Steep, soil‐mantled hillslopes evolve through the downslope movement of soil, driven largely by slope‐dependent transport processes. Most landscape evolution models represent hillslope transport by linear diffusion, in which rates of sediment transport are proportional to slope, such that equilibrium hillslopes should have constant curvature between divides and channels. On many soil‐mantled hillslopes, however, curvature appears to vary systematically, such that slopes are typically convex near the divide and become increasingly planar downslope. This suggests that linear diffusion is not an adequate model to describe the entire morphology of soil‐mantled hillslopes. Here we show that the interaction between local disturbances (such as rainsplash and biogenic activity) and frictional and gravitational forces results in a diffusive transport law that depends nonlinearly on hillslope gradient. Our proposed transport law (1) approximates linear diffusion at low gradients and (2) indicates that sediment flux increases rapidly as gradient approaches a critical value. We calibrated and tested this transport law using high‐resolution topographic data from the Oregon Coast Range. These data, obtained by airborne laser altimetry, allow us to characterize hillslope morphology at ≈2 m scale. At five small basins in our study area, hillslope curvature approaches zero with increasing gradient, consistent with our proposed nonlinear diffusive transport law. Hillslope gradients tend to cluster near values for which sediment flux increases rapidly with slope, such that large changes in erosion rate will correspond to small changes in gradien. Therefore average hillslope gradient is unlikely to be a reliable indicator of rates of tectonic forcing or baselevel lowering. Where hillslope erosion is dominated by nonlinear diffusion, rates of tectonic forcing will be more reliably reflected in hillslope curvature near the divide rather than average hillslope gradient.
[1] In mountainous landscapes the role of periglacial processes in producing sediment is poorly defined, despite evidence of abundant talus slopes. Ice growth in rock has long been recognized as an efficient erosion mechanism, but the effects have not been readily applied to landscape evolution in response to tectonic and climatic forcing. Here, we quantify how and where ice-driven mechanical erosion occurs in cold, bedrock-dominated landscapes using a simple one-dimensional numerical heat flow model. In our model, ice grows by water migration to colder regions in shallow rock by the reduction in chemical potential associated with intermolecular forces between ice and mineral surfaces, a process called segregation ice growth. The depth and intensity of frost cracking is primarily dependent on mean annual temperature (MAT), with positive MAT sites characterized by intense cracking in the top meter of the rock mass and a maximum frost penetration of $4 m. In contrast, negative MAT areas have less intense cracking that primarily occurs at depths between 50 and 800 cm. We compare the depth and intensity of frost cracking predicted by our model with measures of the intensity of frost processes determined in three studies: The first measured the timing of rockfall in the Canadian Rockies, Niagara Escarpment, and Japanese Alps; the second analyzed scree deposits in the Southern Alps, New Zealand; and the third documented rockfall frequency in Utah. These natural examples show that rockfalls tend to nucleate at elevations that coincide with zones of intense frost cracking predicted by our model. As such, climatic variations associated with interglacial-glacial cycles may impart a significant influence on the denudation of mountainous landscapes.
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