2) Probability density functions (PDFs) of 2 m temperature values
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.
Fig. 4 shows the PDFs of the hourly 2 m temperature (Fig. 4 (a–c)), daily maximum 2 m temperature (Tmax ) (Fig. 4 (d–f)), and daily minimum 2 m temperature (Tmin ) (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.