Monthly River Discharge Forecasting Using Hybrid Models Based on Extreme Gradient Boosting Coupled with Wavelet Theory and Lévy–Jaya Optimization Algorithm

River discharge represents critical hydrological data that can be used to monitor the hydrological status of a river basin. The objective of this study was to forecast the monthly river discharge time-series of two gauging hydrometric sites (USGS 06054500 and USGS 06090800) located on the Missouri River, USA. The forecast was performed using two machine learning models based on extreme gradient boosting (XGB) and K-nearest neighbors (KNN). XGB outperformed the KNN framework in forecasting the river flow. Subsequently, wavelet (W) analysis was incorporated to develop the hybrid W-XGB and W-KNN approaches. Finally, two novel hybrid models were established through the hybridization of XGB and the Lévy–Jaya optimization algorithm (LJA) and simultaneous integration of the wavelet analysis and LJA with the XGB, i.e., XGB-LJA and W-XGB-LJA, respectively. The performances of the models were evaluated using the root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), determination coefficient (R ), and Nash–Sutcliffe efficiency (NSE). In the test phase, the best discharge forecasts at USGS 06054500 and USGS 06090800 were obtained using the hybrid WXGB2-LJA (RMSE = 41.303 m /s, MAE = 28.752 m /s, MBE = 3.377 m /s, R = 0.819, NSE = 0.800) and W-XGB4-LJA (RMSE = 39.310 m /s, MAE = 26.804 m /s, MBE = 1.489 m3/s, R = 0.897, NSE = 0.885), respectively.