Pro+: Automated protrusion and critical shear stress estimates from 3D point clouds of gravel beds

Abstract

The dimensionless critical shear stress (τ*_c) needed for the onset of sediment motion is important for a range of studies from river restoration projects to landscape evolution calculations. Many studies simply assume a τ*_c value within the large range of scatter observed in gravel-bedded rivers because direct field estimates are difficult to obtain. Informed choices of reach-scale τ*_c values could instead be obtained from force balance calculations that include particle-scale bed structure and flow conditions. Particle-scale bed structure is also difficult to measure, precluding wide adoption of such force-balance τ*_c values. Recent studies have demonstrated that bed grain size distributions (GSD) can be determined from detailed point clouds (e.g. using G3Point open-source software). We build on these point cloud methods to introduce Pro+, software that estimates particle-scale protrusion distributions and τ*_c for each grain size and for the entire bed using a force-balance model. We validated G3Point and Pro+ using two laboratory flume experiments with different grain size distributions and bed topographies. Commonly used definitions of protrusion may not produce representative τ*_c distributions, and Pro+ includes new protrusion definitions to better include flow and bed structure influences on particle mobility. The combined G3Point/Pro+ provided accurate grain size, protrusion and τ*_c distributions with simple GSD calibration. The largest source of error in protrusion and τ*_c distributions were from incorrect grain boundaries and grain locations in G3Point, and calibration of grain software beyond comparing GSD is likely needed. Pro+ can be coupled with grain identifying software and relatively easily obtainable data to provide informed estimates of τ*_c. These could replace arbitrary choices of τ*_c and potentially improve channel stability and sediment transport estimates.