Manning’s roughness coefficient ($n_c$) is an important parameter characterizing the flow capacity of water transfer channels, and it is also an important and sensitive parameter in one-dimensional (1D) flow simulation. This study focused on the roughness inversion for datasets with different sequence lengths, time steps and anomalous data points. A case study was performed with the datasets of the Shandong Jiaodong Water Transfer Project under steady-state conditions. For sequence lengths, the datasets of 6, 12, 24, 40, 88, and 142 h were selected, all with a time step of 1 min. Subsequently, the time step was changed to 5, 10, 15, 30, 60, and 120 min for the 40 h dataset mentioned above. Finally, the flow data point under a certain moment was selected and changed by 10%, 20%, 30%, and 40% respectively. The results show that there is a quadratic relationship between the $n_c$ value and the objective function value and the optimal $n_c$ value is $n_c=-b/2a$. It is recommended that the $n_c$ value retains four decimal places and is inverted using high-frequency and cleaned datasets.

For an open channel with cascade pumping stations, the water level immediately upstream of the pumping station should be kept constant to ensure pumping stability and lining safety. In this study, a simple method was proposed to determine the control time of the pumping station to ensure a stable water level immediately upstream of the pumping station using reverse analysis. The variable discharge process and fixed water level were taken as the upstream and downstream boundaries of the one-dimensional open channel hydrodynamic model, and the discharge process of the pumping station was obtained under ideal conditions. The control time was determined by the equivalent water volume change considering the step change of the discharge of the pumping station. A case study was performed using the Jiaodong water diversion project from Songzhuang sluice to Huibu pumping station (G1–P1), and the effects of the initial discharge, variable discharge, and downstream water level on the control time were investigated. The results show that (1) the larger the initial discharge, the shorter the control time; (2) increasing the upstream discharge reduced the control time, while decreasing the upstream discharge increased the control time; (3) the control time decreased with the increase of the water depth immediately upstream of the pumping station.

Changes in the opening of gates in open channel water transfer projects will cause fluctuations in the water level and flow of adjacent open channels and thus bring great challenges for real-time water level prediction. In this paper, a novel slope-similar shape method is proposed for real-time water level prediction when the change of gate opening at the next moment is known. The water level data points of three consecutive moments constitute the query. The slope similarity is used to find the historical water level datasets with similar change trend to the query, and then the best slope similarity dataset is determined according to the similarity index and the gate opening change. The water level difference of the next moment of the best similar data point is the water level difference of the predicted moment, and thus the water level at the next moment can be obtained. A case study is performed with the Middle Route of the South-to-North Water Diversion Project of China. The results show that 87.5% of datasets with a water level variation of less than 0.06 m have an error less than 0.03 m, 71.4% of which have an error less than 0.02 m. In conclusion, the proposed method is feasible, effective, and interpretable, and the study provides valuable insights into the development of scheduling schemes.

It is necessary but difficult to accurately predict the water levels in front of the pumping stations of an open-channel water transfer project because of the complex interactions among hydraulic structures. In this study, a novel GRA-NARX (gray relation analysis—nonlinear auto-regressive exogenous) model is proposed based on a gray relation analysis (GRA) and nonlinear auto-regressive exogenous (NARX) neural network for 2 h ahead for the prediction of water levels in front of pumping stations, in which an improved algorithm of the NARX neural network is used to obtain the optimal combination of the time delay and the hidden neurons number, and GRA is used to reduce the prediction complexity and improve the prediction accuracy by filtering input factors. Then, the sensitivity to changes of the training algorithm is analyzed, and the prediction performance is compared with that of the NARX and GRA-BP (gray relation analysis back-propagation) models. A case study is performed in the Tundian pumping station of the Miyun project, China, to demonstrate the reliability and accuracy of the proposed model. It is revealed that the GRA-NARX-BR (gray relation analysis—nonlinear auto-regressive exogenous—Bayesian regularization) model has higher accuracy than the model based only on a NARX neural network and the GRA-BP model with a correlation coefficient (R) of 0.9856 and a mean absolute error (MAE) of 0.00984 m. The proposed model is effective in predicting the water levels in front of the pumping stations of a complex open-channel water transfer project.

A large amount of energy would be consumed for open-channel water transfer projects due to the low efficiency of pumping stations. One measure to improve the efficiency of a pumping station is to install variable-frequency drives (VFDs). In this paper, a discharge optimization model is proposed for a single pumping station equipped with different numbers of variable speed and blade angle-adjustable pump (VSBAP) units, and then a head optimization model is proposed for cascade pumping stations. The study on the Miyun Reservoir Regulation and Storage Project in China shows that the installation of VFDs can increase the number of operable conditions of a single BAP unit by changing the blade angle and speed and ensure the high efficiency of the pumping unit under most operating conditions, thus reducing the energy consumption of the pumping station. It is desirable to install two VFDs in the Tuancheng Lake–Huairou Reservoir section to ensure the long-term operation of the cascade pumping stations in an economically profitable way. In conclusion, the installation of VFDs can effectively reduce the operation cost of cascade pumping stations.