Hillslope drainage development with time: a physical experiment

Rainfall simulator experiments were structured to develop erosion rill-channel networks for 9° and 5° slopes subject to constant rainfall. Quantitative measurements included measurements of rill-channel width, depth, and width-to-depth ratios aggregated over the slope, and measures of the scaling characteristics and space filling tendencies of the networks. Trends in fractal dimensions and width functions with time are presented and compared to previous qualitative descriptions of network evolution. Our results imply that the equilibrium scaling characteristics of rill-channel networks are similar to those of river networks. For a given slope, the fractal dimension increases with time toward an equilibrium value. This equilibrium value is hypothesized to be a function of the effective storm, the initial hillslope-scale slope, and the geologic properties of the substrate. Results also imply that the rate of increase of the fractal dimension of the developing erosion networks (i.e., the rate at which the erosion networks fill space) may increase with increasing hillslope-scale slope. In addition, the growing rill-channel networks possess width functions whose bifurcation characteristics, as described by the power contained in the high wave numbers of the Fourier series fit, remain constant throughout the evolution of the networks.