  Wildfires pose a severe threat to the ecosystem and economy, and risk
assessment is typically based on fire danger indices such as the McArthur
Forest Fire Danger Index (FFDI) used in Australia. Studying the joint tail
dependence structure of high-resolution spatial FFDI data is thus crucial for
estimating current and future extreme wildfire risk. However, existing
likelihood-based inference approaches are computationally prohibitive in high
dimensions due to the need to censor observations in the bulk of the
distribution. To address this, we construct models for spatial FFDI extremes by
leveraging the sparse conditional independence structure of
H\"usler--Reiss-type generalized Pareto processes defined on trees. These
models allow for a simplified likelihood function that is computationally
efficient. Our framework involves a mixture of tree-based multivariate Pareto
distributions with randomly generated tree structures, resulting in a flexible
model that can capture nonstationary spatial dependence structures. We fit the
model to summer FFDI data from different spatial clusters in Mainland Australia
and 14 decadal windows between 1999--2022 to study local spatiotemporal
variability with respect to the magnitude and extent of extreme wildfires. Our
results demonstrate that our proposed method fits the margins and spatial tail
dependence structure adequately, and is helpful to provide extreme wildfire
risk measures.
