## 3 Results
### Annual Solar Energy
* The above conclusion is indeed true because the value of (1) 38.20 kWhm\({}^{-2}\) year\({}^{-1}\) corresponds to just \(\approx\)1.6% of either the annual \(\rm H_{g,BS,ISO}\) value or the annual \(\rm H_{g,BS,HAY}\) one for configuration (i), i.e., (38.20/2414.16) \(\times\) 100% or (38.20/2452.36) \(\times\) 100%, respectively; (2) 196.79 kWhm\({}^{-2}\) year\({}^{-1}\) is equivalent to 6.6% or 6.2% of the annual \(\rm H_{g,\,\rm H,ISO}\) value or the annual \(\rm H_{g,\,\rm H,H\,AY}\) one for configuration (iii), i.e., (196.79/2973.59) \(\times\) 100% or (196.79/3170.38) \(\times\) 100%, respectively; and (3) 225.75 kWhm\({}^{-2}\) year\({}^{-1}\) is translated to 7.3% or 6.8% of the annual \(\rm H_{g,\rm H,ISO}\) value or the annual \(\rm H_{g,\rm H,AY}\) one for configuration (ii), i.e., (225.75/3093.25) \(\times\) 100% or (225.75/3319.00) \(\times\) 100%, respectively. * The ratios \(\rm H_{g,HAY}/H_{g,ISO}\) are: 1.016 (mode (i)), 1.066 (mode (ii)), and 1.073 (mode (iii)). * The differences and the ratios increase from mode (i) to mode (iii). Figure 5 shows the ratio of the annual mean solar energy yields for all sites according to the HAY-modelled estimates to those of the ISO-modelled estimates as a function of the geographical latitude, \(\varphi\) (in degrees N). All three configuration modes have been considered, i.e., configuration mode (i) of \(\rm\beta S\), configuration mode (ii) of \(\rm\beta t\), and configuration mode (iii) of t. The ratios are linear expressions of \(\varphi\). The increasing trend of the linear expressions with \(\varphi\) implies a faster increase in the \(\rm H_{g,HAY}\) values with \(\varphi\) than the \(\rm H_{g,ISO}\) ones. Figure 6 gives explicit answers to these observations. It is seen that the best-fit linear curves to the individual cases of \(\rm H_{g}\) have all negative trends with increasing \(\varphi\), as expected, due to lower solar radiation levels with increasing latitude; nevertheless, the linear expressions for the same configuration mode (see legend of Figure 6) show quicker decreases in the \(\rm H_{g,HAY}\) values with \(\varphi\) than the \(\rm H_{g,ISO}\) ones, except for configuration mode-(i). Figure 4: Annual solar energy yields averaged over the 82 sites in Saudi Arabia and the period 2005–2016 under all-sky conditions. The variations are shown for the 3 solar system configuration-modes and both ISO- and HAY-modelled results. The numbers 1, 2, and 3 on the x-axis represent the configuration modes-(i), -(ii), and -(iii), respectively. The pink arrow shows the lower solar energy in the configuration-(iii) ISO case compared to the configuration-(ii) HAY case. Figure 3: Variation in the annual solar energy yields across the 82 sites of Saudi Arabia and averaged over the period 2005–2016 under all-sky conditions. The modelled variation is shown for the 3 solar system configuration modes and both ISO- and HAY-modelled results. The horizontal lines are the averages of the yields over all sites: the short-dashed ones indicate the ISO model and the solid lines the HAY model. Figure 5: Annual solar energy yield ratios, \(\rm H_{g,HAV}/H_{g,ISO}\). for the 82 sites in Saudi Arabia averaged over the period 2005–2016 as function of the geographical latitude of the site, \(\varphi\), under all-sky conditions. The data are shown for the 3 solar system configuration modes and both ISO- and HAY-modelled results. The best-fit lines have the following expressions: configuration mode-(i), \(\rm H_{g,BS,HAY}/H_{g,BS,ISO}=0.9948+0.0008\)\(\varphi\) with \(\rm R^{2}=0.78\); configuration mode-(ii), \(\rm H_{g,\phi,tHAV}/H_{g,\phi,ISO}=1.0394+0.0011\)\(\varphi\) with \(\rm R^{2}=0.70\); and configuration mode-(iii), \(\rm H_{g,tHAV}/H_{g,tISO}=1.0571+0.0006\)\(\varphi\) with \(\rm R^{2}=0.56\). Figure 6: Annual solar energy yields, \(\rm H_{g}\), at the 82 sites in Saudi Arabia averaged over the period 2005–2016 as a function of the geographical latitude of the site, \(\varphi\), under all-sky conditions.