How important is the spatial distribution of shear stress for bedload transport at formative flows?

Gravel-bed rivers are characterized by a spatial distribution of processes operating across the active channel area, where there is considerable variation in the forces that drive and resist bedload entrainment and transport. Subsequently, researchers have sought to improve upon traditional bedload transport equations that use reach-averaged shear stress values (a 1D approach) by accounting for the frequency distribution of shear stress (a 2D approach). Recent studies have demonstrated that 2D approaches more accurately predict transport, particularly at low flows where the threshold of motion is estimated to occur at shear stresses around or above the mean. In these cases, 1D approaches may significantly underestimate transport, or incorrectly predict zero transport when in fact active bedload may be concentrated in narrow zones of the channel cross-section. We conducted fixed-bank stream table experiments to examine the effect of the shear stress distribution on transport capacity at relatively higher formative flows, and compare the performance of bedload transport equations that spanned 1D, quasi-2D, and 2D approaches. These higher flows are particularly relevant to river management as they are associated with greater volumes of transport and geomorphic change. We adopted a physical modelling approach where width and discharge were systematically varied to produce channels with four classes of width-depth ratio (range: 5-50) and mean shear stress (2.0-3.5 Pa). The experiments yielded a range of channel morphologies (plane bed to alternate bar), bar wavelengths, and shear stress distributions, with almost identical reach-average gradients and grain size distributions. Despite considerable differences in morphology and flow depth distributions, most channels had relatively similar shear stress distributions occurring over the channel area. Time-averaged transport capacity was remarkably well correlated with values estimated by all dimensionless bedload transport equations, both 1D and 2D. The results suggest that although it is important to account for the spatial distribution of shear stress at low flows, at relatively high flows the process of bedload transport may be well characterized by the mean shear stress if transport is appropriately temporally averaged.