The Influence of Gravel-Bed Structure on Grain Mobility Thresholds: Comparison of Force-Balance Approaches

Grain force-balance models utilize grain protrusion and in-situ resistance force data to evaluate the likely distributions of gravel-bed sediment entrainment thresholds, specifically dimensionless critical shear stress (τ*_c). These methods can give insight into the spatial variability of particle mobilities both within a channel, and between different gravel-beds, but are yet to be evaluated across multiple sites with varying texture and fabric. We evaluate two published force-balance approaches: (a) a Monte Carlo style sampling approach using grain size and topography distributions from field measurements; and (b) an automated point cloud segmentation and analysis approach with an updated set of force-balance equations, Pro+. We compare the workflows, assumptions and inputs for each approach, apply them to an extensive UK-wide data set comprising 45 upland riverbeds, and evaluate the estimated τ*_c distributions. We find that mobility thresholds estimated from both methods are variable, with median τ*_c ranging from 0.05 to 0.15, and are consistent with published values of approximately 0.02–0.1. Uncertainties in grain sampling strategy or point cloud segmentation quality lead to markedly different grain size distributions between approaches, but their resulting influences on τ*_c distributions are small relative to the range of estimated τ*_c. Sensitivity analyses on τ*_c distributions for grain-size fractions also show that bed mobilities are sensitive to the roughness height of the velocity profile. We highlight uncertainties associated with these approaches, suggest areas for further targeted comparisons between methods, and provide guidance for the application of grain force-balance models for estimating entrainment thresholds and bed stability in gravel-bed rivers.