Estimating Mean Bedload Transport Rates and Their Uncertainty

Abstract

Measuring bedload transport rates usually involves measuring the flux of sediment or collecting sediment during a certain interval of time Δt. Because bedload transport rates exhibit significant non‐Gaussian fluctuations, their time‐averaged rates depend a great deal on Δt. We begin by exploring this issue theoretically within the framework of Markov processes. We define the bedload transport rate either as the particle flux through a control surface or as a quantity related to the number of moving particles and their velocities in a control volume. These quantities are double averaged; that is, we calculate their ensemble and time averages. Both definitions lead to the same expression for the double‐averaged mean rate and to the same scaling for the variance's dependence on the length of the sampling duration Δt. These findings lead us to propose a protocol for measuring double‐averaged transport rates. We apply this protocol to an experiment we ran in a narrow flume using steady‐state conditions (constant water discharge and sediment feed rates), in which the time variations in the particle flux, the number of moving particles, and their velocities were measured using high‐speed cameras. The data agree well with the previously defined theoretical relationships. Lastly, we apply our experimental protocol to other flow conditions (a long laboratory flume and a gravel‐bed river) to show its potential across various contexts.