Uncertainties in Models Predicting Critical Bed Shear Stress of Cohesionless Particles

Our data show large scatter in the critical Shields stress values for initial sediment motion. The main sources of dispersion are related to the methodological procedures defining the inception of movement (i.e., visual observations or extrapolation of sediment transport rate) and to the estimation of the bed shear stress. The threshold for sediment motion varies with many factors related not only to grain size but also to bed composition (e.g., presence of fine sediments in a coarse matrix), arrangement (e.g., bed roughness, grain orientation, and characteristic lengths of bed structures) and slope. New models to estimate the critical Shields number are proposed using grain size or bed slope or a combination of both. Model parameters and uncertainty are estimated through Bayesian inference using prior knowledge of these parameters and measured data. Apart from the uncertainty in observations, two types of uncertainty can be evaluated: one related to the parameter estimation (i.e., parametric) and one related to the choice of the model (i.e., structural). Finally, a four-parameter model based on the grain size and bed slope yields the best results and demonstrates potential interaction between these two parameters. Model uncertainty, however, remains large, which indicates that other input parameters may be needed to improve the proposed model.