Time scale analysis of bedload discharge over steep slopes: from intermittency to white noise.

Bedload transport remains largely unpredictable in steep slope rivers. Comparing experimental data obtained in a steep slope flume and a stochastic model, we show that bedload discharge statistics strongly depend on the measurement time and spatial scale. We base our talk on a flume experiment that resolved 7 orders of magnitude in time (from 10-2s to 105s) of solid discharge. Computing the variance of the mean solid discharge depending on the sampling time, we distinguished three successive time scales: (1) intermittent (2) correlated and (3) white noise limit. The intermittent time scale is the shortest and is characterized by long periods of time without any transport. Then, we observe a correlation time scale that spread over 3 order of magnitude in time. Correlation can result from various phenomena (bedform migration, collective motion...). The largest scale observed corresponds to the white noise limit, and occurred for time scales larger than 103s. To understand better the dynamics involved, we compare these results to a stochastic model that capture the basic dynamics of particles motion. Along a one-dimensional spatial grid, particles can erode, deposit, or be advected by the flow according to a Markov process. In the continuous limit, this process converges to a stochastic partial differential equation (SPDE) of advection-diffusion-reaction for the variable ρ(x,t), the density of moving particles (or particle activity). We theoretically derived the first and second moments of the SPDE, together with the spatio-temporal correlation function. By integration of the later, we show that the three different scaling are well described by our model. We point out that depending on the chosen measurement technique to sample bedload, one can expect different statistical behaviors. Notably, we distinguish between “local” techniques that sample bedload at a given location through time, and “spatial” techniques that sample bedload also in the spatial dimension