A Probabilistic and Numerical Approach to Explore How Hillslope Length Controls Sediment Yield
Abstract
Sediment yield from rilled hillslopes increases as the three-halves power of slope length. This nonlinear increase in sediment yield is fundamental to accurate predictions of soil erosion rates and ultimately places a limit on how long hillslopes can be before they are susceptible to valley incision. To date, no widely-accepted theory exists to explain this scaling relationship. In this study, we demonstrate how rill networks can increase the sediment transport efficiency on longer hillslopes, using the Scheidegger model for rill networks as a framework. Scheidegger networks are a collection of paths (rills) in which the slope-normal position of paths (rills) varies as a simple random walk and a uniform drainage density is maintained. This behavior imitates the deflection and concentration of water due to microtopography on hillslopes, and tends to increase the variance of contributing area for rills at downslope positions. Increasing variance in contributing area drives larger erosion rates. We model water flow and the associated erosion rates over slopes of variable length and, assuming that soil detachment rates scale linearly with shear stress, show that the spatial distribution of water flow in Scheidegger rill networks results in the three-halves scaling observed in data. In addition, we approach a similar result analytically by developing the joint probability distributions of contributing area, length, depth, and shear stress as functions of total hillslope length. We show that statistical moments and the proportion of rills that exceed a transport capacity increase nonlinearly with total hillslope length. Insofar as Scheidegger networks have been used to explore river networks as a first order model, this work provides a basis for distributions of contributing area and channel length in addition to the application to rilled hillslopes.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMEP51F2179D
- Keywords:
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- 1824 Geomorphology: general;
- HYDROLOGY;
- 1825 Geomorphology: fluvial;
- HYDROLOGY;
- 1826 Geomorphology: hillslope;
- HYDROLOGY;
- 1862 Sediment transport;
- HYDROLOGY