## 4 Model Development and Performance Metrics
The whole dataset of two catchments is divided into two parts: (i) training dataset (80%), and (ii) testing dataset (20%). The training dataset is used in the model calibration period and the calibrated model is used to predict the test dataset. In the training phase, the configuration of the ELM has been undertaken by initializing the input weights (\(w_{l}\)) and hidden neurons biases (b\({}_{l}\)) using the population size of EO. After optimizing the decision variables by EO, output weights (\(\beta_{l}\)) are calculated analytically by the basic ELM procedure. Since the number of hidden neurons (\(l\)) influence the ELM performance, a trail was tested between the number of \(l\) versus mean square error (RMSE) (Equation (26)) to fix \(l\). The training data set of 20 hidden neurons showed the better model performance for lags selection using PACF plots (Figure 5b,d). The final architecture of ELM with optimal number of discharge lags and \(P_{t}\) was set to \(n\) number of input neurons (\(n\) = 7, 6 for Fal at Tregony and Teifi at Glanteifi, respectively), 20 hidden neurons, and the number of training  
Figure 5: Autocorrelation function (ACF) and partial autocorrelation function (PACF) plots for daily discharge data of catchment Fal at Tregony (**a**,**b**) and Teifi at Glanteifi (**c**,**d**), respectively. targets as output neurons. The main purpose of the use of EO and PSO is to optimize the input weight matrix (7 or 6 \(\times\) 20) and hidden biases (20 \(\times\) l) repeated within the number of training samples that minimize the error between predicted discharge and observed discharge value. That error value is calculated by Equation (20). \[error=\frac{1}{q}\underset{j=1}{\overset{q}{\sum}}\left(\gamma^{j}-T^{j} \right)^{2} \tag{20}\]  
where \(\gamma^{j}\) and \(T^{j}\) are the observed and predicted target value of the \(j^{\text{th}}\) sample, \(q\) is the total number of training sample. The total number of concentrations or features for EO and PSO particles is 160 (7 \(\times\) 20 + 20) (for Fal at Tregony) and 140 (6 \(\times\) 20 + 20) (for Teifi at Glanteifi) which are tuned during EO-ELM and PSO-ELM development for each run of EO and PSO, respectively. The size of the population is considered as 20 with 100 iterations for the best model performance for both catchments data with optimal discharge lags and current day precipitation. The optimal value of EO parameters are set \(a_{1}\) = 2, \(a_{2}\) = 1 and \(GP\) = 0.5. The optimal PSO parameters are set to \(C_{1}\) = 1 and \(C_{2}\) = 2. In the case of ELM, 20 hidden neurons are selected based on trials for both catchments. For KELM, 10 number of kernel parameter and \(C\) = 1 regularization coefficient is used based on trails for both datasets. The two-layered DNN model is considered for runoff prediction. After several trial and error, the number of hidden neurons in each layer are selected for best performance of DNN. Therefore, first and second hidden layers consist 10 and 5 neurons respectively for both catchments. The optimal batch size is 10 and epochs are set to 100 for DNN. For wavelet-based sub-series decomposition of rainfall and discharge, nine sub-series and one approximation components feed into to the proposed model. The high-pass filters and low-pass filter rainfall and runoff are shown in Figure 6a-d for both catchments. For both catchments, total number of features or concentrations for EO and PSO particle are 525 (20 \(\times\) 25 + 25) and 252 (20 \(\times\) 12 + 12) which are tuned during WEO-ELM and WPSO-ELM development for Fal at Tregony and Teifi at Glanteifi respectively. The size of the population is considered as 20 with 100 iterations for the best model performance for both catchments data. The optimal value of EO parameters are set \(a_{1}\) = 2, \(a_{2}\) = 1 and \(GP\) = 0.5. The optimal PSO parameters are set to \(C_{1}\) = 1 and \(C_{2}\) = 2. After several trials of WELM, 250 hidden neurons are selected for Fal at Tregony and 50 hidden neurons are selected for Teifi at Glanteifi.