The Properties of Elliptical Wildfire Growth for Time Dependent Fuel and Meteorological Conditions

Abstract

Abstract— This work considers an existing system of differential equations based on Huygens' Principle that can, under some assumptions, trace the position in time of the perimeter of a large wildland fire. These equations in general require a sophisticated numerical solution, however it is demonstrated that if fuel and meteorological conditions are functions of time only, then an analytic solution can be obtained to the equations. The solution is in the form of a definite integral involving the affecting variables expressed as functions of time. For the special case of only time dependent wind velocity, the solution is presented in terms of probability distributions. The solution allows an analysis of its properties giving an insight into the behaviour of wildland fire. A number of general properties are derived, such as how the history of the fire can be traced back in time and how fires from finite length ignition lines can be simulated. For the case of a point source ignition the solution has a simplified form that allows further analysis. It is shown that the perimeter length of the fire is a function of the wind speeds experienced only and independent of the wind directions. An analysis is made of the effect of wind velocity variations on the spread rates and perimeter shape, it is found that such variations can not cause otherwise elliptical fires to be lemniscate or double ellipse shaped, and that even small wind direction variations can result in significant reductions in the length to breadth ratio of the fire perimeter.

Keywords:

• Wildland Fire
• Modelling
• Perimeter Shape