A unified framework for modeling landscape evolution by discrete flows

Topographic features such as branched valley networks and undissected convex‐up hillslopes are observed in disparate physical environments. In some cases, these features are formed by sediment transport processes that occur discretely in space and time, while in others, by transport processes that are uniformly distributed across the landscape. This paper presents an analytical framework that reconciles the basic attributes of such sediment transport processes with the topographic features that they form and casts those in terms that are likely common to different physical environments. In this framework, temporal changes in surface elevation reflect the frequency with which the landscape is traversed by geophysical flows generated discretely in time and space. This frequency depends on the distance to which flows travel downslope, which depends on the dynamics of individual flows, the lithologic and topographic properties of the underlying substrate, and the coevolution of topography, erosion, and the routing of flows over the topographic surface. To explore this framework, we postulate simple formulations for sediment transport and flow runout distance and demonstrate that the conditions for hillslope and channel network formation can be cast in terms of fundamental parameters such as distance from drainage divide and a friction‐like coefficient that describes a flow's resistance to motion. The framework we propose is intentionally general, but the postulated formulas can be substituted with those that aim to describe a specific process and to capture variations in the size distribution of such flow events.