## 3 Results
### Correction Factor  
[PERSON] et al. [1] introduced the notion of the correction factor, CF, which is defined as: \(\mathrm{CF}=\mathrm{H_{g,t,\beta}/\mathrm{pg}}/\mathrm{H_{g,t,\beta}/\mathrm{pg}}\). Actually, CF is the ratio of the annual \(\mathrm{H_{g,t,\beta}}\) sum at each site of the 82, calculated twice, once for \(\mathrm{\rho_{g0}=0.2}\) and a second time for \(\mathrm{\rho_{g}=actual value}\). The meaning of the CF is that it 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 the near-real ground-albedo value. Figure 10 presents the variation of CF as function of \(\beta\) for all 82 sites; the controlling parameter is the ratio \(\mathrm{\rho_{r}=\mathrm{\rho_{g}/\mathrm{\rho_{g0}}}}\). Note that the higher the \(\mathrm{\rho_{r}}\) value is (i.e., for \(\mathrm{\rho_{g}>\mathrm{\rho_{0}}}\)), the more concave the best-fit curve is; in contrast, the lower the \(\mathrm{\rho_{r}}\) value is (i.e., for \(\mathrm{\rho_{g}<\mathrm{\rho_{0}}}\)), the more convex the best-fit curve becomes. In the exceptional case of \(\mathrm{\rho_{g}=\mathrm{\rho_{0}}}\) (as for site #24), \(\mathrm{CF}=1\). All the data points at every \(\beta\) in Figure 10 correspond to the 82 sites. Figure 11 shows the distribution of the \(\mathrm{\rho_{r}}\) values across the 82 sites. A diagram of CF vs. \(\mathrm{\rho_{r}}\) is shown in Figure 12, where a linear relationship exists along all sites at the same \(\beta\). The controlling parameter in this case is \(\beta\); as \(\beta\) increases, so does the slope of the linear fit to the data points. The data points along each line correspond to the 82 sites. of the CF across all sites in the same SEZ, or all SEZs, gives a relationship resembling a site with \(\rho_{\text{r}}>1\). Figure 8: Distribution of the annual (**a**) \(\text{H}_{\text{g}}\) (kWhm\({}^{-2}\)year\({}^{-1}\)) and (**b**) \(\text{H}_{\text{g,t,B/gg}}\) (kWhm\({}^{-2}\)year\({}^{-1}\)) sums over Saudi Arabia, under all-sky conditions and averaged over the period 2005-2016. The different colouring in the \(\text{H}_{\text{g}}\) levels is due to the different colour scales used. Figure 8a is reproduction of Figure 7a in [1]. Figure 10: Variation of the correction factor, CF, as function of the tilt angle of the inclined flat plane, \(\beta\), under all-sky conditions and averaged over the period 2005–2016. The dotted lines are the best-fit curves to the data points for each site, expressed as 3 rd-order polynomials. The blue horizontal line indicates CF = 1. Figure 9: Comparison of monthly mean H\({}_{\rm{g}}\) values from PV-GIS to measured H\({}_{\rm{g}}\) values at ASNOA in the period 2005–2011. The red dashed line represents the best fit to the data points and is expressed by the regression equation: H\({}_{\rm{g}PV\_GIS}\) = 1.06 H\({}_{\rm{g}ASNOA}\) + 14.96 (R\({}^{2}\) = 0.99). The solid black line is the 1:1 (or y = x) line. This figure is reproduction of Figure 8 in [1]. Figure 11: 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. The site #24 has \(\rho_{r}=1\), because its \(\rho_{\rm g}=\rho_{\rm g0}=0.2\). From the above it is confirmed that the curves of CF vs. \(\beta\) (Figure 10) and CF vs. \(\rho_{\rm r}\) (Figure 12) are universal and may be represented graphically as nomograms to allow any one of those variables to be calculated from the other two; this was demonstrated for the first time worldwide by [1].