Estimating the suspended sediment load in the Sefidrood River using meta-heuristic algorithms

Introduction
Suspended sediments are fine particles transported within the water column under turbulent flow conditions, and their movement in rivers is controlled by complex interactions between hydrological processes, flow characteristics, and sediment properties. The deposition of these sediments can significantly reduce river conveyance capacity, increasing flood vulnerability and affecting sustainable water resource management. Rivers, as vital natural systems, are continuously influenced by the transport and accumulation of sediments. Historically, suspended sediment estimation has relied on empirical, statistical, and physically based models. However, in recent years, data-driven approaches, particularly Artificial Neural Networks (ANN) and evolutionary optimization models, have demonstrated considerable potential for improving prediction accuracy. Hybrid ANN models, including ANN-Genetic Algorithm (GA), ANN-Particle Swarm Optimization (PSO), and ANN-Imperialist Competitive Algorithm (ICA), have been widely applied to enhance model optimization, improve convergence performance, and increase the capability of nonlinear prediction. Furthermore, nonlinear machine learning techniques, such as Random Forest (RF) and Support Vector Machine (SVM), have also shown promising performance in suspended sediment load estimation compared with conventional approaches.
This research evaluates a comprehensive set of six models—ANN, ANN-GA, ANN-PSO, ANN-ICA, SVM, and RF—for estimating suspended sediment load in the Sefidrood River. The Sefidrood River is of great importance in northern Iran due to its high sediment transport capacity, considerable rainfall regime, and key role in regional water supply and sediment transfer to the Caspian Sea. The main objective is to compare the predictive performance and generalization capability of different data-driven models to support effective sediment management and future water resource decisions in this region.
Materials and Methods
The Sefidrood River, the largest river in Northern Iran, was selected as the study area. Originating from the Zanjan and Shahrood mountains, the river extends over 765 km, draining a vast catchment area of approximately 59,400 km² into the Caspian Sea. It is characterized by high discharge variability, considerable sediment transport capacity, and a high potential for flooding and sedimentation.
For the simulation, daily discharge and suspended sediment load data were collected from the Gilan Regional Water Authority, covering the statistical period from 2007 to 2022 (1386–1401). The dataset was randomly partitioned, with 70% used for model training and the remaining 30% reserved for independent testing. Prior to modeling, statistical outliers were treated, and the data were normalized using Equation (1) to improve data quality and enhance simulation performance.
Six data-driven models were implemented to estimate suspended sediment load. These included the standard ANN model, three hybrid meta-heuristic versions (ANN-GA, ANN-PSO, and ANN-ICA), and two machine learning techniques (SVM and RF). The models were trained using the available dataset, and their performance was evaluated based on prediction accuracy criteria, including the Root Mean Square Error (RMSE), Mean Squared Error (MSE), and coefficient of determination (R²). The base ANN model was configured with one hidden layer containing 10 neurons, employing the 'tansig' and 'purelin' activation functions for the hidden and output layers, respectively, over 1000 epochs. The hybrid optimizers were set with specific parameters; GA used a population size of 50 with 200 iterations, PSO was implemented with 50 particles and 200 iterations, and ICA utilized 100 countries and 30 imperialists for 150 iterations. Finally, the models were compared using both training and independent testing results to assess predictive accuracy and generalization capability.
Results and Discussion
The performance of the six data-driven models was evaluated using the coefficient of determination (R²), Mean Squared Error (MSE), and Root Mean Square Error (RMSE). During the training phase, the Random Forest (RF) model achieved the highest predictive accuracy (R² = 0.90 and RMSE = 3.49), followed by ANN-GA (R² = 0.87), SVM (R² = 0.86), ANN (R² = 0.85), ANN-ICA (R² = 0.84), and ANN-PSO (R² = 0.76). In the independent testing phase, ANN-ICA produced the best overall performance with the lowest RMSE (4.14) and an R² value of 0.86. ANN-GA achieved the same R² (0.86) with a slightly higher RMSE (4.61), while SVM also demonstrated satisfactory predictive capability (R² = 0.85 and RMSE = 4.37). Although RF showed excellent performance during training, its testing accuracy decreased (R² = 0.83), indicating relatively lower generalization capability than ANN-ICA. Overall, the obtained R² values ranging from approximately 0.76 to 0.90 indicate that all developed models were capable of capturing the nonlinear relationship between discharge and suspended sediment load.
To complement the conventional performance indices, the predictive errors of the six models were statistically compared using the non-parametric Friedman test. The test revealed a highly significant difference among model performances (p = 2.0 × 10⁻⁸ < 0.05), indicating that at least one model differed significantly from the others. The mean-rank analysis showed that ANN obtained the lowest average error rank (2.04), followed by ANN-PSO (3.14), ANN-GA (3.86), ANN-ICA (3.88), SVM (3.88), and RF (4.20). This ranking differs from the RMSE- and R²-based evaluation because the Friedman test considers the ranking of prediction errors at every observation rather than relying on a single summary statistic. Therefore, a model with a lower overall RMSE may still receive a higher mean rank if it produces relatively larger errors at some time steps. Pairwise comparisons were subsequently performed using the Bonferroni post-hoc procedure. The results indicated statistically significant differences between the conventional ANN model and ANN-GA, ANN-ICA, RF, and SVM (p < 0.001), whereas the comparison between ANN and ANN-PSO was marginally non-significant (p = 0.053). No statistically significant differences were detected among ANN-GA, ANN-PSO, ANN-ICA, RF, and SVM (p > 0.05), suggesting that these advanced data-driven approaches provide statistically comparable predictive performance despite slight numerical differences in RMSE and R².
Conclusion
his study evaluated six data-driven approaches, including ANN, ANN-GA, ANN-PSO, ANN-ICA, RF, and SVM, for suspended sediment load estimation in the Sefidrood River. The results demonstrated that model performance differed between the training and testing stages. RF achieved the highest predictive accuracy during training, whereas ANN-ICA provided the best generalization performance during testing by producing the lowest RMSE together with a high coefficient of determination. ANN-GA and SVM also achieved competitive prediction accuracy, confirming the effectiveness of advanced machine learning and hybrid optimization techniques for nonlinear suspended sediment modeling. Beyond the conventional evaluation criteria, the Friedman statistical test confirmed that the overall differences among the six models were statistically significant (p < 0.05). However, the Bonferroni post-hoc analysis showed that these differences were mainly associated with the conventional ANN model, while no significant differences were observed among ANN-GA, ANN-PSO, ANN-ICA, RF, and SVM. These findings demonstrate that model selection should not rely solely on RMSE or R² but should also consider statistical significance tests to provide a more comprehensive assessment of predictive performance.The proposed models can serve as reliable tools for suspended sediment estimation and support sediment management and water resources planning in northern Iran. Nevertheless, the present study was conducted using daily discharge and suspended sediment data from a single hydrometric station during the 2007–2022 period. Therefore, extending the conclusions to other watersheds should be undertaken cautiously. Future research should investigate the applicability of the best-performing models in other river basins and incorporate additional explanatory variables such as rainfall, land use, and morphological characteristics, as well as advanced deep learning approaches, to further improve prediction accuracy and model generalization.