Reliable prediction of water supply dynamics in large-scale canal systems is critical for water allocation and operational decision-making in inter-basin water transfer projects. Uncertainty in lateral offtake discharges evolves over time and often exhibits multi-peaked distributions due to real-time hydraulic states and unplanned gate operations. However, reliably quantifying and interpreting the evolving uncertainty remains difficult under such dynamically changing and small-sample conditions. Here we show that a physics-guided mixture density network (PgMDN) can effectively characterize this uncertainty while remaining physically consistent. In the proposed PgMDN, physical knowledge is incorporated into the loss function through local mass balance and a consistency constraint between predictions and their associated uncertainty, while long short-term memory layers are employed to model temporal dependencies and multi-factor influences. In addition, Shapley additive explanation analysis is used to identify the dominant hydraulic inputs contributing to predictive uncertainty. Tested on real-world canal datasets, the proposed PgMDN outperforms the standard mixture density network, achieving over a 25% reduction in both mean absolute error and root mean square error, together with improved reliability, as measured by the R-index (increasing from 0.45 to 0.82), and stronger generalization. The results further reveal that water level fluctuations and boundary inflow are key drivers of predictive uncertainty, supporting the physical interpretability of the proposed model. Overall, this study provides a scalable and interpretable tool for real-time modeling of environmental infrastructure and the operational management of large-scale water diversion systems.

An Intelligent control can often be required for the multi-level canal systems in practical engineering, particularly with the increasingly large-scale irrigation districts in China. Nevertheless, most research can focus mainly on the single-level cascaded canal systems. Less attention has been paid to the simulation models and control algorithms of the multi-level canal systems. In this study, the Saint-Venant equations and the implicit finite difference algorithm were employed to establish a simulation model for the multi-level canal systems. The structures were also generalized, such as the inverted siphons and water diversion outlets. The HENRY formula was utilized to determine the relationship between the water levels of the main and branch canals and the flow rates at the water diversion gates. In the coupled control of the main and branch canals, a feedforward + feedback controller was adopted to control the openings of the regulating gates along the main canal and the water diversion gates at the heads of the branch canals. Among them, there were the consistence conditions of the water intake. The control algorithm was then optimized for the water diversion gates, according to the flow error threshold for the high stability of the diversion flow. Taking the Quanmutang Irrigation District Project as an example, the coupled model of the main and branch canals was verified to evaluate the channel’s response and the regulation of the gates. The results indicated that the main-canal-only model was basically consistent with the water level trend simulated by the coupled model of the main and branch canals. But there was a significant difference in the deviation amplitude of the water level. The water intake at the branch canals had a certain influence on the water levels of the main and the upstream canals. But there was a negligible influence on the water levels of the downstream main canals. The interval of the gate operations had a notable impact on the times of gate operation and the stabilization time of the water level. A large time interval reduced the times of gate operation, compared with a small time interval. The stabilization time increased. After setting a 3% flow error threshold for the optimized control algorithm of the water diversion gates, the number of gate operations decreased by approximately 77%, compared with the fixed time interval. The deviation of the water intake flow decreased by approximately 26%, compared with the static gates. This finding can also provide a strong reference to construct and control the complex multi-level models of the canal system.

Channels often freeze in cold regions in winter. A control system of horizontal freezing always causes a significant decrease in the water delivery capacity of channels. Improper regulation may even lead to disasters, such as ice jams and ice dams. A large number of studies on the channel ice conditions have been conducted to improve the water delivery capacity and safety during the ice period. However, it is still lacking in the scheduling decisions from the verified numerical simulation, particularly for the spatiotemporal density of observation data. Remote sensing has great potential for the channel ice monitoring, due to the wide range of observation and high timeliness. This study aims to explore the suitable method for the remote sensing monitoring of channel ice conditions in cold regions. The open channel was taken from the Beijing-Shijiazhuang section in the middle route of the south-to-north water transfer project. Three types of feature space datasets were constructed using 11 bands of Sentinel-2 images, including the complete feature, the optimized feature, and the combined feature. These datasets were selected as the inputs for the classification of the support vector machine (SVM), maximum likelihood estimation (MLE), and random forest (RF). Nine classifiers were trained to identify the freezing range of the channel. An experiment was conducted to extract the freezing range of the channel from the images of the Beijuma check-gate. The performance of classification was compared under different classifications and inputs. The results indicated that the near-infrared (NIR), visible light (R, G, and B), and shortwave infrared (SWIR) were the key bands to recognize the range of the channel freezing. The highest accuracy was achieved in the SVM using the limited sample size, with a producer's accuracy (PA) of 85.10%-87.91% and a commission error (CE) of 10.84%-16.08% under different feature inputs; The accuracy of RF classification was close to that of SVM using complete and optimized feature, with PA=84.67%-86.61%, and CE=13.76%-14.41%. But the classification was seriously deviated from the reality under combined features; The MLE classification shared the low accuracy under all three types of features, indicating unsuitable for the recognition of channel icing range. Overall, the SVM had a low sensitivity to the feature space, whereas, the high-precision observation was achieved in the range of channel freezing under different feature inputs; The RF shared a high sensitivity to feature space, where the unstable accuracy was observed when the input features changed. Taking the SVM with complete features as an example, the spatiotemporal generalization of the classifier was finally verified for the model. The lowest mapping accuracy of 82.09% and the highest misclassification error of 13.82% were achieved at different times and channel segments. The classification model with the better accuracy can be expected to effectively identify the icing range of the channel. The finding can provide a new approach to monitoring the ice conditions in water transfer projects in cold regions. The application scenarios of satellite remote sensing can also be extended to the strong reference in the field of ice monitoring.