## 5 Results and Discussion
### DCF Performance  
In this section, the DCF performance for short- and long-term forecasting is presented. To validate its performance and ensure that DCF is a generic model that can be utilised for different locations, forecasts were conducted for three cities, i.e., Denver, Boston, and Seattle. The results for all three cities and both algorithms are presented in Table 7. It can be seen that the SVM model performed even better on the short-term prediction in Seattle and Boston than for Denver, while the general trend remained the same as for the Denver results. For the long-term prediction, Denver displayed the best results in terms of R\({}^{2}\); however, both MAE and RMSE were as low or lower for Boston and Seattle than for Denver. Again, the SVM model mostly outperformed FBP in the 1- and 2-hour forecasts, while the FBP model generally generated better results for 3-hour prediction and in the long term. This was observed similarly in the results and its trend validated the chosen DCF model. Two days of short-term predictions by the DCF algorithm are displayed in Figure 12. It shows that the model was noticeably accurate for sunny days (first day), with smooth irradiance transitions. Furthermore, it captured trends for changes in weather, as can be observed on the second day. Despite the rapid change in irradiance, the model still generated accurate predictions. As shown in Figure 13, DCF was applicable to different locations, conserving the general pattern of performance. This validated the DCF algorithm and provided us with confidence that this model will perform well in other not-yet-tested locations. Results of around 90% (91.2%, 90.6%, and 87.6%) for the 1-hour predictions were achieved for R\({}^{2}\), while MAE ranged from 36 W/m\({}^{2}\) for Seattle to 47 W/m\({}^{2}\) for Denver and RMSE from 75 W/m\({}^{2}\) for Seattle to 107 W/m\({}^{2}\) for Denver. For the 2-hour forecast, the R\({}^{2}\) value declined by about 5%, and MAE and RMSE increased by ca. 12 and 18 W/m\({}^{2}\), respectively, for all locations. The 3-hour prediction still generated R\({}^{2}\) of 78% (Seattle) to about 83% (Denver  
Figure 11: Short-term FBP, SVM predicted, and target values: 1 h ahead. and Boston), while MAE ranged from 56 (Seattle) to about 61 W/m\({}^{2}\) (Denver and Boston) and RMSE from 103 W/m\({}^{2}\) (Seattle) to 116 W/m\({}^{2}\) (Denver and Boston). Even the long-term prediction for one year ahead still generated good results for all cities, with high R\({}^{2}\) values and low error values, as shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Algorithm** & **Horizon** & **Denver** & **Seattle** & **Boston** \\ \hline \multicolumn{6}{c}{**R\({}^{2}\)**} \\ \hline \multirow{3}{*}{SVM} & & 1 h & 87.64\% & 90.62\% & 91.19\% \\  & Short term & 2 h & 83.07\% & 85.80\% & 86.77\% \\  & & 3 h & 80.02\% & 82.32\% & 81.94\% \\ \hline \multicolumn{6}{c}{Long term} & 8760 h & 82.56\% & 78.41\% & 75.92\% \\ \hline \multirow{3}{*}{FBP} & 1 h & 83.55\% & 78.35\% & 83.53\% \\  & Short term & 2 h & 83.46\% & 78.32\% & 83.44\% \\  & & 3 h & 83.41\% & 78.32\% & 83.39\% \\ \hline \multicolumn{6}{c}{**MAE**} \\ \hline \multirow{3}{*}{SVM} & & 1 h & 46.70 & 37.40 & 36.15 \\  & Short term & 2 h & 58.86 & 49.27 & 47.48 \\  & & 3 h & 65.96 & 58.39 & 57.95 \\ \hline \multirow{3}{*}{FBP} & Long term & 8760 h & 56.67 & 52.90 & 58.67 \\  & & 1 h & 60.69 & 55.94 & 60.96 \\  & Short term & 2 h & 60.97 & 56.01 & 61.23 \\  & & 3 h & 61.23 & 56.02 & 61.48 \\ \hline \multicolumn{6}{c}{**RMSE**} \\ \hline \multirow{3}{*}{SVM} & & 1 h & 107.37 & 75.36 & 77.05 \\  & Short term & 2 h & 125.68 & 92.72 & 94.42 \\  & & 3 h & 136.51 & 103.48 & 110.29 \\ \hline \multirow{3}{*}{FBP} & Long term & 8760 h & 119.74 & 106.39 & 116.94 \\  & & 1 h & 116.30 & 103.54 & 116.37 \\  & Short term & 2 h & 116.63 & 103.60 & 116.69 \\  & & 3 h & 116.81 & 103.60 & 116.87 \\ \hline \multicolumn{6}{c}{Long term} & 8760 h & 114.83 & 98.77 & 110.99 \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of SVM and FBP performance in all cities.