The dynamics and statistics of synthetic and historical mid-sized Mediterranean forest fires that occurred in Catalonia (Spain) and Liguria (Italy) regions are investigated using a wildfire simulator PROPAGATOR based on a cellular-automaton scheme. On one hand, the mean, variance, and kurtosis of the synthetic burned area exhibits a non-linear growth during fire spread exacerbated by higher wind speeds and steeper terrain slopes, whereas its skewness decreases. On the other hand, the mean and variance of the burned area for the simulated historical wildfires increase nonlinearly over time, Albenga fire in Liguria region being the one exhibiting the minimum stochasticity. The skewness and kurtosis of all the real cases exhibit an irregular pattern. Z-score and interquartile range standardization methods are applied to find the most suitable parametric model for the statistical distribution of the burned area. Analytic formulae for the shape parameters ( \(\alpha\) , \(\beta\) ) are derived by using a customized method of moments. Both standardization approaches indicate that a four-parameter Beta density function provides the best fit both for the ideal synthetic case under various wind intensities and terrain slopes’ angles, and for all the historical fires studied in Southern Europe. This suggests that this statistical model can serve as a good candidate for a prior distribution in a Bayesian approach. The dynamics of the synthetic forest fire’s shape parameters exhibit the same tendency regardless of meteorological and topographic conditions: \(\alpha\) increases during fire-growth while \(\beta\) becomes constant after a crossover time \(t_x\) ( \(\beta =\beta _\textrm{eq}\) ). In the short-time regime, i.e., \(t < t_x\) , the burned area distribution is right-skewed ( \(\alpha < \beta\) ) highlighting the prevalence of small-size burned areas. At \(t \simeq t_x\) , the distribution is symmetric, and it does not exhibit any bias towards outliers. In the long-time regime, i.e., \(t > t_x\) , the distribution becomes left-skewed ( \(\alpha > \beta\) ), and large-size wildfires lead the process. The real-world cases are characterized by more nuanced dynamics in the long-time regime ( \(t > t_x\) ), where the Beta distribution’s parameters are affected by the complex interplay between the inherent stochastic nature of fire dynamics and the firefighters’ actions, land cover, meteorological, and orographic conditions.
