Characterization of heatwave duration is becoming increasingly important in environmental research as they pose a significant threat to many human lives worldwide. Although several quantification of the extremities of a heatwave have been proposed in literature, they are mostly improvised and there does not exist a universally accepted definition of heatwave. In this article, we devise a probabilistic inferential framework to characterize heatwave and come up with a definition that can capture the essence of all existing ad hoc definitions. We derive an exact distribution on the frequency of such durations for a stationary Markov process and also an approximate distribution of durations for a stationary non‐Markov time series. For a given site, using a daily time series (of ambient temperature or heat‐index), we define a heatwave as the number of sustained days above a given threshold using the probability distribution of the durations. We illustrate the proposed methodology using daily time series of ambient temperature for a fixed site (of Atlanta) and also using the USCRN consisting of 126 sites across the United States. Furthermore, we also derive an empirical quadratic curve based relationship between expected durations and extreme thresholds. The proofs of the theorems, datasets, algorithms, and computer codes are provided in the supplementary materials.

中文翻译：

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热浪持续时间：使用概率推理进行表征

热浪持续时间的表征在环境研究中变得越来越重要，因为它们对全世界许多人的生命构成了重大威胁。尽管文献中已经提出了几种对热浪末端的量化，但它们大多是即兴的，并且不存在普遍接受的热浪定义。在本文中，我们设计了一个概率推理框架来表征热浪，并提出一个可以捕捉所有现有临时定义本质的定义。我们推导出平稳马尔可夫过程的这种持续时间频率的精确分布，以及平稳非马尔可夫时间序列的持续时间近似分布。对于给定的站点，使用每日时间序列（环境温度或热指数），我们使用持续时间的概率分布将热浪定义为高于给定阈值的持续天数。我们使用固定站点（亚特兰大）的每日环境温度时间序列以及由美国 126 个站点组成的 USCRN 来说明所提出的方法。此外，我们还推导出了基于预期持续时间和极端阈值之间的经验二次曲线关系。补充材料中提供了定理、数据集、算法和计算机代码的证明。我们还推导出了基于预期持续时间和极端阈值之间的经验二次曲线关系。补充材料中提供了定理、数据集、算法和计算机代码的证明。我们还推导出了基于预期持续时间和极端阈值之间的经验二次曲线关系。补充材料中提供了定理、数据集、算法和计算机代码的证明。