## 2 Materials and Methods
### Quality Control Procedure
#### 2.5.4 Quality Control of Daily Values  
The quality control process was also extended to the daily sums of global solar radiation and daily sunshine duration values. Firstly, the daily values of global irradiation (\(G_{d}\)) were checked against the extraterrestrial daily irradiation (\(G_{0d}\)) (Table 4). The daily values of \(G_{d}\) should be lower than \(G_{0d}\), but they should be higher than the lowest limit of 0.03 \(\times\)\(G_{d}\) during overcast conditions [43]. As it can be seen in Figure 11, \(G_{d}\) is lower than the upper limits of \(G_{0d}\) and 0.8 \(\times\)\(G_{0d}\). The graph also shows that the daily direct horizontal irradiation (\(B_{d}\)) is lower than the ERL threshold of 0.8 \(\times\)\(G_{0d}\). Similarly, the diffuse irradiation (\(D_{d}\)) is lower than the threshold of \(G_{0d}\)*0.7. Generally, all daily radiation values are within their upper limits defined by PPL and ERL criteria. The second test is a comparison test between the extreme values of daily sums of global irradiation and the respective estimated daily sums on clear days. \(G_{d}\) should be lower than the product of 1.1 \(\times\)\(G_{cd}\). As can be seen in Figure 11, \(G_{d}\) is slightly higher than the product of 1.1 \(\times\)\(G_{cd}\) at least in some cases during the first half of the year. Figure 10: (**a**) linear regression of the estimated sum of the measured irradiances (\(B+D\)) and the relevant global irradiances (\(G\)); and (**b**) Ratio of \(G/(B+D)\) as a function of solar zenith angle (SZA) with the reference lines within the ratio should be detected. The sums of the daily values of direct horizontal and diffuse irradiation (\(B_{d}+D_{d}\)) are closely compared with the daily global irradiation (\(G_{d}\)) as shown in Figure 12.  
Figure 13 shows the linear relationship between the daily clearness index (\(K_{T}\)) and the daily relative sunshine (\(\sigma\)). Most of the values are within the 95% prediction intervals. According to [PERSON] and [PERSON] (2013), if the deviations of the pairs \(K_{T}\) and \(\sigma\) from the regression line are greater than 0.3, then the pairs are considered as suspect. Generally, the deviations are lower than 0.3. Additionally, the daily sums of sunshine duration (\(S_{d}\)) are lower than the astronomical d \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **PPL ERL** & **Upper Limit (MJ/m\({}^{2}\))** \\ \hline Global irradiation (\(G_{d}\)) vs. \(G_{0d}\) & PPL & \(G_{d}<G_{0d}\) \\ \hline Global irradiation (\(G_{d}\)) vs. \(G_{0d}\) & ERL & \(G_{d}<0.8\)\(\times\)\(G_{0d}\) \\ \hline Global irradiation (\(G_{d}\)) vs. \(G_{cd}\) & ERL & \(G_{d}<1.1\)\(\times\)\(G_{cd}\) \\ \hline Diffuse irradiation (\(D_{d}\)) vs. \(G_{0d}\) & PPL & \(D_{d}<1.0\)\(\times\)\(G_{0d}\) \\ \hline Diffuse irradiation (\(D_{d}\)) vs. \(G_{0d}\) & ERL & \(D_{d}<0.7\)\(\times\)\(G_{0d}\) \\ \hline Beam Normal irrad. (\(B_{nd}\)) vs. \(G_{0 nd}\) & PPL & \(B_{nd}<1.0\)\(\times\)\(G_{0 nd}\) \\ \hline Beam Normal irrad. (\(B_{nd}\)) vs. \(G_{0 nd}\) & ERL & \(B_{nd}<0.8\)\(\times\)\(G_{0 nd}\) \\ \hline Beam Horizontal irrad. (\(B_{d}\)) vs. \(G_{0d}\) & PPL & \(B_{d}<1.0\)\(\times\)\(G_{0d}\) \\ \hline Beam Horizontal irrad. (\(B_{d}\)) vs. \(B_{cd}\) & PPL & \(B_{d}<1.1\)\(\times\)\(B_{cd}\) \\ \hline Consistency test [Sum \(B_{d}+D_{d}\))/\(G_{d}\)] & PPL & Range of 0.9 to 1.1 \\ \hline Daily Sunshine Duration (\(S_{d}\)) vs. \(S_{0d}\) & PRL & \(S_{d}<S_{0d}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Daily Upper limits of Physically Possible tests (PPL) and Extremely Rare tests (ERL) (Lower limit of \(G_{d}\) is 0.03 \(\times\)\(G_{0d}\)) [5]. Figure 11: Daily totals of global irradiation (\(G_{d}\)) compared to the respective extraterrestrial (\(G_{0d}\)) and clear-sky irradiation (\(G_{cd}\)). The daily totals of horizontal direct (\(B_{d}\)) and diffuse irradiation (\(D_{d}\)) are also shown in the graph. The time series plots of the daily values of all the shortwave radiation components are illustrated in Figure 14. High variability is observed in spring.