## 4 Conclusions and Discussion  
The main aim of the present study was comparing the global solar radiation on inclined surfaces in three configuration modes by using an isotropic and an anisotropic model for the assessment of the diffuse solar radiation on such surfaces. The solar collector  
Figure 10: Distribution of the annual solar irradiation sums, H\({}_{\text{g}}\), averaged over Saudi Arabia in the period 2005–2016 under all-sky conditions. The left maps (**a,c,e**) were derived by using the ISO model, and the right maps (**b,d,f**) with the HAY one. The solar energy potential is shown in the system configuration: mode (i) in (**a,b**), mode (ii) in (**c,d**), and mode (iii) in (**e,f**). Figure 10a is a reproduction of Figure 7b in [30], Figure 10c is a corrected version of Figure 8b in [31], and Figure 10e is a corrected version of the map in Figure 8b of [32]. The colour code represents the H\({}_{\text{g}}\) levels (in kWhm\({}^{-2}\) year\({}^{-1}\)). types considered were: (i) southward fixed-tilt surface, (ii) fixed-tilt surface tracking the Sun, and (iii) varying-tilt surface tracking the Sun. These types were denoted as mode (i), mode (ii), and mode (iii), respectively. The estimates for all three modes and both isotropic and anisotropic models were compared against each other because of lack of systematic global horizontal or global inclined radiation measurements throughout Saudi Arabia. The isotropic model selected was the Liu-Jordan one (ISO), and the anisotropic model was the Hay (HAY). The analysis showed that for mode (i), the average annual difference of \(\rm H_{g,6S,HAY}-H_{g,6S,ISO}\) estimates was at least (\(\approx\)38 kWhm\({}^{-2}\) year\({}^{-1}\)) over Saudi Arabia. This difference is much smaller than any monthly mean value of \(\rm H_{g}\) (cf. Figure 8). Therefore, the ISO model can be used effectively for mode-(i) estimates. For solar systems in mode-(ii) operation, the difference of \(\approx\)197 kWhm\({}^{-2}\) year\({}^{-1}\) is comparable to a mode-(i) autumn/winter mean monthly \(\rm H_{g}\) value, but definitely less than any monthly value for mode-(ii) systems (cf. Figure 8). This outcome dictates the choice of using the ISO model with a relatively larger estimation error or the HAY model with relatively higher accuracy. For mode-(iii) solar systems, the difference of \(\approx\)225 kWhm\({}^{-2}\) year\({}^{-1}\) is much higher than any mode-(i) monthly mean \(\rm H_{g}\) value, but comparable to any autumn/winter monthly mean \(\rm H_{g}\) value (cf. Figure 8). Therefore, it is recommended that the HAY model must be preferred to the ISO one in this case. The annual mean \(\rm H_{g,HAY}\) (3093.25 kWhm\({}^{-2}\) year\({}^{-1}\)) was found to be less than the \(\rm H_{g,6S,1G}\) (3170.38 kWhm\({}^{-2}\) year\({}^{-1}\)). This discrepancy was attributed to the effect of the ground-albedo variation across Saudi Arabia on the solar radiation estimations for the inclined surfaces in mode-(ii) HAY and mode-(iii) ISO. The ratio \(\rm H_{g,HAY}/H_{g,ISO}\) for the annual mean solar energy yields for all sites and all three modes is a linear function of the geographical latitude, \(\varphi\). The increasing trends of the linear expressions implies a quicker increase in the \(\rm H_{g,HAY}\) values with \(\varphi\) than with the \(\rm H_{g,ISO}\) ones. As stated in Section 2, comparison of the derived results with real measurements could not be feasible because of a lack of systematic solar radiation measurements throughout Saudi Arabia. To overcome this difficulty, comparison of the results between the ISO and the HAY cases was considered by taking the ISO time series as a reference. Specific statistical metrics were employed with the following conclusions:  
* The annual average \(\rm H_{g}\) values estimated for all Saudi Arabia increase from mode-(i) to mode-(iii) solar system operations; a discrepancy, though, exists for the annual \(\rm H_{g,iii-ISO}\) value, it being less than the \(\rm H_{g,ii-HAY}\) one.