## 3 Results and Discussion
### Quality Control: Global Solar Irradiance and Temperature
#### 3.2.2 Performance  
Figures 3-10 show the relationship between the daily clearness index and daily delta of temperature for the studied AWS. Figures 3 and 10 show that there is a moderate linear relationship between the daily clearness index and daily delta of temperature in the Pacific zone. Figure 5 shows that, in _Cerro Paramo_, the clearness index and the delta of temperature possess a moderate linear relationship. In the Andean zone, the clearness index and delta of temperature exhibited a weak linear relationship. Table 11 shows the empirical coefficients of the HS, BC, and ON models and those of the proposed model. The \(a\) and \(b\) empirical constants of the BC model demonstrated a growing trend corresponding to altitude, while the \(c\) empirical constant showed the opposite behavior. The empirical coefficients of the HS model did not present a significant variation among AWS. This means that the AWSs have similar humid conditions, considering the original values given by [9]. The empirical coefficient of the ON model for the _Bitopo_ AWS revealed the unique negative value. More studies and data are necessary to understand this result. However, there were two influencing factors: _Biotopo_ AWS did not have calibration factor, and the data number was the lowest. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Bristow and Campbell**} \\ \hline AWS & \(a\) & \(b\) & \(c\) \\ \hline _Biotopo_ & 0.5075 & 0.0735 & 1.1908 \\ _Viento Libre_ & 0.5942 & 0.1499 & 0.8655 \\ _Cerro Paramo_ & 0.5922 & 0.2595 & 0.6153 \\ _Universidad de Nariño_ & 0.4893 & 0.3282 & 0.6568 \\ _Botana_ & 0.6288 & 0.1964 & 0.6415 \\ _Josefina_ & 0.6039 & 0.2563 & 0.5350 \\ _Parasio_ & 0.5850 & 0.3183 & 0.4818 \\ _Guapi_ & 0.4471 & 0.1156 & 1.2478 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Empirical coefficients. Figure 10: Daily delta of temperature–clearness index for _Guapi_. Table 12 presents the results of seven statistical validation measurements for each AWS. Considering \(RMSE\), \(SD\), \(MAE\), \(U_{95}\), and \(MAPE\), the proposed model had better performance than the other models. That said, the BC model had better results for \(MAE\) and \(MPE\). The proposed model showed better results in AWS located at altitudes above 2500 MASL. In contrast, the HS model showed better performance at altitudes below 2500 MASL. However, if the objective is to use a unique model to estimate solar irradiance from temperature data in the state, the proposed model remains the best. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**[PERSON] and Samani**} \\ \hline AWS & \(a\) & \\ \hline _Bioppo_ & 0.0970 & \\ _Viento Libre_ & 0.1248 & \\ _Cerro Patamo_ & 0.1340 & \\ _Universidad de Nariño_ & 0.1263 & \\ _Botana_ & 0.1169 & \\ _Josefina_ & 0.1138 & \\ _Parasio_ & 0.1199 & \\ _Guapi_ & 0.1208 & \\ \hline \multicolumn{3}{c}{**Okundamiya and Nzeako**} \\ \hline AWS & \(a\) & \(b\) & \(c\) \\ \hline _Bioppo_ & \(-0.1838\) & \(-0.3871\) & 0.0264 \\ _Viento Libre_ & 0.0578 & \(-0.2666\) & 0.0168 \\ _Cerro Patamo_ & 0.1084 & \(-0.1572\) & 0.0257 \\ _Universidad de Nariño_ & 0.2679 & \(-0.2416\) & 0.0112 \\ _Botana_ & 0.0621 & \(-0.1547\) & 0.0191 \\ _Josefina_ & 0.1770 & \(-0.1589\) & 0.0118 \\ _Parasio_ & 0.2617 & \(-0.1775\) & 0.0100 \\ _Guapi_ & 0.0717 & \(-0.5202\) & 0.0228 \\ \hline \multicolumn{3}{c}{**Proposed model**} \\ \hline AWS & \(a\) & \(b\) & \\ \hline _Bioppo_ & \(-2.3058\) & 0.1786 & \\ _Viento Libre_ & \(-1.3499\) & 0.0912 & \\ _Cerro Patamo_ & \(-1.7914\) & 0.1706 & \\ _Universidad de Nariño_ & \(-1.2211\) & 0.0747 & \\ _Botana_ & \(-1.4489\) & 0.0898 & \\ _Josefina_ & \(-1.2299\) & 0.0608 & \\ _Parasio_ & \(-1.1667\) & 0.0607 & \\ _Guapi_ & \(-1.8043\) & 0.1495 & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._