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

Area of Science:

• Wildland fire science
• Combustion physics
• Percolation theory
• Reaction-diffusion systems

Background:

• Wildland fires operate across diverse spatial and temporal scales, connecting local combustion to continental burned area patterns.
• Existing models lack a quantitative link between microscale ignition and macroscale fire spread, using empirical data or simplified combustion states.

Purpose of the Study:

• To develop a unified theoretical framework connecting microscale ignition physics to macroscale wildland fire propagation.
• To derive ignition probabilities from fundamental energy-balance principles.
• To explain scale-free burned-area distributions and abrupt fire regime transitions.

Main Methods:

• Derived ignition probabilities from an energy-balance law.
• Embedded ignition probabilities in a branching-process formulation linked to percolation theory.
• Connected discrete and continuum models using a real-space-renormalization invariant.

Main Results:

• Developed a framework yielding closed-form fuel-load thresholds for fire ignition.
• Explained the observed scale-free distributions of burned areas in wildland fires.
• Clarified the role of meteorological changes in precipitating transitions from smoldering to landscape-spanning fires.

Conclusions:

• The derived framework provides a quantitative bridge between microscale ignition and macroscale fire spread.
• The model successfully explains key characteristics of wildland fire behavior, including burned-area distributions and regime shifts.
• This approach offers new insights into predicting and understanding the dynamics of large-scale wildland fires.