Daily Streamflow Prediction of the Simineh River Using Machine and Deep Learning Models Enhanced with the Aquila Optimizer Algorithm

Introduction
Accurate prediction of river discharge is a fundamental requirement for effective water resources management, flood risk mitigation, reservoir operation, and climate change adaptation strategies. However, process-based hydrological models are often associated with considerable uncertainties arising from parameter estimation, model structure, and the complex nonlinear nature of rainfall–runoff processes, particularly in semi-arid and mountainous catchments. These challenges are exacerbated in regions with limited or heterogeneous hydro-meteorological observations. In recent years, data-driven approaches, including machine learning (ML) and deep learning (DL) models, have emerged as powerful alternatives to traditional physically based models due to their ability to capture nonlinear relationships without explicit representation of physical processes.Among various ML and DL techniques, Artificial Neural Networks (ANN), Random Forests (RF), and Long Short-Term Memory (LSTM) networks have been widely applied to hydrological forecasting problems. Nevertheless, the performance of these models strongly depends on the selection of appropriate input variables, hyperparameter tuning, and the balance between model complexity and generalization capability. Metaheuristic optimization algorithms have recently gained attention as efficient tools for automated hyperparameter optimization, enabling improved predictive accuracy and robustness. The Aquila Optimization (AO) algorithm, inspired by the hunting behavior of eagles, is a relatively new population-based metaheuristic that has demonstrated strong global search capability and fast convergence. The primary objective of this study is to evaluate and compare the performance of ANN, RF, and LSTM models optimized using the Aquila Optimization algorithm (ANN-AO, RF-AO, and LSTM-AO) for daily river discharge prediction. The Simineh River basin, located in West Azerbaijan Province, Iran, was selected as the study area due to its hydrological importance and exposure to hydroclimatic variability. Special emphasis is placed on assessing the impact of different input combinations and identifying the most robust and generalizable modeling scenario.
Materials and Methods
Daily hydro-meteorological data spanning a 40-year period (1982–2022) were used in this study. Observed river discharge and precipitation data were obtained from the Iran Water Resources Management Company, while additional hydroclimatological variables were extracted from NASA POWER satellite products. The input variables included bias-corrected precipitation (mm/day), two-meter air temperature range (°C), relative humidity at two meters (%), wind speed range at ten meters (m/s), and antecedent river discharge with one- to three-day time lags (m³/s). The target output variable was daily river discharge (m³/s). Prior to modeling, an extensive data preprocessing procedure was conducted, including homogeneity testing, detection and removal of outliers, reconstruction of missing values, and linear normalization. Pearson correlation coefficient (PCC) analysis was employed to quantify the relationships between candidate input variables and river discharge. Based on this analysis, seven different input scenarios were defined to systematically investigate the role of hydroclimatic variables and hydrological memory in model performance. The dataset was divided into training (70%) and testing (30%) subsets. The Aquila Optimization algorithm was applied to optimize the hyperparameters of all three models to ensure a fair and objective comparison. Model performance was evaluated using Root Mean Square Error (RMSE), coefficient of determination (R²), and Nash–Sutcliffe Efficiency (NSE) in both training and testing phases, with particular emphasis on testing performance as an indicator of generalization capability.
Results and Discussion
The results demonstrate that all three optimized models were capable of capturing the general dynamics of daily river discharge; however, their predictive accuracies and generalization behaviors varied considerably across different input scenarios. For the ANN-AO model, the best testing performance was achieved under Scenario SN6, which exhibited balanced errors between training and testing phases, indicating reduced overfitting. Nevertheless, the overall predictive accuracy of ANN-AO was lower than that of RF-AO and LSTM-AO. The RF-AO model consistently outperformed the other models in terms of robustness and generalization. In the testing phase, Scenario SN4 yielded the best results with RMSE = 11.931 m³/s, R² = 0.834, and NSE = 88.0%. This scenario combined key hydroclimatic variables with selected discharge lags, achieving an optimal balance between model complexity and predictive power. Notably, scenarios with excessively rich input combinations, such as SN7, showed slightly better performance during training but experienced degradation in testing accuracy, highlighting the negative impact of over-parameterization on generalization. The LSTM-AO model demonstrated competitive performance, particularly in scenarios with limited but informative inputs. The best testing performance for LSTM-AO was observed under Scenario SN1 (RMSE = 10.541 m³/s, R² = 0.862, NSE = 86.0%). However, when all hydroclimatic variables and discharge lags were included, LSTM performance deteriorated, suggesting increased sensitivity to noise and reduced robustness under daily time-step conditions. Overall, the comparative analysis revealed that RF-AO provided the most stable and accurate predictions across scenarios, outperforming LSTM-AO and ANN-AO by approximately 2.3% and 36.0% in NSE, respectively. These findings emphasize that increasing the number of input variables does not necessarily improve predictive performance and that intelligent feature selection plays a more critical role than model complexity alone.
Conclusion
This study confirms the high potential of data-driven models, particularly Random Forest combined with metaheuristic optimization, for reliable daily river discharge prediction in hydroclimatically complex basins. The superior performance of RF-AO highlights the effectiveness of ensemble-based algorithms in reducing variance and enhancing generalization without requiring explicit sequential memory or complex network architectures. The results further demonstrate that excessive input enrichment can negatively affect model robustness, especially in ANN and LSTM frameworks. The findings provide valuable insights for developing intelligent decision-support systems for water resources management, flood forecasting, and climate change impact assessment in data-scarce regions.
Acknowledgement
The authors gratefully acknowledge the Iran Water Resources Management Company for providing hydrological data and NASA POWER for supplying hydroclimatological datasets used in this study.