During 2000–2018, annual averages of observed global and diffuse solar irradiance (n= 92,941) were 0.59 and 0.29 MJ m⁻², thus, the direct horizontal irradiance was a little larger than the diffuse irradiance at the surface, average of S/G was 0.64, and averages of surface air temperature and relative humidity were 0.76 °C (ranged from −39.90 to 31.50 °C) and 80.31%, respectively.

Applying the empirical model of global solar irradiance, hourly global irradiance was calculated for Sodankylä during 1 January 2000 to 31 December, 2018. The input data were observed hourly global and diffuse solar irradiance for S/G and water vapor pressure at the ground. Global solar irradiance in December was too low and not considered in the later analysis, and n decreased to 69,171. The calculated and observed hourly global solar irradiance varied similarly, and calculated values were larger than the observed by 18.11% for the average in 2000–2018. It is reasonable that the empirical model represents the global irradiance and its relationships with absorbing and scattering processes at relative clean atmospheric conditions (i.e., relative low S/G at 0.50 in 2008–2011 in the model development). The calculated and observed monthly global irradiance, diffuse irradiance and S/G are shown in Figure 5. Global solar irradiance in June or July was higher over clean atmospheric conditions, e.g., 2001 to 2003, 2007 and 2011 at low S/G (<0.60), but lower over high GLP loading, e.g., 2008, 2009 and 2017 at high S/G (>0.60). Scattering factor S/G was lower during April to September and higher in October to March.

During 19 years, the monthly averages of the calculated global irradiance decreased by 0.01% and diffuse irradiance increased by 0.11% per year, respectively. They were associated with the increases of S/G by 0.14% and water vapor by 0.06%. Air temperature and relative humidity increased by 0.83% (corresponding to 0.01 °C) and 0.23% for monthly average, respectively. On the average, the annual air temperature increased about 2.09 °C during 2000–2018, also indicating the Arctic warming [27].

Long term interannual variations were also investigated during 2000–2018 (Figure 6 and Figure 7). The calculated annual global solar irradiance decreased by 0.92% and diffuse irradiance increased by 1.28% per year, respectively. Both were associated with the increases of S/G by 1.73% and water vapor by 0.43% per year. Annual air temperature increased by 4.64% (corresponding to 0.07 °C), and relative humidity increased by 0.23% per year, respectively. The annual air temperature showed a higher correlation with water vapor (R = 0.79) than with relative humidity (R = 0.20). A good correlation was determined in annual water vapor pressure (E) and air temperature (T) and relative humidity (RH) as E = 0.293 × T + 0.024 × RH + 3.994 (R = 0.828, n = 19, α = 0.001).

Based on above as well as the following integrated results, the increase of air temperature is evidently associated with the increased GLPs, as well as water vapor. If the output of the Sun remains, solar global radiation at the ground would decrease and air temperature increase with the increase of atmospheric substances in the future.

The global solar irradiance losses caused by absorbing and scattering GLPs (G_LA and G_LS) were calculated by using A₁(1-e^−kWm×cos(Z)) and A₂(1-e^−S/G), respectively. The total loss G_L is G_LA + G_LS. The monthly losses due to absorption G_LA dominated the total loss G_L and showed clear seasonal variations, lower in April–September and higher in October–March, whereas G_LS did not have evident seasonal variation and most peaks appeared in October–February. During January 2000 to December, 2018, (1) monthly G_LA decreased slightly by 0.003%, associated with the increase of water vapor by 0.06%; (2) monthly G_LS increased by 0.06%, associated with the increase of S/G by 0.14%; and (3) monthly G_L increased by 0.02% (Figure 8).

For the annual losses of global solar irradiance during 2000–2018, G_LA decreased by 0.02% per year, associating with the increase of E by 0.43%; G_LS increased by 0.72% per year, associating with the increase of S/G by 1.73%; annual G_L increased by 0.24% per year.

The contributions of monthly mean absorbing and scattering losses (R_LA and R_LS) to monthly mean total loss were 63.33% (ranged from 53.95 to 71.99%) and 36.67% (28.01–46.05%), respectively, during January 2000 to December 2018 (Figure 9), corresponding to the monthly averages of water vapor at 6.48 hPa (0.57–14.33) and S/G at 0.55 (0.30–0.94). Generally, R_LA was lower in April–September and higher in October–March, whereas R_LS varied inversely compared to R_LA (i.e., most peaks appeared in October–February). The corresponding annual mean absorbing and scattering losses (R_LA and R_LS) to annual mean total loss were 63.32% (60.09–65.48%) and 36.68% (34.52–39.04%), respectively.

During 2000–2018 at Sodankylä, the annual mean monthly loss of G_LA, G_LS and G_L were 1.94 (1.57–2.41), 1.17 (0.82–1.53) and 3.11 (2.50–3.90) MJ m⁻², corresponding to 539.82, 323.86 and 863.68 W m⁻², respectively.