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

Hongbo Ma, Joris Heyman, Xudong Fu, Francois Mettra, Christophe Ancey, Gary Parker

Research output: Contribution to journalArticlepeer-review


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 (蠐tI), an invariant stage (tI < t < tc), and a memoryless stage (蠑 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.

Original languageEnglish (US)
Pages (from-to)2653-2673
Number of pages21
JournalJournal of Geophysical Research: Earth Surface
Issue number12
StatePublished - Dec 2014


  • bed load transport
  • fluctuation
  • stochastic theory
  • three-regime relation
  • timescale dependence

ASJC Scopus subject areas

  • Earth-Surface Processes
  • Geophysics


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