A Channelization Model of Landscape Evolution

Abstract

The geomorphic evolution of many landscapes is fundamentally deter- mined by the evolution of the river channels and their interactions with hillslopes. Consequently, models of landscape evolution ought to track the evolution of the channel geometry so as to quantify the rate of erosion of channel bottoms and to follow the changes in hillslope-channel coupling over time. Unfortunately, the spatial resolution required to describe channel morphology adequately is computationally impractical. It is also beyond the resolution of most digital elevation data. What is required is a parameterization scheme for approximating fine scale channel morphol- ogy at a coarse pixel scale. Such a parameterization is already implicitly employed in most models by assuming channel equilibrium, which ties the width and depth of a model channel to the square root of discharge through a pixel. Channel fluxes are thereby predictable, and a closed form of the governing equations is attained. In reality, mountain river channels do not take a simple equilibrium form and show great spatial variability and evident disequilibrium geometry. Since the time scales of changes in channel geometry, bedrock channel erosion, and hillslope response are all closely related, it is reasonable to infer that the spatio-temporal development of the landscape is determined by their interaction and that channel disequilibrium is a fundamental factor in the dynamics of landscape evolution. If this is the case, we need an alternative sub-grid scale parameterization that aggregates channel properties such as surface morphology, roughness, cross-sectional geometry, so that the time depen- dent behavior of these properties can be estimated at the coarse pixel scale. We introduce such a parameterization measure, which we term channelization, after extensive investigation of the pixel resolution dependence of topographic relief. We focus in particular on the effect of coarse graining on digital elevation data for derived measures such as channel slope and upstream area and demonstrate that we can approximately correct for this effect. We show that a very simple geomorphic model can be constructed around the channelization parameter and the resolution-invariant topographic measures. This model demonstrates that channel disequilibrium may play a significant role in mountain landscape dynamics. It also shows how geomorphic models in general could be modified to incorporate such sub-pixel scale complexities and to better model these dynamics.