## 6 Conclusions  
This paper developed two data-driven daily R-R modeling approaches, called EO-ELM and DNN, for two different benchmark stations of the catchment in the UK. The ELM, KELM, PSO-ANN, SVR, ANN, GBM were considered to validate the prediction performance of the proposed models. Initially, for an optimal number of input features, a PACF plot was used to feed the models. The main contributions of this paper are:  
1. The use of a new metaheuristic algorithm (called EO) to optimize the input weights and hidden neuron biases of ELM are adequate for the better prediction performance by reducing the prediction error.
2. The DWT is used to decompose the current day rainfall series (previous days rainfall series is already reflected in current day runoff series) and a runoff series (the highest correlated lag from PACF plot) to enhance the prediction performance of the proposed models (EO-ELM and DNN).
3. Finally, the UA and two-tailed \(t\)-test confirm that EO-ELM performs best in optimal lag-based scenario and WDNN best for the wavelet-based scenario. WEO-ELM performs better compared to the other six models  
For lag-based input, the experimental results showed that the one day-ahead discharge forecast performance of EO-ELM was better than the ELM, KELM, PSO-ELM, DNN, SVR, ANN, GBM. For wavelet-based input, the results showed that WDNN performed better due to enhancement of input features. However, WEO-ELM out-performed compared to WELM, WKLEM, WPSO-ELM, WSVR, WANN and WGBM.  
In future, the proposed model should be evaluated on other catchments' data, and the performance of the other machine learning models should be compared to check the prediction capability of the proposed models. The proposed models can be applied to other time series hydrological variable predictions.  
B.R.; Conceptualization, methodology, investigation data curation, original draft preparation, writing--original draft preparation, writing--review and editing, visualization, M.P.S.; supervision, resources, D.K. and R.K.; writing--review and editing, formal analysis, M.R.K.; writing--review and editing, visualization J.-W.H.; review and editing, funding acquisition, W.-S.H., review and editing. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Incheon National University Research Grant in 2021.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Lag-Based** & **ELM** & **RBF-ELM** & **PSO-ELM** & **EOELM** & **DNN** & **SVM** & **ANN** & **GBM** \\ \hline Difference in mean abs. & \multirow{2}{*}{5.15} & \multirow{2}{*}{4.79} & \multirow{2}{*}{4.59} & \multirow{2}{*}{4.46} & \multirow{2}{*}{5.17} & \multirow{2}{*}{7.56} & \multirow{2}{*}{5.10} & \multirow{2}{*}{6.13} \\ error & & &  
Data Availability Statement: Data is available on [[https://nrfa.ceh.ac.uk/](https://nrfa.ceh.ac.uk/)]([https://nrfa.ceh.ac.uk/](https://nrfa.ceh.ac.uk/)) accessed on 5 August 2019 and can be downloaded on request.  
This work was supported by Incheon National University Research Grant in 2021.  
The authors declare no conflict of interest.