## 2 Materials and Methods
### Quality Control Procedure
#### 2.5.3 Comparison Tests
(2015) [35] are:  
* \(k_{d}<1.05\ \mathrm{for}\ \mathrm{SZA}<75^{\circ}\);
* \(k_{d}<1.1\ \mathrm{for}\ \mathrm{SZA}>75^{\circ}\);
* \(k_{d}<0.95\ \mathrm{for}\ k_{t}>0.6\);
* \(k_{t}<1\)  
The tests performed in the \(k_{n}\)-\(k_{t}\) space have the following limits:  
Figure 8: Comparison based on the Rayleigh limit for data points that have \(k_{d}<0.8\) and \(G>500\) W/m\({}^{2}\). * \(k_{n}>k_{t}\);
* \(k_{n}<0.8\);
* \(k_{t}<1\). The results of this quality control process are shown in Figure 9a,b. The dotted red lines represent the different tests that are conducted. As it is indicated from the graphs all the measurements satisfy the test conditions, except three points that exceed the limits of \(k_{t}\) and these are the cases of enhancing global irradiances due to the reflections of the clouds. In Figure 9a, the limits of various situations are noted. For example, the limits for \(k_{t}<0.2\) and \(k_{d}<0.85\), show overcast conditions [42]. The condition \(k_{t}>0.5\) and \(k_{d}>0.8\) tests the misalignment [36], while [PERSON] (2004) [2] suggested that if there are observations in the space of \(0.2<k_{t}<0.5\) and \(k_{d}<0.2\), then debris are present in the dome of the sensor. Similar results for the control envelopes are obtained through a statistical outlier analysis as proposed by [PERSON] et al., (2005) [29]. The whole \(k_{t}\) range (from 0 to 1) was divided into ten equal intervals. For every interval the mean and standard deviation of the diffuse fraction (\(k_{d}\)) and the direct normal transmittance (\(k_{n}\)) were calculated. From this information an envelope may be drawn that connects those points that, respectively, represent the top (\(\overline{k}_{d}+3*\sigma_{k_{d}}\)) and bottom curves (\(\overline{k}_{d}-3*\sigma_{k_{d}}\)). In a similar way the top and bottom curves are defined for the \(k_{n}\) vs. \(k_{t}\) graph. A mathematical description of the envelope is obtained by fitting second degree polynomial curves (Figure 9c,d). The quadratic equations obtained for the lower and upper curves for the data sets of \(k_{d}\) vs. \(k_{t}\) are the following:  
\[flower(k_{t}) =0.723-1.355*k_{t}+0.539*k_{t}^{2}R^{2}=0.98 \tag{21}\] \[fupper(k_{t}) =0.763+1.007*k_{t}-1.254*k_{t}^{2}R^{2}=0.98 \tag{22}\]  
Figure 7:0 _Cont._  
The respective equations for the graph of \(k_{n}\) vs. \(k_{t}\) have the following forms:  
Figure 7:1 Figure 7:2  
Figure 9c shows that some points are outside the limits defined by the lower curve, coinciding with the graph of Figure 9a, as shown with the reference curves. Finally, the three-component test is intended to compare the measured global (\(G\)) irradiance by the pyranometer and the calculated sum from diffuse (\(D\)) and direct horizontal irradiance (\(B\)) which are measured independently:  
Figure 7:3  
Figure 7:4  
Ideally, the ratio of measured and estimated global irradiance should be 1.0, but due the instruments' inaccuracy, values far from unity, are often obtained. However, it is not possible to detect which of the three components is wrong. Figure 10a shows the regression analysis for the measured and estimated global irradiances. Although the coefficient of determination is quite high (\(R^{2}\) = 0.993), there is a set of points which are outside the 95% confidence intervals, indicating that one of the components is probably wrong. A misalignment error seems to affect the solar tracking system during the period 25 March 2021-8 April 2021. Figure 10b shows similar results, using the ratio of \(G\) to the sum of \(B+D\). The reference lines show the limits within which the values of the ratio should be detected. Generally, there is a higher dispersion of points at low elevation angles (or high SZA), which can be attributed to the cosine and directional response error of the pyranometers.