## 4 Evaluation and Discussion
### Performance of Forecasting Based on Augmented and Original Dataset  
This Section provides a comprehensive examination of the performance of modeling tests carried out to predict global horizontal irradiance an hour in advance. The performance of six forecasting models has been compared, including SVM, ANN, LSTM, CNN, CNN-LSTM, and LSTM-CNN, to showcase the enhanced accuracy of the forecasting models utilizing augmented data over the models relying solely on original data. Table 3 illustrates that the GAN-CSVR model-based data augmentation exhibits significant potential in improving the accuracy of deep learning forecasting models compared to the original data. Unlike machine learning models, their efficiency remains constant as the amount of input data increases for three cities: San Diego, San Francisco, and Los Angeles. The evaluation metrics whose values are deemed to be the best across all models are given in bold for each site. The results indicate that the proposed forecasting models, when employed with augmented datasets, exhibit greater forecasting accuracy for the three locations compared to the same models applied with the original datasets. The following is an in-depth account of the study findings:  
* The proposed models utilizing augmented datasets outperformed, with RMSE values of 68.56 Wm\({}^{2}\), 60.39 Wm\({}^{2}\), and 83.18 Wm\({}^{2}\) for SVM and 61.07 Wm\({}^{2}\), 57.27 Wm\({}^{2}\), and 74.59 Wm\({}^{2}\) for ANN in Los Angeles, San Diego, and San Francisco, respectively. Figure 5: The CDF curve of GHI data for the original and augmented dataset. Furthermore, in Los Angeles, San Diego, and San Francisco, the LSTM model outperformed, with RMSE values of 36.91 Wm\({}^{2}\), 33.28 Wm\({}^{2}\), and 43.43 Wm\({}^{2}\), while the CNN model outperformed with RMSE values of 48.84 Wm\({}^{2}\), 44.23 Wm\({}^{2}\), and 58.74 Wm\({}^{2}\). However, the hybrid CNN-LSTM outperformed, with RMSE values of 29.68 Wm\({}^{2}\), 23.64 Wm\({}^{2}\), and 34.16 Wm\({}^{2}\). Finally, LSTM-CNN outperformed, with RMSE values of 25.97 Wm\({}^{2}\), 22.26 Wm\({}^{2}\), and 29.14 Wm\({}^{2}\) in Los Angeles, San Diego, and San Francisco, respectively. * The proposed forecasting models utilizing augmented data exhibited superior performance compared to their original data, yielding highly accurate projections for the specified three sites according to the Correlation Coefficient (R) metric. San Francisco has the highest accurate forecast (R = 0.9313), followed by San Diego (R = 0.9589) and Los Angeles (R = 0.9356) in the SVM model, and San Francisco (R = 0.9361), San Diego (R = 0.9501), and Los Angeles (R = 0.9538) in the ANN model. Furthermore, San Francisco (R = 0.9678), San Diego (R = 0.9693), and Los Angeles (R = 0.9695) in the LSTM model, and San Diego (R = 0.9165), San Diego (R = 0.9408) and Los Angeles (R = 0.9392) in the CNN model. Following that, San Francisco (R = 0.9699), followed by San Diego (R = 0.9687) and Los Angeles (R = 0.9691) in the CNN-LSTM model. Finally, in the LSTM-CNN model, San Francisco has the highest accurate forecast (R = 0.9889), followed by San Diego (R = 0.9832) and Los Angeles (R = 0.9836), as shown in Table 3.
* The performance of the proposed forecasting models utilizing augmented data vs. the original data is more accurate when comparing the RMSE and MAE values, as shown in Figure 6. For example, the enhancement of machine learning models utilizing augmented data over original data with respect to MAE is 1.55% to 1.74% for SVM and 4.09% to 4.78% for ANN for San Francisco, San Diego, and Los Angeles, respectively. According to our observations, the efficiency of machine learning models does not change as input data grow in quantity compared to deep learning models. The enhancement of the CNN model utilizing augmented data was 34.13%, 33.44%, and 32.64% for Los Angeles, San Diego, and San Francisco, respectively.