Wildfires as Far-From-Equilibrium Systems: A Theoretical Framework

Wildfires inherently represent complex systems that are far from equilibrium, possibly leading to deep ecological and societal consequences. The challenge of wildfire spread modeling is to adequately describe its front evolution along largei a considerable length and time scales in an heterogeneous environment. Environmental heterogeneities range from abrupt landscape variations together with spatial alternations of different vegetation types having distinct fuel structures and moisture levels. We introduce a $(3 + 1)$-state lattice model to describe the stochastic nature of wildfire propagation, where each state represents unburned, burning, and burned vegetation, as well as, an additional inert state representing a lattice site without vegetation. In addition, the model requires three parameters defined as the fuel content (load), a threshold for ignition, and the wildfire rate of spread. Based on these few assumptions, a formal framework is developed to describe the kinetics of the stochastic wildfire model. The model is validated using kinetic Monte Carlo simulations for two initial conditions which we denote as the line and point sources of ignited vegetation. The stochastic wildfire model successfully describes wildfire front evolution in both the absence and presence of wind.