## 2 Materials and Methods
### CEEMDAN-CNN-ATT-LSTM Model
\begin{table}
\begin{tabular}{l l c c c} \hline \hline \multirow{2}{*}{**Resampled**} & \multirow{2}{*}{**Metric**} & \multicolumn{3}{c}{**Time Interval**} \\ \cline{3-5}  & & **1 h** & **6 h** & **12 h** \\ \hline \multirow{4}{*}{10 min (Winter)} & MAE & 111.31 & 117.39 & 116.46 \\  & RMSE & 148.62 & 169.62 & 173.08 \\  & \(R^{2}\) & 0.50 & 0.35 & 0.33 \\  & MAPE & 1,737,572.90 & 1,438,205.13 & 892,101.04 \\ \hline \multirow{4}{*}{10 min (Summer)} & MAE & 116.10 & 222.91 & 218.22 \\  & RMSE & 147.68 & 275.98 & 266.95 \\  & \(R^{2}\) & 0.66 & \(-\)0.17 & \(-\)0.09 \\  & MAPE & 1,865,474.68 & 4,790,196.73 & 4,305,417.09 \\ \hline \multirow{4}{*}{30 min (Winter)} & MAE & 109.64 & 107.95 & 112.63 \\  & RMSE & 147.07 & 151.30 & 154.51 \\  & \(R^{2}\) & 0.44 & 0.42 & 0.39 \\  & MAPE & 650.25 & 546.71 & 645.45 \\ \hline \multirow{4}{*}{30 min (Summer)} & MAE & 114.45 & 119.14 & 128.85 \\  & RMSE & 146.83 & 161.69 & 160.40 \\  & \(R^{2}\) & 0.63 & 0.55 & 0.56 \\  & MAPE & 251.63 & 227.55 & 281.15 \\ \hline \multirow{4}{*}{1 h (Winter)} & MAE & 116.47 & 100.12 & 99.89 \\  & RMSE & 148.78 & 134.13 & 130.42 \\  & \(R^{2}\) & 0.59 & 0.48 & 0.51 \\  & MAPE & 127.96 & 173.36 & 172.79 \\ \hline \multirow{4}{*}{1 h (Summer)} & MAE & 100.22 & 110.30 & 110.43 \\  & RMSE & 135.16 & 146.13 & 141.15 \\ \cline{1-1}  & \(R^{2}\) & 0.46 & 0.61 & 0.64 \\ \cline{1-1}  & MAPE & 157.99 & 126.76 & 144.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of metrics for irradiance prediction with different resampling and forecast horizons. long-term forecasts. The difference in errors for the summer and winter seasons can be attributed to the seasonal effect, as summer tends to have a more compact error distribution than winter. Figure 14: Boxplot of MAE across different time horizons. (**a**) Summer forecast errors. (**b**) Winter forecast errors. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**Season**} \\ \cline{3-4}  & & **Winter** & **Summer** \\ \hline \multirow{4}{*}{Our Model} & MAE & **116.47** & **110.43** \\  & RMSE & **148.78** & **135.16** \\  & \(R^{2}\) & **0.59** & **0.64** \\  & MAPE & **127.96** & **157.99** \\ \hline \multirow{4}{*}{Baseline LSTM} & MAE & 120.52 & 115.32 \\  & RMSE & 151.89 & 140.21 \\  & \(R^{2}\) & 0.55 & 0.60 \\  & MAPE & 130.25 & 162.35 \\ \hline \multirow{4}{*}{Autoencoder} & MAE & 118.73 & 112.57 \\  & RMSE & 150.03 & 137.98 \\  & \(R^{2}\) & 0.57 & 0.62 \\  & MAPE & 129.45 & 160.84 \\ \hline \multirow{4}{*}{Transformer} & MAE & 118.00 & 113.50 \\  & RMSE & 148.50 & 140.75 \\ \cline{1-1}  & \(R^{2}\) & 0.56 & 0.61 \\ \cline{1-1}  & MAPE & 132.50 & 158.25 \\ \hline \hline \end{tabular} Note: In bold are the best results

\end{table} 
Table 8: Comparison of metrics for 12 h ahead irradiance prediction in winter and summer with 1 h resampling. ## 4 Conclusions

This research presents a novel methodology for forecasting solar irradiance in complex areas, combining advanced techniques such as a CEEMDAN, CNNs, attention mechanisms, and LSTM networks in a hybrid architecture. We integrated a CEEMDAN to decompose the solar irradiance variable into more interpretable components, which facilitated the identification of specific patterns in different time zones. The CEEMDAN proved effective in improving the accuracy of the forecasts in our model, providing a robust solution for integrating solar energy into the power grid and outperforming traditional approaches in terms of accuracy and generalization. Our CEEMDAN-CNN-ATT-LSTM model demonstrated its ability to handle the variability and uncertain behavior of solar irradiance by combining the strengths of CNNs to capture spatial relationships between variables, the ability of LSTM networks to extract short-term temporal information, and the integrated attention mechanism to improve the ability to capture long-term spatial and temporal relationships by focusing on the most critical long-term features.