## 5 Results and Analysis
### Discrete Wavelet Transform (DWT)-Based  
In UK catchments, the discharge prediction using rainfall and runoff modelling is a challenging task [60; 78; 79]. In order to achieve better prediction result of runoff in both catchments, the authors used the DWT-based time series data pre-processing technique in the rainfall and runoff dataset. Both current day rainfall and current day runoff (the highest correlated runoff data which has greater than 0.8 correlation observed from PACF plots for both catchments (Figure 5b,d) series are decomposed by estimated optimal number of sub-series (D1 to D9) with an approximation (A9) using Equation (19). The decomposed  
Figure 11: Prediction capability of the eight models in train case (**a**) ELM, (**b**) KELM, (**c**) PSO-ELM, (**d**) EO-ELM, (**e**) DNN, (**f**) SVR, (**g**) ANN, and (**h**) GBM for the catchment Teifi at Glanteifi. Figure 12: Prediction capability of the eight models in test case (**a**) ELM, (**b**) KELM, (**c**) PSO-ELM, (**d**) EO-ELM, (**e**) DNN, (**f**) SVR, (**g**) ANN, and (**h**) GBM for the catchment Teifi at Glanteifi. series of rainfall and discharge data are fed into models and next day discharge value is the predicted output value. The performance of the wavelet-based models for the catchment Fal at Tregony is shown in Table 5. It is apparent that the proposed WEO-ELM and WDNN exhibits better prediction in train and test phase compared to others in terms of all measured matrices (Table 5). For this catchment, the prediction accuracy of WDNN is comparable to WEO-ELM and better compared to WELM, WKELM, WPSO-ELM, WSVR, WANN and WGBM  
Figure 13: Statistical comparison for all models for catchment Teifi at Glanteifi: (**a**) train and (**b**) test. (Table 5). It is evident from Table 5 that WEO-ELM model with rank 44 in training and 45 in testing (having MAE = 0.18, MAPE = 11.26, NSE = 0.96, R\({}^{2}\) = 0.96, RMSE = 0.33, VAF = 96.19 in training and MAE = 0.24, MAPE = 11.81, NSE = 0.98, R\({}^{2}\) = 0.96, RMSE\(=\) 0.47, VAF = 96.18 in testing) which is comparable with WDNN model with rank 46 in training and 43 in testing (having MAE = 0.21, MAPE = 13.60, NSE = 0.97, R\({}^{2}\) = 0.97, RMSE = 0.31, VAF = 97.09 in training and MAE = 0.30, MAPE = 15.70, NSE = 0.98, R\({}^{2}\) = 0.97, RMSE = 0.44, VAF = 96.04 in testing). Figures 14 and 15 exhibit better prediction performance of WEO-ELM and WDNN in the train and test case respectively compared to other models with their linear equations for predicted and measured values. Figure 14d,e shows better prediction in train case for WEO-ELM and WDNN respectively against observed values. From Figure 14a-h, it is confirmed that WDNN (R\({}^{2}\) = 0.972) performed better compared to other six ML models. Similarly, Figure 15d,e shows better prediction in test case for WEO-ELM and WDNN, respectively, against observed values. From Figure 15a-h, it is confirmed that WDNN (R\({}^{2}\) = 0.965) performed better compared to the other six ML models. The Taylor plots (Figure 16a,b) confirm the better prediction performance of WDNN in terms of the statistical comparison of all models. Figure 14: Prediction capability of the eight models in train case (**a**) WELM, (**b**) WKELM, (**c**) WPSO-ELM, (**d**) WEO-ELM, (**e**) WDNN, (**f**) WSVR, (**g**) WANN, and (**h**) WGBM for the catchment Fal at Tregony. Figure 15: Prediction capability of the eight models in test case (**a**) WELM, (**b**) WKELM, (**c**) WPSO-ELM, (**d**) WEO-ELM, (**e**) WDNN, (**f**) WSVR, (**g**) WANN, and (**h**) WGBM for the catchment Fal at Tregony. The performance of the wavelet-based models for the catchment Teifi at Glanteifi is shown in Table 6. It is apparent that the proposed WDNN exhibits better prediction in train and test phase compared to others in terms of all measured matrices (Table 6). For this catchment, the prediction accuracy of WEO-ELM follows WDNN and better compared to WKELM, WPSO-ELM, WELM, WANN, WSVR, and WGBM (Table 6).