Forest fire modeling
Forest fire modeling is a critical tool used in forestry management to predict the behavior and spread of both controlled burns and wildfires. These models leverage mathematical equations and simulations to analyze various factors influencing fire dynamics, including vegetation type, terrain, weather conditions, and available fuel. The first mathematical model for fire spread was introduced in 1946, and since then, models have evolved in complexity with advancements in computational technology, allowing for more sophisticated simulations that incorporate a wide range of parameters.
Today’s forest fire models can simulate thousands of trees in a grid format, assessing the likelihood of fire spread based on the conditions of surrounding vegetation and environmental factors. This predictive capability aids firefighters and forestry officials in making informed decisions about fire management and intervention strategies. However, accurately estimating the parameters used in these models remains challenging, as many environmental factors can change rapidly and unpredictably.
Applications of forest fire models are vast, encompassing both the prediction of potential fire behavior and the analysis of past incidents to improve future outcomes. While these models provide significant insights, they are not without limitations; inaccurate parameter estimation can lead to severe consequences, as evidenced by historical incidents where controlled burns turned catastrophic. In summary, forest fire modeling plays an essential role in understanding and mitigating the impacts of wildfires, with ongoing research aimed at refining these predictive tools.
Forest fire modeling
Summary: The spread of forest fires has been modeled for decades to guide firefighting decisions.
Forest service officials have often used controlled burns to reduce the risk of fires spreading by burning the dry vegetation that builds up on the forest floor. Predicting the spread of a fire, whether a controlled burn or a wildfire burning out of control, is of great interest in forest management. Mathematical models take into account various parameters, indices, and activity levels.
Brief History of Forest Fire Modeling
According to Forest Service (a branch of the U.S. Department of Agriculture) documents, the first mathematical model of the spread of fires was developed in 1946 by W. R. Fons. Fons’s model was based on approximating the spread as a series of ignitions, with the key elements being ignition time and the distance between particles. Over the years, fire models became more sophisticated, using increasingly complicated mathematical equations, as in Richard C. Rothermel’s 1972 differential and integral equation model of fire spread.
With the development of high-speed computers in the last quarter of the twentieth century, simulation models that use large numbers of relatively simple probabilistic and geometric relationships have become more common. In these models, forest fires are represented by a grid of trees where a variety of parameters are set for each tree.
Examples of Forest Fire Models
A very simple simulation of a forest fire can be modeled with a grid of evenly spaced trees and a number cube. Set a forest dryness factor—a set of numbers that, when rolled on a six-sided die, indicate that a tree will catch fire if one of its four neighbors is on fire. For example, a dry forest might be represented by the numbers 1, 2, 3, and 4. In this example, 4/6 or 2/3 of the time, the fire would spread to neighbor trees.
To see how such a simple model works, set the tree in position (3,2) on fire in the grid below and then roll the number cube for the trees in positions (3,1), (2,2), (3,3) and (4,2) to see if they will catch fire as the original tree “burns out.”
Suppose the number cube rolls are 5, 2, 3, and 2, respectively; then the fire would spread as pictured, with the tree in position (3, 1) remaining unlit.
To complete the simulation, continue rolling the number cube to see if the trees adjacent to the three now on fire will burn. As with all models involving probabilities, it is important to run the simulation a large number of times and to look at the average or most common results rather than to rely on one run of the simulation, such as the forest fire simulation screen shot below:
The simulations in use today to model forest fires are very sophisticated. They include thousands of trees and hundreds of parameters, such as tree size, distribution, and dryness; wind speed and direction; humidity and ambient air temperature; leaf litter buildup; heating, ignition, and burn time; and the geometry of the terrain. These parameters contribute to the calculation of the probability that a tree will catch fire when its neighbors are on fire. Computer visualization software of the early twenty-first century allows programmers to build sophisticated user interfaces for these models in which the spread of the fire can be watched on screen and users can interact with the model, clearing a firebreak or starting a backfire.
Applications of Forest Fire Models
These models can be used to predict how a hypothetical fire might behave or to determine the best intervention in an existing fire, provided the parameter values used in the model accurately reflect the real conditions in the forest. Estimating these parameters poses a challenge to forestry officials—terrain and tree size and distribution are constant in a given forest at a specific time but other parameters, such as tree dryness, wind speed and direction, humidity, and ambient air temperature, vary over time, sometimes significantly.
Failure to accurately gauge parameters in a model can lead to disastrous results. In 2000, the National Park Service developed a fire plan for a controlled burn at the Bandolier National Monument in New Mexico. Now known as the Cerro Grande fire, the wind shifted and strengthened unpredictably, causing the fire to rage out of control, damaging more than 200 homes and 48,000 acres of land in and around the town of Los Alamos.
Agencies and firefighters use a wide variety of National Fire-Danger Rating System (NFDRS) indices and activity levels to monitor and make decisions about fires. For example, the Occurrence Index predicts the potential fire incidence within a rated area. Fire behavior researchers, like George Byram, defined many quantitative measures of fire behavior, such as the definition for fire intensity as the rate of heat energy release per unit time per unit length of fire front, which is defined independently of the depth or width of the fire. The Burning Index (BI) is commonly used to indicate the amount of effort that is needed to contain a given fire. The BI is calculated based on the material that is burning and other factors, including a modification of an equation defined by Byram for flame length. Some people have criticized agencies for failure to use historic data in making future predictions of wildfire hazards, such as recent burn areas in which wildfire is rarely likely to spread.
Newer mathematical models may improve fire forecasts and replace indices like the BI. Statistician Frederic Schoenberg collected and analyzed historic wildfire data in order to build statistical models that clarify relationships such as the apparent linear association between wildfire hazard and average temperature for those that fall below 21 degrees Celsius. While drought is a demonstrated predictor of fires, climatology statistician Sam Shen, atmospheric physicist Robert Field, and earth scientist Guido van der Werf also linked fires in Indonesia with changes in land use and population density. These types of studies have led to quips that only mathematics can prevent forest fires.
Bibliography
Cohen, Jack, and John Deeming. The National Fire Danger Rating System: Basic Equations. Berkeley, CA: Pacific Southwest Forest and Range Experiment Station, 1985.
Johnson, Edward, and Kiyoko Miyanishi. Forest Fires: Behavior and Ecological Effects. San Diego, CA: Academic Press, 2001.
National Science Foundation. “NSF Discoveries—Improving Fire Forecasts.” http://www.nsf.gov/discoveries/disc‗summ.jsp?cntn‗id=100272&org=NSF.
Rothermel, Richard C. A Mathematical Model for Predicting Fire Spread in Wildland Fuels. Report from the Intermountain Forest and Range Experiment Station, Forest Service, U.S. Department of Agriculture, 1972. http://www.treesearch.fs.fed.us/pubs/32533.
Shodor Education Foundation, Inc. “Interactivate: Fire!” http://www.shodor.org/interactivate/activities/Fire.