## 5 Results and Analysis
### Optimal Lags-Based  
Initially the optimal number of runoff lags from PACF plots and current day precipitation is used for model prediction of next day runoff value. The performance of the models for the smaller catchment Fal at Tregony is shown in Table 3. It is apparent that the proposed EO-ELM exhibits better prediction in the train and test phases compared to other applied models in terms of all measured matrices (Table 3). Furthermore, the prediction accuracy of DNN performed less compared to ELM, KELM, PSO-ELM, ANN, SVR and better compared to GBM (Table 3). It is evident from Table 3 that the EO-ELM model with rank 48 in both training and testing (having MAE = 0.25, MAPE = 11.75, NSE = 0.87, R2 = 0.86, RMSE = 0.62, VAF = 86.34 in training and MAE = 0.29, MAPE = 11.18, NSE = 0.96, R2 = 0.91, RMSE = 0.68, VAF = 91.13 in testing) achieved better results as compared to PSO-ELM model with rank 42 in training and 40 in testing (having MAE = 0.26, MAPE = 12.21, NSE = 0.86, R2 = 0.85, RMSE = 0.65, VAF = 85.26 in training and MAE = 0.31, MAPE = 11.29, NSE = 0.95, R2 = 0.90, RMSE = 0.72, VAF = 89.85 in testing). Figures 7 and 8 exhibit better prediction performance of EO-ELM in the train (Figure 7d) and test (Figure 8d) cases respectively compared to other models with their linear equations for predicted and measured values. Figure 9 shows the precise prediction line for EO-ELM (Figure 9a) against observed values in the test case compared to PSO-ELM (Figure 9b). The overfitting lines of peak discharge values are higher and underfitting lines of low discharge values for PSO-ELM are lower compared to EO-ELM (Figure 9). The Taylor plot (Figure 10a,b) confirms the better prediction performance of EO-ELM in terms of statistical comparison of all the models. The performance of the models for the larger catchment of Teifi at Glanteifi is shown in Table 4. It is apparent that the proposed EO-ELM exhibits better prediction in test phase compared to other applied models in terms of all measured matrices (Table 4). Furthermore, the prediction accuracy of DNN performed less compared ELM, KELM PSO-ELM, ANN and better compared to SVR, GBM (Table 4). It is evident from Table 4 that EO-ELM model with rank 48 in training and 47 in testing (having MAE = 3.58, MAPE = 11.77, NSE = 0.95, R2 = 0.95, RMSE = 7.64, VAF = 94.50 in training and MAE = 4.46, MAPE = 11.67, NSE = 0.95, R2 = 0.94, RMSE = 10.18, VAF = 93.46 in testing) achieved better results as compared to PSO-ELM model with rank 42 in both training and testing (having MAE = 0.64, MAPE = 11.26, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **MAE** & **MAPE** & **NSE** & **R2** & **RMSE** & **VAF** & **TOTAL** \\ \hline \multirow{4}{*}{ANN} & Train & 0.28 & 13.71 & 0.85 & 0.84 & 0.68 & 83.93 & \\ \cline{2-9}  & Rank & 6 & 6 & 6 & 6 & 6 & 6 & 36 \\ \cline{2-9}  & Test & 0.34 & 13.48 & 0.94 & 0.89 & 0.77 & 88.61 & \\ \cline{2-9}  & Rank & 5 & 5 & 4 & 4 & 4 & 4 & 26 \\ \hline \multirow{4}{*}{GBM} & Train & 0.42 & 39.1 & 0.83 & 0.83 & 0.72 & 83.04 & \\ \cline{2-9}  & Rank & 1 & 1 & 1 & 1 & 1 & 3 & 8 \\ \cline{2-9}  & Test & 0.66 & 47.97 & 0.89 & 0.78 & 1.09 & 77.72 & \\ \cline{2-9}  & Rank & 1 & 1 & 1 & 1 & 1 & 1 & 6 \\ \hline \hline \end{tabular} ELM: Extreme Learning Machine; KELM: Kernel ELM; PSO-ELM: Particle Swarm Optimization coupled ELM; EO-ELM: Equilibrium Optimizer coupled ELM; DNN: Deep Neural Network; SVR: Support Vector Regression; ANN: Artificial Neural Network; GBM: Gradient Boosting Machine.  
\end{table} 
Table 3: _Cont._  
Figure 7: 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 Fal at Tregony. NSE = 0.94, R2 = 0.94, RMSE = 7.87, VAF = 94.16 in training and MAE = 4.5, MAPE = 12.44, NSE = 0.95, R2 = 0.93, RMSE = 10.45, VAF = 93.10 in testing).