Quantifying the Uncertainty Associated with Estimating Sediment Concentrations in Open Channel Flows Using the Stochastic Particle Tracking Method

Abstract

Suspended sediment concentrations are typically estimated using either the advection-diffusion equation or sediment rating curves in a deterministic manner. This study attempts to develop a stochastic approach for quantifying the probabilistic characteristics of sediment concentrations that can account for the uncertainty associated with flow randomness. Turbulence is a primary cause of particle diffusion in a flow. Impacts from such flow randomness on particle diffusion can be observed from two aspects: (1) the degree of spreading of a particle cloud, and (2) variability in concentration curves observed in different releases of particles under the same turbulence intensity. While the former diffusion has been extensively studied, the latter has not been fully investigated, in spite of its significance in terms of identifying the uncertainty associated with estimating concentrations. Herein, the effect of probabilistic characteristics attributed to turbulence on sediment concentrations is evaluated through multiple realizations of a Lagrangian-based stochastic differential equation for particle trajectory. Both the resuspension and deposition of particles are considered in the transport processes. Sediment concentrations can then be estimated from the spatial distribution of particles. As a result of the ensemble standard deviation, it is found that estimating higher-concentration regions is subject to a higher uncertainty. The coefficient of variation representing the extent of variability relative to their mean in lower-concentration regions is found to be more variable than that in higher-concentration regions. It is observed that when the ensemble standard deviation of the concentration is normalized by the square root of the particle number, the magnitude of the variability of concentration curves tends to approach asymptotically to one single curve.