Optimizing the Numerical Simulation of Debris Flows: A New Exploration of the Hexagonal Cellular Automaton Method

Abstract

Debris flow, driven by natural events like heavy rainfall and snowmelt, involves sediment, rocks, and water, posing destructive threats to life and infrastructure. The accurate prediction of its activity range is crucial for prevention and mitigation efforts. Cellular automata circumvent is the cumbersome process of solving partial differential equations, thereby efficiently simulating complex dynamic systems. Given the anisotropic characteristics of square cells in the simulation of dynamic systems, this paper proposes a novel approach, utilizing a hexagonal cellular automaton for the numerical simulation of debris flows, where the direction judgment efficiency increased by 25%. Employing cubic interpolation, the model thereby determines the central elevation of each hexagonal cell. By modifying the flow direction function and stopping conditions, it achieves more accurate predictions of the debris flow run-out extent. This method was applied to the 2010 Yohutagawa debris flow event and the flume test. To evaluate the simulation’s accuracy, the Ω value and Fβ score were used. The Ω value is a comprehensive evaluation factor that takes into account missed or misjudgment areas. On this basis, the Fβ score emphasizes that the missed identification of debris flow areas will bring greater harm. Research indicates that the Ω value showed improvements of 6.47% and 3.96%, respectively, while the Fβ score improved by 3.10% and 4.61%.