A Physically Based Channel Network and Catchment Evolution Model

Abstract

A catchment evolution and channel network growth model is presented. Elevations within the catchment are simulated by a sediment transport continuity equation applied over geologic time. Sediment transport may by modelled by both fluvial (e.g. Einstein-Brown) and mass movement (e.g. creep and landsliding) mechanisms. An explicit differentiation between the channel and the hillslope is made with different transport processes in each regime. The growth of the channel network is governed by a physically based threshold, which is nonlinearly dependent on discharge and slope and thus governed by hillslope form. Hillslopes and the growing channel network interact through the different sediment transport processes and the preferred drainage to the channels to produce the long term form of the catchment. General requirements for network formation in physically based models are examined by use of a previously reported leaf vein growth model. Elements of chaos were discovered that result in apparently random networks being generated. It was argued that this is also true for the catchment and connections with topologically random networks were provided. Synthetic catchments were simulated using a numerical implementation of the model and statistics for the catchments are analyzed. Drainage density and elevation characteristics are correlated with nondimensional numbers arising from a nondimensionalization of the governing equations. These nondimensional numbers parameterize rates of tectonic uplift, sediment transport, both in the channel and the hillslope, channel growth, and resistance to channelization. Runoff rate, erodability and flood frequencies arise explicitly in these numbers. A fundamental measure of catchment dissection based on one of the nondimensional numbers is proposed. It follows that drainage density and hillslope length are dependent, in a well defined way, on runoff rate, slopes and catchment erodability. Simulation results are compared with reported field data and small scale experimental catchment evolution studies and found to be consistent. A linear log-log relationship between channel slope and area, observed in the field, is also observed in the simulation data at dynamic equilibrium. An explanation based on model physics is proposed, a central feature being the balance between tectonic uplift and fluvial erosion at dynamic equilibrium. This explanation also accounts for observed deviations from the linear log-log relationship where slopes are reduced for small areas; these small areas are dominated by diffusive transport processes in the hillslope. The channelization threshold based on discharge and slope is compared with recently reported data of hillslope slopes and contributing areas at channel heads; the threshold is consistent with the field data. Observed differences between hypsometric curves, previously attributed to catchment age, are found to result from differences in the tectonic uplift regime. A scheme for landscape classification, based on the nondimensional numbers, is proposed which is more consistent with the governing physical processes than previous work. A one-dimensional advection-diffusion reformulation of the sediment transport equation is proposed that predicts rates of hillslope retreat and hillslope degradation, and provides a link to observed hillslope transport mechanisms.