Joint Stochastic Bedload Transport and Bed Elevation Model: Variance Regulation and Power Law Rests

Abstract

We describe the joint dynamics of bedload transport and bed elevation changes with a stochastic population model, and we analyze (1) the dependence of bedload flux statistics on local bed elevations and (2) resting time distributions for sediment undergoing burial in the fluctuating sedimentary bed. The model involves entrainment and deposition in a control volume characterized by elevation‐dependent rates, and it exhibits a statistical regulation effect, whereby bed aggradation suppresses the variance of the bedload flux while degradation enhances it. This variance regulation effect is contingent on collective entrainment, whereby moving grains destabilize stationary grains in a positive feedback. When collective entrainment is turned off,bedload transport fluctuations become independent of the bed elevation. Return times from above in the bed elevation time series provide heavy‐tailed power law distributions of resting times with tail behavior characterized by the mean erosion rate and the active layer depth. These results imply bedload statistics measurements on relatively short timescales can be strongly biased by bed elevation changes when collective entrainment occurs, and they support the growing consensus that sediment burial generates heavy‐tailed sediment resting times that ultimately generate anomalous bedload diffusion.