## 2 Materials and Methods
### Data Processing and Analysis  
The processing of the H\({}_{\rm b,0}\) and H\({}_{\rm d,0}\) hourly values (in Wm\({}^{-2}\)) obtained from the PV-GIS platform was the same as that described in a previous work concerning the solar energy potential of Saudi Arabia [32], i.e., steps 1-5; therefore, that procedure is not reported here. The hourly global horizontal solar irradiance values, H\({}_{\rm g,0}\) (in Wm\({}^{-2}\)), were calculated as the sums of the H\({}_{\rm b,0}\) and H\({}_{\rm d,0}\) ones. Estimates of the inclined global solar irradiance on a flat-plate surface with (i) optimally selected, southward fixed-tilt angle, H\({}_{\rm g,\beta s}\), (ii) optimally selected fixed-tilt angle tracking the Sun, H\({}_{\rm g,\beta t}\), and (iii) varying-tilt angle tracking the Sun, H\({}_{\rm g,t}\) (all in Wm\({}^{-2}\)) were performed in the respective works of [30; 31; 32], by using the isotropic transposition L-J model [10]. The calculations in those studies used near-real ground-albedo values, \(\rho_{\rm g}\), retrieved from the Giovanni platform [39], instead of utilising the reference value of \(\rho_{\rm g0}\) = 0.2. This method was followed in the present study too. The estimation of the global solar irradiance on an inclined surface in any of the above-mentioned types of solar systems is:  
\[{\rm H}_{\rm g,x}={\rm H}_{\rm b,x}+{\rm H}_{\rm d,x}+{\rm H}_{\rm r,x}, \tag{1}\]  
where the subscript x denotes \(\beta\)S, \(\beta\)t, or t according to the configuration of the solar system as (i), (ii), or (iii), respectively. The individual parameters on the right-hand side of Equation (1) are estimated through the following expressions [40]:  
\[{\rm H}_{\rm b,x}={\rm H}_{\rm b,0}.{\rm R}_{\rm b} \tag{2}\]  
Figure 1: Distribution of the 82 sites in Saudi Arabia. The numbers in the circles refer to those in column 1 of Table 1 reported in [30]. This figure is a reproduction of Figure 1 in [30]. \[H_{d,x}=H_{d,0}\cdot R_{d,MODEL} \tag{3}\] \[H_{rx}=H_{g,0}\cdot R_{r}\cdot\beta_{g},\] (4) \[R_{b}=max(cos\theta/sin\gamma,0),\] (5) \[R_{d,ISO}=(1+\cos\beta)/2\] (6) \[R_{d,HAY}=K_{b}\cdot R_{b}+(1-K_{b})\cdot R_{d,ISO}\] (7) \[R_{r}=(1-\cos\beta)/2\] (8) \[\cos\theta=\sin\beta\cdot cos\gamma\cdot cos(\psi-\psi^{\prime})+\cos\beta \cdot sin\gamma.\] (9) \[{\rm H}_{\rm b,x}={\rm H}_{\rm b,0}.{\rm R}_{\rm b} \tag{2}\]0 (10) \[{\rm H}_{\rm b,x}={\rm H}_{\rm b,0}.{\rm R}_{\rm b} \tag{2}\]1 (11) \[{\rm H}_{\rm b,x}={\rm H}_{\rm b,0}.{\rm R}_{\rm b} \tag{2}\]2  
In the above expressions:  
* \(\theta\) 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, in degrees);
* \(\beta\) is the inclination of the tilted surface with respect to the local horizon (in degrees);
* \(\psi\) and \(\psi^{\prime}\) are the solar azimuths of the Sun and of the inclined plane, respectively (in degrees);
* \(\gamma\) is the solar elevation (or solar altitude, in degrees);
* in the case of (a) a southward fixed-tilt-angle surface (configuration-(i) system), \(\beta\) = constant, \(\psi\) = constant \(\
eq\psi^{\prime}\), \(\theta\
eq 0^{\circ}\); (b) a fixed-tilt-angle surface tracking the Sun (configuration-(ii) system), \(\beta\) = constant, \(\psi\) = \(\psi^{\prime}\), \(\theta\
eq 0^{\circ}\); and (c) a varying-tilt-angle surface tracking the Sun (configuration-(iii) system), \(\beta\) = \(90^{\circ}-\gamma\), \(\psi\) = \(\psi^{\prime}\), \(\theta\) = \(0^{\circ}\);
* the subscripts ISO and HAY denote the isotropic L-J and anisotropic Hay models, respectively, and will be used as such in the rest of the work;
* the subscript MODEL denotes either ISO or HAY;
* H\({}_{0}\) is the solar constant of 1361.1 W m\({}^{-2}\)[41];
* S is the Sun-Earth distance correction factor [42];
* N is the day-of-the-year (N = 1 for 1 January, N = 365 or 366 for 31 December in a non-lep or leap year, respectively).