Statistical Characterization of Wildfire Dynamics: Studying the Relation Between Burned Area and Head of the Fire
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We show that the probability density function (PDF) of an area enclosed by a random perimeter is driven by the PDF of the integration bounds and the mean value of the perimeter function. With reference to wildfires, if the integration interval is aligned with the main direction of propagation, the PDF of the burned area is driven by the PDF of the position of the head of the fire times the mean value of the fire front. We show that if the random fire front perimeter is modelled as an ellipse-like curve with stochastic noise, the relation between the probability distribution of the burned area and the one of the head of the fire is linear, with the constant mean value of the perimeter as a factor. Different random noise models have been developed and implemented for this purpose. Different behaviours of the stochastic position of the head of the fire have been studied, including Viegas’ rate of spread model. We show that for the realistic propagation model given by the operational wildfire cellular automata simulator Propagator , the PDF of the burned area is still driven by the position of the head of the fire and the mean value of the fire front perimeter, and the shape of the perimeter is not relevant. This has been shown for 5 case studies, ranging from easy ones to realistic complicated cases.