as in Bavaria. The negative trend of cloud fractional cover (CFC T ) in April of −4.1%/10 yr favors this development, further details on CFC T can be found in Figure 6 and are given in the corresponding text in [20]. From Eastern to Southwestern Germany, an area with a value of SIS T around 5 W/m 2 /10 yr is discernible. Again, this behavior can be explained by the variability in CFC.
The month with the most pronounced trends in SIS and TAS is April (Figure 4). The most significant increase of SIST up to 15 W/m 2 /10 yr can be seen in Northwestern Germany as well as in Bavaria. The negative trend of cloud fractional cover (CFCT) in April of −4.1%/10 yr favors this development, further details on CFCT can be found in Figure 6 and are given in the corresponding text in [20]. From Eastern to Southwestern Germany, an area with a value of SIST around 5 W/m 2 /10 yr is discernible. Again, this behavior can be explained by the variability in CFC.
Regarding TAST in April, Germany is divided into two parts: In the northern part there is hardly any trend (<0.5 K/10 yr), while the southern part of Germany shows values up to 1.2 K/10 yr. This is in line with a previous study [5] that found an average trend of TAS in Northern Germany of 0.30 K/10 yr and for Southern Germany of 0.28 K/10 yr for a 65-year period .
This underlines the well-known fact that there has been a significant increase in TAS, especially in the last decade of the study period analyzed by [5]. An increase in TAS can be expected when the NI is positive [31]. In almost all years, the NI values are positive in April.  Regarding TAS T in April, Germany is divided into two parts: In the northern part there is hardly any trend (<0.5 K/10 yr), while the southern part of Germany shows values up to 1.2 K/10 yr. This is in line with a previous study [5] that found an average trend of TAS in Northern Germany of 0.30 K/10 yr and for Southern Germany of 0.28 K/10 yr for a 65-year period .
This underlines the well-known fact that there has been a significant increase in TAS, especially in the last decade of the study period analyzed by [5]. An increase in TAS can be expected when the NI is positive [31]. In almost all years, the NI values are positive in April.
Since Figure 3 shows the most striking trend in SIS and to some extent also in TAS in spring, the seasonal anomalies of SIS (SIS MAM ) and TAS (TAS MAM ) in spring are shown in Figure 5. Increasing SIS MAM coincides with an increase in TAS MAM . In addition to the correlation between SIS MAM and TAS MAM , the fluctuations of SIS MAM and TAS MAM within the study period were investigated. It was found that large fluctuations of SIS MAM are associated with large fluctuations of TAS MAM . For Europe, a correlation coefficient between R = 0.73 and R = 0.86 was found in [2]. Especially for the years from 1990 onwards, the authors calculated high correlation values for the summer months.
Meteorology 2022, 2, FOR PEER REVIEW 8 Since Figure 3 shows the most striking trend in SIS and to some extent also in TAS in spring, the seasonal anomalies of SIS (SISMAM) and TAS (TASMAM) in spring are shown in Figure 5. Increasing SISMAM coincides with an increase in TASMAM. In addition to the correlation between SISMAM and TASMAM, the fluctuations of SISMAM and TASMAM within the study period were investigated. It was found that large fluctuations of SISMAM are associated with large fluctuations of TASMAM. For Europe, a correlation coefficient between R = 0.73 and R = 0.86 was found in [2]. Especially for the years from 1990 onwards, the authors calculated high correlation values for the summer months.

Changes in High SISMAM and TASMAM Values
For the dimensioning of PV plants, their operators do not need the long-term means of SIS and TAS, but rather, information on how often the given thresholds are exceeded. Corresponding results are given here.

Changes in High SIS MAM and TAS MAM Values
For the dimensioning of PV plants, their operators do not need the long-term means of SIS and TAS, but rather, information on how often the given thresholds are exceeded. Corresponding results are given here.
Since the most significant changes in SIS and TAS are to be expected in spring, Figure 6a displays the spatial patterns of SIS MAM . In Southern Germany, higher SIS MAM values are found than in the north. The low mountains in Central Germany are characterized by significantly lower SIS MAM values.
Meteorology 2022, 2, FOR PEER REVIEW 9 is exceeded in between 5% and 10% of all cases. The limit value of 20 °C is exceeded in only 3% of all cases.  The long-term means of SIS MAM are between 120 and 190 W/m 2 . In cases of cloudless sky, the average daily irradiance in the study area may be up to 500 W/m 2 .
Since hardly a significant number of events could be detected above 300 W/m 2 , the number of SIS MAM values exceeding the thresholds of 150, 200, and 250 W/m 2 was investigated. Figure 6c- In at least 50% of all cells, TAS MAM = 10 • C is exceeded. The lowlands are marked with 15% and the Rhine Valley with 60% of all the cases. The limit value of TAS MAM = 15 • C is exceeded in 22% of all cases in the Rhine Valley. In the other areas of Germany, this limit is exceeded in between 5% and 10% of all cases. The limit value of 20 • C is exceeded in only 3% of all cases.
Additional information on the long-term increase of SIS MAM and TAS MAM can be obtained by studying the increase in the number of events in individual SIS MAM and TAS MAM ranges. Due to the development of solar energy applications over recent years, there is an increasing need to study the transition of SIS MAM and TAS MAM to higher levels. Therefore, the long-term change in the number of events in the SIS MAM range of 150-200 W/m 2 and in the TAS MAM range of 10-15 • C is displayed in Figure 7. The trends of SIS MAM and TAS MAM significantly increase.
Meteorology 2022, 2, FOR PEER REVIEW 10 Additional information on the long-term increase of SISMAM and TASMAM can be obtained by studying the increase in the number of events in individual SISMAM and TASMAM ranges. Due to the development of solar energy applications over recent years, there is an increasing need to study the transition of SISMAM and TASMAM to higher levels. Therefore, the long-term change in the number of events in the SISMAM range of 150-200 W/m 2 and in the TASMAM range of 10-15 °C is displayed in Figure 7. The trends of SISMAM and TASMAM significantly increase.

Influence of the NAO Index on SIS and TAS
As an example, for April, the correlations between NI and SIS (SISApril) and NI and TAS (TASApril) are shown in Figure 8.

Influence of the NAO Index on SIS and TAS
As an example, for April, the correlations between NI and SIS (SIS April ) and NI and TAS (TAS April ) are shown in Figure 8.

Influence of the NAO Index on SIS and TAS
As an example, for April, the correlations between NI and SIS (SISApril) and NI and TAS (TASApril) are shown in Figure 8.   Table 2. We found, similar to the study of [6], an interdependence of SIS, TAS, and NI of about 0.40-0.60 for the study area.
With the exception of January, the monthly R SIS,TAS is positive. In July, which has the longest light days, R SIS,TAS = 0.93. The correlation from April to September is significant at p < 0.05.
In the winter months, the high and also significant R NI,TAS values are striking. During this time, TAS is essentially determined by high NI, which is responsible for a pronounced westerly wind circulation. The same was found for the BSRN station Tartu-Tõravere in Estonia [6] which indicates that atmospheric circulation is an important factor controlling TAS in the study areas.
The results in [6] differ slightly from those of our study for several reasons: (1) we used data records from a larger area (48 • N-55 • N/6 • E-15 • E) rather than from a single station (BSRN station Tartu-Tõravere in Estonia), (2) the station is located about 5 • further north (about 500 km) than the northernmost point of Germany. Thus, in the winter months, the days of light are significantly shorter than those in Germany. In the summer months, the ratio reverses in favor of Tartu-Tõravere. (3) The two study periods are not identical: The author [6] used data records from the period 1955-2007.

Correlation between SIS and TAS
The similar long-term increase in SIS and TAS in April and October presented in Figure 3 stimulated a correlation analysis of these two variables. A good correlation between these variables was also found by [3].

Ratio of Temperature and Solar Radiation
Finally, the regional structure of the long-term ratio TAS/SIS in the four seasons is given in Figure 10a-d. In all four seasons, the ratio is between 0 and 0.15 K/W/m 2 . The larger the quotient (light areas), the more TAS reacts on an increase in SIS. This is clearly visible in all four seasons in the large basins in Southwestern Germany. While spring and autumn have hardly any regional structure but a strong correlation, the strong increase in autumn is particularly noticeable in Northern Germany. In winter, the sign of K/W/m 2 reverses in Southern Germany and in the low mountains, while in the north it remains positive. This regional two-part behavior is also evident from the fact that the correlation between SIS and TAS is unstructured in these seasons. This behavior is determined on the one hand by changes in the NI and the lower inter-annual variability of cloud cover [20].

Ratio of Temperature and Solar Radiation
Finally, the regional structure of the long-term ratio TAS/SIS in the four seasons is given in Figure 10a-d. In all four seasons, the ratio is between 0 and 0.15 K/W/m 2 . The larger the quotient (light areas), the more TAS reacts on an increase in SIS. This is clearly visible in all four seasons in the large basins in Southwestern Germany. While spring and autumn have hardly any regional structure but a strong correlation, the strong increase in autumn is particularly noticeable in Northern Germany. In winter, the sign of K/W/m 2 reverses in Southern Germany and in the low mountains, while in the north it remains positive. This regional two-part behavior is also evident from the fact that the correlation between SIS and TAS is unstructured in these seasons. This behavior is determined on the one hand by changes in the NI and the lower inter-annual variability of cloud cover [20].

Conclusions
To mitigate climate change, solar energy must play an increasingly important role in today and tomorrow's global energy supply. Before deciding to install PV systems in a particular area, a thorough analysis of the long-term spatial and temporal trends of solar radiation and surface air temperature is required. The following characteristic parameters of surface incoming solar radiation and surface air temperature are important for PV system operators to optimize their systems: long-term averages in the individual regions, the long-term trend of mean values and their variability, and finally an increase in exceedances of specified thresholds.
For the climate of the study area, we found a simultaneous long-term increase in incoming solar radiation and air temperature in spring. A further increase in surface air temperature was observed in autumn. The annual variability of incoming solar radiation and surface air temperature is much greater than their long-term variability.
Although an increase in solar radiation does not directly result in an increase in surface air temperature, an influence of solar radiation on surface air temperature was shown.
It was found that the TAS/SIS ratio is always positive, except in winter. This indicates a slight but almost equal interdependence of the two variables in the whole study area. Due to the short period of light days in winter, the ratios are unclear in this season.
The variable input of solar radiation in the study area influences the large-scale circulation, expressed by the variability of the NAO index. This quantity then controls the change in surface air temperature. These interdependencies are responsible for the efficiency of the PV systems and must therefore be considered by the operators of PV systems.

Conclusions
To mitigate climate change, solar energy must play an increasingly important role in today and tomorrow's global energy supply. Before deciding to install PV systems in a particular area, a thorough analysis of the long-term spatial and temporal trends of solar radiation and surface air temperature is required. The following characteristic parameters of surface incoming solar radiation and surface air temperature are important for PV system operators to optimize their systems: long-term averages in the individual regions, the long-term trend of mean values and their variability, and finally an increase in exceedances of specified thresholds.
For the climate of the study area, we found a simultaneous long-term increase in incoming solar radiation and air temperature in spring. A further increase in surface air temperature was observed in autumn. The annual variability of incoming solar radiation and surface air temperature is much greater than their long-term variability.
Although an increase in solar radiation does not directly result in an increase in surface air temperature, an influence of solar radiation on surface air temperature was shown.
It was found that the TAS/SIS ratio is always positive, except in winter. This indicates a slight but almost equal interdependence of the two variables in the whole study area. Due to the short period of light days in winter, the ratios are unclear in this season.
The variable input of solar radiation in the study area influences the large-scale circulation, expressed by the variability of the NAO index. This quantity then controls the change in surface air temperature. These interdependencies are responsible for the efficiency of the PV systems and must therefore be considered by the operators of PV systems. Data Availability Statement: SIS-data are available online: https://wui.cmsaf.eu/safira/action/ viewProduktDetails;jsessionid=A57DBBCF8B91A1018C4978343231BB1B.ku_1?fid=28&eid=21833_22 009, TAS-data are available online: https://opendata.dwd.de/climate_environment/CDC/grids_ germany/daily/hyras_de/air_temperature_mean/, NAO-Index-Data are available online: https: //www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/norm.nao.monthly.b5001.current.ascii.

Conflicts of Interest:
The author declares no conflict of interest.