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.

中文翻译：

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爱尔兰都柏林郡最高气温贝叶斯空间极值分析

在这项研究中，我们开始全面表征爱尔兰 1981-2010 年期间的极端温度。我们生成了 1981 年至 2010 年 30 年间爱尔兰某地区每日最高气温异常的异常回归水平。我们采用极值理论 (EVT) 使用广义帕累托分布 (GPD) 作为三级贝叶斯分层模型的一部分对数据进行建模。我们使用预测过程来解决在非常密集的空间场上建模数据的计算难题。据我们所知，这是第一项以这种方式结合预测过程和 EVT 的研究。该模型使用马尔可夫链蒙特卡罗 (MCMC) 算法进行拟合。除了天气站的特定站点分析外，还产生后验参数估计和返回水平面，包括凯斯门特机场和都柏林机场。2011-2018 年期间的观测数据包含在该站点分析中，以确定是否有证据表明观测到的极端情况发生了变化。在此期间，观察到极端异常的频率增加，但严重性没有增加。我们发现 2011-2018 年在 Casement Aerodrome 和 Phoenix Park 天气站观测到的极端异常频率分别超过模型可信区间的上限 20% 和 7%。