Wildland fire propagation modeling: fire-spotting parametrisation and energy balance

Abstract

Present research concerns the physical background of a wild-fire propagation model based on the split of the front motion into two parts - drifting and fluctuating. The drifting part is solved by the level set method and the fluctuating part describes turbulence and fire-spotting. These phenomena have a random nature and can be modeled as a stochastic process with the appropriate probability density function. Thus, wildland fire propagation results to be described by a nonlinear partial differential equation (PDE) of the reaction-diffusion type. A numerical study of the effects of the atmospheric stability on wildfire propagation is performed through its effects on fire-spotting. Moreover, it is shown that the solution of the PDE as an indicator function allows to construct the energy balance equation in terms of the temperature.