Are Forest Fires Predictable?

TL;DR

This paper applies dynamic mean field theory and Monte Carlo simulations to analyze forest fire predictability, revealing chaotic behavior and stability windows in the evolution of forest density.

Contribution

It introduces a novel application of mean field theory and bifurcation analysis to forest fire modeling, linking microscopic simulations with macroscopic dynamics.

Findings

Time evolution of forest density is chaotic.

Bifurcation diagram shows stability windows and periodic orbits.

Results qualitatively match historical forest fire data.

Abstract

Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We get the map $p_n\to p_{n+1}$, where $p_n$ is the probability of finding a tree in a cell, and $n$ is the discrete time. We demonstrate that the time evolution of $p$ is chaotic. The arguments are provided by the calculation of the bifurcation diagram and the Lyapunov exponent. The bifurcation diagram reveals several windows of stability, including periodic orbits of length three, five and seven. For smaller lattices, the results of the iteration are in qualitative agreement with the statistics of the forest fires in Canada in years 1970--2000.