Stochastic bedload transport in mountain streams

Describing bedload transport as a stochastic process is an idea that emerged in the 1930s with the pioneering work of Einstein. For a long time, the stochastic approach attracted marginal attention, but the situation has radically changed over the last decade with the recent advances in the theory of bedload transport. In parallel, the implementation of bedload monitoring techniques at high temporal resolution has produced a wealth of interesting results showing, among other things, that classic empirical bedload transport equations do not capture neither the mean behavior of sediment transport rates qs nor its order of magnitude, especially at low sediment transport rates (a case that is most frequent in mountain streams). We have developed a stochastic model, which takes inspiration from population dynamics and provides a stochastic partial differential equation for the number of moving particles. Taking the ensemble average leads to a fairly simple advection diffusion equation for particle activity (i.e., the number of moving particles per unit streambed area). The model has a number of unique features. For instance, it yields the probability distribution of the bedload transport rate and predicts bedform formation for a wide range of Froude numbers.