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 (RH), 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.

中文翻译：

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基于河流流量预测的多元气候变量，使用受自然启发的混合长短期记忆算法


可靠的河流流量预测对防洪、水资源规划和管理有很大贡献。最近，几种机器学习 （ML） 模型已被用于预测河流流量，表明它们的性能优于传统的统计模型。在这项研究中，基于长短期记忆 （LSTM） 与改进的 Harris hawks 优化 （IHHO） 算法的混合开发了一种新的混合 ML 模型，以理解每月河流流量时间序列的非线性和线性成分。不同的气候变量，包括降水 （P）、气温 （T）、相对湿度 （RH）、蒸散 （E） 和水文变量，即印度奥里萨邦马哈纳迪河流域的水位;用于模型的开发。为了确定 LSTM 模型的超参数，将 HHO、salp swarm 算法 （SSA） 、正弦余弦优化算法 （SCO） 、灰狼优化 （GWO） 和粒子群优化 （PSO） 算法与 LSTM 集成。使用 Willmott 指数 （WI） 、均方根误差 （RMSE） 、决定系数 （R2） 、PBIAS 和平均绝对百分比误差 （MAPE） 对这些模型的性能进行统计评估。获得的结果表明，与 LSTM-HHO、LSTM-SSA、LSTM-SCO、LSTM-GWO、LSTM-PSO 和独立的 LSTM 模型相比，混合 LSTM-IHHO 模型可以产生更精确和可靠的预测。LSTM-IHHO 模型执行了出色的预测结果，RMSE = 19.3658，WI = 0.9614，R2 = 0.9663，PBIAS = −3.5467，RMSE = 19.9854，WI = 0.9608，R2 = 0.9657，PBIAS = 2.3665 对于 Kesinga，RMSE = 20.0019，WI = 0.9605，R2 = 0.96547，PBIAS = −0.351 对于 Salebhata，RMSE = 19.5321，WI = 0.961，R2 = 0.9659，PBIAS = −0。Sundergarh 在测试阶段为 9264。与其他方法相比，LSTM-IHHO 模型还能够以最低的 MAPE 和 RMSE 提供更具体的峰值放电估计值。所提出的混合 LSTM-IHHO 模型非常擅长捕获时间序列的线性和非线性元素以预测河流排放事件。