Does the flow of information in a landscape have direction?

There is an emerging viewpoint that the sediment flux at a given point on the landscape may be influenced by landscape properties in a region extending away from the point of interest. Using a general sediment transport model that incorporates this non-local nature via fractional derivatives, we find a strong asymmetry in the direction in which the non-locality affects a given point: For erosional landscapes, physically plausible elevation profiles are obtained only when the spatial influence is restricted to the region upstream of the point of interest. By contrast, in depositional landscapes, the non-local model is guaranteed to produce physically plausible topographic profiles only when the spatial influence is restricted to the region downstream of the point of interest. These results suggest that information flows downstream in an erosional landscape and upstream in depositional landscapes.