Forest fire in heterogeneous environments: the role of enlarged active neighborhoods and random forbidden sites

Abstract

In the present work, the spread of forest fires in heterogeneous environments is studied through cellular automata (CA) models, that are commonly used to simulate contact processes, and display a critical self-organized dynamics. The concept of self-organized criticality (SOC) is related to the ability of a dynamical system to evolve towards a critical phase spontaneously. The signature of these processes is the scale invariance (power-law behavior) of its observables. The forest fire model proposed by Drossel and Schawbl (DSFFM) in 1992, regards an homogeneous population of trees and its fire-size and fire duration distributions suggest typical SOC behaviors. In the other hand, the literature reports wildland fires whose frequency-area histograms are either power-law distributions or ‘heavy-tailed’ distributions. In 2011, Camelo-Neto and Coutinho proposed a CA model in which two distinct populations of trees are considered: one comprising trees with low flammability (with a parameter R of resistance to ignite) and the other composed by high flammability (susceptible trees). Aiming to generalize this model, some ingredients have been added in order to amplify or constrain the effective reach of the fire spreading. By increasing the reach of the interactions, the system performs fires that spread more like a ‘field’ of heat than like a contact process as in the DSFFM. Another novel aspect of the model – related to the heterogeneity of the population – is the addition of a fraction s of forbidden sites (randomly placed), at which trees are not allowed to sprout. Moreover, theses forbidden sites do not interact with fire. Results have showed that the fire-size distributions can display either a ‘heavy-tailed’ behavior or a power-law behavior, depending on the resistance parameter R and on the fraction s of forbidden site.