## 5 Results and Discussion
### Clustering with Two Parameters  
So far, the analyses have been performed for one dimension k-means clustering for the classification. In previous studies such as [45; 52], two variables are used to classify the day. Therefore, we have performed classification with two parameters and compare the performance of the forecasting with a single parameter classification-based model. To see the effects of two parameters on classification, one site is considered for further analysis. For this purpose, the cloud covers are considered with a clearness index to define a sunny and cloudy day. If the percentage of the cloud covers is high and the clearness index is low, then the day is more likely to be classified as cloudy. Figure 11 shows the classification for Golden, Colorado (USA) with two parameters.  
The results for various forecasting techniques considering both sunny and cloudy days are presented in Table 7. Results show the supremacy of LSTM among other models as expected. Average NRMSE for LSTM, FFNN, SVM and persistence models are recorded as 4.65%, 5.46%, 5.76% and 11.58%, respectively. Errors for this approach are closely comparable with the former classification approach, however, performance is not improved. Therefore, the classification using one parameter is suitable for forecasting with the advantage of better accuracy and less computation burden as more computation time is required for a classification task that uses two parameters.  
Overall, the proposed model is showing better performance for forecasting the SI, however, it has some limitations for a practical system. As in this study, inputs are obtained from the weather stations that are measured values and are assumed as the perfectly forecasted values for the proposed approach. However, in a real system, these exogenous features are used as the forecasted metrological data for the next day to predict the SI. Therefore, the accuracy of the SI prediction may be affected by a forecasted error of the meteorological data. This is the limitation of the data-driven forecasting approach that uses exogenous features as inputs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**RMSE (W/m\({}^{2}\))**} & \multicolumn{3}{c}{**NRMSE (\%)**} \\ \cline{2-7}  & **Sunny** & **Cloudy** & **Avg.** & **Sunny** & **Cloudy** & **Avg.** \\ \hline LSTM & 49.51 & 50.82 & 50.17 & 4.56 & 4.73 & 4.65 \\ FFNN & 53.81 & 64.01 & 58.91 & 4.96 & 5.95 & 5.46 \\ SVM & 57.34 & 67.06 & 62.20 & 5.29 & 6.23 & 5.76 \\ Pers. & 98.63 & 151.22 & 124.93 & 9.10 & 14.06 & 11.58 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results for the proposed and other models with two parameters clustering for Golden.  
Figure 11: Classification with two parameters for Golden.  
Another limitation is related to the data availability. We trained the model using several years' measured data. However, in practice, it might be difficult to obtained measured data of several years to train the model, specifically, for a new site. The proposed solution to the limitation is the generalization of the model for SI forecasting [68]. The model can be generalized using the data from the nearby weather station and the use for the new site. The performance of the generalized model may vary however, but can be improved with time. The model can be trained continuously using upcoming data for a particular site.