Reconstruction of Fire Spread with a Markov Random Field Mixture Model

Sammanfattning: This thesis revolves around reconstructing fire sizes for historical fires in Jämtgaveln, Sweden based on data of fire scars in trees. We propose a Hidden Markov Model (HMM), where the domain is divided into quadratic grid cells of 250 $\times$ 250 m and with these grid cells we associate a binary Markov random field taking values 0 or 1 corresponding to no fire and fire respectively. Furthermore, we let the fire tendency vary locally based on landscape related covariates and previous fire in the area. The model for the observed fire scars contains a detection probability, representing the likelihood that a fire leaves a scar in a tree, that we also estimate. For estimation we use a modified Maximum Likelihood method with a pesudo-likelihood for the Markov random field, where the estimation is performed with a Monte Carlo EM method (MCEM). The posterior distribution is estimated through Gibbs sampling. The detection probability was estimated to 0.59 and fraction of lakes in a grid cell was found to have a significant negative effect on the spread of the fire. We also found a weak negative dependence between fire tendencies for consecutive fires at the same location.