Fighting Fire with Mathematical Models

Computer simulations help researchers and professionals fight forest fires

Fighting Fire with Mathematical Models

Research teams are developing models to predict the way fires will behave. Information from these simulations is bringing valuable information to firefighters’ relentless struggle against forest fires.

Research teams are developing models to predict the way fires will behave. Information from these simulations is bringing valuable information to firefighters’ relentless struggle against forest fires.

This article is a translation of “Des modèles mathématiques à l’assaut du feu!”. It was translated from French by Timothée Froelich.


25,000 hectares of forest burn every year in France. To better fight against wildfires, multidisciplinary research teams are using mathematical models. These computer simulations help them understand fire and better manage the land.

Anticipating fire behavior

Wildfire modeling consists of creating a mathematical representation of a forest fire. “It makes it possible to see how a wildfire evolves with the different characteristics of the terrain,” summarizes Lucile Rossi, associate professor specialized in signal processing at the University of Corsica. The models used are simplified and take into account the chemical characteristics of plants, but also wind speed and the slope of the ground. “We made the choice not to use a statistical model, but a model more similar to the physical processes involved in wildfires,” explains Eric Rigolot, deputy director of INRA’s research unit on Mediterranean forest ecology. From these mathematical models, scientists are able to make computer simulations that can predict a given fire’s intensity (heat flow and temperature), speed and direction.


Forest fire models include parameters on vegetation, topology and weather conditions.

Source: Wikimedia Commons/Cameron Strandberg


Researchers work on practical data in order to compare the simulation with reality. “We conduct experiments in the lab, but also in nature,” points out Lucile Rossi. The scientists use cameras that record at both visible and infrared wavelengths during a forest fire. The team from the University of Corsica even uses stereovision, a technique that involves two cameras recording the same image from different angles, to develop 3D models. “3D modeling makes it possible to describe the flames’ angle, for instance, whereas 2D modeling only gives information about the ground footprint,” explains Lucile Rossi.

Invaluable help for firefighters

Modeling generates a wealth of information useful to fire professionals. It helps them to better adapt their methods and deployment of their teams to fight a fire. “We can identify the strategic points where the fire is weak,” explains Lucile Rossi. For example, they can adapt the response of fire-fighting planes according to the concentration of the heat radiated by the fire. In addition, this knowledge adds to local know-how in terms of fighting fire with fire. This technique, traditionally used by farmers, can aggravate a wildfire when it is not well mastered. It consists of starting a fire on a given plot to clear it completely, thereby preventing expansion of future fires. “It’s in the common interest of firefighters and farmers to leave these controlled fires in the hands of trained and equipped professionals,” argues Eric Rigolot.

Fireflux model of a prairie fire.

Video source: Jean Batiste Filippi/Fireflux


Other fires are started by researchers to conduct experiments in the field. Researchers rent a helicopter to transport equipment to the plots. “It requires quite a significant budget, especially since we also need portable tools that can resist very high temperatures. We cannot do experiments as much as we’d like, because moving all this equipment around takes a lot of time and money,” Lucile Rossi laments.

A multidisciplinary field

To take into account all the ground parameters in these models, multidisciplinarity is absolutely necessary. Teams of mathematicians, physicists, chemists and even ecologists work together to improve understanding of the entire fire phenomenon and its effect on ecosystems.

A promising line of research consists in studying volatile organic compounds (VOCs). These chemical compounds given off by plants are mostly consumed by the fire. One hypothesis suggests that these compounds could be responsible for the phenomenon of flare-ups, when a fire suddenly spreads or intensifies quickly. Some plants, stressed by the approach of fire, may release massive quantities of these organic molecules that could fan the fire. If this hypothesis is true, it could significantly improve simulations and control of forest fires!


To find out more:

Website of the European project Fireparadoxe                                       

A stereovision system for fire characteristics estimation, by Lucile Rossi, Moulay Akhloufi, Thierry Molinier and Yves Tison