Approximate solution of the probability density function of bedload transport rate over multiple time scales

Bedload transport rate in mountain rivers is highly fluctuating and has strong stochastic behavior even under steady flow conditions. Its stochastic description thus offers deeper insights into its dynamics than the deterministic one. As a random quantity, it is sampled from experimental devices at a given time resolution i.e. the sampling time scale. Previous studies showed that bedload transport behaves as a scale-dependent process. (Singh et al., 2009). In this study, we report bedload transport rate characteristics over different sampling time scales from an experimental study. Then, starting from Ancey's Markov model (Ancey et al., 2008), we propose a theoretical expression for bedload transport rate that is valid across multiple sampling time scales. Although the complete probability density function(PDF) cannot be analytically obtained, all