## 4 Conclusions and Discussion
* The annual standard deviation of \(\rm H_{g}\) values for all Saudi Arabia increase from mode-(i) to mode-(iii) solar system operations; nevertheless, these values are almost equal for the configuration mode-(i) ISO and HAY cases. * Application of the \(t\)-test to the annual mean values for the (\(\rm H_{g,ISO}\), \(\rm H_{g,HAY}\)) data-series pairs showed that the data series of the (\(\rm H_{g,6S,ISO}\), \(\rm H_{g,6S,HAY}\)) pair had no statistically significantly different mean values at the confidence level of 95%, whereas the opposite existed for the pairs (\(\rm H_{g,6S,1G}\), \(\rm H_{g,6S,HAY}\)) and (\(\rm H_{g,4,ISO}\), \(\rm H_{g,4,HAY}\)). * The Levene test confirmed the equality-of-the-annual-variances hypothesis at the confidence level of 95% for the ISO and the HAY models by considering all three configuration modes in each case. * The ANOVA test showed that there exists an inequality of the annual means in the ISO or the HAY data series at the confidence level of 95%, by considering all three configuration modes in each case. * The post hoc test agreed with the ANOVA findings (confidence level of 95%). * To investigate the influence of the ISO- or the HAY-diffuse model on the estimation of \(\rm H_{g}\), the Fisher-Snedecor test showed that the application of the diffuse model has a significant effect no matter what solar system configuration mode is used. \"Wells\" of annual mean solar energy ratios \(\rm H_{g,HAY}/H_{g,ISO}\) were formed in their 3D plots against \(\varphi\) and \(\rm\rho_{r}\) (see Figure 9). These dips were spotted in the ranges \(28.5^{\circ}\leq\varphi\leq 31.0^{\circ}\) and \(1.15\leq\rho_{\rm r}\leq 1.55\), and were attributed to the combination of low \(\rm H_{g}\)-ratio levels with rather high \(\rm\rho_{r}\) values and high \(\varphi\) ones. Moreover, this phenomenon was formed due to lower \(\rm H_{g,HAY}\) values that approached low \(\rm H_{g,ISO}\) ones over the specified \(\varphi\) and \(\rm\rho_{r}\) ranges. The solar energy potential maps of Saudi Arabia that consist of annual mean \(\rm H_{g,ISO}\) and \(\rm H_{g,HAY}\) values showed very similar patterns for all three solar system configuration modes. Any differences in the solar energy isoline patterns for the three configuration modes and the two models used may be attributed to the anisotropic ground-albedo pattern around the selected sites. The above conclusions led to the verification of the initial hypothesis that \"no transposition model has an eminent performance\"; at least, this became true for the two models used. Some considerations should be noted regarding the estimation of the solar energy potential of Saudi Arabia on flat-plate surfaces operating under fixed-tilt toward the south, fixed-tilt tracking the Sun, and varying-tilt tracking the Sun modes. * The first thing is the credibility of the results presented in this study, since no evaluation of the ISO and the HAY models took place against real solar radiation measurements. This could be considered a handicap of the study if such measurements were available. Since no such stations exist in Saudi Arabia that perform solar radiation measurements on inclined surfaces, or at least on a horizontal plane, the inter-comparison of the ISO- and the HAY-estimated solar radiation on the considered tilted flat-plate collectors was one way. Nevertheless, this handicap was overcome by invoking specific statistical metrics that verified the credibility of the results by considering the ISO values as a reference. * A second is the verification of the results of this study against real solar radiation measurements in the near future with the build-up of one or more stations at some location(s) of the 82 sites of the study. * A third observation, an outcome of the study, is the utility of adopting as simple as possible solar models for the estimation of the solar energy potential at a site or region. This is particularly important to solar energy engineers or solar energy investors, who incline to make use of simple solar algorithms or tools.