## 2 Materials and Methods
### CEEMDAN-CNN-ATT-LSTM Model
This suggests that the model is more accurate during summer in estimating solar irradiance, especially for larger resampling intervals, and remains reasonably accurate in winter. ### Forecasting at 6 h Ahead with Different Resampling for Winter and Summer

Figure 12 represents the 6 h ahead predictions with different resampling configurations. The figures on the right represent the summer, and those on the left represent the winter. The results show how the model performs under these resampling configurations, considering the effect of seasonal variations. For the 10 min resampling in winter (Figure 12a), the MAE is 117.39, the RMSE is 169.62, and the \(R^{2}\) is 0.35, indicating moderate performance for a 6 h

Figure 11: Predictions 1 h ahead with different resamplings. (**a**) 10 min resampled to 1 h forecasts in winter. (**b**) 10 min resampled to 1 h forecasts in summer. (**c**) 30 min resampled to 1 h forecasts in winter. (**d**) 30 min resampled to 1 h forecasts in summer. (**e**) 1 h resampled to 1 h forecasts in winter. (**f**) 1 h resampled to 1 h forecasts in summer. prediction. The resampling in summer (Figure 12b) yields an MAE of 222.91, an RMSE of 275.98, and a negative \(R^{2}\) of \(-0.17\), reflecting lower prediction accuracy due to increased seasonal variability. During winter (Figure 12c), the RMSE is 151.30, the MAE is 107.95, and the \(R^{2}\) improves to 0.42, showing enhanced accuracy with a larger resampling interval. During summer (Figure 12d), the RMSE is 161.69, the MAE is 119.14, and the \(R^{2}\) improves to 0.55, indicating better prediction accuracy. In winter (Figure 12e), the MAE is 100.12, the RMSE is 134.13, and the \(R^{2}\) is 0.48, reflecting better accuracy in long-term forecasts compared to smaller resampling intervals. In summer, the RMSE decreases to 141.15, the MAE to 110.43, and the \(R^{2}\) reaches 0.64, reflecting the model's ability to capture seasonal patterns in long-term predictions with larger resampling intervals. ### Forecasting at 12 h Ahead with Different Resampling for Winter and Summer

Figure 13 presents the results of 12 h ahead forecasts with varying resampling intervals, comparing winter (left column) and summer (right column). For the 10 min resampled forecasts in winter (Figure 13a), the model achieves an MAE of 116.46, an RMSE of 173.08, and an \(R^{2}\) of 0.33, indicating moderate accuracy. However, in summer (Figure 13b), the error increases significantly with an MAE of 218.22, an RMSE of 266.95, and a negative \(R^{2}\) of \(-0.09\), reflecting higher seasonal variability. The 30 min resampled results in winter (Figure 13c) improve slightly, with an MAE of 112.63, an RMSE of 154.51, and an \(R^{2}\) of 0.39, showing better accuracy over longer intervals. For summer (Figure 13d), the model achieves an MAE of 128.85, an RMSE of 160.40, and an \(R^{2}\) of 0.56, indicating an improvement in forecast precision compared to shorter resampling intervals. Finally, for the 1 h resampling,

Figure 12: Predictions 6 h ahead with different resamplings. (**a**) 10 min resampled to 6 h forecasts in winter. (**b**) 10 min resampled to 6 h forecasts in summer. (**c**) 30 min resampled to 6 h forecasts in winter. (**d**) 30 min resampled to 6 h forecasts in summer. (**e**) 1 h resampled to 6 h forecasts in winter. (**f**) 1 h resampled to 6 h forecasts in summer. the winter predictions (Figure 13e) demonstrate a significant increase in accuracy, with an MAE of 99.89, an RMSE of 130.42, and an \(R^{2}\) of 0.51, while the summer predictions (Figure 13f) also show improved results, with an MAE of 110.43, an RMSE of 141.15, and an \(R^{2}\) of 0.64. These results show that larger resampling intervals improve forecast accuracy, especially over longer prediction horizons such as 12 h ahead. Table 7 summarizes the performance metrics for irradiance prediction at different resampling intervals (10 min, 30 min, and 1 h) and forecast horizons (1 h, 6 h, and 12 h) for both winter and summer seasons. The metrics presented include the MAE, RMSE, \(R^{2}\), and MAPE.