River discharge prediction based multivariate climatological variables using hybridized long short-term memory with nature inspired algorithm

Reliable prediction of river discharge can contribute remarkably for flood control, water resources planning and management. In recent times, several machine learning (ML) models have been utilized to predict river discharge, revealing that their performances are superior to conventional statistical models. In this study, a new hybrid ML model was developed based on the hybridization of Long Short-Term Memory (LSTM) with improved Harris hawks optimization (IHHO) algorithm to apprehend the non-linear and linear constituents of monthly river discharge time series. Different climatological variables including precipitation (P), air temperature (T), relative humidity (R_H), evapotranspiration (E) and hydrological variable i.e., water level of Mahanadi river basin in Odisha, India; were used for the model's development. To determine hyper-parameters of LSTM model, HHO, salp swarm algorithm (SSA), sine cosine optimization algorithm (SCO), grey wolf optimization (GWO), and particle swarm optimization (PSO) algorithms were integrated with LSTM. The performance of these models was statistically evaluated using Willmott Index (WI), root mean squared error (RMSE), coefficient of determination (R²), PBIAS and mean absolute percentage error (MAPE). The obtained results revealed that the hybrid LSTM-IHHO model could generate more precise and reliable prediction compared to LSTM-HHO, LSTM-SSA, LSTM-SCO, LSTM-GWO, LSTM-PSO, and the standalone LSTM models. The LSTM-IHHO model performed superior prediction results with RMSE = 19.3658, WI = 0.9614, R² = 0.9663, PBIAS = −3.5467 for Kantamal, RMSE = 19.9854, WI = 0.9608, R² = 0.9657, PBIAS = 2.3665 for Kesinga, RMSE = 20.0019, WI = 0.9605, R² = 0.96547, PBIAS = −0.351 for Salebhata and RMSE = 19.5321, WI = 0.961, R² = 0.9659, PBIAS = −0.9264 for Sundergarh over the testing phase. LSTM-IHHO model was also capable of providing more specific estimates of peak discharge with lowest MAPE and RMSE compared to other methods. The proposed hybridized LSTM-IHHO model was extremely proficient in capturing linear and non-linear elements of the time series for forecasting river discharge events.