A power series formulation for two-dimensional wildfire shapes
J. E. Hilton A C , C. Miller A and A. L. Sullivan B
+ Author Affiliations
- Author Affiliations
A CSIRO, Private Bag 10, Clayton South, Vic. 3169, Australia.
B CSIRO, GPO Box 1700, Canberra, ACT 2601, Australia.
C Corresponding author. Email: james.hilton@csiro.au
International Journal of Wildland Fire 25(9) 970-979 https://doi.org/10.1071/WF15191
Submitted: 28 October 2015 Accepted: 28 April 2016 Published: 5 July 2016
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.
Additional keywords: perimeter propagation, simulation.
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