## 1 Introduction

[2] Steep slope streams carry large amounts of sediment from glaciers down to valleys. As the mean diameter of grains is relatively large in these rivers, sediment transport mainly takes the form of bedload: particles are never carried entirely by the fluid but slide, roll, and move downstream by small jumps (saltation).

[3] Despite being a key process in mountainous landscape evolution, bedload transport in steep slope rivers is still poorly understood and largely unpredictable. For instance, prediction from modern formulae may diverge by between 1 and 4 orders of magnitude from field data, leaving little hope of quantifying any cumulative sediment volume at long times.

[4] There exist several reasons for the failure of traditional equations when applied to steep slope streams, the most important one being the complexity of the flow in such rivers. For instance, large protruding boulders significantly reduce the transport capacity of the streams and thus often lead to over-prediction of solid discharge [*Yager et al*., 2012]. On the other hand, full transport capacity is also limited by sediment availability, which in turn is difficult to estimate in the field.

[5] Furthermore, the dynamics of moving particles on steep slopes are known to be highly nonlinear and intermittent. The particle flow rate may exhibit chaotic behavior at certain scales. Early experimental results have already pinpointed the fluctuating behavior of bedload discharge, even in precisely controlled flows and under idealized conditions [*Kuhnle and Southard*, 1988]. Recent results show that steep slope channels are particularly prone to such variability [*Ancey et al*., 2006; *Zimmermann et al*., 2010] and strongly suggest the use of a probabilistic framework to model bedload transport.

[6] The first attempt to derive a statistical equation is attributed to *Einstein* [1950]. Analyzing the random motion of particles, Einstein found that bedload discharge should follow a Poisson distribution. Since then, many probabilistic equations have been derived for erosion/deposition models [*Lajeunesse et al*., 2010]. *Turowski* [2010] derived the probability density function (pdf) of the cumulative solid discharge assuming that the distribution of the waiting time between two moving particles is known and that all particles move independently. The Poisson distribution is recovered when waiting times are exponentially distributed. However, Poissonian models seem to underpredict the variability of bedload transport over steep slopes [*Ancey et al*., 2006].

[7] Recently, many studies have shown the singular fractal and intermittent characteristics of bedload data series and their probable origin in long-range correlated processes [*Singh et al*., 2009]. *Ancey et al*. [2008] proposed a Markovian model based on a reduced set of possible particle movements and showed that large fluctuations around the mean and correlation were possible. Based on their experimental observations, *Ancey et al*. [2008] introduced a collective entrainment parameter to account for the collective motion of particles.

[8] Here, we present the results of an experimental study of bedload transport in a steep laboratory flume. We show that there exists a net separation between time scales in the statistics of the solid discharge. Moreover, we demonstrate that the Markovian model of *Ancey et al*. [2008] also predicts a separation between time scales when collective dynamics are considered and for flow close to the onset of particle motion. Thus, we conclude that collective dynamics are of particular relevance in bedload transport over steep slopes at incipient motion conditions.