## 3 Results
### Statistical Analysis of the Annual Solar Energy Values  
The mean and standard-deviation values of the annual solar energy sums for all 82 sites and the three configuration modes are shown in Table 1. Attention must be paid to the standard-deviation values, which show that the dispersion of the solar energy sums across Saudi Arabia is rather uniform for the mode-(i) systems (181.08 kWhm\({}^{-2}\) year\({}^{-1}\) and 181.47 kWhm\({}^{-2}\) year\({}^{-1}\) for the ISO and HAY cases, respectively), but higher for the HAY-estimated values in the configuration mode-(ii) and -(iii) solar systems (compare 182.68 to 191.2 kWhm\({}^{-2}\) year\({}^{-1}\) and 186.88 to 198.49 kWhm\({}^{-2}\) year\({}^{-1}\)). Configuration modes (ii) and (iii) indicate that the ground-albedo value has a higher effect on the estimation of solar radiation on the inclined surface. Moreover, the comparable standard deviations for the ISO solar energy values estimated under all configuration modes (compare 181.08, 182.68, and 186.88 kWhm\({}^{-2}\) year\({}^{-1}\)) justify the insignificant effect of the ground-albedo value on isotropic modelling simulations. The correlation coefficients of the estimated annual solar energy sums across all 82 sites between the ISO- and HAY-modelled results are 0.999, 0.997, and 0.999 for the configuration modes (i), (ii), and (iii), respectively. These are considered high, as they show the absolute co-variability of the annual solar energy sums from the ISO and HAY models over all Saudi Arabia. Despite the co-variability in the data series discussed above, a 2-sided \(t\)-test was applied to the annual mean values from the ISO model and those from the HAY model in the same configuration mode. This was done in order to find whether the data series of the individual average values are significantly different or not for the ISO- and HAY-derived solar radiation estimations in the same configuration mode. In all cases, the ISO data series were taken as the reference. The null hypothesis was that the average value of the HAY data series is equal to the mean value of the ISO data series, and the alternative hypothesis was that the mean values are different. The results of the \(t\)-tests are shown in Table 2. It is seen that the data series of the pair (H\({}_{\text{g,g,ISSO}}\), H\({}_{\text{g,g,HAY}}\)) shows no statistically significant differences between their mean values at the confidence level of 95% (\(t\)-test \(>\) t\({}_{\text{cr}}\)), whereas the opposite exists for the pairs (H\({}_{\text{g,B,t,ISO}}\), H\({}_{\text{g,B,t,HAY}}\)) and (H\({}_{\text{g,LISO}}\), H\({}_{\text{g,L,HAY}}\)) (\(t\)-test \(<\) t\({}_{\text{cr}}\)). In other words, the mean values of the H\({}_{\text{g,g,HAY}}\) time series are equal or very close to the mean values of the H\({}_{\text{g,g,ISSO}}\) data series. The opposite (greater) is the case for the mean values of the H\({}_{\text{g,B,t,HAY}}\) and the H\({}_{\text{g,t,HAY}}\) time series in comparison to those of the H\({}_{\text{g,B,t,ISO}}\) and the H\({}_{\text{g,t,ISO}}\) time series. These results justify the average values shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical Indicator**} & \multicolumn{2}{c}{**Configuration Mode-(i)**} & \multicolumn{2}{c}{**Configuration Mode-(ii)**} & \multicolumn{2}{c}{**Configuration Mode-(iii)**} \\ \cline{2-7}  & **ISO Model** & **HAY Model** & **ISO Model** & **HAY Model** & **ISO Model** & **HAY Model** \\ \hline AVG & 2414.16 & 2452.36 & 2973.56 & 3170.38 & 3093.25 & 3319.00 \\ SD & 181.08 & 181.47 & 182.68 & 191.21 & 186.88 & 198.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Averages (AVG) and standard deviations (SD) of the ISO- and HAY-estimated annual solar energy sums across Saudi Arabia in the period 2005–2016 under all-sky conditions.