Forest-Fire Model with Resistant Trees

TL;DR

This paper investigates how heterogeneity in tree resistance affects forest fire dynamics using cellular automata and mean field models, revealing phase transitions in fire size distributions based on resistance levels.

Contribution

It introduces a model incorporating varying tree resistance and analyzes the resulting fire-size distributions, highlighting a transition from power-law to exponential behavior.

Findings

Power-law distributions occur at low resistance levels.

Exponential distributions dominate at high resistance levels.

Intermediate resistance shows a transition with possible percolation behavior.

Abstract

The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with distinct strengths of resistance to burn. The scaling analysis of fire-size and fire-lifetime frequency distributions in the non-interacting fire steady-state limit indicates the breakdown of the power-law behavior whenever the resistance strength parameter R exceeds a certain value. For higher resistant strength, exponential behavior characterizes the frequency distributions, while power-law like behavior was observed for the lower resistant case in the same manner as reported in the literature for a homogeneous counterpart model. For the intermediate resistance strength, however, it may be described either by a stretched exponential or by a power-law plot whenever the fraction of recovering empty cells by susceptible trees not-exceeds or exceeds a certain threshold respectively, also suggesting a dynamical percolation transition with respect to the stationary forest density.