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.