Topographic evolution and morphology of surfaces evolving in response to coupled fluvial and hillslope sediment transport

This paper quantifies how the ratio of sediment transport on hillslopes to sediment transport in channels influences surface and channel network morphologies and the dynamics of topographic evolution. This problem is investigated by development and investigation of a simple deterministic model incorporating mass balance of sediment and runoff coupled with a law combining dispersive and concentrative sediment transport processes. Our analysis includes the identification of a new nondimensional parameter D-e that is a function of rainfall, system size, rock type, and hydraulic regime and that is a measure of the relative importance of fluvial and hillslope sediment transport. We show that D-e has an important influence on the surface morphology (e.g., total exposed surface area and interface width which reflects surface roughness and relief), channel network form (e.g., channel sinuosity), channel spacing, and timescale of surface evolution. Surface and channel network morphologies are also strongly influenced by the overall surface slope relative to the magnitude of initial topographic roughness. Topographic evolution occurs in distinct phases of relief growth and decay, the transition between which is controlled by a saturation phenomenon related to the growth of spatial correlations. The scaling behavior of simulated topography with respect to both time and space is obtained and is shown to be independent of D-e. Roughness exponents are found to be independent of D-e but dependent on the magnitude of initial roughness. Interface width is shown to grow and decay as a logarithm of time.