## 3 Case Study
### Model Performance Analysis for DWT-CNN-LSTM Model with Different WD Level  
In the proposed DWT-CNN-LSTM model, the first step is to decompose the raw solar irradiance sequence of certain weather type into several approximate subsequences and detailed subsequences. The key of this step is the determination of decomposition level. As for the solar irradiance forecasting based on certain dataset, both the higher and lower WD level are not conducive to the performance improvement of subsequent forecasting models. Therefore, in this part, the performance comparison of DWT-CNN-LSTM model with different WD level is conducted using two different datasets, namely the dataset of Elizabeth City State University and Desert Rock Station. The detailed results are respectively shown in Tables 5 and 6. As shown in Table 5, under the sunny weather type, the DWT-CNN-LSTM model without WD performs better than that with WD level 1 to 4. This is mainly because the solar irradiance curve of sunny days is smooth and less fluctuating. Therefore, the application of WD will not bring very obvious improvement of the forecasting performance.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Weather Types**} & \multirow{2}{*}{**Error Index**} & \multicolumn{5}{c}{**Wavelet Decomposition (WD) Level**} \\ \cline{3-7}  & & **Level 1** & **Level 2** & **Level 3** & **Level 4** & **without WD** \\ \hline \multirow{3}{*}{Sunny} & MAE & 23.174 & 23.474 & 24.213 & 24.848 & **22.560** \\  & RMSE & 36.548 & 36.363 & 40.323 & 41.244 & **36.226** \\  & R & 0.991 & 0.991 & 0.989 & 0.989 & **0.992** \\ \hline \multirow{3}{*}{Cloudy} & MAE & 86.313 & **81.466** & 83.547 & 88.731 & 86.754 \\  & RMSE & 121.506 & 118.645 & 124.364 & 126.149 & 121.922 \\  & R & 0.926 & 0.928 & 0.925 & 0.919 & 0.925 \\ \hline \multirow{3}{*}{Rainy} & MAE & 95.1758 & 89.503 & 93.126 & 93.695 & 93.694 \\  & RMSE & 145.219 & 139.133 & 143.919 & 142.998 & 142.194 \\  & R & 0.748 & 0.757 & 0.741 & 0.741 & 0.743 \\ \hline \multirow{3}{*}{Heavy rainy} & MAE & 41.234 & 38.642 & 39.981 & 42.774 & 43.435 \\  & RMSE & 68.742 & 67.574 & 68.981 & 70.885 & 70.410 \\ \cline{1-1}  & R & 0.628 & 0.641 & 0.634 & 0.611 & 0.615 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The performance comparison of DWT-CNN-LSTM model at different WD levels using the dataset of Elizabeth City State University.  
Nevertheless, for other three weather types (i.e. cloudy, rainy and heavy rainy) shown in Table 5, DWT based solar irradiance sequence decomposition does enhance the corresponding forecasting performance to a different extent. This can be explained by the fact that the solar irradiance curve of cloudy, rainy and heavy rainy days presents higher volatility, variability and randomness than that of sunny days. Therefore, the raw solar irradiance sequence of cloudy, rainy and heavy rainy days probably includes nonlinear and dynamic components in the form of spikes and fluctuations. The existence of these components will undoubtedly deteriorate the precision of the solar irradiance forecasting models. Additionally, the application of WD can mitigate the above problems.  
To summarize the information provided in Table 5, WD cannot effectively improve the forecasting performance of sunny days. Under the other three weather types, DWT-CNN-LSTM model performs best at WD level 2 when using the dataset of Elizabeth City State University. The results of performance comparison shown in Table 6 are different. Specifically speaking, DWT-CNN-LSTM model of cloudy days performs best at WD level 1 rather than WD level 2 when using the dataset of Desert Rock Station. Therefore, we can draw the conclusion that the influence of WD on forecasting performance, as well as the best WD level, generally varies under different weather types and validation datasets.