## 2 Materials and Methods  
### Data Collection  
For the implementation of the study hourly values of the following parameters were collected: direct, H\({}_{\text{b}}\) (in Wm\({}^{-2}\)), and diffuse, H\({}_{\text{d}}\) (in Wm\({}^{-2}\)), horizontal solar radiation. These values were downloaded from the PV--Geographical Information System (PV-GIS) tool [10] using the latest Surface Solar Radiation Data Set--Heliostat (SARAH) 2005-2016 data base (12 years) [11; 12]. The PV-GIS provides solar radiation data for any location in Europe, Africa, Middle East including Saudi Arabia, central and southeast Asia and most parts of the Americas. Solar radiation in the PV-GIS platform is calculated from satellite observations and modelling [13; 14].  
A set of 82 sites in Saudi Arabia was selected to cover the whole territory of the country. Hourly values of H\({}_{\text{b}}\) and H\({}_{\text{d}}\) were downloaded from PV-GIS for all 82 sites; Table 1 shows the names and provides the geographical coordinates of these sites, while Figure 1 is a map of Saudi Arabia showing their location. The criterion for selecting these sites is mentioned in [1].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \# & **Site** & **\(\varphi\) (Degrees N)** & \(\lambda\) (Degrees E)** \\ \hline
1 & Dammam & 26.42 & 50.09 \\
2 & Al Jubail & 26.96 & 49.57 \\
3 & Ras Tanura & 26.77 & 50.00 \\
4 & Abqaiq & 25.92 & 49.67 \\
5 & Al Hoftuf & 25.38 & 49.59 \\
6 & Arar & 30.96 & 41.06 \\
7 & Sakaka & 29.88 & 40.10 \\
8 & Tabuk & 28.38 & 36.57 \\
9 & Al Jawf & 29.89 & 39.32 \\
10 & Riyadh & 24.71 & 46.68 \\
11 & Al Qassim & 26.21 & 43.48 \\
12 & Hafar Al Batin & 28.38 & 45.96 \\
13 & Buraydah & 26.36 & 43.98 \\
14 & Al Majma’ah & 25.88 & 45.37 \\
15 & Hail & 27.51 & 41.72 \\
16 & Jeddah & 21.49 & 39.19 \\
17 & Jazan & 16.89 & 42.57 \\
18 & Mecca & 21.39 & 39.86 \\
19 & Medina & 24.52 & 39.57 \\
20 & Taif & 21.28 & 40.42 \\
21 & Yanbu & 24.02 & 38.19 \\
22 & King Abdullah Economic City & 22.45 & 39.13 \\
23 & Najran & 17.57 & 44.23 \\
24 & Abha & 18.25 & 42.51 \\
25 & Bisha & 19.98 & 42.59 \\
26 & Al Sahmah & 20.10 & 54.94 \\
27 & Thabhloten & 19.83 & 53.90 \\
28 & Ardah & 21.22 & 55.24 \\
29 & Shaybah & 22.52 & 54.00 \\
30 & Al Kharkhir & 18.87 & 51.13 \\
31 & Umm Al Melh & 19.11 & 50.11 \\
32 & Ash Shalfa & 21.87 & 49.71 \\
33 & Oroug Bani Maradh Wildlife & 19.41 & 45.88 \\
34 & Wadi ad Dawasir & 20.49 & 44.86 \\
35 & Al Badie Al Shamali & 21.99 & 46.58 \\
36 & Howtat Bani Tamim & 23.52 & 46.84 \\
37 & Al Duwadimi & 24.50 & 44.39 \\
38 & Shaqra & 25.23 & 45.24 \\
39 & Afif & 24.02 & 42.95 \\
40 & New Muwayh & 22.43 & 41.74 \\
41 & [PERSON] & 23.49 & 40.85 \\
42 & Ar Rass & 25.84 & 43.54 \\
43 & Uglat Asugour & 25.85 & 42.15 \\
44 & Al Henakiyah & 24.93 & 40.54 \\
45 & Ar Rawdah & 26.81 & 41.68 \\
46 & Asbtar & 26.96 & 40.28 \\
47 & Tayma & 27.62 & 38.48 \\
48 & Al Khanafah Wildlife Sanctuary & 28.81 & 38.92 \\
49 & Madain Saleh & 26.92 & 38.04 \\
50 & Altubaiq Natural Reserve & 29.51 & 37.23 \\
51 & [PERSON] & 31.28 & 40.07 \\
52 & Turaf & 31.68 & 38.69 \\
53 & Al Qurayvat & 31.34 & 37.37 \\
54 & Harrat al Harrah Conservation & 30.61 & 39.48 \\
55 & Al Uwayqilah & 30.33 & 42.25 \\
56 & Rafha & 29.63 & 43.49 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The 82 sites selected over Saudi Arabia to cover the whole territory of the country; \(\varphi\) is the geographical latitude, and \(\lambda\) the geographical longitude in the WGS84 geodetic system. This table is reproduction of Table 1 in [1].  
Figure 1: Distribution of the selected 82 locations in Saudi Arabia. The numbers in the circles refer to those in column 1 of Table 1. This figure is reproduction of Figure 1 in [1].