Scarp diffusion model (${\partial }_{t}h=\kappa {\partial }_x^{2}h$)

A simple model of hillslope smoothing in which sediment flux is proportional to negative slope. For constant transport coefficient $\kappa$, an ideal initial step broadens on scale $\sqrt{\kappa t}$. Real free-face collapse, nonlinear transport, changing climate and deposition can invalidate the linear diffusion equation approximation.