A coupled channel network growth and hillslope evolution model: 1. Theory

TLDR

Catchments differ in channel and hillslope behavior, with sediment transport driven by fluvial processes, creep, rockslides, and tectonic uplift influencing overall elevations. The study introduces a model to simulate long‑term catchment evolution, including drainage network growth and elevation changes in channels and hillslopes. The model couples flow and sediment transport continuity equations for channels and hillslopes, differentiates their physics, and uses a discharge‑ and slope‑dependent initiation function to drive channel head advance and network growth, implemented computationally with simple simulations.

Abstract

This paper presents a model of the long‐term evolution of catchments, the growth of their drainage networks, and the changes in elevations within both the channels and the hillslopes. Elevation changes are determined from continuity equations for flow and sediment transport, with sediment transport being related to discharge and slope. The central feature of the model is that it explicitly differentiates between the sediment transport behavior of the channels and the hillslopes on the basis of observed physics, and the channel network extension results solely from physically based flow interactions on the hillslopes. The difference in behavior of channels and hillslopes is one of the most important properties of a catchment. The flow and sediment transport continuity equations in the channel and the hillslope are coupled and account for the long‐term interactions of the elevations in the hillslope and in the channels. Sediment transport can be due to fluvial processes, creep, and rockslides. Tectonic uplift may increase overall catchment elevations. The dynamics of channel head advance, and thus network growth, are modeled using a physically based mechanism for channel initiation and growth where a channel head advances when a channel initiation function, nonlinearly dependent on discharge and slope, exceeds a threshold. This threshold controls the drainage density of the basin. A computer implementation of the model is introduced, some simple simulations presented, and the numerics of the solution technique described.