[1] 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 À1 ). 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.

Fluvial landscapes are dissected by channels, and at their upstream termini are channel heads.Accurate reconstruction of the fluvial domain is fundamental to understanding runoff generation, storm hydrology, sediment transport, biogeochemical cycling, and landscape evolution. Many methods have been proposed for predicting channel head locations using topographic data, yet none have been tested against a robust field data set of mapped channel heads across multiple landscapes. In this study, four methods of channel head prediction were tested against field data from four sites with high-resolution DEMs: slopearea scaling relationships; two techniques based on landscape tangential curvature; and a new method presented here, which identifies the change from channel to hillslope topography along a profile using a transformed longitudinal coordinate system. Our method requires only two user-defined parameters, determined via independent statistical analysis. Slope-area plots are traditionally used to identify the fluvialhillslope transition, but we observe no clear relationship between this transition and field-mapped channel heads. Of the four methods assessed, one of the tangential curvature methods and our new method most accurately reproduce the measured channel heads in all four field sites (Feather River CA, Mid Bailey Run OH, Indian Creek OH, Piedmont VA), with mean errors of 211, 27, 5, and 224 m and 34, 3, 12, and 258 m, respectively. Negative values indicate channel heads located upslope of those mapped in the field. Importantly, these two independent methods produce mutually consistent estimates, providing two tests of channel head locations based on independent topographic signatures.

Abstract. The characteristics of the sediment transported by rivers (e.g. sediment flux, grain size distribution – GSD) dictate whether rivers aggrade or erode their substrate. They also condition the architecture and properties of sedimentary successions in basins. In this study, we investigate the relationship between landscape steepness and the grain size of hillslope and fluvial sediments. The study area is located within the Feather River basin in northern California, and studied basins are underlain exclusively by tonalite lithology. Erosion rates in the study area vary over an order of magnitude, from >250 mm ka−1 in the Feather River canyon to <15 mm ka−1 on an adjacent low-relief plateau. We find that the coarseness of hillslope sediment increases with increasing hillslope steepness and erosion rates. We hypothesise that, in our soil samples, the measured 10-fold increase in D50 and doubling of the amount of fragments larger than 1 mm when slope increases from 0.38 to 0.83 m m−1 is due to a decrease in the residence time of rock fragments, causing particles to be exposed for shorter periods of time to processes that can reduce grain size. For slopes in excess of 0.7 m m−1, landslides and scree cones supply much coarser sediment to rivers, with D50 and D84 more than one order of magnitude larger than in soils. In the tributary basins of the Feather River, a prominent break in slope developed in response to the rapid incision of the Feather River. Downstream of the break in slope, fluvial sediment grain size increases, due to an increase in flow competence (mostly driven by channel steepening) as well as a change in sediment source and in sediment dynamics: on the plateau upstream of the break in slope, rivers transport easily mobilised fine-grained sediment derived exclusively from soils. Downstream of the break in slope, mass wasting processes supply a wide range of grain sizes that rivers entrain selectively, depending on the competence of their flow. Our results also suggest that, in this study site, hillslopes respond rapidly to an increase in the rate of base-level lowering compared to rivers.

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope-area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope-area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length-relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end-member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length-relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient.