Steady-state forms of channel profiles shaped by debris-flow and fluvial processes

Abstract. Debris flows regularly traverse bedrock channels that dissect steep landscapes, but our understanding of the dominant controls that set rates and spatial patterns of landscape evolution by debris flows is still rudimentary. As a result, much of our understanding of steep bedrock channel networks is derived from application of geomorphic transport laws designed to represent erosion by water-dominated flows. To quantify the link between debris-flow mechanics and steep channel network form, establishment of a geomorphic transport law that quantifies bedrock erosion by debris flows and development of methods capable of handling the transient, non-local behavior of debris flows throughout the steep channel network are needed. Here, we propose a landscape evolution model to simulate longitudinal channel profiles that evolve in response to both debris-flow and fluvial processes. The model framework, which includes a methodology to explicitly track spatial variations in bulk debris-flow properties (e.g. flow depth, velocity) along the length of the channel profile, is designed to allow for the exploration of a range of potential debris-flow incision laws. We propose a relationship in which the debris-flow erosion rate is a function of debris-flow depth and channel slope. By comparing the morphology of modeled channel profiles to that typically seen in natural channels, we place constraints on a debris-flow incision law with this general form. Modeled channel profiles are consistent with observations of channel morphology in debris-flow-dominated terrain when the debris-flow incision rate is related to local channel slope raised to a power greater than one and approximately linearly related to debris-flow depth. Model results indicate that erosion by debris flows can explain the occurrence of a scaling break in the slope-area curve at low drainage areas and that upper-network channel morphology may be useful for inferring catchment-averaged erosion rates in quasi-steady landscapes. These results improve our ability to interpret topographic signals within steep channel networks and provide a general framework for exploring the role of debris-flow erosion within landscape evolution models