Extreme learning machine coupled with Heuristic algorithms for daily streamflow modeling at Lake Ziway Watershed, Ethiopia

Streamflow modeling on a daily scale is essential for managing water resources, such as drought warning, flood mitigation, and reservoir operation. This study aims to predict the daily streamflow by integrating multi-linear regression (MLR) and extreme learning machine (ELM) with metaheuristic algorithms, namely Grey Wolf Optimization (GWO), butterfly optimization algorithm (BOA), Harris Hawks Optimization (HHO), and Whale Optimization Algorithm (WOA). The study was conducted in two steps. First, streamflow modeling was performed using MLR, ELM, and optimized ELM methods (BOA-ELM, HHO-ELM, GWO-ELM, and ELM-WOA) (strategy 1). Afterward, the hybrid linear-nonlinear models were developed by integrating the linear MLR with optimized ELM methods (i.e., MLR-BOA-ELM, MLR-HHO-ELM, MLR-GWO-ELM, and MLR-WOA-ELM) (strategy 2) to estimate streamflow in the Ziway catchment in Ethiopia. The prediction power of the employed models was evaluated using percent bias (Pbias), root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), determination coefficient (R²), as well as different visual measures. The result of the study demonstrated that optimizing ELM with different techniques improved modelling accuracy. During testing, the best streamflow modelling results at Meki and Abura stations were obtained using the hybrid MLR-GWO-ELM with NSE = 0.937 and 0.971, Pbias = -2.517 % and −0.753 %, RMSE = 2.58 m³ /s and 3.454 m³/s, R² = 0.942 and 0.9715, respectively. The MLR-GWO-ELM method improved the NSE value of models in strategy1 (i.e., optimized ELM methods) by 4.551 %-17.897 %, and 3.298 %-21.375 %, at Meki and Abura, respectively. Overall, the findings revealed that the proposed linear-nonlinear hybrid models can potentially model the streamflow in data-scarce watersheds effectively.