Joint Estimation of Extreme Precipitation at Different Spatial Scales through Mixture Modelling

Parsimonious and effective models for the extremes of precipitation aggregates that can capture their joint behaviour at different spatial resolutions must be built with knowledge of the underlying spatial process. Precipitation is driven by a mixture of processes acting at different scales and intensities. The specific process that drives the extremal behaviour of the aggregate will be dependent on the aggregate resolution; whilst high-intensity, spatially-localised convective events cause extreme high-resolution spatial aggregates, the contribution of low-intensity, large-scale fronts is likely to increase with the scale of the aggregate. Thus, to jointly model low- and high-resolution spatial aggregates, we require a model that can capture both convective and frontal events. We propose a novel spatial extreme values model which is a mixture of two components with different marginal and dependence models that are able to capture the extremal behaviour of convective and frontal rainfall. Modelling extremes of the frontal component raises new challenges due to it exhibiting strong long-range extremal spatial dependence. Our modelling approach is applied to fine-scale, high-dimensional, gridded precipitation data, where we show that accounting for the mixture structure improves the joint inference on extremes of spatial aggregates over multiple regions of different sizes.