Modelling extremes of spatial aggregates of precipitation using conditional methods

Abstract

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 (J. R. Stat. Soc. Ser. B. Stat. Methodol. 66 (2004) 497–546) 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 subregions 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.