Accurately predicting suspended sediment concentrations (SSC) is vital for effective reservoir planning, water resource optimization, and ecological restoration. This study proposes a hybrid ensemble model—VMD-MGGP-NGO-BiLSTM-NGO—which integrates Variational Mode Decomposition (VMD) for signal decomposition, Multi-Gene Genetic Programming (MGGP) for feature filtering, and a double-optimized NGO-BiLSTM-NGO (Northern Goshawk Optimization) structure for enhanced predictive learning. The model was trained and validated using daily discharge and SSC data from the Tangnaihai Hydrological Station on the upper Yellow River. The main findings are as follows: (1) The proposed model achieved an NSC improvement of 19.93% over the Extreme Gradient Boosting (XGBoost) and 15.26% over the Convolutional Neural Network—Long Short-Term Memory network (CNN-LSTM). (2) Compared to GWO- and PSO-based BiLSTM ensembles, the NGO-optimized VMD-MGGP-NGO- BiLSTM-NGO model achieved superior accuracy and robustness, with an average testing-phase NSC of 0.964, outperforming the Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) counterparts. (3) On testing data, the model attained an NSC of 0.9708, indicating strong generalization across time. Overall, the VMD-MGGP-NGO-BiLSTM-NGO model demonstrates outstanding predictive capacity and structural synergy, serving as a reliable reference for future research on SSC forecasting and environmental modeling.

The roughness of a river’s boundary significantly influences the sediment transport process and the ultimate configuration of the river’s stable cross-section. This interplay between boundary roughness and river morphology is crucial to a river’s overall behavior and form. This study aims to analyze the influence of the relative roughness of riverbanks to a riverbed $\lambda$ on the equilibrium form of alluvial rivers using a variational method. The results show the following: (1) As the parameter $\lambda$ transitions from smaller to larger values, noteworthy variations are observed in a river’s characteristics. Specifically, there is a discernible reduction in the calculated maximum sediment discharge, coupled with a corresponding expansion in the optimal width–depth ratio. For instance, when $\lambda$ changes from 1 to 0.1, the optimal width–depth ratio increases by 45%, while the calculated maximum sediment discharge experiences a decrease of 1.62%. (2) An examination of hydraulic geometric relationships, derived by assigning distinct values to the relative roughness of riverbanks to the riverbed, highlights the significant influence of this relative roughness on the ultimate equilibrium configuration of the river channel. Remarkably, this effect remains consistent and stands independently of other variables such as sediment discharge, flow discharge, channel gradient, and sediment size. (3) The critical and average hydraulic geometric relationships deduced in this study closely align with previous research findings. Notably, this research contributes to addressing the existing gap in understanding the mechanistic underpinnings of how river boundary conditions impact the equilibrium forms of rivers, thereby advancing our knowledge of river morphology. Nevertheless, it is imperative to emphasize that while this study provides valuable theoretical insights, the practical application of these findings in the context of river morphological evolution necessitates further in-depth research. It calls for a more comprehensive exploration of the transition from theoretical constructs to real-world applications, thus promoting a deeper understanding of the dynamics that shape river systems.

Riverbanks vary considerably in anti-scourability and consequently take various profiles. By using an isosceles trapezoid as the generalized form of river channel cross-sections and then incorporating the effects of bank angle into the variational analytical approach developed by Huang and Nanson (2000), this study presents a detailed theoretical investigation of the self-adjustment of alluvial channel forms. It is demonstrated that when alluvial channel flow achieves stable equilibrium, a significant decrease in riverbank steepness leads to a slight decrease in maximum sediment (bedload) discharge, and yet results in a significant increase in optimal channel width and a considerable decrease in optimal channel depth. The hydraulic geometry relations, theoretically derived for bank steepness to vary across a wide range, show that among the multivariant controls, the roles of bed sediment size, channel roughness, flow discharge and sediment (bedload) discharge are independent of bank steepness. While the effects of bank steepness illustrated in the theoretically derived hydraulic geometry relations are highly consistent with the results of threshold theory and previous empirical studies, limitations on using bank angle to reflect the anti-scourability of natural riverbanks are also highlighted.