Statistical description of firebrand size and shape distribution from coniferous trees for use in Metropolis Monte Carlo simulations of firebrand flight distance

• A pair of simple mechanical failure model of ember break-off process is proposed.
• Geometric scaling analysis of embers is conducted.
• Detailed statistical analysis of the size and shape of the embers is presented.
• It is shown that the size distribution of embers is less dependent on a simple geometric relationship with the tree height.

The process of ember/firebrand formation, lofting, wind driven transport, and resulting spot fire ignition during a wildfire is still poorly understood. Lack of a tractable firebrand formation model along with a detailed statistical description of the size and shape distribution of typical firebrand that could be used in simulations of firebrand flight and combustion may result in unrealistic outcomes. In this regard, a simple, yet quite informative, mechanical failure model of the firebrand break-off process is proposed. This model suggests that the previous laboratory scale firebrand generation experiments would likely provide a reasonable analogue for the formation process in a full scale wildfire. In addition, geometric scaling analysis is conducted and shows that the firebrand surface area scales with the firebrand mass raised to the 2/3rds2/3rds power. This is in close agreement with measurements of firebrand from previously published data in the literature that are obtained under controlled laboratory combustion of coniferous tress of different sizes. Also, a detailed statistical characterization of the size and shape of these firebrands are presented. A nonlinear regression model on the firebrands' data led to the generation of a set of virtual firebrands. The resulting data could be used as inputs to a Monte-Carlo simulation of firebrands' transport through the velocity field induced by the interaction of a fire plume and the atmospheric boundary layer. Moreover, it is shown that the size distribution of firebrands is more dependent on the mechanics of combustion and limb failure than on a simple geometric relationship with the tree height.