  Relationships between sediment flux and geomorphic processes are combined
with statements of mass conservation, in order to create continuum models of
hillslope evolution. These models have parameters which can be calibrated using
available topographical data. This contrasts the use of particle-based models,
which may be more difficult to calibrate, but are simpler, easier to implement,
and have the potential to provide insight into the statistics of grain motion.
The realms of individual particles and the continuum, while disparate in
geomorphological modeling, can be connected using scaling techniques commonly
employed in probability theory. Here, we motivate the choice of a
particle-based model of hillslope evolution, whose stationary distributions we
characterize. We then provide a heuristic scaling argument, which identifies a
candidate for their continuum limit. By simulating instances of the particle
model, we obtain equilibrium hillslope profiles and probe their response to
perturbations. These results provide a proof-of-concept in the unification of
microscopic and macroscopic descriptions of hillslope evolution through
probabilistic techniques, and simplify the study of hillslope response to
external influences.
