# Solar Potential in Saudi Arabia for Southward-Inclined Flat-Plate Surfaces
## 2 Materials and Methods
### Data Processing and Analysis  
In step 1, the downloaded hourly data from the PV-GIS website were transferred from the coordinated universal time (UTC) into the Saudi Arabia local standard one (LST = UTC + 3 h). It must be mentioned here that the PV-GIS solar radiation values were provided at different UTC times for the various sites considered, e.g., at hh:48 or hh:09, where hh stands for any hour between 00 and 23. In step 2, the hourly global horizontal radiation, H\({}_{\rm g,0}\), values were estimated as the sum H\({}_{\rm g,0}\) = H\({}_{\rm b,0}\) + H\({}_{\rm d,0}\). In step 3, the original Sun's azimuth and elevation (SUNAE) routine introduced by [PERSON] [36], together with its modifications [37; 38; 39; 40] renaming SUNAE to XRONOS (meaning time in Greek, X is pronounced CH), ran for the geographical coordinates of the 82 sites in the period 2005-2016 to derive the solar altitudes, \(\gamma\); the XRONOS algorithm computed \(\gamma\) at the LST times so calculated in step 1. In step 4, all radiation and solar geometry values were assigned to the nearest LST hour (i.e., values at hh:48 LST or hh:09 LST were assigned to just hh:00 LST). That was done in order to have all values in the data base at integer hours. In the next step 5, only those hourly solar radiation values were retained for analysis that were greater than 0 Wm\({}^{-2}\), and for \(\gamma\geq 5^{\circ}\) (to avoid the cosine effect). Also, the criterion of H\({}_{\rm d,0}\leq\) H\({}_{\rm g,0}\) should be met at hourly level. \begin{table}
\begin{tabular}{c c c c} \hline \hline \# & **Site** & \(\varphi\) (\({}^{\circ}\) N) & \(\lambda\) (\({}^{\circ}\) E) \\
51 & Hazem Aljalamid & 31.28 & 40.07 \\
52 & Turaif & 31.68 & 38.69 \\
53 & Al Qurayyat & 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 \\
57 & Khafi & 28.41 & 48.50 \\  
\hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._For estimating global solar irradiance on an inclined plane facing south, H\({}_{\rm g,BS}\) (in Wm\({}^{-2}\)), the isotropic model of Liu-Jordan [41] was adopted (\(\beta\) is the tilt angle of the inclined plane in respect to the local horizon, in degrees). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, H\({}_{\rm g,BS}\) (in Wm\({}^{-2}\)), received on the inclined flat surface. This model has been adopted in the present study because it has proved as efficient in providing the tilted total solar radiation in many parts of the world as other more sophisticated models [42]. For a south-facing surface the received total solar radiation is given by [43]:  
\[{\rm H_{g,BS}=H_{b,BS}+H_{d,BS}+H_{r,BS}}, \tag{1}\]  
where the subscript S denotes the south orientation of the inclined surface. According to [PERSON] [41]:  
\[{\rm H_{d,\beta S}=H_{d,0}.R_{di}}, \tag{2}\]  
\[{\rm H_{r,BS}=H_{g,0}.R_{r}.\rho_{g0}}, \tag{3}\]  
\[{\rm R_{di}=(1+cos\beta)/2}, \tag{4}\]  
\[{\rm R_{r}=(1-cos\beta)/2}, \tag{5}\]  
\[{\rm H_{b,\beta S}=H_{b,0}.cos\theta/sin\gamma}, \tag{6}\]  
\[{\rm cos\theta=sin\beta\cdot cos\gamma\cdot cos(\psi-\psi^{\prime})+cos\beta \cdot sin\gamma}. \tag{7}\]  
where \(\theta\) is the incidence angle (the angle formed by the normal to the inclined surface and the line joining the surface with the centre of the Sun), and \(\psi\), \(\psi^{\prime}\) are the solar azimuths of the Sun and of the inclined plane, respectively; the latter two solar parameters were estimated through the XRONOS algorithm, while \(\psi^{\prime}\) was always equal to 180 degrees to  
Figure 1: Distribution of the 82 selected sites in Saudi Arabia. The numbers in the circles refer to those in column 1 of Table 1.  
south. The parameters \(\mathrm{R_{di}}\) and \(\mathrm{R_{r}}\) are called the isotropic sky-configuration and ground-inclined plane-configuration factors, respectively. In the Liu-Jordan model the ground albedo usually takes the value of \(\mathrm{\rho_{g0}}\) = 0.2 (Equation (3)).