Improving a multi-grain size total sediment load model through a new standardized reference shear stress for incipient motion and an adjusted saltation height description

Abstract. Modelling sediment transport is important to understand how fluvial systems respond to climatic change or other transient conditions such as catastrophic sediment release. In natural rivers, heterogeneity of sediment properties and variability of flow regime result in different modes of transport that all contribute to the total sediment load. Le Minor et al. (2022) presented a sediment transport law for rivers that extends from bed load to suspended load while being relevant for a wide range of grain sizes but not specifically addressing the case of a distribution of grain sizes, which must also consider the interactions between grain classes that are mainly important during the sediment erosion phase. If these interactions are not properly considered, the model overestimates transport rates compared to measured ones. We present a new formalism for the reference shear stress of multiple-size sediments, a parameter governing the onset of transport. We show that using a reference shear stress standardized across datasets improves transport rate predictions made with the model of Le Minor et al. (2022). We show that considering the bed roughness length as a reference transport height for single- and multiple-size sediments significantly improves transport rate predictions. We also suggest that, for multiple-size sediments where the bed surface is not fully mobile, the entrainment coefficient should include a dependency on the fraction of mobile grain sizes at the bed surface, although data are insufficient to add this effect in a definite parameterization. Therefore, using a standardized reference shear stress and a transport length adjusted with a common reference height across all sizes appear to be two critical ingredients of a fully functional multi grain-size total sediment load model based on the disequilibrium length. This adjusted model offers the potential to quantify grain-size specific sediment fluxes when different modes of transport may be observed simultaneously, paving the way for more informed numerical modelling of fluvial morphodynamics and sediment transfers.