## 2 Materials and Methods
### Data Quality Control
#### 2.2.1 Solar Irradiance Data Quality Control  
The first step consists of checking database structure. In our case, the data exhibited the following structure: AWS code, weather variable code, date, hour, and value. This step only maintains the values with the described structure [15]. For the fixed-range step, UNE500540 suggests using the most restrictive condition between the measurement device limit and the physical phenomenon limit. Narino's AWS have Kipp & Zonen CMP11 pyranometers with an upper operation limit of 4000 W/m\({}^{2}\)[24]. The physical limit is the  
Figure 1: Automatic and conventional weather stations in Narín. Source: made by the authors with information from OpenStreetMap. maximum extraterrestrial solar irradiance \(I_{0}\) of each location computed with the following equation [25]:  
\[I_{0} =I_{sc}\times\Big{[}1+0,033*\cos\Big{(}360*\frac{D-3}{365}\Big{)} \Big{]}*\sin(\beta),\] \[\sin(\beta) =\cos(\varphi)\times\cos(\delta)\times\cos(\omega_{s})\ +\sin( \varphi)\times\sin(\delta)\]  
where \(I_{sc}\) is the solar constant, \(D\) is the Julian day, \(\beta\) is the solar altitude, and \(\delta\) is the declination calculated as follows:  
\[\delta=23.45\times sin\bigg{[}\frac{360\times(D+284)}{365}\bigg{]},\]  
where \(\varphi\) is the latitude, and \(\omega_{s}\) is the hour angle calculated as follows. \[\omega_{s}=\cos^{-1}[-\tan(\delta)\tan(\varphi)].\]  
Therefore, the most restrictive condition is the extraterrestrial solar irradiance [22]. Consequently, \(I_{0}\geq I_{mt}\), where \(I_{mt}\) is the measured global solar irradiance by a pyranometer at time \(t\). For the flexible range test, UNE500540 suggests comparing the time series with the maximum and minimum values of a validated time series. In this case, there was no time series previously validated; therefore, we used, as an alternative, the restriction proposed for [PERSON] et al. with one modification. Namely, instead of using \(I_{0}\), we used the following range defined by the clear-sky global solar irradiance: \((0.03*I_{\text{cs}}\leq I_{mt}\leq I_{\text{cs}})\)[21]. The clear-sky global solar irradiance is equal to \(\tau\) times \(I_{0}\), \(I_{cs}=I_{0}*\tau\), and \(\tau\) is the atmospheric transmittance estimated with [PERSON]'s model as follows [25]:  
\[\tau=0.56\times\Big{(}e^{-0.65\times m}+e^{-0.095\times m}\Big{)}\]  
where the air mass \(m\) is defined as follows. \[m=\frac{1}{\sin(\beta)}\]  
The fourth step consists of analyzing changes in global solar irradiance hour by hour. This analysis, known as time consistency, follows the restriction \(|I_{\text{{\it{\it{\it{\it{\it{\it{  
researchers. [PERSON] et al. recommended a temperature interval between \(-50\)\({}^{\circ}\)C and \(70\)\({}^{\circ}\)C, while [PERSON] et al. suggested a range of \(-30\)\({}^{\circ}\)C to \(50\)\({}^{\circ}\)C. We followed [PERSON] et al. 's recommendation because it is within the temperature range of the sensor. Likewise, the analysis of the step test, internal consistency test, and persistency test also followed [PERSON] et al. 's quality control process because it offered promising data analysis results in Spain [22,27]. The step test requires the fulfillment of the following requirements: \(\left|T_{h}-T_{h-1}\right|\ <4\); \(\left|T_{h}-T_{h-2}\right|\ <7\); \(\left|T_{h}-T_{h-3}\right|\ <9\); \(\left|T_{h}-T_{h-6}\right|\ <15\); and \(\left|T_{h}-T_{h-12}\right|\ <25\), where \(T_{h}\) is the air temperature measured at time \(h\). Although this evaluation does not consider other climatology aspects that can affect temperature variation, such as humidity, wind speed, cloudiness, and precipitation, the authors of this study applied these restrictions. Another fundamental requirement is that the daily step restriction fulfills the following condition: \(T_{max}-T_{min}<30\)\({}^{\circ}\)C, where \(T_{max}\) and \(T_{min}\) are the maximum and minimum daily temperatures [26].