Functional relationships between denudation and hillslope form and relief

Functional relationships between landscape morphology and denudation rate allow for the estimation of sediment fluxes using readily available topographic information. Empirical studies of topography-erosion linkages typically employ data with diverse temporal and broad spatial scales, such that heterogeneity in properties and processes may cloud fundamental process-scale feedbacks between tectonics, climate, and landscape development. Here, we use a previously proposed nonlinear model for sediment transport on hillslopes to formulate 1-D dimensionless functions for hillslope morphology as well as a generalized expression relating steady-state hillslope relief to erosion rate, hillslope transport parameters, and hillslope length. For study sites in the Oregon Coast Range and Gabilan Mesa, CA, model predictions of local relief and average hillslope gradient compare well with values derived from high-resolution topographic data acquired via airborne laser altimetry. Our formulation yields a nondimensional number describing the extent to which the nonlinearity in our gradient-flux model affects slope morphology and landscape response to tectonic and climatic forcing. These results should be useful for inferring rates of hillslope denudation and sediment flux from topography, or for coarse-scale landscape evolution simulations, in that first-order hillslope properties can be calculated without explicit modeling of individual hillslopes.