## 2 Equipment and Methodology
### Statistical Parameters and Estimators  
In addition to the experimental measurements (I\({}_{\rm{GH}}\), I\({}_{\rm{DH}}\), and I\({}_{\rm{BH}}\), as indicated above), other meteorological variables easily obtained from those values were used. \(\Delta\) is the sky's brightness, as shown in Equation (2). It quantifies cloud thickness or aerosol loading. \[\Delta=\frac{\rm{I}_{\rm{DH}}*\rm{m}}{\rm{B}_{\rm{sc}}\cdot\epsilon_{0}} \tag{2}\]  
where B\({}_{\rm{sc}}\) is the extraterrestrial irradiance constant (=1361.1 W/m\({}^{2}\)[40]) and m is the relative optical air mass. The sky's clearness index, \(\epsilon\), predicts cloud conditions using the ratio between the diffuse horizontal irradiance and the direct one on the same plane, as shown in Equation (3), where k = 1.041 for Z in radians. \[\epsilon=\left(\frac{\rm{I}_{\rm{DH}}+\rm{I}}{\rm{I}_{\rm{DH}}}+\rm{k}Z^{3} \right)/\left(1+\rm{k}Z^{3}\right) \tag{3}\]  
The clearness index, k\({}_{\rm{tr}}\), obtained with Equation (4), defined as the ratio of the global horizontal irradiance at ground level and the extra-terrestrial global solar irradiance, measures the fraction of the solar radiation transmitted through the atmosphere. \[\rm{k}_{t}=\frac{\rm{I}_{\rm{GH}}}{\rm{B}_{\rm{sc}}\cdot\epsilon_{0}\cdot \cos Z} \tag{4}\]  
The sky ratio or diffuse fraction, D, as shown in Equation (5), is defined as the ratio of horizontal diffuse irradiance to horizontal global irradiance. It refers to the cloudiness of the sky and/or the turbidity of the atmosphere. \[\rm{D}=\frac{\rm{I}_{\rm{DH}}}{\rm{I}_{\rm{GH}}} \tag{5}\]  
Figure 1: Experimental equipment. The goodness-of-fit of the models was calculated in terms of nMBE (\(\%\)) (normalized mean bias error) and nRMSE (\(\%\)) (normalized root mean square error). Equations (6) and (7) show the statistical estimators employed in this study. \[\text{nMBE }(\%)=100\frac{\sum_{n}(\text{X}_{\text{model}}-\text{X}_{\text{ measured}})}{\sum_{n}\text{X}_{\text{measured}}} \tag{6}\]  
\[\text{nRMSE }(\%)=100\frac{\sqrt{\frac{\sum_{n}(\text{X}_{\text{model}}- \text{X}_{\text{measured}})^{2}}{n}}}{\frac{\sum_{n}\text{X}_{\text{measured}}}{n}} \tag{7}\]  
The Pearson correlation coefficient was used to determine the degree of correlation between \(\text{I}_{\text{UV}}\) and the meteorological variables under study. The Pearson criterion is based on the Pearson correlation coefficient, r. If there is a strong correlation between \(\text{I}_{\text{UV}}\) and the selected variable, then the Pearson coefficient will be either 1 (direct correlation) or \(-1\) (inverse correlation). However, a Pearson coefficient close to 0 implies a weak or null correlation. The rule of thumb [41] established five r intervals for the correlation: direct (1 \(\geq\left|\text{r}\right|\geq 0.9\)), strong (0.9 \(>\left|\text{r}\right|\geq 0.7\)), moderate (0.7 \(>\left|\text{r}\right|\geq 0.5\)), weak (0.5 \(>\left|\text{r}\right|\geq 0.3\)), and negligible (\(\left|\text{r}\right|<0.3\)). Figure 2 shows the correlation between all variables considered in the study. The correlation of \(\text{I}_{\text{UV}}\) with the independent meteorological variables is obtained from the last row/column of the correlation matrix shown in Figure 2. The influence of these variables on \(\text{I}_{\text{UV}}\) can also be seen graphically in Figure 3, where the input variables have been ordered according to the correlation with \(\text{I}_{\text{UV}}\). The meteorological variables with r(\(\text{I}_{\text{UV}},\text{ variable})<0.4\) were discarded as inputs for the models, after which only the variables included in Table 1 were considered. As Figure 3 shows, \(\text{I}_{\text{GH}}\) has the strongest correlation with \(\text{I}_{\text{UV}}\), followed by the solar altitude angle, \(\alpha\), and the clearness index, \(\text{k}_{\text{t}}\). Only D and Cc presented weak inverse correlation with \(\text{I}_{\text{UV}}\). The results were coherent with those in the literature review.