  In gravel-bed rivers, bedload transport exhibits considerable variability in
time and space. Recently, stochastic bedload transport theories have been
developed to address the mechanisms and effects of bedload transport
fluctuations. Stochastic models involve parameters such as particle
diffusivity, entrainment and deposition rates. The lack of hard information on
how these parameters vary with flow conditions is a clear impediment to their
application to real-world scenarios. In this paper, we determined the closure
equations for the above parameters from laboratory experiments. We focused on
shallow supercritical flow on a sloping mobile bed in straight channels, a
setting that was representative of flow conditions in mountain rivers.
Experiments were run at low sediment transport rates under steady nonuniform
flow conditions (i.e., the water discharge was kept constant, but bedforms
developed and migrated upstream, making flow nonuniform). Using image
processing, we reconstructed particle paths to deduce the particle velocity and
its probability distribution, particle diffusivity, and rates of deposition and
entrainment. We found that on average, particle acceleration, velocity and
deposition rate were responsive to local flow conditions, whereas entrainment
rate depended strongly on local bed activity. Particle diffusivity varied
linearly with the depth-averaged flow velocity. The empirical probability
distribution of particle velocity was well approximated by a Gaussian
distribution when all particle positions were considered together. In contrast,
the particles located in close vicinity to the bed had exponentially
distributed velocities. Our experimental results provide closure equations for
stochastic or deterministic bedload transport models.
