Inference on the extremal behaviour of spatial aggregates of precipitation
is important for quantifying river flood risk. There are two classes of previous
approach, with one failing to ensure self-consistency in inference across
different regions of aggregation and the other imposing highly restrictive assumptions. To overcome these issues, we propose a model for high-resolution
precipitation data, from which we can simulate realistic fields and explore
the behaviour of spatial aggregates. Recent developments have seen spatial
extensions of the Heffernan and Tawn (2004) model for conditional multivariate
extremes, which can handle a wide range of dependence structures.
Our contribution is twofold: extensions and improvements of this approach
and its model inference for high-dimensional data; and a novel framework for
deriving aggregates addressing edge effects and sub-regions without rain.We
apply our modelling approach to gridded East-Anglia, UK precipitation data.
Return-level curves for spatial aggregates over different regions of various
sizes are estimated and shown to fit very well to the data.