Abstract
Modeling the suspended sediment load (SSL) in rivers is of great importance in various fields, e.g. hydrological sciences, water resources management, and dams engineering. In this study, the daily SSL time series at two distinct stations are modeled. The machine learning methods of random forest (RF) and long short-term memory (LSTM) are implemented. The outcomes state that the RF yielded better SSL predictions compared with LSTM. Besides the aforementioned individual models, this study improves the SSL forecasts through the development of hybrid versions of RF and LSTM. To achieve this, an optimizer, i.e. the immune system algorithm (ISA), was initially coupled to the RF. Next, recurrent neural networks (RNN) were hybridized with an LSTM. Therefore, the hybrid forms of RF and LSTM, i.e. RF-ISA and RNN-LSTM, were proposed. The findings reveal that both hybrid models, specifically RNN-LSTM, outperformed their relevant individual forms. The RF-ISA model, with its optimized hyperparameter selection, demonstrated better generalization compared to the baseline RF model, while the RNN-LSTM model effectively captured temporal trends in SSL fluctuations. The values of evaluation error metrics, namely root mean square error (RMSE), normalized RMSE (NRMSE), correlation coefficient (R), Nash-Sutcliffe efficiency (NSE), Willmott’s index (WI), and percent bias (PBIAS) in the test phase for the best model of RNN-LSTM were achieved as follows: R = 0.9434, RMSE = 105567 ton/day, NRMSE = 0.0291, NSE = 0.8893, WI = 0.9701, PBIAS = −0.7135% (first station), and R = 0.9824, RMSE = 57238 ton/day, NRMSE = 0.0311, NSE = 0.9632, WI = 0.9912, PBIAS = 0.0271% (second station). The outcomes of SHapley Additive exPlanations (SHAP) explainer exhibited that one-day delayed SSL and river discharge data represented the greatest and least impacts on the models' output, respectively.