A NUMERICAL MODELING INVESTIGATION OF STEADY STATE CHANNEL PROFILES INCISED BY DEBRIS FLOW AND FLUVIAL PROCESSES

The longitudinal profiles of quasi-steady state channels can encode valuable information about climate and tectonics. Extracting this information requires a better understanding of how debris flow and fluvial processes combine to incise channels. Despite the observation that debris flows traverse many moderately and steeply sloping reaches of bedrock channels, we currently lack a geomorphic transport law to represent debris flow erosion in landscape evolution models. In this study, we develop a 1d landscape evolution model to simulate longitudinal channel profiles that evolve due to both debris flow and fluvial processes. The model utilizes an empirical routing algorithm to estimate spatial patterns in debris flow depth and velocity throughout the channel network that can then be used to estimate a debris flow incision rate. Using this framework, we compared modeled and observed channel profiles to test a family of potential debris flow erosion laws that relate slope, debris flow depth, and debris flow velocity to an incision rate. Simulations indicate that modeled profiles are most consistent with those observed in debris-flow dominated landscapes when the debris flow incision rate increases nonlinearly with slope and roughly linearly with flow depth. In these cases, the model reproduces the observed break in the scaling relationship between channel slope and drainage area that is often interpreted as a topographic signature of debris flow erosion. Furthermore, the model suggests that the morphology of debris-flow dominated channel profiles can provide constraints on catchment-averaged erosion rates in steady state landscapes. Results provide a general form for a debris-flow erosion law as well as insight into the relative importance of debris flow versus fluvial processes in shaping channel profiles in steep landscapes.