Evaluating hillslope diffusion and terrace riser degradation in New Zealand and Idaho

[1] The relationship of sediment flux to surface slope is a predominant control on the evolution of transport-limited hillslopes. Although both linear and nonlinear sediment flux models have been proposed and widely debated, this functional relationship remains one of the outstanding questions in geomorphology. We examine degradation of fluvial terrace risers in New Zealand and Idaho in order to test the linear diffusion model and to better understand the relationship between sediment flux and slope. We implement three techniques based on the linear diffusion model, as well as a geometric scaling method that uses proportional relationships in riser geometry rather than a specific transport equation model, to assess rates of degradation. We show that techniques that utilize the riser midpoint slope as the primary metric of degradation, as opposed to the full scarp profile, offer the simplest and most reliable assessment of riser degradation. Our findings suggest that the linear diffusion model does not accurately describe terrace riser degradation, except for low-angle risers for which linear and nonlinear forms are indistinguishable. Results from the geometric scaling method show that degradation rates in both regions differ by a factor of two between equator- and pole-facing risers and that diffusion ages of Idaho risers are approximately 2 times those of New Zealand risers. Similar geometric trends in riser evolution from both regions reveal that terrace riser degradation is governed by a widely applicable relationship between sediment flux and slope.