## 2 Materials and Methods
### Quality Control Procedure
#### 2.5.3 Comparison Tests  
The tests of this category refer to (a) comparisons between the average and extreme values of the shortwave components, (b) comparisons between the pyranometers which are installed at the station, (c) comparison of diffuse irradiance with the Rayleigh limit, (d) comparisons of the radiation indices, and (e) comparison tests based on three radiation components (\(G=B+D\)). The results of these comparisons showed high quality of the data. Regarding the comparisons of the four pyranometers, the process showed that the coefficients of determination (\(R^{2}\)) are close to 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Lower Bound (W/m\({}^{2}\))**} & \multicolumn{2}{c}{**Upper Bound (W/m\({}^{2}\))**} & \multicolumn{2}{c}{**Upper Bound (W/m\({}^{2}\))**} \\ \hline
**Parameter** & **PPL** & **ERL** & **PPL** & **ERL** & **CCL** & **Level** \\ \hline \(G\) & \(-4\) & \(-2\) & min(\(1.2^{*}G_{0n},1.5^{*}G_{0n}\)*(cos\(\theta_{2}\))\({}^{1,2}+100\)) & \(1.2^{*}G_{0n}\)*(cos\(\theta_{2}\))\({}^{1,2}+50\) & \(0.97^{*}G_{0n}\)*(cos\(\theta_{2}\))\({}^{1,2}+55\) & 2 nd \\  & & & & \(0.92^{*}G_{0n}\)*(cos\(\theta_{2}\))\({}^{1,2}+50\) & 1 st \\ \Figure 6: (**a**) graphical representation of PPL, ERL and CCL tests of the average 10 min irradiances of the pyranometer on solar tracker (\(G\)) as a function of solar zenith angle (SZA); and (**b**) graphical representation of PPL, ERL and CCL tests of the maximum 10 min irradiances of the pyranometer on solar tracker (\(G\)) as a function of extraterrestrial irradiance at the top of the atmosphere (\(G_{0}\)). Figure 7: Graphical representation of PPL, ERL and CCL tests of the average 10 min irradiances of: (**a**) the diffuse on solar tracker (\(D\)); (**b**) direct horizontal (\(B\)); (**c**) reflected (\(R\)); and (**d**) direct normal irradiance as a function of solar zenith angle (SZA). Regarding diffuse irradiance the upper limit is 700 W/m\({}^{2}\), while the lower limit is the Rayleigh limit which is estimated during clear-sky conditions. The Rayleigh diffuse limit (\(R_{L}\)) is estimated from the following formula [33]:  
\[R_{L}=209.3*\mu-708.3*\mu^{2}+1128.7*\mu^{3}-911.2*\mu^{4}+287.85*\mu^{5}+0.0467 25*\mathrm{P} \tag{17}\]  
where \(\mu\) is the cosine of the solar zenith angle and \(P\) is the station surface pressure in millibars. Then, the limit of diffuse irradiance is defined as:  
\[D>R_{L}-1\ \mathrm{for}\ k_{d}\ <\ 0.8\ \mathrm{and}\ G\ >\ 50\ \mathrm{W/m^{2}} \tag{18}\]  
The results of this test are shown in Figure 8. Only, limited number of points is lower than \(R_{L}\) limit. The points are located mostly at SZA \(>60^{\circ}\). The radiation indices tests refer to the diffuse fraction and to NREL SERIS K tests. The diffuse fraction test involves the examination of the consistency of independent measurements. In this case, the components of global and diffuse irradiances are compared based on the following relations, for cases of global \(>50\) W/m\({}^{2}\)[42]:  
\[k_{d}=D/G<1.05\ \mathrm{for}\ \mathrm{SZA}\ <\ 75^{\circ} \tag{19}\]  
\[k_{d}=D/G<1.1\ \mathrm{for}\ 75^{\circ}\ <\ \mathrm{SZA}\ <\ 93^{\circ} \tag{20}\]  
All the measurements are lower than the limits shown in the above equations. The NREL-SERIS K tests were originally proposed by NREL with solar irradiance normalized to extraterrestrial values. The tests are based on the calculation of the diffuse fraction (\(k_{d}\)), the clearness index (\(k_{t}\)) and the direct normal transmittance (\(k_{n}\)). We can define two tests to qualify 'k-values': a test in the \(k_{d}\)-\(k_{t}\) space and a second in the \(k_{n}\)-\(k_{t}\) space. The limits of measurements in the \(k_{d}\)-\(k_{t}\) space as defined by [PERSON] et al.