Fractal analysis of wildfire pattern dynamics using a Small World Network model

Abstract

The dynamics of a spreading wildfire is modeled by using a variant of the Small World Network stochastic model (Zekri et al., 2005). The temporal evolution of the fire front width and its pattern’s fractal dimension exhibits an anomalous relaxation process before the extinction of the initial fire-line that is well described by a Kohlrausch–Williams–Watts-like relaxation function. The decrease of the fire pattern’s dimension corresponds to a transition from a structured fire front induced by the collective effects of burning fuels to a dispersed one caused by their individual effects. This anomalous relaxation with an exponent γ≈0.5 indicates the existence of a sub-diffusion process of the spreading fire regardless of the impact length and fuel occupation density. After the extinction of the initial fire-line, the fractal dimension of the fire pattern fluctuates around an average value corresponding to an average spread rate of fire and front intensity. The amplitude of these fluctuations decreases as the impact length of the burning fuel or the occupation density increases. The analysis of the local scale exponents shows that the fractal (self-similar) behavior of the fire pattern is observed in the spatial resolution range delimited by the mean free path and the pattern size. Further discussion on the competition effect between the heat release rate of the flame and the mean free path on fire behavior is provided.