A Multi-Scale Network with Percolation Model to Describe the Spreading of Forest Fires

Sara Aleixo Perestrelo,Maria Clara Grácio,Nuno de Almeida Ribeiro,Luís Mário Lopes

doi:10.3390/math10040588

Sara Aleixo Perestrelo, Maria Clara Grácio + Show 2 more

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https://doi.org/10.3390/math10040588

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Abstract

Forest fires have been a major threat to forest ecosystems and its biodiversity, as well as the environment in general, particularly in the Mediterranean regions. To mitigate fire spreading, this study aims at finding a fire-break solution for territories prone to fire occurrence. To the effect, here follows a model to map and predict phase transitions in fire regimes (spanning fires vs. penetrating fires) based on terrain morphology. The structure consists of a 2-scale network using site percolation and SIR epidemiology rules in a cellular automata to model local fire Dynamics. The target area for the application is the region of Serra de Ossa in Portugal, due to its wildfire incidence. The study considers the cases for a Moore neighbourhood of warm cells of radius 1 and 2 and also considers a heterogeneous terrain with 3 classes of vegetation. Phase transitions are found for different combinations of fire risk for each of these classes and use these values to parametrize the resulting landscape network.

Highlights

Forest ecosystems and their biodiversity are currently threatened by forest fires, as well as the environment in general
A clear phase transition is observed for the classical case (Figure 8), in a homogeneous terrain
At critical density dc ≈ 0.41, fire spreading ceases its extinction regime to the uncontrollable regime, where the generated cluster increases with the patch size

Summary

Introduction

Forest ecosystems and their biodiversity are currently threatened by forest fires, as well as the environment in general. Fire behaves according to three interacting physical factors: fuel availability (morphological and physiological characteristics of vegetation), weather (wind speed and direction, temperature, and relative humidity) and terrain (slope and aspect) [6,7]—throughout this article these factors will be referred to as FWT conditions. These factors, along with the data of the initial fire condition, allow for the possibility to model fire behaviour [8]. These fuel models may include the environmental parameters of wind, slope, and expected moisture changes [9]

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