# A New Way to Look at Fire: Using Artificial Intelligence to Describe Fire and Plume Behavior

The global increase in destructive and costly large-scale wildfires reveals a pressing need for better understanding and accurate prediction of fire and plume behavior. However, this multiphysics problem is challenging to efficiently model and simulate due to the presence of nonlinear and non-local effects, complex heterogeneous environments, and multiple time and length scales. These factors contribute to a variety of structures and behaviors that must be measured, modeled, simulated, and analyzed across diverse fire environments.

One approach that addresses the high computational cost of fire system simulation is the development of simplified models for operational settings that complement fire practitioners’ expertise [1, 3, 5]. In order to validate these models with experimental results prior to use, we quantify fire and plume behavior by applying computer vision principles and graph theory techniques to videos of fire. The resulting data describe the transport of heat and fire spread, turbulent statistics, and near-field plume structure. This novel approach generates a new statistical framework that better illustrates fire and plume dynamics [8].

### Extracting Data From Videos

Many critical dynamics of fire behavior occur at centimeter or sub-centimeter scales, but these small-scale dynamics both inform and influence larger-scale fire behavior. To capture small-scale dynamics in the field, we employ visual and infrared cameras to record prescribed burn experiments. Animation 1 provides visual and infrared recordings of a 2-meter \(\times\) 2-meter pine straw burn and its calculated fire progression map.

Our algorithm uses these videos to extract a fire’s path of travel via a series of steps that incorporate thresholding, clustering, Dijkstra’s algorithm, and a modified assignment problem. The assignment problem calculates a bijection to minimize \(\sum\nolimits_i \| \boldsymbol{a}_i - \boldsymbol{b}_i \|\), where \(\boldsymbol{a} = (\boldsymbol{a_1}, ..., \boldsymbol{a_n})\) and \(\boldsymbol{b} = (\boldsymbol{b_1}, ..., \boldsymbol{b_n})\) are fire fronts that are isolated in consecutive video frames (see Figure 1a). The spatial and temporal scales that are resolved by this method are limited only by the camera’s features; many modern cellphone cameras can capture sufficient videos for centimeter- or sub-centimeter-scale results. This method requires minimal equipment and can be set up outside of the fire area, thus enabling the study of many processes that occur in a wide range of fire scenarios.

In the field, the rate of spread is commonly presented as a single value that is associated with a set of wind, fuel, and slope conditions [7]. In contrast, our method yields spatially- and temporally-varying rates of spread that represent the fire front’s movement — thereby allowing more precise analysis of its critical dynamics. The strong relationship between fire behavior and atmospheric dynamics permitted us to interpret these results with atmospheric and fluid dynamics principles.

### Analysis and Conclusions

Fire fronts propagate with variable speeds and directions. As a consequence, the fronts divide into some portions that spread in the downwind positive longitudinal direction (head fire) and others that spread in the upwind negative longitudinal direction (backfire). This variation in speed creates a frontal burning zone (see Figure 2a). The frontal burning zone propagates with a net forward motion, so positive longitudinal components of the calculated rates of spread represent its motion. Figure 1b displays an exponential fit to the distribution of these positive longitudinal velocities. A Markov chain Monte Carlo (MCMC) method—which produced a normalized root mean square error (RMSE) of \(5.88 \times 10^{-4}\) centimeters per second—yielded the best experimental fit. Since exponential distributions are memoryless, our results suggest that we can appropriately model forward fire spread as a memoryless random process at this scale. Other laboratory and field studies have identified similar behaviors, even across larger spatial scales [4, 6].

Temperature data from an infrared camera offered supplementary information. Figure 2b depicts a distribution of the amount of time that each pixel actively burns during the 2-meter \(\times\) 2-meter pine straw experiment. We used MCMC to fit an Erlang distribution to this data, which produced a normalized RMSE of \(4.23 \times 10^{-5}\) seconds. Erlang distributions are generalizations of exponential distributions and arise as a convolution thereof, hence suggesting that the burn time of a fuel element relies on multiple exponential factors and stems from the interaction of turbulent and thermodynamic combustion processes. Previous studies have observed similar distributions in data from much larger-scale burns [2].

Both exponential and Erlang distributions are examples of gamma distributions and represent memoryless processes. We can thus interpret the Erlang burn time distribution as an underlying random process for extinguishing events — just as we can model the forward fire spread as a random process at this scale. This outcome speaks to the complex dynamics that affect fire spread, as well as the useful analysis and synthesis that a statistical description provides.

Using modern computing and physical science, we returned physical values and statistics that contribute to our understanding of fire behavior in diverse situations. Future research could apply the same framework to recordings of flame-atmosphere interactions, plume evolution, and additional configurations of fire spread across the surface layer. Furthermore, we found that combining visual and infrared results yields a more informative and complete picture of the intricate dynamics that are at play.

*Daryn Sagel delivered a minisymposium presentation on this research at the 2022 SIAM Conference on Mathematics of Planet Earth (MPE22), which took place concurrently with the 2022 SIAM Annual Meeting in Pittsburgh, Pa., last year. She received funding to attend MPE22 through a SIAM Student Travel Award. To learn more about Student Travel Awards and submit an application, visit the online page.*

*SIAM Student Travel Awards are made possible in part by the generous support of our community. To make a gift to the Student Travel Fund, visit the SIAM website. *

References[1] Achtemeier, G.L., Goodrick, S.A., Liu, Y., Garcia-Menendez, F., Hu, Y., & Odman, M.T. (2011). Modeling smoke plume-rise and dispersion from southern United States prescribed burns with Daysmoke.

Atmosphere,2(3), 358-388.

[2] Butler, B., Teske, C., Jimenez, D., O’Brien, J., Sopko, P., Wold, C., ... Loudermilk, E.L. (2016). Observations of energy transport and rate of spreads from low-intensity fires in longleaf pine habitat-RxCADRE 2012.Int. J. Wildland Fire,25(1), 76-89.

[3] Finney, M.A. (2006). An overview of FlamMap fire modeling capabilities. In P.L. Andrews & B.W. Butler (Eds.),Fuels management – how to measure success: Conference proceedings (Proceedings RMRS-P-41)(pp. 213-220). Fort Collins, CO: U.S. Department of Agriculture.

[4] Johnston, J.M., Wheatley, M.J., Wooster, M.J., Paugam, R., Davies, G.M., & DeBoer, K.A. (2018). Flame-front rate of spread estimates for moderate scale experimental fires are strongly influenced by measurement approach.Fire,1(1), 16.

[5] Linn, R.R., Goodrick, S.L., Brambilla, S., Brown, M.J., Middleton, R.S., O'Brien, J.J., & Hiers, J.K. (2020). QUIC-fire: A fast-running simulation tool for prescribed fire planning.Environ. Model. Softw.,125, 104616.

[6] Morandini, F., Silvani, X., & Susset, A. (2012). Feasibility of particle image velocimetry in vegetative fire spread experiments.Exp. Fluids,53(1), 237-244.

[7] Rothermel, R.C. (1972).A mathematical model for predicting fire spread in wildland fuels(Research paper INT-115). Ogden, UT: U.S. Department of Agriculture.

[8] Sagel, D., Speer, K., Pokswinski, S., & Quaife, B. (2021). Fine-scale fire spread in pine straw.Fire,4(4), 69.

### About the Authors

#### Daryn Sagel

##### Ph.D. candidate, Florida State University

Daryn Sagel is a Ph.D. candidate in the Geophysical Fluid Dynamics Institute and Department of Scientific Computing at Florida State University. Her research interests include the development of computer vision and statistical algorithms for fire and fluid behavior analysis.

#### Kevin Speer

##### Director, Geophysical Fluid Dynamics Institute

Kevin Speer is director of the Geophysical Fluid Dynamics Institute and a professor in the Department of Scientific Computing at Florida State University. His research focuses on applications of fluid dynamics that range from oceanography to fire behavior.

#### Bryan Quaife

##### Professor, Florida State University

Bryan Quaife is a professor in the Department of Scientific Computing at Florida State University. He is interested in the development of integral equation methods for complex fluids and fire dynamics.

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