The influence of gravel-bed structure on grain mobility thresholds: Comparison of force-balance approaches

Abstract

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.

Key Points

• Two different novel force-balance models are used to estimate grain mobility thresholds using resistance force and microtopography data
• An automated point cloud segmentation approach is compared against a Monte Carlo approach which samples inputs from field distributions
• Site-average mobility thresholds are consistent with published values (τ*_c = 0.05 to 0.15). Both approaches produce similar τ*_c estimates

Plain Language Summary

The forces required to mobilize riverbed material in gravel-dominated rivers is important in understanding whether a river is likely to erode into its bed. This force is typically assumed, based on how steep the river is, or how large the material is. We test two process-based approaches, which evaluate the forces acting on a single grain to estimate the forces required to transport it, using data acquired from field measurements and 3D digitized riverbeds. The first approach randomly selects inputs from data observed in the field to evaluate different combinations of gravel sizes, arrangements and stabilities that are most likely to be observed in the field. The second approach automatically identifies individual grains and extracts real data for each identified gravel to estimate the forces required to begin grain movement. We perform each method on 45 upland rivers across the UK, compare their predicted erosion thresholds, and discuss potential limitations and sensitivities for each approach. Our estimated bed erosion thresholds are consistent with those used in other studies but enable a smaller-scale evaluation of their variabilities (e.g., variabilities within rivers, rather than assuming a value for an entire channel), which can be useful in river management.