Stochasticity in fire spread and the fire size distribution

We present an alternative model that is able to generate both heavy-tailed distributions and the steepness range observed in the data. The model considers that fire size is controlled by the stochastic dynamics of the fire front. The range of steepness (exponent -1.9 to -1.3) observed in the data is obtained by varying the average success of a fire front to travel across the fuel, which regrows locally depending on the time since last fire. For a critical parameter value, the model analytically predicts a power-law distribution of fire sizes of exponent -1.5. We conclude that regionally characteristic stochasticity during the spread of a fire is able to generate the observed fire size distributions. We discuss the role of vegetation, topography and climate in generating this stochasticity and its implications for associated control strategies.