Transient emergence of ramified river channels: simulations of geographical cycle by Erosion-Diffusion Model (EDM)

Abstract

We present a minimal version of Landscape Evolution Models (LEMs) to capture the essence of tree-shaped channel network formation on the assumption of two mechanisms, soil erosion and diffusion. The continuous tectonic uplift is not required, which affects landscape evolution only at the starting point. We refer to the mathematical model as the Erosion-Diffusion Model (EDM). No steady state exists in the EDM except for the perfectly flat plane, which is realized at the ultimate final stage of the landform transition. It is suggested that generated channel patterns are temporal and transient creatures during long-term gravitational and erosional processes on the earth.