Numerical simulation for run-out extent of debris flows using an improved cellular automaton model

Numerical simulation of the debris-flow process is commonly based on the shallow water equations. However, as a two-phase anisotropic mixture, debris flows display complex rheological behavior, making it difficult to model or to simulate these using standard approaches. In this paper, an improved cellular automaton (CA) model is developed for simulating the extent of debris-flow run-out. The CA model consists of three essential components: cellular space, lattice relation, and transition function. A two-dimensional rectangular cellular space is generated from mesh grid in the digital terrain model data, and the Moore neighborhood type is selected as the lattice relation. We also use a transition function based on a Monte Carlo iteration algorithm to automatically search the flow direction and flow routine. Specifically, this new transition function combines the topography function and persistence function (due to the flow inertia), and is advanced in its ability to avoid certain illogical lateral spreading due to abrupt changes in topography. In addition, in contrast to previous studies, in the present work, we regressed the persistence function from a well-documented flume experiment, rather than using a manipulated constant value as described in earlier empirical studies. Our results show that the debris-flow persistence function is closely related to the channel slope. It approximates the law of cosines at a steep slope and Gamma law at a gentle slope. To illustrate the performance of the improved CA model, we selected the 2010 Yohutagawa debris-flow event in Japan as a case study. Our results show that the simulated deposition perimeter pattern and run-out distance are in high accordance with the data from in situ investigation.