Probabilistic Versus Deterministic Descriptions of Bed Load Sediment Transport: Clarifying the Inherent Variability in Transport Rates

Abstract

Bed load sediment transport often occurs under rarefied conditions in which particle fluxes have decided uncertainties; as such, probabilistic descriptions that acknowledge a range of outcomes are better suited than deterministic ones. We examine four hours of transport rates of a gravel mixture as measured in a 15-meter experimental channel during steady conditions. Because particle-particle interactions during transport are infrequent in rarefied conditions, we assume sediment crossing events at the end of the flume are random in time such that the flux can be modeled as a Poisson process. Based on experimentally estimated rate constants for each particle size, we compare the resulting theoretical Poisson distributions to the experimental data for varying time intervals. Visual comparison of the distributions combined with chi-square test statistics suggest that larger grain sizes are well described by a Poisson process for all time intervals; in rarefied conditions, this suggests that the entrainment rate is also Poissonian. In contrast, smaller grain sizes exhibit overdispersion, and a compound Poisson process captures the behavior of the flux of small grain sizes at small time intervals more accurately than a simple Poisson process. However, the variance of the smaller grain sizes increases nonlinearly with increasing time interval, and therefore cannot be described by a compound Poisson process or a renewal process; this likely indicates the presence of non-stationarity. This also highlights the need for a better physical understanding of the mechanisms of entrainment for the finer grains that contributes to the intermittency that is only partly reflected in a compound Poisson process. Our results are particularly significant for experimentalists and practitioners; the large natural variability apparent in the experimental data highlights the stochasticity inherent to bed load transport in rarefied conditions, and calls attention to the need for probabilistic descriptions that formally characterize this variability in behavior as well as the uncertainty associated with experimentally estimated parameters. A probabilistic approach provides practitioners with a more holistic view of the system, facilitating more informed predictions and enabling more robust management strategies.