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Thermal-image-based wildfire spread simulation using a linearized model of an advection–diffusion–reaction equation

This paper models the fire spread at Cleveland National Forest in California using a partial differential equation (PDE) in two space dimensions and observed data. We consider the linearized model of the advection–diffusion–reaction equation to test the feasibility with the available sparse wind data and the thermal images. The model equation is simple enough to be executed in minutes on a desktop or laptop to provide immediate and effective fire-fighting planning during a crisis. We incorporate the real time update and reinitialization with the available thermal images and wind data for the simulation. The update is done by fitting the solution and the coefficients of the model equation. We implement the linear regression and second-order finite difference methods with Strang splitting. We consider several possible scenarios to test the feasibility of the model equation and present the numerical results. With adequate data, our simple model is effective enough to produce accurate results within a minute for short time intervals, which may be sufficiently long for immediate fire-fighting planning.