Using hilltop curvature to derive the spatial distribution of erosion rates

Erosion rates dictate the morphology of landscapes, and therefore quantifying them is a critical part of many geomorphic studies. Methods to directly measure erosion rates are expensive and time consuming, whereas topographic analysis facilitates prediction of erosion rates rapidly and over large spatial extents. If hillslope sediment flux is nonlinearly dependent on slope then the curvature of hilltops will be linearly proportional to erosion rates. In this contribution we develop new techniques to extract hilltop networks and sample their adjacent hillslopes in order to test the utility of hilltop curvature for estimating erosion rates using high-resolution (1 m) digital elevation data. Published and new cosmogenic radionuclide analyses in the Feather River basin, California, suggest that erosion rates vary by over an order of magnitude (10 to 250 mm kyr^-1). Hilltop curvature increases with erosion rates, allowing calibration of the hillslope sediment transport coefficient, which controls the relationship between gradient and sediment flux. Having constraints on sediment transport efficiency allows estimation of erosion rates throughout the landscape by mapping the spatial distribution of hilltop curvature. Additionally, we show that hilltop curvature continues to increase with rising erosion rates after gradient-limited hillslopes have emerged. Hence hilltop curvature can potentially reflect higher erosion rates than can be predicted by hillslope gradient, providing soil production on hilltops can keep pace with erosion. Finally, hilltop curvature can be used to estimate erosion rates in landscapes undergoing a transient adjustment to changing boundary conditions if the response timescale of hillslopes is short relative to channels.