A power series formulation for two-dimensional wildfire shapes

This is the authors' abstract. We don't add key points for this paper.

Computational simulations of wildfires require a model for the two-dimensional expansion of a fire perimeter. Although many expressions exist for the one-dimensional rate of spread of a fire front, there are currently no agreed mathematical expressions for the two-dimensional outward speed of a fire perimeter. Multiple two-dimensional shapes such as elliptical and oval-shaped perimeters have been observed and reported in the literature, and several studies have attempted to classify these shapes using geometric approximations. Here we show that a two-dimensional outward speed based on a power series results in a perimeter that can match many of these observed shapes. The power series is based on the dot product between the vector normal to the perimeter and a fixed wind vector. The formulation allows the evolution and shape of a fire perimeter to be expressed using a small set of scalar coefficients. The formulation is implemented using the level set method, and computed perimeters are shown to provide a good match to perimeters of small-scale experimental fires. The method could provide a framework for statistical matching of wildfire shapes or be used to improve current wildfire prediction systems.