# Solar Potential in Saudi Arabia for Southward-Inclined Flat-Plate Surfaces
## 3 Results  
### Annual Energy Sums and Solar Energy Zones  
Table 2 shows the maximum annual \(\mathrm{H_{g,opt.~{}\mathrm{g}}}\) sums for all sites with their corresponding tilt angles, \(\beta\). The derivation of those energy values was based on the optimum angle \(\beta\) (in the range 15\({}^{\circ}\)-55\({}^{\circ}\) in steps of 5\({}^{\circ}\)) for which maximum \(\mathrm{H_{g,BS}}\) was obtained. Along with each maximum \(\mathrm{H_{g,opt.~{}\mathrm{g}}}\) the corresponding optimum \(\beta\) is shown. Differences of the annual energy sums, \(\Delta\mathrm{H_{g,BS}}\), were then derived through using \(\mathrm{\rho_{g}}\) and \(\mathrm{\rho_{g0}}\) in Equation (3), i.e., \(\Delta\mathrm{H_{g,BS}}=\mathrm{H_{g,BS/\mathrm{\rho_{g}}}}\). - \(\mathrm{H_{g,BS/\mathrm{\rho_{g0}}}}\). Note that the optimum \(\beta\)s differ between the two cases (columns 2 and 3 in Table 2, respectively). The truth is that the reference value of \(\mathrm{\rho_{g0}}\) is applicable to grassland areas; surfaces with different vegetation or no vegetation (e.g., tundras, deserts, snow-covered areas) may have reflectance far from 0.2 [42]. The differences \(\Delta\mathrm{H_{g,BS}}\) are shown in Figure 2 for all 82 sites. From these Figs. it is seen that almost all differences are positive. This occurs for the sites having \(\mathrm{\rho_{g}}\) > \(\mathrm{\rho_{g0}}\), i.e., for a ground albedo greater than 0.2; the negative differences correspond to sites having \(\mathrm{\rho_{g}}\) < \(\mathrm{\rho_{g0}}\), i.e., for a ground albedo less than 0.2. It is considered that the \(\mathrm{H_{g,opt.~{}\mathrm{g}}}\)/\(\mathrm{\rho_{g0}}\) values are closer to reality because of the use of the near-real ground-albedo values \(\mathrm{\rho_{g}}\); therefore, the present study deals with these \"pragmatic\" annual solar energy sums in the rest of the analysis. Figure 3 shows the distribution of \(\mathrm{\rho_{g}}\) over Saudi Arabia. Considering the maximum energy sums and optimal tilt angles given in column 3 of Table 2, a new map was derived in Figure 4, where the 82 sites are shown in different colours and symbols; the sites are grouped according to the same optimum \(\beta\). It is apparent that 3 distinct solar energy zones (SEZ) are formed: (i) SEZ-A (red circles) with optimum \(\beta\) = 20\({}^{\circ}\) S, (ii) SEZ-B (orange circles) with optimum \(\beta\) = 25\({}^{\circ}\) S, and (iii) SEZ-C (green circles) with optimum \(\beta\) = 30\({}^{\circ}\) S. Contrary to this result, [PERSON] et al. [27] divided the country into 5 geographical regions (central, eastern, southern, western, western inland) for the purpose of analysing the solar radiation data from [45]. Nevertheless, the division of [PERSON] et al. 's did not obey any solar radiation criteria, while the SEZs in the present work really meet the mentioned energy criteria; therefore, it is of no practical value. Figure 2: (**a**) Differences of annual maximum solar energy sums, \(\Delta\)H\({}_{\text{g-ept. $\beta$S}}\), on flat planes with optimally-derived tilt angles Figure 1. and (**b**) 44–82, under all-sky conditions and averaged over the period 2005–2016. \(\Delta\)H\({}_{\text{g-ept. $\beta$S}}=\) H\({}_{\text{g-ept. $\beta$S}/\rho_{\text{g-}}}-\) H\({}_{\text{g-ept. $\beta$S}/\rho_{\text{g-0}}}\), where opt. \(\beta\) refers to the angles shown in Table 2 for both ground-albedo cases of \(\rho_{\text{g}}\) and \(\rho_{\text{g0}}\). [PERSON] et al. (2019) estimated 12 optimal angles \(\beta\) for the 12 months of the year for Tabuk (#8 in Table 1), Al Jawf (#9), Riyadh (#10), Jeddah (#16), and Abha (#24). These angles were derived from modelling and they, therefore, have a purely theoretical value, since it is not practical at all to change the tilt angle of the solar panel frame every month. To the contrary, the present work gives a constant tilt angle throughout the year at any site in Saudi Arabia belonging to the same SEZ. [PERSON] et al.