A Versatile Physics-Based Rate of Spread Model for Backfires and Steep Terrain Conditions.

A versatile physics-based rate of spread model for backfires and steep terrain conditions.

Aurélien Costes¹, and Adam Kochanski¹

¹ Wildfire Interdisciplinary Research Center, San Jose State University, San Jose, United States of America

Wildfires are complex phenomena influenced by various factors, including wind, topography, and fuel moisture. Most tools dedicated to forecasting and studying large wildfires rely on a simplified representation of the fire dynamics. They assume the fire is a moving front separating an unburnt area from a burnt area. The speed of this front is called the rate of spread.

Two main categories of rate of spread models can be distinguished. Empirical/semi-empirical models (Rothermel 1972; Anderson et al. 2015) are based on small-scale experiments and provide a mathematical representation of the rate of spread with fitted parameters. Physics-based models (De Mestre et al. 1989; Balbi et al. 2009; Chatelon et al. 2022) compute the rate of spread by using heat transfer laws. The latter should be able to represent better complex configurations that were not in the scope of the experiments used during the calibration process of the empirical models, for example, a backfire on steep slope terrain (positive or negative slope). However, most of the current physics-based models are primarily defined for head fires, and their physical representation of heat transfer could not be applied in certain conditions (for example wind in the opposite direction of fire propagation).

We propose a physics-based rate of spread model that will be able to handle any wind and slope configuration. This model solves the energy balance over the surface stratum of dead fuel. It considers the flame radiative heat fluxes as well as heating and cooling convective heat fluxes in the fuel. Two radiative emission sources are considered: the flame base, from the ground to fuel height, and the flame sheet, above the fuel stratum. A surface-to-surface method (Schröder and Hanrahan 1993; Howell 2010) is used to compute the amount of radiative energy received at the vegetation top and sides. The fuel is considered as a highly porous media that can absorb a fraction of the energy received at its boundaries. The convective heat flux coefficients are computed using the method described by Mueller et al. (2022). The fire-induced flow is computed by using the potential flow theory.

The model can represent two extinction mechanisms, either the fuel may be too wet to burn, or the heat generated by the flame may not be sufficient to sustain the combustion.

The energy balance is calculated over a preheating distance defined by the equilibrium between radiative heating and convective cooling. We assume that the flame does not influence the fuel temperature beyond this point. The validation of the model has been conducted with an extensive comparison to experimental datasets. Results show a very good agreement between the model and the experiments. The model has also been implemented in WRF-SFIRE (Mandel et al. 2011).

References

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Chatelon, F. J., Balbi, J. H., Cruz, M. G., Morvan, D., Rossi, J. L., Awad, C., Frangieh, N., Fayad, J., & Marcelli, T. (2022). Extension of the Balbi fire spread model to include the field scale conditions of shrubland fires. International Journal of Wildland Fire, 31(2), 176–192. https://doi.org/10.1071/WF21082

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