# Bayesian spatial extreme value analysis of maximum temperatures in County Dublin, Ireland

## TL;DR

This paper develops a Bayesian hierarchical model combining predictive processes and extreme value theory to analyze spatial temperature extremes in Ireland, providing detailed return level estimates and site-specific analysis over 1981-2010.

## Contribution

It introduces the first integration of predictive processes with EVT in a Bayesian framework for spatial extreme temperature analysis.

## Key findings

- Observed increase in extreme anomaly frequency from 2011-2018.
- Site-specific anomalies exceed model credible intervals by 20% and 7%.
- Model provides detailed return level surfaces and site analyses.

## Abstract

In this study, we begin a comprehensive characterisation of temperature extremes in Ireland for the period 1981-2010. We produce return levels of anomalies of daily maximum temperature extremes for an area over Ireland, for the 30-year period 1981-2010. We employ extreme value theory (EVT) to model the data using the generalised Pareto distribution (GPD) as part of a three-level Bayesian hierarchical model. We use predictive processes in order to solve the computationally difficult problem of modelling data over a very dense spatial field. To our knowledge, this is the first study to combine predictive processes and EVT in this manner. The model is fit using Markov chain Monte Carlo (MCMC) algorithms. Posterior parameter estimates and return level surfaces are produced, in addition to specific site analysis at synoptic stations, including Casement Aerodrome and Dublin Airport. Observational data from the period 2011-2018 is included in this site analysis to determine if there is evidence of a change in the observed extremes. An increase in the frequency of extreme anomalies, but not the severity, is observed for this period. We found that the frequency of observed extreme anomalies from 2011-2018 at the Casement Aerodrome and Phoenix Park synoptic stations exceed the upper bounds of the credible intervals from the model by 20% and 7% respectively.