## 5 Results and Discussion
### Data-Driven Model Results  
The initial model was based on historical solar radiation data and the respective algorithm. SVM outperformed FBP in the 1-hour ahead prediction in terms of R\({}^{2}\) and RMSE (Table 4). It also had the lowest MAE for all three horizons. For 2-hour prediction, the FBP yielded similar results in R\({}^{2}\) and MAE to SVM, while beyond this horizon, it outperformed the SVM model. This is because SVM displayed a stark decline in accuracy with the increase in prediction horizon. For the long-term forecast, FBP resulted in a better R\({}^{2}\) and RMSE, while SVM yielded a better MAE (Table 5). Adding extraterrestrial radiation to the model enhanced the performance of SVM and FBP for both the short- and long-term predictions (Tables 4 and 5). For the short-term prediction, R\({}^{2}\) increased by ca. 7% for FBP, and between 5% (for 1 hour ahead) and 10.5%, (for 3 hours ahead) for the SVM model. MAE decreased noticeably for FBP, by ca. 34 W/m\({}^{2}\), and also, but less drastically, for the SVM model. RMSE also decreased for both algorithms. The SVM model, which included global and extraterrestrial radiation of the same hour and day, 1 and 2 years ago, yielded the best results. The R\({}^{2}\) value in the long-term model increased by 7% for FBP and 17% for SVM. Furthermore, MAE and RMSE were reduced substantially. Overall, the addition of extraterrestrial radiation resulted in considerable improvements of all models. Extraterrestrial radiation on a horizontal surface is a good indicator of potential global horizontal irradiance, stating how much solar radiation is received at the top of the atmosphere for a certain location [51]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & **Data-Driven** & & **Contextual** & \\ \hline \multirow{2}{*}{**Algorithm**} & **Forecast** & **Initial** & **Additional** & **Tuned** & **Negative Elimination** & **Overall** \\  & **Horizon** & **Features** & **Features** & **and Night Hours** & **Improvement** \\ \hline \multicolumn{8}{c}{**R\({}^{2}\)**} \\ \hline \multirow{3}{*}{SVM} & 1 h & 83.27\% & 87.45\% & 87.64\% & 87.64\% & 5.25\% \\  & 2 h & 76.02\% & 82.74\% & 83.07\% & 83.07\% & 9.27\% \\  & 3 h & 72.05\% & 79.56\% & 80.02\% & 80.02\% & 11.07\% \\ \hline \multirow{3}{*}{FBP} & 1 h & 77.84\% & 83.46\% & 83.46\% & 83.55\% & 7.34\% \\  & 2 h & 77.82\% & 83.37\% & 83.37\% & 83.46\% & 7.24\% \\  & 3 h & 77.82\% & 83.33\% & 83.33\% & 83.41\% & 7.18\% \\ \hline \multicolumn{8}{c}{**MAE**} \\ \hline \multirow{3}{*}{SVM} & 1 h & 73.42 & 55.2 & 46.88 & 46.70 & 36.40\% \\  & 2 h & 84.71 & 67.5 & 58.86 & 58.86 & 30.51\% \\  & 3 h & 89.98 & 74.65 & 65.99 & 65.96 & 26.69\% \\ \hline \multirow{3}{*}{FBP} & 1 h & 99.49 & 65.39 & 65.39 & 60.69 & 39.00\% \\  & 2 h & 99.53 & 65.62 & 65.62 & 60.97 & 38.74\% \\  & 3 h & 99.54 & 65.79 & 65.79 & 61.23 & 38.49\% \\ \hline \multicolumn{8}{c}{**RMSE**} \\ \hline \multirow{3}{*}{SVM} & 1 h & 124.93 & 108.2 & 107.37 & 107.37 & 14.06\% \\  & 2 h & 149.55 & 126.90 & 125.68 & 125.68 & 15.96\% \\  & 3 h & 161.48 & 138.07 & 136.51 & 136.51 & 15.47\% \\ \hline \multirow{3}{*}{FBP} & 1 h & 135.03 & 116.47 & 116.47 & 116.30 & 13.87\% \\  & 2 h & 135.07 & 116.78 & 116.78 & 116.63 & 13.65\% \\ \cline{1-1}  & 3 h & 135.09 & 116.94 & 116.94 & 116.81 & 13.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Short-term results using data-driven and contextual optimisation. The hyperparameters were tuned for the SVM model, using grid search cross validation. The tunable parameters were the regularisation parameter \(C\), the size of the error tube \(\epsilon\), and the width of the RBF kernel \(\gamma\). The influence of \(\epsilon\) and \(\gamma\) were minimal, leading to improvements of less than 0.0004% in R\({}^{2}\). Therefore, it was focused on tuning the regulation parameter \(C\). SVMs are generally strongly dependent on their hyperparameters [10]. However, tuning the hyperparameters for these models did not lead to significant improvements. For the short-term prediction, \(C=120\) led to the best results.