Heatwave duration: Characterizations using probabilistic inference

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.