# Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun
## 3 Results
### The Correction Factor  
[PERSON] et al. [1] introduced the notion of the correction factor, CF, which, for the purpose of the present work, is defined as: CF = H\({}_{\rm g,t/pg}\)/H\({}_{\rm g,t/pg0}\). CF is, therefore, the ratio of the annual H\({}_{\rm g,t}\) sum at each site of the 82, calculated twice, once for \(\rho_{\rm g0}\) = 0.2 and a second time for \(\rho_{\rm g}\) = actual value. The practicality of using CF is that it corrects the solar energy incident on an inclined surface under the influence of a ground albedo equal to 0.2 to that which is under the influence of a near-real ground-albedo value. Despite the variation of CF as function of \(\beta\) for all 82 sites in [1; 2], the present analysis of the H\({}_{\rm g,t}\) values does not depend on this parameter at all because of the ever varying tilt angle of the receiving flat-plate surface during the operation of a mode (iii) system. Therefore, a different graph was prepared, i.e., a graph of CF as function of the ground-albedo ratio, \(\rho_{\rm r}\) = \(\rho_{\rm g0}\)/\(\rho_{\rm g}\). Figure 11 shows this dependence, which is linear: CF = 0.0203\(\cdot\)pr + 0.9797 with R\({}^{2}\) = 0.98 at the 95% confidence level; similar dependence was firstly found by [PERSON] et al. [1; 2]. The two lines CF = 1 and \(\rho_{\rm r}\) = 1 in Figure 11 cross each other at the site #24, which has a ground albedo \(\rho_{\rm g}\) = \(\rho_{\rm g0}\) = 0.2, and, therefore, H\({}_{\rm g,t/pg}\) = H\({}_{\rm g,t/pg0}\). The blue and red bands show the confidence and prediction intervals around the best-fit line, respectively. It is seen that many sites are within the blue zone, but most of them are accommodated in the red band. Only four sites lie outside the prediction interval. This observation means that some of the sites (i.e., their CF-\(\rho_{\rm r}\) data pairs) that lie within the confidence interval are significant at the 95% level, while others that are within the prediction zone will be significant at the 95% level in the future (i.e., they will tend to be significant), and those four sites that are outside the prediction zone will be non-significant at the 95% level anyway.  
Figure 11: Variation of the correction factor, CF, as function of the ground-albedo ratio, \(\rho_{\rm r}\), under all-sky conditions; both CF and \(\rho_{\rm r}\) data points are annual averages over each site and over the period 2005–2016. The straight dotted green line expresses the best fit to the data points. The blue and the red zones are the confidence and prediction intervals at the 95% level, respectively. The horizontal black dash-dotted line and the vertical black dashed line indicate the crossing point of CF = 1 and \(\rho_{\rm r}\) = 1.  
Further, by defining the ratio of the annual solar energy sum differences, \(\mathrm{RAH_{g}}=(\mathrm{H_{g,t/pg}}-\mathrm{H_{g,g,S/pg}})/(\mathrm{H_{g,t/pg}}- \mathrm{H_{g,g,t/pg}})\), we derived two more plots. Figure 12a shows the dependence of CF on \(\mathrm{RAH_{g}}\), and Figure 12b the dependence of \(\mathrm{\rho_{r}}\) on \(\mathrm{RAH_{g}}\). Both plots show the mean \(\mathrm{RAH_{g}}\) (black lines) and the (mean \(\mathrm{RAH_{g}}+1\sigma\), mean \(\mathrm{RAH_{g}}-1\sigma\)) zone; this zone includes most of the 82 sites, a fact that is interpreted as meaning that most of the \(\mathrm{RAH_{g}}\) values are statistically significant at the 95% level in relation to those of CF vs. \(\mathrm{\rho_{r}}\) (Figure 11). The other 24 sites outside the band (as #24 for which \(\mathrm{CF}=\mathrm{\rho_{r}}=1\)) can be characterised as reflecting a loose dependence of CF or \(\mathrm{\rho_{r}}\) on \(\mathrm{RAH_{g}}\); this may occur because of the following reasons: (i) inaccurate estimation of \(\mathrm{\rho_{g}}\) at the Giovanni platform, (ii) inaccurate estimation of \(\mathrm{H_{g}}\) by the PV-GIS tool, or (iii) both.  
Figure 12: _Cont._