Gielis superformula and wildfire models

TL;DR

This paper demonstrates that wildfire spread shapes can be effectively modeled using the Gielis superformula, with firefronts computed via lightlike geodesics in a Finsler spacetime, providing a novel geometric approach.

Contribution

It introduces a new geometric model for wildfire propagation based on the Gielis superformula and Finsler spacetime, linking wildfire shapes to advanced mathematical structures.

Findings

Wildfire spread shapes are well approximated by the Gielis superformula.

The model accurately captures the double semi-elliptical wildfire shape.

Efficient geodesic equations are derived for the firefront computation.

Abstract

Experimental data on the propagation of wildfires show that its short-time spread has a double semi-elliptical shape. Our main goal is to show that this shape can be accurately approximated in polar coordinates by choosing suitable parameters in Gielis superformula and, then, implemented in a geometrical model for wildfire propagation. In this model, the firefront can be determined by computing the lightlike geodesics of a specific Finsler spacetime, and we derive a concise and efficient expression of the geodesic equations in these coordinates.