@article{ref1,
title="A power series formulation for two-dimensional wildfire shapes",
journal="International journal of wildland fire",
year="2016",
author="Hilton, J. E. and Miller, C. and Sullivan, A. L.",
volume="25",
number="9",
pages="970-979",
abstract="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.<p /><p>Language: en</p>",
language="en",
issn="1049-8001",
doi="10.1071/WF15191",
url="http://dx.doi.org/10.1071/WF15191"
}