Bed load transport over a broad range of timescales: Determination of three regimes of fluctuations

• Published in: Journal of geophysical research. Earth surface Vol. 119; no. 12; pp. 2653 - 2673
• Main Authors: Ma, Hongbo, Heyman, Joris, Fu, Xudong, Mettra, Francois, Ancey, Christophe, Parker, Gary
• Format: Journal Article
• Language: English
• Published: Washington Blackwell Publishing Ltd 01-12-2014
• Subjects: Bed load; bed load transport; Earth science; Fluctuation; Fluctuations; Flux; Geophysics; Invariants; Load distribution; Probability distribution; Sampling; Sediment transport; Statistics; stochastic theory; three-regime relation; timescale dependence; Titanium; Transport; Variance
• ISSN: 2169-9003; 2169-9011
• DOI: 10.1002/2014JF003308

This paper describes the relationship between the statistics of bed load transport flux and the timescale over which it is sampled. A stochastic formulation is developed for the probability distribution function of bed load transport flux, based on the Ancey et al. (2008) theory. An analytical solution for the variance of bed load transport flux over differing sampling timescales is presented. The solution demonstrates that the timescale dependence of the variance of bed load transport flux reduces to a three‐regime relation demarcated by an intermittency timescale (tI) and a memory timescale (tc). As the sampling timescale increases, this variance passes through an intermittent stage (≪tI), an invariant stage (tI < t < tc), and a memoryless stage (≫ tc). We propose a dimensionless number (Ra) to represent the relative strength of fluctuation, which provides a common ground for comparison of fluctuation strength among different experiments, as well as different sampling timescales for each experiment. Our analysis indicates that correlated motion and the discrete nature of bed load particles are responsible for this three‐regime behavior. We use the data from three experiments with high temporal resolution of bed load transport flux to validate the proposed three‐regime behavior. The theoretical solution for the variance agrees well with all three sets of experimental data. Our findings contribute to the understanding of the observed fluctuations of bed load transport flux over monosize/multiple‐size grain beds, to the characterization of an inherent connection between short‐term measurements and long‐term statistics, and to the design of appropriate sampling strategies for bed load transport flux.
Key Points
Bed load transport flux shows timescale‐dependent fluctuations with scale breaksThese breaks define three regimes: intermittent, invariant, and memorylessTheory explains regimes via particle discreteness and correlated particle motion