## 2 Materials and Methods
### Data Processing and Analysis  
This section consists of five steps, which are briefly described as more details can be found in the companion paper [1]. Step 1: The downloaded hourly data from the PV-GIS platform were converted from the universal time coordinate (UTC) into local standard time (LST = UTC + 3 h). Step 2: The hourly global horizontal radiation, \(\mathrm{H_{g}}\) (in Wm\({}^{-2}\)), values were estimated as the sum \(\mathrm{H_{g}}=\mathrm{H_{b}}+\mathrm{H_{d}}\). Step 3: Use of the XRONOS.bas algorithm was made to calculate the solar altitudes, \(\gamma\), for all sites in LST; this code is based on the SUNAE routine introduced by [PERSON] [15], and all subsequent modifications [16; 17]. Step 4: All radiation and solar geometry values were assigned to the nearest LST hour (i.e., values at h:mm LST were assigned to hh:00 LST). Step 5: All hourly solar radiation values were retained for subsequent analysis that (i) were greater than 0 Wm\({}^{-2}\), (ii) corresponded to \(\gamma\geq 5^{\circ}\), and (iii) \(\mathrm{H_{d}}\leq\mathrm{H_{g}}\). For estimating global solar irradiance on an inclined plane fixed on a one-vertical axis tracker, \(\mathrm{H_{g,t,\beta}}\) (in Wm\({}^{-2}\)), there was adopted the isotropic model of Liu-Jordan (L-J) [18] (the subscript t stands for 'tracking', and \(\beta\) is the tilt angle of the inclined plane with respect to the local horizon, in degrees). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, \(\mathrm{H_{r,t,\beta}}\) (in Wm\({}^{-2}\)), received on the inclined flat-plate surface. The L-J model has proved to be as efficient as other more sophisticated models in providing the tilted total solar radiation in many parts of the world [19]. For a Sun-tracking surface mounted on a vertical axis the received total solar radiation is given by a slight modification of Equation (1) in [1]  
\[\mathrm{H_{g,t,\beta}}=\mathrm{H_{b,t,\beta}}+\mathrm{H_{d,t,\beta}}+\mathrm{H _{r,t,\beta}}, \tag{1}\]  
where the subscript t denotes tracking by the inclined surface. According to [PERSON] [18]  
\[\mathrm{H_{d,t,\beta}}=\mathrm{H_{d}}\cdot\mathrm{R_{di}}, \tag{2}\]  
\[\mathrm{H_{r,t,\beta}}=\mathrm{H_{g}}\cdot\mathrm{R_{r}}\cdot\mathrm{\rho_{g0 }}, \tag{3}\]  
\[\mathrm{R_{di}}=(1+\cos\beta)/2, \tag{4}\]  
\[\mathrm{R_{r}}=(1-\cos\beta)/2, \tag{5}\]  
\[\mathrm{H_{b,t,\beta}}=\mathrm{H_{b}}\cdot\mathrm{cos\theta}/\mathrm{sin \gamma}, \tag{6}\]  
\[\mathrm{cos\theta}=\mathrm{sin\beta}\cdot\mathrm{cos\gamma}\cdot\mathrm{cos (\psi-\psi^{\prime})}+\mathrm{cos\beta}\cdot\mathrm{sin\gamma}. \tag{7}\]  
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; \(\psi=\psi^{\prime}\) in this case. The parameters \(\mathrm{R_{di}}\) and \(\mathrm{R_{r}}\) are called the isotropic sky-configuration and ground-inclined plane-configuration factors, respectively. In the L-J model the ground albedo usually takes the value of \(\mathrm{\rho_{g0}}=0.2\) (Equation (3)), which is considered as reference in solar radiation modelling, although it refers to grassland areas [19]. Also, close-to-reality ground-albedo values, \(\mathrm{\rho_{g}}\), were used in this work. To retrieve such values for the 82 sites, use of the Giovanni portal [20] was made (details in [1]). Annual mean \(\mathrm{\rho_{g}}\) values were then computed and used to re-calculate \(\mathrm{H_{g,t,\beta}}\). The tilt angle in the present study varied in the range \(5^{\circ}\)-\(55^{\circ}\) in increments of \(5^{\circ}\) (i.e., \(11\) tilt angles). This range fully covers all latitudes of Saudi Arabia (from \(\approx\)18\({}^{\circ}\) N to 32\({}^{\circ}\) N). For every site and tilt angle, hourly values of \(\mathrm{H_{g,t,\beta}}\) were estimated from Equation (1) for both \(\mathrm{\rho_{g0}}=0.2\) and \(\mathrm{\rho_{g}}\).