Age-based morphodynamic formulation for streamwise and vertical advection and dispersion of tracer particles in rivers

Bed load tracer particles have been widely used to understand the advection and dispersion of bed load in rivers. Recently, consecutive works on advection-dispersion of pebble tracers in rivers have led to the formulation of an Exner-based Master Equation for the dispersal of bedload tracer particles that has no active layer and embeds an age-specific population dynamic model. This formulation not only provides a probabilistic framework for sediment conservation that captures the vertical structure of bed elevation variation as particles erode and deposit but also a way to characterize particle waiting time as a function of depth of burial. The formulation sets an age zero to a particle when first deposited at some elevation and allows age to increase until the bed erodes down to that level and the particle is re-entrained in bed motion. Here we outline the development of this age-based waiting time formulation. We then compute the level-specific particle waiting time probability density function (i.e. the joint probability that a particle has an assigned age at a certain level) from laboratory gravel transport experiments. Using this pdf in the Master Equation and solving numerically, we demonstrate the character of streamwise and vertical advection-dispersion of tracer particles.