Modelling hillslope evolution: linear and nonlinear transport relations

Many recent models of landscape evolution have used a diffusion relation to simulate hillslope transport. In this study, a linear diffusion equation for slow, quasi-continuous mass movement (e.g., creep), which is based on a large data compilation, is adopted in the hillslope model. Transport relations for rapid, episodic mass movements are based on an extensive data set covering a 40-yr period from the Queen Charlotte Islands, British Columbia. A hyperbolic tangent relation, in which transport increases nonlinearly with gradient above some threshold gradient, provided the best fit to the data. Model runs were undertaken for typical hillslope profiles found in small drainage basins in the Queen Charlotte Islands. Results, based on linear diffusivity values defined in the present study, are compared to results based on diffusivities used in earlier studies. Linear diffusivities, adopted in several earlier studies, generally did not provide adequate approximations of hillslope evolution. The nonlinear transport relation was tested and found to provide acceptable simulations of hillslope evolution. Weathering is introduced into the final set of model runs. The incorporation of weathering into the model decreases the rate of hillslope change when theoretical rates of sediment transport exceed sediment supply. The incorporation of weathering into the model is essential to ensuring that transport rates at high gradients obtained in the model reasonably replicate conditions observed in real landscapes. An outline of landscape progression is proposed based on model results. Hillslope change initially occurs at a rapid rate following events that result in oversteepened gradients (e.g., tectonic forcing, glaciation, fluvial undercutting). Steep gradients are eventually eliminated and hillslope transport is reduced significantly.