A bed load transport equation based on the spatial distribution of shear stress – Oak Creek revisited

Abstract

Abstract. Bed load transport formulations for gravel-bed rivers are often based on reach-averaged shear stress values. However, the complexity of the flow field in these systems results in wide distributions of shear stress, whose effects on bed load transport are not well captured by the frequently used equations, leading to inaccurate estimates of sediment transport. Here, we modified a subsurface-based bed load transport equation to include the complete distributions of shear stress generated by a given flow within a reach. The equation was calibrated and verified using bed load data measured at Oak Creek, OR. The spatially variable flow field characterization was obtained using a two-dimensional flow model calibrated over a wide range of flows between 0.1 and 1.0 of bankfull discharge. The shape of the distributions of shear stress was remarkably similar across different discharge levels, which allowed it to be parameterized in terms of discharge using a gamma function. When discharge is high enough to mobilize the pavement layer (1.0 m3 s−1 in Oak Creek), the proposed transport equation had a similar performance to the original formulation based on reach-averaged shear stress values. In addition, the proposed equation predicts bed load transport rates for lower flows when the pavement layer is still present because it accounts for bed load transport occurring in a small fraction of the channel bed that experiences high values of shear stress. This is an improvement over the original equation, which fails to estimate this bed load flux by relying solely on reach-average shear stress values.