## 3 Case Study
### Simulation Discussion  
In this paper, an improved DL model (i.e., DWT-CNN-LSTM) based on WD, CNN, and LSTM is proposed for day-ahead solar irradiance forecasting. In the actual simulation based on two datasets, the model performance of DWT-CNN-LSTM model with Different WD Level is assessed for four general weather types (i.e., sunny, cloudy, rainy, and heavy rainy). At the same time, the DWT-CNN-LSTM model with certain WD Level is also compared with other DL models (e.g., CNN and LSTM) and traditional forecasting models (e.g., ANN, persistence forecast and ARIMA) for each weather type. The information previously shown in Tables 5-15 is vividly described in the following Figures 11-14, which is conducive to further summary. The changing trends of bars in these four figures are similar, which can be summarized as follows. Figure 10: Actual and forecasted solar irradiance on heavy rainy day pattern using dataset of Elizabeth City State University. Figure 11: The MAE of different forecasting models for sunny, cloudy, rainy and heavy rainy days using the dataset of Elizabeth City State University. Figure 12: The RMSE of different forecasting models for sunny, cloudy, rainy and heavy rainy days using the dataset of Elizabeth City State University. Figure 13: The MAE of different forecasting models for sunny, cloudy, rainy and heavy rainy days using the dataset of Desert Rock Station. First of all, it can be concluded that the influence of WD on forecasting performance, as well as the best WD level, generally varies under different weather types and validation datasets. Additionally, the introduction of certain WD level can improving the forecasting performance of DWT-CNN-LSTM model for cloudy, rainy and heavy rainy days, excluding sunny day. The conclusions are revealed by the fact in Figures 11-14 that the heights of all the blue bars (represent DWT-CNN-LSTM models with different WD Level) of sunny day are higher than the dark green bars (represents CNN-LSTM model). 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 could mitigate the above problems. Secondly, the proposed DWT-CNN-LSTM models with suitable WD Level are always superior to other DL models (e.g., CNN and LSTM) and traditional forecasting models (e.g., ANN, persistence forecast and ARIMA) for cloudy, rainy and heavy rainy days. For sunny days, the CNN-LSTM model without WD also performs better than other DL models and traditional forecasting models. The performance enhancement can be attributed to the application of WD and the reasonable tandem connection of CNN and LSTM. WD is used to decompose the raw solar irradiance sequence data of certain weather types into several subsequences with better behaviors (e.g., more stable variances and fewer outliers). CNN is good at automatically and effectively extracting representative and significant information from the raw subsequence data. As shown in Figure 15, the sequential characteristics with low and high frequency are well captured by CNN. LSTM is able to find the long dependencies of the time series input. In the end, it should be noted that the applicability degree of DWT-CNN-LSTM model under the different weather is not the same. Specifically speaking, the height differences of bars under different weather types reveal that our proposed DWT-CNN-LSTM model obviously performs better than traditional forecasting models (e.g., ARMIA) under cloudy, rainy and heavy rainy days. In other words, our proposed model is more applicable for the solar irradiance forecasting of extreme weather conditions.