A new formula for predicting movable bed roughness coefficient in the Middle Yangtze River

Computing movable bed roughness plays an important role in the modeling of flood routing and bed deformation, and the magnitude of movable bed roughness is closely associated with complex bedform configurations that change with the sand wave motion. The motion of sand wave is dependent on the incoming flow and sediment conditions and channel boundary. After the operation of the Three Gorges Project, the flow and sediment regime changed remarkably in the Middle Yangtze River (MYR), followed by significant channel adjustments. A dramatic decrease in sediment concentration caused continuous channel degradation and significant variations in cross-sectional profiles of the MYR. These adjustments in the channel boundary influence the motion of sand wave, which can further affect the magnitude of movable bed roughness. A new formula for predicting the movable bed roughness coefficient is developed, which can be expressed by a power function of both Froude number and relative water depth. The proposed formula was first calibrated using 1266 datasets of measurements at five hydrometric stations in the MYR during 2001–2012. A back-calculation process shows that the roughness coefficients calculated by the proposed formula agree well with the observations, with the determination coefficient being equal to 0.88. The proposed formula was further verified using 651 datasets of measurements at these hydrometric stations during 2013–2017. Furthermore, four common roughness formulas selected from the literature were tested for comparison. The results indicate that the calculation accuracy of the proposed formula is significantly higher than that of the previous formulas, and the Manning roughness coefficients predicted by the proposed formula have the errors less than ±30% for 96% of the datasets. Therefore, the new bed roughness predictor proposed in this study can accurately calculate the roughness coefficients straightforwardly without iterative solution and graphical interpolation, and the parameters required in the roughness predictor are easily obtained from the hydrometric observations.