Applications of Randers geodesics for wildfire spread modelling

Abstract

Here, by using the validity of the Huygens’ envelope principle for wavefronts in Randers spaces, we present some models for wildfire propagation in a flat land under the presence of wind. The wind could be constant or space-dependent. In the models, the height of the propagation is considered, trajectories of fire particles are tracked, and the equations that give the wavefront at each time are provided. Furthermore, we determine the paths of great importance in the process of wildfire management, called strategic paths. These paths can be used to determine the locations of barriers that we make to block the fire and stop it from propagation toward some special area; or to determine the paths through which the fire surrounds, for instance, the transmission lines of the power system. Finally, we provide several interesting examples of spreading the wildfire with different conditions. We implement the examples in the MATLAB environment to solve and provide the models of fire propagations.