<div>2) Probability density functions (PDFs) of 2 m temperature values</div><div>PDFs were calculated to investigate the distribution of the land hourly
temperatures over different decades in different scenarios. This section
focuses on the hourly 2 m temperatures over land in each scenario for
current and future periods. The associated PDFs are nonparametric curves
constructed through kernel density estimation and Gaussian smoothening.
The vertical lines in the plots denote the statistical value of the mean
of each PDF. Three statistical metrics characterizing the PDF are
calculated, including the mean, variance, and skewness (Donat and
Alexander 2012). Skewness measures the extent to which the distribution
of temperatures is skewed, with positive values indicating a longer tail
on the right side of the curve. The sign of the skewness (positive or
negative) only indicates the direction of the skewness, not its
magnitude. The magnitude of different distributions is determined by the
absolute value of the skewness. Variance measures the spread of the
distribution from the mean, with higher values indicating greater
dispersion. In meteorology, positive skewness means more extreme high
than low temperatures.</div><div>Fig. 4 shows the PDFs of the hourly 2 m temperature (Fig. 4 (a–c)),
daily maximum 2 m temperature (<i>T<sub>max</sub></i> ) (Fig. 4
(d–f)), and daily minimum 2 m temperature (<i>T<sub>min</sub></i> )
(Fig. 4 (g–i)) on land in each scenario. Under SSP2-4.5, the hourly 2 m
temperature distribution shifts to the hotter side of the curve with
time, with mean values of 28.97 °C, 29.76 °C, and 30.6 °C for the 2010s,
2040s, and 2090s, respectively. Skewness increases over time, with
values of 0.18, 0.37, and 0.35 for the same decades, indicating longer
tails in high temperatures and more extreme hot temperatures in the
future. The increased mean and variance in daily maximum and minimum
temperature distributions have implications for extreme heat events, not
only in the daytime but also at nighttime. Under SSP5-8.5, the PDF
changes with time are similar to those under SSP2-4.5 but more profound.
The distribution is more skewed toward the hotter side of the curve,
with larger mean values, greater variance, indicating a higher
likelihood of extreme hot temperatures in the future decades. In
contrast, the sustainable pathway of SSP1-2.6 shows a decrease in mean
values of hourly 2 m temperature, daily maximum, and minimum temperature
in the 2090s compared to the 2040s. The skewness of hourly 2 m
temperature in the 2090s is smaller than that in the 2040s, with values
of 0.28 and 0.37, respectively. This suggests a shorter tail in the
distribution of high temperatures in the 2090s. The magnitude of
negative skewness of daily maximum and minimum temperatures in the 2090s
is larger than that in the 2040s, implying a longer tail on the colder
side of the curve and a reduced likelihood of extreme high temperatures
in the 2090s.</div>