An analysis of nonlinearity effects on bed load transport prediction

Because bed load equations are nonlinear and because parameters describing the flow and the bed can have large variance, different results are expected when integrating bed load over a cross section with respect to spatially variable local data (2D), or when computing bed load from cross-section-averaged data, which reduces the problem to uniform conditions (1D). Evidence of these effects is shown by comparing 1D (flume-derived) equations with 2D field measurements, and by comparing a 2D (field-derived) equation with 1D flume measurements, leading to the conclusion that different equations should be used depending on whether local or averaged data are used. However, whereas nonlinearity effects are considerable for low-transport stages, they tend to disappear for higher-flow conditions. Probability distribution functions describing the variance in flow and bed grain size distribution (GSD) are proposed, and the width-integrated bed load data (implicitly containing the natural variance in bed and flow parameters) are used to calibrate these functions. The method consists of using a Monte Carlo approach to match the measured 2D bed load transport rates with 1D computations, artificially reproducing the natural variance associated with the mean input parameters. The Wilcock and Crowe equation was used for the 1D computation because it was considered representative of 1D transport. The results suggest that nonlinearity effects are mostly sensitive to the variance in shear stress, modeled here with a gamma function, whose shape coefficient was shown to increase linearly with the transport stage. This variance in shear stress suggests that even for very low flow conditions, shear stress can locally exceed the critical shear stress for the bed armor, generating local armor breakup. This could explain why the bed load GSD is usually very similar to subsurface GSD, even in the presence of complete armor.