One Dimensional Hydraulic Flow Routing Incorporating a Variable Grain Roughness Coefficient

The reach-average impacts of frictional forces, which retard flows in man-made channels and natural streams, are basically taken into account by flow resistance coefficients. These coefficients have been commonly treated as either a constant or a variable parameter, while the latter is only feasible through a tedious calibration process considering different flow and channel-boundary conditions. When neither historical records are available nor flow measurement is possible, applying a fixed-value roughness coefficient is practically inevitable. Although variation of Manning's coefficient (n) with flow characteristics has been established in the literature, it has not been systematically implemented into hydraulic flow routing models, particularly because of the absence of a flow-dependent bed roughness predictor (BRP) suitable for numerical applications. In this study, a new grain roughness predictor, which provides derivations of n in respect with discharge and stage, is proposed. This grain roughness estimator, which enables to consider flow-dependent variation of n, is implemented in casting of governing equations of one-dimensional hydraulic flow routing method. In the numerical experiments designed to assess this implementation, three scenarios for n were considered: (1) constant n, (2) variable n computed using the new roughness predictor, and (3) variable n calculated based on the observed data. The third scenario, which requires a significant amount of field measurements, was considered as the benchmark solution. The obtained results showed that applying the proposed BRP to the hydraulic flow routing improved estimated outflows more than 40% based on the mean absolute relative error. The achieved improvement obviously demonstrates that considering variable resistance coefficient, like the one suggested in this study, may considerably improve the results of the flow-related numerical modeling.