Direct Observation of Heavy-Tailed Storage Times of Bed Load Tracer Particles Causing Anomalous Superdiffusion

A consensus has formed that the step length distribution of fluvial bed load is thin tailed and that the observed anomalous superdiffusion of bed load tracer particles must arise from heavy-tailed resting times. However, heavy-tailed resting times have never been directly observed in the field over multiple floods. Using 9years of data from a large bed load tracer experiment, I show that the spatial variance of the tracer plume scales faster than linearly with integrated excess stream power, indicating anomalous superdiffusion. The superdiffusion is caused by a heavy-tailed distribution of observed storage times that is fit with a truncated Pareto distribution with a tail parameter that is predicted by anomalous diffusion theory. The heavy-tailed distribution of storage times causes the tracer virtual velocity to slow over time, indicated by a sublinear increase in the mean displacement that is predicted by the storage time distribution tail parameter. Plain Language Summary The way a plume of river sediment spreads out depends on the length of particle travel distances and the length of time between episodes of motion. If the probability of long stationary periods is particularly high, the sediment can, somewhat counter-intuitively, spread out faster than expected. This paper presents observational evidence that the burial of sediment in a stream bed can cause this faster than expected spreading.