Geomorphic Transport laws: Non-local Flux with Classical Mass Balance By

Most geomorphic transport laws proposed to date are local in character, i.e., they express the sediment flux at a point as a function of the elevation gradient or curvature or other geomorphic quantities at that point only. We argue that non-local constitutive laws, in which the flux at a point depends on the conditions in some larger neighborhood around this point in space and/or time, present a physically-motivated alternative which can handle the presence of heterogeneities known to exist in landscapes over a large range of scales. A particularly attractive subclass of these non-local constitute laws involves fractional (non-integer) derivatives in time and/or space and provides a rich class of models extensively studied in other fields of science. We draw on two examples to illustrate the scale dependency of the parameters of local geomorphic transport equations and suggest that this dependency has the potential to be alleviated by non-local constitutive laws.