# Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun
## 3 Results
### Monthly Energy Sums  
The intra-annual variation of \(\mathrm{H_{g,I/pg}}\) for all sites is shown in Figure 5. It is seen that the variations of almost all sites are very close to each other, creating a bundle, a zone. There are, however, two sites that present exceptional monthly yields and, therefore, lay above the bundle (i.e., sites #28, and 52). Site #28 lies in the very southeastern part of Saudi Arabia and receives high solar insolation throughout the year. On the contrary, site #52 lies in the very northern part of the country, and lower solar insolation would be expected; this unevenness could probably be attributed to local climatology with very clear skies  
Figure 4: Annual solar energy aggregate (sum, yield) across all 82 sites in Saudi Arabia for each type of installation; 0: horizontal surface; 1: mode (i) static system; 2: mode (ii) dynamic system; 3: mode (iii) dynamic system.  
occurring most time of the year or miscalculation of the ground albedo at the Giovanni platform or inaccurate estimation of solar radiation by the PV-GIS tool or a combination of them. The exceptional performance of solar energy at these two sites is also depicted in Figure 3.  
From Figure 5, one can detect the energy yield per site. Nevertheless, this task is not very informative for solar energy engineers and entrepreneurs, as they would like to have a \"compass\" that would show them an (even approximate) estimate of the monthly solar energy yield. For this reason, the average monthly energy sums for all sites were estimated, and their intra-annual variation for all Saudi Arabia is shown in Figure 6. It might have been anticipated that all curves (mean and mean \(\pm\) 1\(\sigma\)) in Figure 6 would be smoother than those actually derived because of the continuous normality of the solar rays on the inclined flat-plate surface. Nevertheless, the differentiation in the ground-albedo values across the whole territory of Saudi Arabia and the variation in local climatology provided the shapes seen in Figure 6. The mean \(+\) 1\(\sigma\) curve shows a peak in August and a secondary one in October. Since this statistic is related to the dispersion of the 82 H\({}_{\text{gt}}\) values within some limits (i.e., the band of mean \(\pm\) 1\(\sigma\)), the upper limit (mean \(+\) 1\(\sigma\)) corresponds to the dispersion of the higher solar energy values and the lower limit (mean \(-\) 1\(\sigma\)) to the dispersion of the lower solar energy values. In other words, the red line in Figure 6 denotes the weighting of the higher values in the whole sample of the 82 H\({}_{\text{gt}}\) values, while the blue line is weighted towards the lower values in the same sample. This implies that the upper limit is dominated by the high H\({}_{\text{gt}}\) values in the south of the country (i.e., SEZ-A, Figure 3 in [2]), while the lower limit by the low H\({}_{\text{gt}}\) values that occurred in the northern part of Saudi Arabia (i.e., SEZ-C, Figure 3 in [2]). Therefore, the upper limit is influenced by a solar energy pattern with maximum in the summer (August), and the lower limit by a solar energy pattern with a main peak in the summer (June, July) and minor peaks in April and September. These observations are justified by Figure 5 in [2]. Table 3 provides the expression for the monthly H\({}_{\text{gt}}\) values over all Saudi Arabia as function of the month  
Figure 5: Intra-annual variation of H\({}_{\text{gt}/\text{pg}}\) under all-sky conditions for all 82 sites. The monthly values are sums of the hourly solar radiation ones for each site and averaged over the period 2005–2016. The numbers in the legend correspond to the sites shown in column 1, Table 1.  
number, s (s = 1,...,12); the regression equation has a very high R\({}^{2}\) equal to 0.96, implying an almost perfect fit to the data.