# Analytical Fire Modeling: Fire in its Environment

Team: 77

School: RIO RANCHO HIGH

Area of Science: Environmental Sciences

Interim:

Primary Goal:
Create a three-dimensional program with two-dimensional exactness.

Problem Definition:
How can the flow of heat required to ignite a fire on all levels of a forest environment be accurately modeled using Huygen's principles and other mathematical equations.
How to model the spread of heat using equations that model convection, conduction, and heat radiation which all effect fire flow.

On average, nearly six and a half million acres of woodland forest burn in the United States every year (O'Driscoll, 2005). The recent Cerro Grande Fire of 2000 which quickly got out of hand and burned 47,650 acres of federal forest, cost the Federal Government 10 million dollars to contain (nifc.gov, 2002) and caused more than a billion dollars in damage (Masse, 2003).

In the previous year's project, a program was created in C++ to randomly model the forest environment. Heat flow was achieved by averaging temperatures between neighboring patches of forest. Fire spread was achieved by programming logic into each patch so that if one were on fire, then the other patches around it would ignite and further spread the fire.

The new program will differ in that it will include vertical fire spread from the ground up into the tree top canopy. Huygens principle, which models fire spread from the origin based on wind and characteristics of the burning fuel to create an elliptical fire flow path. This will allow the program to more accurately spread based on a dynamic environment. The new program will be able to model fire over a larger area; will incorporate movement from tree to tree and overall growth of the fire in that environment. This data will be recorded and used for statistical interpretation then it will be validated by comparing the results to the USFS data.

Problem Solution:
The program will function on a two-dimensional plane using Huygen's principles (Finey, 2002) for flow in elliptical cells. The program will then proceed to encompass equations used in the Farsite program to incorporate the fire spread and wind specifics on the edge of a fire and accurately spread it in a three-dimensional pattern. Crown fire is the most important factor because the tree top crown will burn with more heat and will therefore flow more intensity.

Progress to Date:
To date, a two-dimensional program has been created which allows for the forest environment to be accurately drawn in a single plane. The two-dimensional program can then be incorporated into a separate three-dimensional program, which is still in development. Combined, the two programs will be used to model three-dimensional fire spread on multiple levels of the forest. The team has also analyzed and incorporated Newton's Law of Cooling (wikipedia.com, 2005), and Fourier's Law of Conduction (wikipedia.com, 2005) and are close to including Huygen's equation (Finey, 2002) which will allow for more accurate elliptical flow.

Expected Results:
Once the three-dimensional program is completed, the team expects this model to accurately portray how a fire spreads in a three-dimensional environment based on heat, oxygen, and fuel supply. The program could be used to take the place of fire modeling programs like Farsite which neglects many of the variables inherent in heat flow, and may someday help to predict how a fire travels in various forest settings and conditions. It could possibly be used to determine if it is safe to attempt a prescribed burn given certain conditions in the forest. One day, it may even be used to predict the threat of another large scale fire like the Cerro Grande.

References:
Masse, B. & Nisengard, J. (2003). Cerro Grange Fire Assessment Project Cultural Resources Report No. 211.

O'Driscoll, P. (2005). Studies at odds over logging after wildfires. USA Today Nov. 2nd

Finey, M. (2002) Austrailian Mathematical Society Fire growth using minimum travel time methods

www.nifc.gov (last updated, 2002). Historical Wildfire Statistics. Retrieved December 6th 2005 http://www.nifc.gov/stats/historicalstats.html