Record-breaking temperature events are now very frequently in the news, viewed as evidence of climate change. With this as motivation, we undertake the first substantial spatial modeling investigation of temperature record-breaking across years for any given day within the year. We work with a dataset consisting of over sixty years (1960-2021) of daily maximum temperatures across peninsular Spain. Formal statistical analysis of record-breaking events is an area that has received attention primarily within the probability community, dominated by results for the stationary record-breaking setting with some additional work addressing trends. Such effort is inadequate for analyzing actual record-breaking data. Effective analysis requires rich modeling of the indicator events which define record-breaking sequences. Resulting from novel and detailed exploratory data analysis, we propose hierarchical conditional models for the indicator events. After suitable model selection, we discover explicit trend behavior, necessary autoregression, significance of distance to the coast, useful interactions, helpful spatial random effects, and very strong daily random effects. Illustratively, the model estimates that global warming trends have increased the number of records expected in the past decade almost two-fold, 1.93 (1.89,1.98), but also estimates highly differentiated climate warming rates in space and by season.

翻译：破纪录高温事件如今频繁见诸新闻，被视为气候变化的证据。以此为动机，我们首次对全年任意日期温度破纪录现象开展了系统性的空间建模研究。本研究使用的数据集涵盖西班牙半岛六十余年（1960-2021年）的每日最高气温。破纪录事件的正式统计分析此前主要受到概率学界的关注，该领域以平稳破纪录场景下的研究成果为主，仅有少量涉及趋势分析的工作。此类方法不足以分析真实的破纪录数据。有效分析需要对定义破纪录序列的指标事件进行丰富建模。通过新颖细致的探索性数据分析，我们提出了指标事件的分层条件模型。经过合适的模型选择，我们发现了明确的趋势行为、必要的自回归效应、海岸距离的显著性、有价值的交互作用、有益的空间随机效应以及极强的日随机效应。模型估算表明，全球变暖趋势使过去十年预期破纪录次数增加近一倍（1.93, 1.89-1.98），同时还揭示了空间和季节维度上高度分化的气候增温速率。