Statistical models for the location of lightning-caused wildfire ignitions
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2018 Dr. Nicholas Read
Lightning-caused wildfire is a significant concern for fire management agencies worldwide. Unlike other ignition sources, lightning fires often occur in remote and inaccessible locations making detection and suppression particularly challenging. Furthermore, individual lightning storms result in a large number of fires clustered in space and time which can overwhelm suppression efforts. Victoria, Australia, is one of the most fire prone environments in the world and the increased frequency of large-scale landscape fires over the last decade is of particular concern to local wildfire management authorities. This thesis is concerned with modeling lightning-caused wildfire ignition locations in Victoria. Such models could be used for predicting daily lightning-caused ignition likelihood as well as simulating realistic point patterns for use in fire spread models for risk analyses. The first half of this thesis looks at regression models. We review methods for the model selection, validation, approximation and interpretation of generalised additive models. A review of performance metrics, such as the AUC, shows the difficulties and subtleties involved in evaluating the predictive performance of models. We apply this theory to construct a non-linear logistic regression model for lightning-caused wildfires in Victoria. The model operates on a daily time scale, with a spatial resolution of 20 km and uses covariate data including fuel moisture indices, vegetation type, a lightning potential index and weather. We develop a simple method to deconstruct model output into contributions from each of the individual covariates, allowing predictions to be explained in terms of the weather conditions driving them. Using these ideas, we discuss ranking the relative 'importance' of covariates in the model, leading to an approximating model with similar performance to the full model. The second half of this thesis looks at point process models for lightning-caused ignitions. We introduce general theory for point processes, focusing on the inhomogeneous Poisson process, cluster processes and replicated point patterns. The K-function is a useful summary function for describing the spatial correlation point patterns and for fitting models. We present a method for pooling multiple estimates of the K-function, such as those that arise when using replicated point patterns, intended to reduce bias. We fit an inhomogeneous Poisson process model as well as a Thomas and Cauchy cluster process model to the Victorian lightning-caused ignition data set. The cluster process models prove to have significantly better fit than the Poisson process model, but still struggle to reproduce the complex behaviour of the physical process.
Keywordsprobability; statistics; point processes; regression; wildfire; lightning ignitions
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