  Modelling the extremal dependence structure of spatial data is considerably
easier if that structure is stationary. However, for data observed over large
or complicated domains, non-stationarity will often prevail. Current methods
for modelling non-stationarity in extremal dependence rely on models that are
either computationally difficult to fit or require prior knowledge of
covariates. Sampson and Guttorp (1992) proposed a simple technique for handling
non-stationarity in spatial dependence by smoothly mapping the sampling
locations of the process from the original geographical space to a latent space
where stationarity can be reasonably assumed. We present an extension of this
method to a spatial extremes framework by considering least squares
minimisation of pairwise theoretical and empirical extremal dependence
measures. Along with some practical advice on applying these deformations, we
provide a detailed simulation study in which we propose three spatial processes
with varying degrees of non-stationarity in their extremal and central
dependence structures. The methodology is applied to Australian summer
temperature extremes and UK precipitation to illustrate its efficacy compared
to a naive modelling approach.
