There is increasing evidence that global warming manifests itself in more frequent warm days and that heat waves will become more frequent. Presently, a formal definition of a heat wave is not agreed upon in the literature. To avoid this debate, we consider extreme heat events, which, at a given location, are well-defined as a run of consecutive days above an associated local threshold. Characteristics of extreme heat events (EHEs) are of primary interest, such as incidence and duration, as well as the magnitude of the average exceedance and maximum exceedance above the threshold during the EHE. Using approximately 60-year time series of daily maximum temperature data collected at 18 locations in a given region, we propose a spatio-temporal model to study the characteristics of EHEs over time. The model enables prediction of the behaviour of EHE characteristics at unobserved locations within the region. Specifically, our approach employs a two-state space–time model for EHEs with local thresholds where one state defines above threshold daily maximum temperatures and the other below threshold temperatures. We show that our model is able to recover the EHE characteristics of interest and outperforms a corresponding autoregressive model that ignores thresholds based on out-of-sample prediction.

中文翻译：

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极端高温事件特征的长期空间建模

越来越多的证据表明，全球变暖在更频繁的温暖日子里表现出来，热浪将变得更加频繁。目前，文献中并未就热浪的正式定义达成一致。为了避免这种争论，我们考虑了极端高温事件，在给定位置，这些事件被明确定义为连续几天高于相关的局部阈值。极端高温事件 (EHE) 的特征是主要关注点，例如发生率和持续时间，以及 EHE 期间平均超出阈值和最大超出阈值的幅度。使用在给定区域的 18 个地点收集的大约 60 年的每日最高温度数据的时间序列，我们提出了一个时空模型来研究 EHE 随时间的特征。该模型能够预测该区域内未观察到的位置的 EHE 特征的行为。具体来说，我们的方法对具有局部阈值的 EHE 使用双态时空模型，其中一个状态定义高于阈值的每日最高温度，另一个定义低于阈值温度。我们表明，我们的模型能够恢复感兴趣的 EHE 特征，并且优于忽略基于样本外预测的阈值的相应自回归模型。