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

Debris flows regularly traverse bedrock channels that dissect steep landscapes, but our understanding of bedrock erosion by debris flows and their impact on steepland morphology is still rudimentary. Quantitative models of steep bedrock channel networks are based on geomorphic transport laws designed to represent erosion by water-dominated flows. To quantify the impact of debris flow erosion on steep channel network form, it is first necessary to develop methods to estimate spatial variations in bulk debris flow properties (e.g., flow depth, velocity) throughout the channel network that can be integrated into landscape evolution models. Here, we propose and evaluate two methods to estimate spatial variations in bulk debris flow properties along the length of a channel profile. We incorporate both methods into a model designed to simulate the evolution of longitudinal channel profiles that evolve in response to debris flow and fluvial processes. To explore this model framework, we propose a general family of debris flow erosion laws where erosion rate is a function of debris flow depth and channel slope. 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. Validating specific forms of a debris flow incision law, however, would require more detailed model-data comparisons in specific landscapes where input parameters and channel morphometry can be better constrained. Results improve our ability to interpret topographic signals within steep channel networks and identify observational targets critical for constraining a debris flow incision law.