## 2 Materials and Methods  
### Site and Dataset  
The weather stations located in Narino, Colombia (00\({}^{\circ}\)31/08\({}^{\prime\prime}\) N and 02\({}^{\circ}\)41/08\({}^{\prime\prime}\) N latitude; 76\({}^{\circ}\)51/19\({}^{\prime\prime}\) W and 79\({}^{\circ}\)01/34\({}^{\prime\prime}\) W longitude), measured solar irradiance and temperatures used as input for the empirical models. The proximity to the Equator and the Intertropical Convergence Zone influences the weather of this place, causing unimodal or bimodal rainy seasons and increasing cloud cover due to high humidity in low altitudes. Additionally, the western mountain range is a barrier for the moist air masses from the Pacific Ocean; thus, the Pacific foothills become more humid and tend to maintain this humidity [17]. Hence, it is appropriate to divide the weather and orographic conditions of Narino into three environmental regions: the Pacific, the Andean, and the Amazon [18]. The Pacific zone covers 52% of the total territory of Narino, and this zone includes the _Mira-Mataje_ binational watershed and a mangrove forest located in the _Sanquianga_ natural reserve. Additionally, the region has two climatic zones: the Pacific flatlands and the Pacific foothills. The Pacific flatlands have a humidity level higher than 80%, an average temperature higher than 26 \({}^{\circ}\)C, and annual precipitation of between 3000 and 5000 mm/year. The Pacific foothills have high humidity, an average temperature between 18 \({}^{\circ}\)C and 24 \({}^{\circ}\)C, and annual precipitation between 4000 and 6000 mm/year. However, between the _Junit_ and _Barbaocas_ localities, the annual precipitation is approximately 9000 mm/year [17; 18; 19]. The Andean zone constitutes 40% of the total area of Narino, and in this zone, the Andes split into two ranges: western and central [17; 20]. The western mountain range exhibits bimodal precipitation behavior between 800 and 2200 mm/year, with peaks in April-May and October-November. In the central mountain range, the temperatures vary between 16 \({}^{\circ}\)C to 24 \({}^{\circ}\)C, and precipitation averages between 1000 to 1800 mm/year. In the north zone toward _Patia_, annual precipitation is less than 1000 mm/year, with temperatures typically above 24 \({}^{\circ}\)C [19]. The Amazon zone covers 8% of the Narino territory and has two climate zones: mountainous and flatland. The mountainous zone is located between the _Patia_ and _Putumago_ rivers with temperatures averaging between 6 \({}^{\circ}\)C and 11 \({}^{\circ}\)C and annual precipitation of about 2000 mm/year. The flatland zone has tropical weather influenced by the cloudy jungle and precipitation between 500 to 1500 mm/year [19]. There are 9 AWSs measuring solar irradiance, 8 located in Narino and 1 positioned in the neighboring state of Cauca, and 16 Conventional Weather Stations (CWS) measuring temperature (see Tables 1 and 2), located as shown in Figure 1. In the Pacific region, there are three AWSs. The altitude of these AWS ranges between 16 and 512 MASL. In the Andean region, there are five AWSs located at altitudes between 1005 and 3120 MASL. Finally, in the Amazon region, there is one AWS at an altitude of 3577 MASL. The maximum altitude difference between all AWSs is 3561 MASL. This difference allows evaluating solar irradiance behavior in a wide range of altitudes in the three diverse environmental regions. We reviewed a study on the same zone that used Landsat 7 (1999-2015), MODIS (2005-2015) and VAISALA 3 TIER (2000-2015) satellite data; however, when comparing the satellite and ground data, we found a significant difference between them. The satellite data resulted in a maximum solar irradiance potential of approximately 245 W/m\({}^{2}\) day with MODIS and Landsat 7 database [21]. In contrast, the ground measurements show a maximum potential of approximately 3800 W/m\({}^{2}\) day. Furthermore, the results of the national Solar Atlas are closer to our results than satellite ones.