## 3 Case Study
### Performance Comparison Analysis of Different Solar Irradiance Forecasting Models
#### 3.5.4 Comparison Analysis under Heavy rainy Days  
Regarding the weather type of rainy days, the corresponding simulation result in Section 3.5 reveals that the DWT-CNN-LSTM model can reach the best precision at WD level 2. Therefore, the DWT-CNN-LSTM (WD level 2) is adopted once again to be compared with other forecasting models. Similar to the cloudy and rainy days, the solar irradiance data under heavy rainy days is also volatile and fluctuates. The introduction of DWT based sequence decomposition is able to mitigate the adverse influence of fluctuation on forecasting models. This idea is in accordance with comparison results shown in Tables 14 and 15.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Forecasting Models** & **MAE** & **RMSE** & **R** \\ \hline DWT-CNN-LSTM (WD level 2) & 62.160 & 94.979 & 0.680 \\ CNN-LSTM & 63.448 & 95.374 & 0.647 \\ CNN & 64.743 & 96.774 & 0.640 \\ LSTM & 65.014 & 97.096 & 0.641 \\ Manually extracted features-ANN & 81.249 & 138.689 & 0.454 \\ ANN & 66.312 & 99.863 & 0.615 \\ Persistence forecasting & 75.029 & 115.696 & 0.497 \\ ARIMA & 79.473 & 120.744 & 0.477 \\ \hline \end{tabular}
\end{table}
Table 15: The performance comparison of different heavy rainy days’ forecasting models using the dataset of Desert Rock Station.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Forecasting Models** & **MAE** & **RMSE** & **R** \\ \hline DWT-CNN-LSTM (WD level 2) & 38.642 & 67.574 & 0.641 \\ CNN-LSTM & 43.435 & 70.410 & 0.616 \\ CNN & 45.775 & 73.377 & 0.611 \\ LSTM & 44.373 & 74.086 & 0.611 \\ Manually extracted features-ANN & 54.580 & 120.495 & 0.354 \\ ANN & 48.956 & 77.034 & 0.589 \\ Persistence forecasting & 64.416 & 107.290 & 0.401 \\ ARIMA & 63.848 & 110.735 & 0.388 \\ \hline \end{tabular}
\end{table}
Table 14: The performance comparison of different heavy rainy days’ forecasting models using the dataset of Elizabeth City State University.  
Figure 9: Actual and forecasted solar irradiance on rainy day pattern using dataset of Elizabeth City State University.  
Additionally, the great performance improvement is also achieved via automatic feature extraction and long dependency identification, especially under unstable weather conditions. This can also be verified by the following results shown in Table 14. For example, the MAE is reduced a lot from 64.416 in persistence forecasting to 38.642 in DWT-CNN-LSTM (WD level 2). The RMSE is reduced a lot from 107.290 in persistence forecasting to 67.574 in DWT-CNN-LSTM (WD level 2). Additionally, the R is enhanced from 0.401 in persistence forecasting to 0.641 in DWT-CNN-LSTM (WD level 2). The performance improvement achieved by DWT-CNN-LSTM (WD level 2) can also be found when compared with other forecasting models shown in Table 14.  
Moreover, it should be noted the applicability degree of DWT-CNN-LSTM model in different weather conditions is different. For instance, as mentioned in Section 3.5.1, the MAE of sunny days' forecasting is decreased little with 30.271 in the persistence forecasting model and 23.174 in the DWT-CNN-LSTM model. Nevertheless, in Table 12, the MAE of heavy rainy' forecasting is reduced a lot from 64.416 in the persistence forecasting model to 38.642 in the DWT-CNN-LSTM model. This further indicates that our proposed model is more applicable for the solar irradiance forecasting of extreme weather conditions. Similar results can also be found in Table 15. Figure 10 shows the actual and forecasted solar irradiance curve for rainy day pattern using dataset of Elizabeth City State University.