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Parameter estimation of fire propagation models using level set methods. (English) Zbl 1481.49035

Summary: The availability of wildland fire propagation models with parameters estimated in an accurate way starting from measurements of fire fronts is crucial to predict the evolution of fire and allocate resources for firefighting. Thus, we propose an approach to estimate the parameters of a wildland fire propagation model combining an empirical rate of spread and level set methods to describe the evolution of the fire front over time and space. The estimation of parameters affecting the rate of spread is performed by using fire front shapes measured at different time instants as well as wind velocity and direction, landscape elevation, and vegetation distribution. Parameter estimation is done by solving an optimization problem, where the objective function to be minimized is the symmetric difference between predicted and measured fronts at different time instants. Numerical results obtained by the application of the proposed method are reported in two simulated scenarios and in a case study based on data originated by the 2002 Troy fire in Southern California. The obtained results showcase the effectiveness of the proposed approach both from qualitative and quantitative viewpoints.

MSC:

49N45 Inverse problems in optimal control
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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