Formula of movable bed roughness for the Middle Yangtze River

The computation of movable bed roughness is an important step in morphodynamic models. After the operation of the Three Gorges Project (TGP), a dramatic decrease of sediment load entering the Middle Yangtze River (MYR) caused the processes of channel degradation and coarsening of bed material, and the variation characteristics of the movable bed roughness became more complicated. Therefore, it is necessary to propose the formula of movable bed roughness for the MYR. Based on the 1 266 runs of measurements at five hydrometric stations such as Zhicheng, Shashi, and Hankou during the period 2001—2012, Froude number (Fr) and relative water depth (h/D₅₀) were selected as the main factors influencing the magnitude of movable bed roughness. Based on the theory of flow regime partition, the formula of movable bed roughness was established and calibrated by these measurements using the method of multiple nonlinear regression. Finally, the predictive accuracy of the proposed formula was verified against 651 runs of independent measurements at those stations from the MYR during the period 2013—2017. The results indicate that:① the alluvial resistances in the MYR are in the lower or transitional flow regime for most of the time; and ② the calculation accuracy of the proposed formula based on the flow regime partition is significantly higher than the existing formulas with the determination coefficient (R²) of 0.89. Moreover, the Manning's roughness coefficients predicted by the new formula have the errors less than ±30% for 97.7% of the measurements.