e. Return period definition
A return period is often considered in calculating the period of recurrence of extreme events such as earthquakes and floods. We applied this measure to extreme heat events. Unlike the definitions of heatwaves, we evaluated the highest hourly temperature in each grid cell from 2011 to 2020 as a 10-year extreme heat event. The highest temperature in each grid in the 2010s was used as a benchmark to calculate the return period of a 10-year extreme heat event in each scenario in future decades. The return period was calculated using Weibull’s formula (Horton et al. 2016).
\begin{equation} \begin{matrix}\mathrm{return\ period=}\frac{\mathrm{n+1}}{\mathrm{m}}\\ \end{matrix}\nonumber \\ \end{equation}
where n is the sample size, and m is the rank of the values in decreasing order. In this study, m is the descending order rank of the highest temperatures in the 2010s, 2040s and 2090s.