The relationship between drainage density, erosion rate, and hilltop curvature: implications for sediment transport processes

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 non-linear 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.