Abstract
Drainage density is a fundamental landscape metric describing the extent of the fluvial network. We compare the relationship between drainage density (Dd) and erosion rate (E) using the Channel‐Hillslope Integrated Landscape Development (CHILD) numerical model. We find that varying the channel slope exponent (n) in detachment‐limited fluvial incision models controls the relationship between Dd and E, with n > 1 resulting in increasing Dd with E if all other parameters are held constant. This result is consistent when modeling both linear and nonlinear hillslope sediment flux. We also test the relationship between Dd and E in five soil‐mantled landscapes throughout the USA: Feather River, CA; San Gabriel Mountains, CA; Boulder Creek, CO; Guadalupe Mountains, NM; and Bitterroot National Forest, ID. For two of these field sites we compare Dd to cosmogenic radionuclide (CRN)‐derived erosion rates, and for each site we use mean hilltop curvature as a proxy for erosion rate where CRN‐derived erosion rates are not available. We find that there is a significant positive relationship between Dd, E, and hilltop curvature across every site, with the exception of the San Gabriel Mountains, CA. This relationship is consistent with an n exponent greater than 1, suggesting that at higher erosion rates, the transition between advective and diffusive processes occurs at smaller contributing areas in soil‐mantled landscapes.
Highlights
One of the most distinctive features of soil-mantled upland landscapes is the repeating patterns of ridges and valleys
With linear hillslope sediment transport, there is a positive relationship between drainage density and uplift rate for n = 2; a negative relationship for n = 0.7 and n = 0.4; and that drainage density is invariant with uplift rate for n = 1
We find a significant positive relationship between mean CHT and uplift rate for both the linear and non-linear hillslope sediment transport scenarios
Summary
One of the most distinctive features of soil-mantled upland landscapes is the repeating patterns of ridges and valleys. The spacing of these ridges and valleys is fundamentally controlled by the competition between creep-like sediment transport processes, which tend to smooth the landscape, and fluvial processes, which incise the landscape [Tarboton et al, 1992; Tucker and Bras, 1998; Perron et al, 2012]. The erosion rate of the landscape plays a major role in controlling the spacing of ridges and valleys, by affecting the relative efficacy of fluvial and hillslope transport processes [Tucker and Bras, 1998; Perron et al, 2008]. Fluvial incision can be modeled using a detachment-limited scenario in which the incision rate E is a power-law function of upstream drainage area A and channel slope SCH [e.g. Whipple and Tucker , 1999]:
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