Kriged Kalman filtering for predicting the wildfire temperature evolution

Existing wildfire evolution models have been mostly developed in a deterministic modelling framework. As a complementary alternative, this thesis presents a stochastic framework based on the Kriged Kalman filter to obtain global temperature predictions given local temperature measurements. By solving the heat transfer partial differential equation driving the wildfire evolution, it is shown that the spatio-temporal mean temperature process associated with a wildfire evolving in a finite spatial domain under certain prescribed conditions can be approximated by a Fourier series. The potential of the proposed Kriged Kalman filtering framework in predicting the wildfire temperature evolution is demonstrated in simulations on temperature data generated by a simplified physical wildfire propagation model. The performance of the Kriged Kalman filter in predicting the wildfire temperature evolution is compared to that of standard Gaussian process regression.