A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

Abstract

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasiempirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.

Forest Fire Spread Simulation and Fire Extinguishing Visualization Research

“…After the researchers digitize the parameters affecting the fire, the forest fire spread model constructed can express the relationship between forest fire behavior and parameters and the quantitative relationship between them. Based on whether the model is based on a statistical analysis of experimentally obtained data and whether it involves chemical or physical principles of combustion and fire spread processes, existing fire spread models can be divided into three categories: physical models, empirical models, and semi-empirical models [1,[4][5][6].…”

“…Sullivan, A.L. [4][5][6] conducted extensive and in-depth discussions on the methods of these researchers, categorized the construction methods of the models reasonably, and further helped us understand the relevant concepts of forest fire models, which are mainly summarized into three categories: physical models, empirical models, and semi-empirical models.…”

Self-organising swarms of firefighting drones: Harnessing the power of collective intelligence in decentralised multi-robot systems

“…Sullivan [80,81,82] proposes three broad categories, which in fact become six: 1) physical models, which attempt to represent the physics and chemistry of fire spread; 2) quasi-physical models, which attempt to represent only the physics; 3) empirical models, which contain no physical basis; 4) quasi-empirical model, which use some physical framework upon which to base the empirical model; 5) simulation models, which implement the preceding types of models in a computer simulation environment; and 6) mathematical analogous models, which use mathematical precepts rather than physical ones.…”

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

“…The first chapter offers an analysis of the types of wildland fires and the existing methods of modelling surface-type fires. It also includes a brief overview of Sullivan's classification [8][9][10]. A short description of Rothermel's mathematical model of the spread of surface fire is included.…”

“…2) Based on the Sillivan's overview [8,10] and the analysis from the information bulletins published on the page of the International Association of Wildland Fires (IAWF), we can conclude that climate change is one of the main triggers for defining fire danger zones on the world map.…”