Math on Fire

Math on Fire

1 November 2007

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USA — Mathematicians are building a model to predict wildfire movement

Firefighters are constantly trying to predict what a fire will do next, and awrong guess can lead to death. Now, a group of mathematicians and scientists isworking to provide a new tool for making more accurate predictions.

The new model is based on a fundamental and longstanding observation that theSanta Ana winds powering the recent conflagration in Southern Californiaemphasize: weather is a crucial driver of wildfire. But wildfire also createsits own weather. It sucks air from the surroundings, which results in winds thatfan the flames.

The researchers realized that the only way to predict with reasonableaccuracy what a fire is going to do is to build a model that combines fire andweather patterns. Firefighters already use programs that calculate expected firespeed on the basis of the slope of the terrain and the type of vegetationcovering it, along with air temperature and wind speed, but such predictionsserve only as the roughest of guides.

In 2002, the Big Elk Fire burned more than 4,000 acres in Colorado. This still image is taken from a computer simulation of the fire. The arrows show the direction of the wind near the ground. To see videos of the full simulation, click on the image above, or go to
National Center for Atmospheric Research

The challenge is formidable. “Fire is very unpredictable,” says JanMandel, the principal investigator for the project and a mathematician at theUniversity of Colorado at Denver. “It can go this way; it can go that way;that’s just the nature of the beast.” The best the researchers can hope todo is to figure out probabilities that will help guide firefighters, showing notjust the most likely scenarios but also others that are less likely but stillpossible.

To improve their model’s predictive powers, the experts are creating ways toupdate the model every half-hour with the latest fire and weather information.That requires developing new methods to gather such data on the spot—quickly.

One of the team’s methods is to have planes fly above the fire with thermaland infrared sensors that can see through the smoke and clouds to find hot spotswithin the fire. Mandel and his colleagues are building software that canautomatically process data from the sensors.

The team is also developing small, autonomous fire detectors that can bedropped into the area from airplanes or carried in by firefighters. Thedetectors would be equipped with radio transmitters, GPS, and a variety ofsensors for measuring factors such as smoke, carbon monoxide, temperature, orhumidity. The team is designing the devices so that a fire can burn right overthem without causing any damage. Once the flames pass, the sensor would resumesending data.

The aerial and ground sensors would send their data to a supercomputer at aremote location. The supercomputer would then use this information, along withcontinually updated weather information, to calculate in what direction the fireis likely to spread and how quickly. It would send the results to handheldcomputers that firefighters would carry with them in the field.

The project has a $2 million dollar budget from the National ScienceFoundation and involves a team of ten researchers, including mathematicians,computer scientists, fire scientists, and meteorologists. In addition todesigning the model itself, the scientists are designing the autonomous sensors,figuring out how to process data from the infrared sensors, and working out thedetails of how to communicate reliably with firefighters in remote locations.

The logistical challenges are formidable. Supercomputing resources would needto be accessible as soon as a fire breaks out. Data about terrain and vegetationwould need to be available for all fire-prone areas, in formats that themodeling software can use at a moment’s notice.

The team has now completed its initial version of the model and is startingto test it on historical fire data. One of the fires chosen is the Esperanza,Calif. fire of 2006, which killed five firefighters who were defending a house.The fire moved so fast that the firefighters didn’t have time to reach shelterin their nearby fire engine. Janice Coen, a meteorologist at the National Centerfor Atmospheric Research in Boulder, Colo. and one of the model’s developers,says that the model is helping to show why that fire became so intense sosuddenly.

Coen is hesitant to claim that the model will save firefighters’ livesbecause “there’s not ever one mistake, there are many mistakes that cometogether to create a fatality.” But if the model helps to prevent a mistakeor two, that might be enough to tip the balance. And it certainly may help setfirefighters’ minds at ease to have a little guidance as they guess what thefire will do next.


Mandel, J.L. . . . J.L. Coen, et al. In press. Awildland fire model with data assimilation. CCM Report 233 Mathematics andComputers in Simulation. Abstract and preprint available at

Coen, J.L. . . . J.L. Mandel, et al. 2007. Awildland fire dynamic data-driven application system. 11th Symposium onIntegrated Observing and Assimilation Systems for the Atmosphere, Oceans, andLand Surface (IOAS-AOLS). Jan. 14-18. San Antonio. Abstract available at

To see videos of the 2002 Big Elk Fire simulation, go to

More information about this project is available at

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