The shape of soil-mantled hillslopes is typically attributed to erosion rate and the transport efficiency of the various processes that contribute to soil creep. While climate is generally hypothesized to have an important influence on soil creep rates, a lack of uniformity in the measurement of transport efficiency has been an obstacle to evaluating the controls on this important landscape parameter. We addressed this problem by compiling a data set in which the transport efficiency has been calculated using a single method, the analysis of hilltop curvatures using 1-m LiDAR data, and the erosion rates have also been determined via a single method, in-situ ¬cosmogenic 10Be concentrations. Moreover, to control for lithology, we chose sites that are only underlain by resistant bedrock. The sites span a range of erosion rates (6 – 922 mm/kyr), mean annual precipitation (39 – 320 cm/yr), and aridity index (0.08 – 1.38). Surprisingly, we find that hilltop curvature varies with the square root of erosion rate, whereas previous studies predict a linear relationship. In addition, we find that the inferred transport coefficient also varies with the square root of erosion rate but is insensitive to climate. We explore various mechanisms that might link the transport coefficient to the erosion rate and conclude that present theory regarding soil-mantled hillslopes is unable to explain our results and is, therefore, incomplete. Finally, we tentatively suggest that processes occurding in the bedrock (e.g., fracture generation) may play a role in the shape of hillslope profiles at our sites.

The concavity index, $\theta$, describes how quickly river channel gradient declines downstream. It is used in calculations of normalized channel steepness index, $k_{sn}$, a metric for comparing the relative steepness of channels with different drainage area. It is also used in calculating a transformed longitudinal coordinate, $\chi$, which has been employed to search for migrating drainage divides. Here we quantify the variability in $\theta$ across multiple landscapes distributed across the globe. We describe the degree to which both the spatial distribution and magnitude of $k_{sn}$ and $\chi$ can be distorted if $\theta$ is assumed, not constrained. Differences between constrained and assumed $\theta$ of 0.1 or less are unlikely to affect the spatial distribution and relative magnitude of $k_{sn}$ values, but larger differences can change the spatial distribution of $k_{sn}$ and in extreme cases invert differences in relative steepness: relatively steep areas can appear relatively gentle areas as quantified by $k_{sn}$. These inversions are function of the range of drainage area in the considered watersheds. We also demonstrate that the $\chi$ coordinate, and therefore the detection of migrating drainage divides, is sensitive to varying values of $\theta$. The median of most likely $\theta$ across a wide range of mountainous and upland environments is 0.425, with first and third quartile values of 0.225 and 0.575. This wide range of variability suggests workers should not assume any value for $\theta$, but should instead calculate a representative $\theta$ for the landscape of interest, and exclude basins for which this value is a poor fit.