Self-Similar Criticality: A Model for Forest Fire Burn Areas

Many natural phenomena exhibit power-law frequency-size distributions and are modeled as self-organized critical (SOC) systems. Examples include earthquakes, forest fires, and landslides, which are associated with the slider-block, forest fire, and sand pile SOC models, respectively. As originally proposed, SOC models generate event frequency-size distributions that follow a power law with a single scaling exponent. The slider-block SOC model was modified to produce a range of scaling exponents, consistent with distributions observed for naturally occurring earthquakes. Forest fire burn areas have been found to follow power law frequency-size distributions with scaling exponents that depend on study location. In the original forest fire SOC model, events are triggered at randomly selected locations and follow a cumulative distribution described by a single scaling exponent. In self-similar criticality (SSC) models, events are triggered on a fractal distribution of critical grid cells and the scaling exponent of the resulting distribution depends on the fractal dimension of the critical cells. The SSC model applied to forest fires generates distributions with a range of scaling exponents, as is observed for forest fire burn areas in nature. The SSC model may provide a link between fractal geometry of topography and observed power law frequency-size distributions of forest fire burn areas.