# Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun
## 2 Materials and Methods
### Data Processing and Analysis  
To process the data used in this work, we followed the following 5 steps:  
Step 1. The downloaded hourly data from the PV-GIS website were transferred from universal time coordinate (UTC) into Saudi Arabian local standard time (LST = UTC + 3 h). It must be mentioned that the PV-GIS solar radiation values were provided at different UTC times for the 82 sites considered, e.g., at hh:48 or hh:09, where hh stands for any hour between 00 and 23. Step 2. The hourly global horizontal solar radiation, \(\mathrm{H_{g}}\), values were estimated at all sites as the sum \(\mathrm{H_{g}}=\mathrm{H_{b}}+\mathrm{H_{d}}\). Step 3. The routine SUNAE introduced by [PERSON] [27] was used to derive the solar azimuths and elevations. The original SUNAE algorithm has, however, been renamed to XRONOS (meaning time in Greek, X is pronounced CH) because of added modifications due to the right ascension and atmospheric refraction effects [28; 29]. XRONOS ran for the geographical coordinates of the 82 sites in the period 2005-2016 to derive the solar altitudes, \(\gamma\), at all LST times calculated in step 1. Step 4. All solar 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 hh:00 LST). This was done in order to have all values in the data base as integer hours. Step 5. Only those hourly solar radiation values greater than 0 Wm\({}^{-2}\) and corresponding to \(\gamma\geq 5^{\circ}\) (to avoid the cosine effect) were retained for further analysis. Moreover, the criterion of \(\mathrm{H_{d,0}}\leq\mathrm{H_{g,0}}\) was required to be met at the hourly level. For estimating global solar irradiance on an inclined plane that continuously tracks the sun, \(\mathrm{H_{g,t}}\) (in Wm\({}^{-2}\)), the isotropic model of Liu-Jordan [30] was adopted (the subscript t stands for \"tracking\"). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, \(\mathrm{H_{r,t}}\) (in Wm\({}^{-2}\)), received on the inclined plane. This model was adopted in the present study because of its simplicity and effectiveness in comparison to other anisotropic models in providing the tilted total solar radiation in many parts of the world; the good performance of the isotropic model has been verified by various studies (e.g., [31; 32; 33; 34; 35]). Figure 2 provides a schematic for a tilted surface receiving solar radiation. Deliberately, the tilted surface is not aligned along the direction of the sun in order to show the various angles formed, i.e., the tilt angle of the surface, \(\beta\); the solar altitude, \(\gamma\); the solar zenithal angle, \(\theta_{2}\); the incidence angle, \(\theta\) (the angle between the normal to the surface and the direction toward the sun); the solar azimuth, \(\psi\); and the azimuth of the tilted plane, \(\psi^{\prime}\). In this graph, the sun lies in the N-S plane that is normal to the local horizon (therefore, \(\psi=180^{\circ}\)). In the case of a surface tracking of the sun, it is easy to conclude that \(\theta=0^{\circ}\) (the solar rays are normal to the tilted surface), \(\beta=90^{\circ}-\gamma\), and \(\psi=\psi^{\prime}\). 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. This figure is reproduction of Figure 1 in [1,2]. For a sun-tracking surface, the received total solar radiation is given by the following well-known expression:  
\[\mathrm{H_{g,t}}=\mathrm{H_{b,t}}+\mathrm{H_{d,t}}+\mathrm{H_{r,t}}, \tag{1}\]  
where the subscript t implies \"tracking\" the sun by the receiving surface.