Assimilation of data into a fire-spread model is formulated as an optimization problem. The level set equation, which relates the fire arrival time and the rate of spread, is allowed to be satisfied only approximately, and we minimize a norm of the residual. Previous methods based on modification of the fire arrival time either used an additive correction to the fire arrival time, or made a position correction. Unlike additive fire arrival time corrections, the new method respects the dependence of the fire rate of spread on diurnal changes of fuel moisture and on weather changes, and, unlike position corrections, it respects the dependence of the fire spread on fuels and terrain as well. The method is used to interpolate the fire arrival time between two perimeters by imposing the fire arrival time at the perimeters as constraints.
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