## 2 Materials and Methods  
The methodology of this work is based on the application of five well-known mathematical models. These models estimate the amount of solar irradiance that can be captured on a flat surface for different orientations and tilt angles. The models' input data are the beam, diffuse, and global irradiance on a horizontal surface, the orientation, and tilt angles of the capturing flat surface. Then, each model obtains as output the amount of solar irradiance captured for different positions. In this way, it is possible to know the optimal position of a flat surface to capture solar energy at a given location. To determine the optimal position of flat surfaces, various parameters should be taken into account, which are listed as follows:  
* Solar insolation: The amount of solar radiation received from the Sun and expressed in \(\mathrm{Wh/m^{2}}\). * Solar irradiance: The instantaneous power per unit area received from the Sun on the Earth's surface and expressed in \(\mathrm{W/m^{2}}\). The irradiance is measured in the wavelength range of the measuring instrument. * Ground reflectance (albedo): The portion of solar insolation incident on the ground that is reflected. * Sky clarity index: The ratio of measured insolation relative to insolation outside the atmosphere calculated in the given location. The analyzed data in Cuenca was collected from a meteorological station located in the Salesian Polytechnic University. The weather data were obtained using VAISALA weather station, Datalogger QML201C, and the VAISALA HydroMetTM Automatic Weather Station Client Software (AWS Client). The AWS Client includes outlier detection as a tool of Quality Control. The data collected is from a VAISALA weather station with a data logger QML201C. The weather station is exposed directly to the environment. The meteorological data are transmitted to a PC station with VAISALA HydroMetTM Automatic Weather Station Client Software (AWS Client), a graphical and end-user software. The time interval of the data is 15 min. The solar radiation is measured with a Hukseflux thermal sensor SR11, HFS Shadow-Ring. The authors have selected Ecuador's case study since, firstly, we had the available information of the most populated cities in the country that are distributed in different regions. Moreover, this is a particularly interesting case study since the equatorial line crosses the country, so the influence of the local climate and the geographical position can influence the optimal orientation and inclination of the solar insolation capturing surfaces. The characteristics of the selected cities are summarized in Table 1 and the corresponding map is depicted in Figure 1. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**City** & \begin{tabular}{l} **Population** \\ **[millions]** \\ \end{tabular} & \begin{tabular}{l} **Latitude** [\({}^{\circ}\)] \\ \end{tabular} & \begin{tabular}{l} **Longitude** [\({}^{\circ}\)] \\ \end{tabular} & \
\begin{tabular}{l} **Elevation [m]** \\ \end{tabular} &
\begin{tabular}{l} **Data Source** \\ \end{tabular} \\ \hline Quito & 2 & \(-0.22\) & \(-78.51\) & \(2850\) & TMY file \\ Guayaquil & 2.7 & \(-2.2\) & \(-79.9\) & \(4\) & TMY file \\ Cuenca & 0.34 & \(-2.88\) & \(-79.02\) & \(2550\) & Vaisala Weather \\  & & & & Station \\ Machala & 0.24 & \(-3.26\) & \(-79.96\) & \(6\) & TMY file \\ Loja & 0.29 & \(-4\) & \(-79.2\) & \(2060\) & TMY file \\ Santo & 0.27 & \(-0.25\) & \(-79.17\) & \(635\) & TMY file \\ Domingo & 0.21 & \(-1.06\) & \(-80.47\) & \(53\) & TMY file \\ Portoviejo & 0.17 & \(-1.24\) & \(-78.63\) & \(2580\) & TMY file \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the selected cities in Ecuador. The collected data from the meteorological station of the Salesian Polytechnic University in the city of Cuenca have been tabulated in a statistical and mathematical analysis computer tool for its estimation and analysis as a function of time. In this analysis, each variable's hourly and daily average has been carried out.