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Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that has the potentiality to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a kernel function that can take into account wind conditions, land slope, spotting phenomena, and so on, bringing to a system of integrodifferential equations whose solutions provide the evolution in time of the subprobability densities. That makes the model complementary to models based on cellular automata that furnish single instantiations of the stochastic phenomenon. Moreover, stochastic models based on cellular automata can be derived from the present model by space and time discretization. Existence and uniqueness of the solutions is proved by using Banach's fixed‐point theorem. The asymptotic behavior of the model is analyzed as well. By specifying a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving toward a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. The kernel could be slightly modified to include firefighters interventions and weather changes.
Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that has the potentiality to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a kernel function that can take into account wind conditions, land slope, spotting phenomena, and so on, bringing to a system of integrodifferential equations whose solutions provide the evolution in time of the subprobability densities. That makes the model complementary to models based on cellular automata that furnish single instantiations of the stochastic phenomenon. Moreover, stochastic models based on cellular automata can be derived from the present model by space and time discretization. Existence and uniqueness of the solutions is proved by using Banach's fixed‐point theorem. The asymptotic behavior of the model is analyzed as well. By specifying a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving toward a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. The kernel could be slightly modified to include firefighters interventions and weather changes.
In the Mediterranean basin, coniferous reforestation mainly comprises forest stands highly susceptible to fires. When silvicultural treatments have not been performed for decades after plantation, these stands often exhibit high vertical and horizontal tree density, along with a significant occurrence of lying and standing deadwood, thereby increasing the fuel load. On average, these pine forests are characterized by high values of above-ground biomass, ranging from 175 to 254 Mg ha−1 for the younger and the older ones, respectively. The theoretical heat energy produced per surface unit, in the case of the total combustion of the above-ground biomass, is also high, varying from 300 to 450 MJ ha−1 depending on the stage of stand development. In this study, we demonstrated the importance of silvicultural interventions in reducing the pyrological potential in pine reforested stands located in southern Italy, also giving attention to the water savings needed during extinction phases. In detail, we applied a preliminary mathematical reaction-diffusion model aimed at predicting the development of forest fires. The model was applied using data obtained through the estimation of the pyrological potential in terms of heat energy produced per surface unit (1 hectare) and the variation in the critical surface intensity. We verified that, when silvicultural interventions are applied, they induce a reduction of heat energy ranging between 17 and 21%, while the extinguishing water saved ranges between 600 and 1000 Mg ha−1. Moreover, when the silvicultural interventions are implemented, the probability of the transition from surface fire to crown fire can be reduced by up to 31%. The most effective results on fire risk mitigation are mainly obtained when thinning aimed at reducing canopy and tree density is carried out in the younger phases of the reforested pine stands.
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