Multivariate modelling of spatial extremes based on copulas

To model extreme spatial events, a general approach is to use the generalized extreme value (GEV) distribution with spatially varying parameters such as spatial GEV models and latent variable models. In the literature, this approach is mostly used to capture spatial dependence for only one type of event. This limits the applications to air pollutants data as different pollutants may chemically interact with each other. A recent advancement in spatial extremes modelling for multiple variables is the multivariate max-stable processes. Similarly to univariate max-stable processes, the multivariate version also assumes standard distributions such as unit-Fréchet as margins. Additional modelling is required for applications such as spatial prediction. In this paper, we extend the marginal methods such as spatial GEV models and latent variable models into a multivariate setting based on copulas so that it is capable of handling both the spatial dependence and the dependence among multiple pollutants. We apply our proposed model to analyse weekly maxima of nitrogen dioxide, sulphur dioxide, respirable suspended particles, fine suspended particles, and ozone collected in Pearl River Delta in China.