From spark to conflagration: A multiscale thermodynamic-percolation framework for wildland-fire spread

Abstract

Wildland fire operates across multiple spatial and temporal scales, linking local combustion chemistry and turbulent heat transport to continental patterns of burned area. A quantitative bridge between microscale ignition physics and macroscale propagation has remained elusive because operational simulators treat ignition empirically, while statistical lattice models simplify combustion to binary states. This study derives ignition probabilities from an energy-balance law, embeds them in a branching-process formulation allied to percolation theory, and connects the discrete description to a reaction-diffusion continuum via a real-space-renormalization invariant. The resulting framework yields closed-form fuel-load thresholds, explains scale-free burned-area distributions, and clarifies why modest meteorological changes can precipitate abrupt transitions from smouldering to landscape-spanning fire.