The missing dimension: effects of lateral variation on 1-D calculations of fluvial bedload transport

Most calculations of bedload transport in rivers, including those in numerical models of aggradation and degradation, are 1-D: all hydraulic and transport-rate calculations are averaged over the channel width. Because bedload transport laws are nonlinear, width-averaged calculations will underestimate the true bedload flux if there is any local spatial variation in either the bed or the flow. This paper analyses the effects on bedload transport capacity of spatial variation in applied (τ) and critical (τc) shear stress, separately and in combination. A simple but versatile statistical model is used to represent variability in τ, with allowance for differences between sand- and gravel-bed rivers and for below-bankfull flow. Bedload flux is shown to increase greatly with the variance of τ, especially in gravel-bed rivers. Variability in τc through bed patchiness may increase, reduce, or make little difference to bedload flux depending on the correlation between τ and τc. Simple width averaging leads to severe underestimation of bedload transport in most conditions; some alternatives are considered. The findings have implications for sediment routing models (SRMs), but further research is needed to explore the issue fully.