The impacts of individual heat wave characteristics can be amplified when considered concurrently (e.g. However, current univariate indicators often underestimate the impacts of heat waves because they fail to characterize the extreme event in a comprehensive manner 23, 34, 35. Current metrics evaluate individual heat wave characteristics, such as the hottest day of each year or longest duration of consecutive hot days 7, 17, 22, 29, 31, 33. For a comprehensive review of traditional heatwave definitions, and a toolbox to identify heatwaves and their statistics at a global scale refer to Raei, 2018 32. The threshold is often based on a percentile of each month’s daily temperatures or a fixed value 30, 31, 32. Although there is no universal definition, heat waves are typically described as a consecutive period of hot days with temperatures above a given threshold 7, 29. Most studies investigate different features of heat waves independently, and ignore their relationships 25, 26, 27, 28. Rising global temperatures are expected to increase the intensity, duration, and frequency of heat waves around the world 16, 17, 18, 19, 20, 21, 22, 23, 24. These cancellations produced a domino effect on the entire air transportation system, which demonstrate how impacts of regional heat waves can expand to a national or even global level. Phoenix Sky Harbor Airport was forced to cancel nearly 50 flights due to extreme temperatures in the summer of 2017, when temperatures soared as high as 120 ☏. Extreme temperatures and heat wave events have also caused problems in the transportation sector. France, Europe’s main electricity exporter, was forced to cut power exports by more than half during the heat wave, because power plants were operating at significantly reduced capacity 14, 15. The 2003 European heat wave also caused electricity demand to soar and energy efficiency to plummet 13. For example, the 2003 European heat wave and 2010 Russian heat wave killed over 70,000 and 56,000 people, respectively 8, 9, 10, 11, 12. Heat waves are also considered to be one of the deadliest natural hazards, and cause high mortality rates in both developed and developing countries 7. In addition, heat waves have been connected to the increased risk of forest fires 6. Heat waves have significant negative implications on human health, urban air quality, ecological and environmental conditions, as well as agricultural and energy sectors 1, 2, 3, 4, 5. For example, in Los Angeles, CA, HIDF analysis shows that we can attribute the 21% increase in the likelihood of a four-day heat wave (temperature > 31 ☌) to anthropogenic emissions. We then employ HIDF curves to attribute changes in heat waves to anthropogenic warming by comparing GCM simulations with and without anthropogenic emissions. Here we show how HIDF curves can be used in various locations to quantitatively describe the likelihood of heat waves with different intensities and durations. We propose a multivariate approach to construct heat wave intensity, duration, frequency (HIDF) curves, which enables the concurrent analysis of all heat wave properties. While most studies investigate one feature at a time, heat wave characteristics are often interdependent and ignoring the relationships between them can lead to substantial biases in frequency (hazard) analyses. Atmospheric warming is projected to intensify heat wave events, as quantified by multiple descriptors, including intensity, duration, and frequency.

Wave intensity