# Solar Potential in Saudi Arabia for Southward-Inclined Flat-Plate Surfaces
## 3 Results
### Definition and Variation of the Correction Factor  
This Section uses the notion of the correction factor, CF. This factor is defined by: CF = H\({}_{\rm g,opt.\ \ BS/\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{ \rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{{\rm{\rm{{\rm{ }}}}}}}}}{{{{}}{{}{}{}{}{}{}{{} {{}}{{{}{}{{  
renders the maximum annual solar energy sum on a flat plane at a site in Saudi Arabia inclined to the south under the influence of the real terrain surrounding the location if this energy maximum value is known for an albedo value of 0.2. In other words, CF corrects the energy on an inclined surface under the influence of a ground albedo equal to 0.2 to that which is under the influence of near-real ground-albedo value. Figure 9 presents the variation of CF as function of \(\beta\) for all 82 sites; the controlling parameter is the ratio \(\rho_{\rm r}=\rho_{\rm g}/\rho_{\rm g0}\), which takes a different value at each site. It is seen that the higher the \(\rho_{\rm r}\) value is, the more concave the best-fit curve is (for CF \(>\) 1); to the contrary, the lower the \(\rho_{\rm r}\) value is, the more convex the best-fit curve becomes (for CF \(<\) 1). All the data points at every \(\beta\) correspond to the 82 sites. The distribution of \(\rho_{\rm r}\) at the 82 sites is shown in Figure 10.  
Further, a diagram of CF vs. \(\rho_{\rm r}\) is shown in Figure 11, where a linear relationship is revealed and is shown for all sites. The controlling parameter in this case is \(\beta\); as \(\beta\) increases, the slope of the linear fit to the data points decreases. The data points along each line correspond to the 82 sites. Figure 9: Variation of the correction factor, CF, as function of the tilt angle of the inclined flat plane, \(\beta\), towards south (S), under all-sky conditions and averaged over the period 2005–2016. The blue straight line represents CF = 1; site #24 is very close to this value (0.98, Figure 10a). The dotted lines are the best-fit curves to the data points of each site. The best-fit lines are expressed by 3 rd-order polynomials. For example, the upper best-fit curve is: CF = 2\(\cdot\)10\({}^{-7}\)\(\beta^{3}\) + 5\(\cdot\)10\({}^{-6}\)\(\beta^{2}\) + 1\(\cdot\)10\({}^{-4}\)\(\beta\) + 0.9977 (R\({}^{2}\) = 1), while the lowest one: CF = \(-\)5\(\cdot\)10\({}^{-8}\)\(\beta^{3}\) – 2\(\cdot\)10\({}^{-6}\)\(\beta^{2}\) – 9\(\cdot\)10\({}^{-5}\)\(\beta\) + 1.0006 (R\({}^{2}\) = 1). The blue horizontal line indicates CF = 1. Figure 10: Annual mean ratios of ground albedo, \(\rho_{r}\), for the 82 sites in Saudi Arabia; (**a**) sites 1–43, (**b**) sites 44–82, averaged over the period 2005–2016. Despite the above, a more detailed analysis was performed for the function CF. In this analysis, the average values of CF were calculated for all \(\beta\)s and all sites belonging to the same SEZ, as well as all sites irrespective of SEZ. The results are shown in Figure 12, where the variation of CF with \(\beta\) in the range 15\({}^{\circ}\)-55\({}^{\circ}\) is shown. More particularly, the graphs give the variation of CF in a specific SEZ having the same optimum \(\beta\), if the optimum tilt angle includes all values in the above range, i.e., if all \(\beta\)s become optimum in a specific SEZ. Table 4 gives the regression equations for the lines that best fit the data points in each SEZ and all SEZs too. These regression relationships have the same shape as those in Figure 9.