Coupling 2D hydro-sedimentary modelling with tracer-based flow competence estimation to determine critical bed shear stress

The critical dimensionless shear stress for particle motion ${\theta }_{cr}$ is one of the most influential parameters in estimating bedload transport rates and modelling river morphodynamics. The estimation of this parameter remains, however, challenging as particle motion depends on riverbed properties (grain size distribution, slope, flow history, etc.), which vary in space and time. This study presents a new, robust method for estimating the critical Shields parameter for two-dimensional hydro-sedimentary modelling in gravel-bed rivers, such as the “Wild Moselle” River (France). This method is based on flow competence estimated from two independent measurements of particle motion (painted bed patches and bedload tracers) and (ii) accurate computations of the maximum grain shear stress derived from a high-resolution and well-calibrated two-dimensional hydro-sedimentary model. The flow competence estimated from each approach provided complementary insights: (i) measuring the $D_{95}$ mobilized out of partially eroded patches enabled us the determination ${\theta }_{cr,D95}$, while (ii) identifying the threshold above which nearly all bedload tracers of a given size were mobilized allowed us to determine the most suitable hiding factor $b$. The ability of the two-dimensional hydro-sedimentary model to predict the motion of the bed surface $D_{50}$ size, using the estimated values ${\theta }_{cr,D50}=0.035$ and $b=-0.6$, was confirmed, as the computed bed shear stress exceeded the critical threshold over more than 80% of the observed eroded areas. This procedure validates both the accuracy of the estimated threshold and the effectiveness of the proposed method for determining it.