## 2 Materials and Methods
### Estimation of Radiation Indices  
The following indices are used for the assessment of radiation levels on the surface: \(k_{n}\), \(k_{t}\), \(k_{b}\), and \(k_{d}\). \(K_{n}\) is the ratio of direct normal irradiance (\(B_{n}\)) to the extraterrestrial one (\(G_{0n}\)). The ratio of horizontal beam irradiance (\(B\)) to the global irradiance \(G\) is defined as \(k_{b}\); \(k_{d}\) is the fraction of diffuse irradiance (\(D\)) to the global (\(G\)); \(k_{t}\) is the clearness index, i.e., the ratio of global irradiance to the horizontal extraterrestrial irradiance:  
\[k_{n}=B_{n}/G_{0n} \tag{12}\]  
\[k_{t}=G/G_{0} \tag{13}\]  
\[k_{b}=B/G \tag{14}\]  
\[k_{d}=D/G \tag{15}\]  
The upper bound of the ratios is 1, although \(k_{d}\) can be slightly higher than 1 (i.e., 1.15). This usually occurs in the morning after sunrise or in the afternoon before sunset when the solar elevation angle is low, and the diffuse irradiance is slightly higher than that of global irradiance due to the cosine effect of the lower sun angles. Therefore, to avoid this problem, cases of diffuse irradiances below 5\({}^{\circ}\) of sun elevation angle were excluded from the data set [29]. Only few observations are considered invalid when low \(k_{t}\) values are associated with low \(k_{t}\) values. This occurs when the sensor is covered with environmental debris. The above ratios can be obtained from both the hourly and daily values. The capital letters and subscripts represent the daily values, while the small letters represent the hourly values. Sky Conditions Classification  
Prior to the analysis of the global solar irradiance, it is constructive to categorize the sky conditions at Athalassa. For this purpose, four sky categories have been proposed by [PERSON] et al. (2009) [30], based on the relation between hourly irradiances of global, direct and diffuse radiation and the clearness index (\(k_{t}\)). Figure 2 indicates the block-averaged curves for global, direct and diffuse solar radiation in terms of \(k_{t}\) (0-1) into subintervals of 0.05 sizes. The four intervals of sky conditions are defined as follows:  
_Interval i_: \(k_{t}\leq 0.35\) and the direct component of the global solar radiation at the surface is practically zero. Therefore, global and diffuse solar radiations are equal, and the sky condition is defined as totally covered by clouds or cloudy sky;  
_Interval ii_: \(0.35<k_{t}\leq 0.55\). The global solar radiation is composed by a fraction of diffuse component which is larger than the fraction of direct component, and the diffuse fraction is decreasing with increasing \(k_{t}\). The upper limit of this interval is set where diffuse equals direct component of the solar radiation (approximately at 100 W/m\({}^{2}\) and at \(k_{t}=0.55\)). In this case, the sky condition is defined as partially cloudy with predominance of diffuse component of the solar radiation because the radiation field is predominantly composed by diffuse radiation;  
_Interval iii_: \(0.55<k_{t}\leq 0.65\). The global solar radiation is composed by a fraction of diffuse component that is smaller than the fraction of direct component and the diffuse fraction is decreasing with \(k_{t}\) until 0.65, which is considered as the end of the partially cloudy interval. In this case, the sky condition is partially cloudy with the predominance of a direct component of the solar radiation;  
Figure 2: Block-average values of global, diffuse and direct components of solar radiation, at the surface, in terms of clearness index intervals. Vertical dashed lines define regions of \(k_{t}\) values associated to sky conditions and identified by i (cloudy sky), ii (partially cloudy with predominance of diffuse component), iii (partially cloudy with predominance of direct component) and iv (clear sky) interval. _Interval iv:_\(k_{t}>0.65\). The global solar radiation at the surface is composed by mainly the direct component of solar radiation and the diffuse contribution is very small, indicating that there is no significant cloud cover.