A stochastic landscape evolution model framework for debris flow and fluvial processes

Debris flow is an important process that shapes steep landscapes, connecting the hillslopes and fluvial domains. Yet, it is unclear how debris flows quantitatively influence the topography. Here, we propose and develop a new framework considering debris flows as stochastic processes in long-term landscape evolution. We assume that debris flows occur randomly in time with different initial debris flow volumes, which we model using five different distribution functions. Debris flows propagate along the channel and increase their volume by eroding additional material using deterministic equations. The model predicts the slope-area relationship that is generally assumed to be indicative of debris-flow-dominated landscapes. We suggest a new equation to fit the slope-area relationship, including both debris flow and fluvial domains. This equation features a total of five metrics, two of which are power law exponents, two are representative areas, and one representative slope. The topography in the debris flow-dominated domain is sensitive to the properties of the debris flow, e.g., the initial volume of debris flow, frequency, erosion coefficient, Manning coefficient, uplift rate, and channel width and length. The representative slope and area are primarily sensitive to the total initial volumes of the debris flow, and secondarily to the frequency of occurrence of debris flows. The type and shape parameters of distributions and the debris flows volume and frequency have limited effects on the slope-area relationship.