3.1 Apparent temperature characteristics
A brief ERA5 assessment of Tmax, Tmin, and RH is generally required for reproducing humid heat and wet cold events. On the daily scale, the ERA5 can accurately reflect Tmax characteristics (Fig. 3a), with a high r (0.997) and low Bias (− 0.61℃), RB (− 2.6%, slightly underestimated), RMSE (0.952℃), and DISO (0.049) values. The simulated effect of the ERA5 data for the daily time period (UTC + 8, 20:00 − 20:00) corresponding to the observed value was slightly better than that of the original daily ERA5 (UTC 0) (Zhang et al. 2021b). The ability of ERA5 to simulate Tmin (Fig. 3b) was similar to that of the Tmax, but it was slightly overestimated. The ERA5's ability to simulate RH (DISO = 0.115) was slightly inferior to temperature, with r = 0.925, RB = − 4.2% (slightly underestimated), Bias = − 3.3%, and RMSE = 6.1% (Fig. 3c). In general, ERA5 performed well in simulating Tmax, Tmin, and RH in the GRB.
We extracted the average daily apparent temperatures based on Tmax and Tmin from 1961 to 2018 in the GRB to draw probability density curves via the kernel probability density function (PDF). For the probability distributions of the apparent temperatures based on Tmax, we focused on the right curves. As shown in Fig. 4a, the kurtosis of apparent temperatures were smaller than the Tmax values. Apparent temperature curves extended to the right side more obviously, especially those of the ATc and HI. This implied that the RH amplifies the severity of heat events. The PDFs of ATc and HI at high temperatures approximately coincided in the GRB. The distributions of apparent temperatures reproduced by ERA5 (Fig. 4b) were consistent with the observed values, except that the probability values of ATc and HI at extreme high temperatures were slightly smaller than the observed values. For the probability distributions of the apparent temperatures based on Tmin, we emphasized the left curves. As shown in Fig. 4c, the kurtosis of apparent temperatures were smaller than the Tmin values. The curves of the apparent temperatures at low temperatures, except for those of the WBGT, were distributed more to the left than the Tmin values. The difference between apparent temperature and Tmin on the left side at a low temperature was not as large as that between apparent temperature and Tmax on the right side at a high temperature. This indicated that the RH amplifies the severity of a high temperature more than a low temperature in the GRB. The ERA5 simulated apparent temperature based on Tmin was basically the same as the observed value (Fig. 4d), except that the inclination of the ATc to the left was slightly different at a low temperature.
As shown in Fig. 5a, under the condition of Tmax > 90th percentile threshold, Tmax and RH showed an obvious negative correlation, indicating that warm-drying was robust in the GRB under high temperature conditions. Apparent temperatures based on Tmax were higher than Tmax values. ATc and HI increased more than ATw and WBGT as RH values increased. The characteristics of apparent temperatures reflected by ERA5 (Fig. 5b) were similar to those of observed temperatures, and the ATc and HI reproduced by ERA5 were smaller than those of the observations. The relationships between apparent temperatures and their RH values under conditions of Tmax > 95th percentiles (Fig. 5c, d) were similar to those under conditions of Tmax> 90th percentiles. The increments (slopes) of apparent temperatures with RH values were generally larger for Tmax > 95th than Tmax > 90th percentile thresholds. For example, the slope value of ATc was 0.462 for observations and 0.378 for ERA5 at the Tmax > 95th percentile threshold, which were higher than those at the Tmax > 90th percentile threshold (0.279 for observations and 0.294 for ERA5).
Under conditions of Tmin < 10th (Fig. 6a, b) and < 5th (Fig. 6c, d) percentile thresholds, the Tmin did not show significant upward or downward trends as the RH increased. HI, ATw, and WBGT increased slightly along with the RH, whereas ATc showed a significant decreasing trend. The decreasing rates of ATc as the RH values increased at the Tmin < 5th percentile threshold (− 0.134 for observations and − 0.121 for ERA5) were slightly greater than those at the Tmin < 10th percentile threshold (− 0.122 for observations and − 0.108 for ERA5). The characteristics of apparent temperatures based on Tmin with increasing RH values in ERA5 were consistent with the observed values.
ATc and HI were very close at high temperatures, and their specific values and slopes as RH increased were obviously higher than those of ATw and WBGT. However, only ATc showed significant downward trends with increasing RH values at low temperatures. Therefore, ATc better reflects humid heat and cold events.
3.2 Temporal and spatial characteristics of humid heat and cold waves
We extracted heat waves using the 90th percentile threshold of the ATc (Tmax) data series, and calculated AHWMI and its corresponding HWMI values. As shown in Fig. 7a, the annual variation of AHWMI was consistent with that of the HWMI, but the specific value was approximately twice that of HWMI. Both AHWMI and HWMI showed overall upward trends, with rates of 2.21/decade and 0.91/decade, respectively. The increasing rates of AHWMI and HWMI during 1997 − 2018 were approximately three times those of the decreasing rates during 1961 − 1997. The AHWMI and HWMI variations in ERA5 were similar to those of the observations (Fig. 7b). The overall increasing rates for AHWMI and HWMI were greater than those of the observations during 1961 − 2018. The increasing rates of AHWMI and HWMI during 1997 − 2018 were much greater than the decreasing rates before the turning point in 1997. On the annual scale, the AHWMI in ERA5 reasonably reflected the features of the observed dataset, with a high r (0.77) value and a low DISO (0.348) value (Fig. 7c). As shown in Fig. 7d, the ability of ERA5 in simulating the HWMI was similar to that of the AHWMI.
The AHWMI values in the northern and southernmost parts of the GRB were higher than for other areas, indicating that humid heat waves in these regions were more severe (Fig. 8a). The spatial patterns of the HWMI and AHWMI were roughly similar (Fig. 8b), and both presented more severe heat waves in the northern parts of the basin (Fig. 8b). The AHWMI (Fig. 8c) and HWMI (Fig. 8d) values for ERA5 were smaller than the observed values in the northern parts of the basin. The AHWMI values were approximately twice as high as the corresponding HWMI values for both the observations and ERA5, indicating that a high RH can significantly amplify the severity of heat waves in the GRB. The values of AHWMI and corresponding HWMI of ERA5 were smaller than those of the observed dataset, mainly owing to the slight underestimations of Tmax and RH in the GRB by ERA5.
The ACWMI and the corresponding CWMI consistently showed significant downward trends, with rates of − 5.97/decade and − 5.58/decade, respectively (Fig. 9a). This indicated that the cold waves showed significant decreasing trends in the GRB. The ACWMI values were slightly larger than the CWMI values, indicating that RH slightly amplified the severity of the cold waves in the GRB. The changes in ACWMI and CWMI values of ERA5 were consistent with the observations, and the decreasing rates were slightly smaller than the observations (Fig. 9b). On the annual scale, the ACWMI of ERA5 reasonably reflected the features of the observations, with a high r (0.84) value and a low DISO (0.266) value (Fig. 9c). As shown in Fig. 9d, the ability of ERA5 in simulating the CWMI was similar to that of the ACWMI. Overall, the ability of ERA5 to simulate the annual variation in the ACWMI was slightly better than that of the AHWMI in the GRB.
The distribution of the annual mean ACWMI showed a north–south gradient (Fig. 10a) decreasing from > 46 in the southern parts of the basin to < 42 in the northern parts of the basin. The spatial distribution of the annual mean CWMI was similar to that of the ACWMI, presenting an overall north–south transition (Fig. 10b). The large magnitudes of the humid cold waves in the southern parts of the basin were attributed to the high RH. The ACWMI value was slightly greater than the corresponding CWMI value, indicating that the RH slightly magnified the severity of the cold wave event because the specific Tmin of the GRB was not too low (the average Tmin in January was 3.5℃). The spatial patterns of the ACWMI and CWMI of ERA5 were similar to those of the observations. In general, ERA5 was more effective in simulating the spatial characteristics of the ACWMI than the AHWMI in the GRB.
We separately explored the spatiotemporal characteristics of the annual number (frequency) of ATc (Tmax) heat waves (AHWN), annual sum of participating heat wave days (AHWP), annual number of ATc (Tmin) cold waves (ACWN), and annual sum of participating cold wave days (ACWP). As shown in Fig. 11a, the AHWN in ERA5 showed a more pronounced upward trend than in the observations (0.26 events/decade in ERA5 and 0.116 events/decade in observations). Except for 1965 and 1966, ERA5 reasonably reflected the annual changes in the AHWN (r = 0.77 and DISO = 0.297) in the GRB. The AHWP changes were similar to those of the AHWN (Fig. 11b), showing increasing trends in the GRB. The ACWN showed clear downward trends in both observations and ERA5 (Fig. 11c), and the decreasing rates exceeded those of the AHWN. The ability of ERA5 (r = 0.85 and DISO = 0.228) to simulate the ACWN was slightly stronger than that of the AHWN. The annual variations in the ACWP were consistent with those of ACWN, showing significant downward trends (Fig. 11d). Overall, the upward trends of the AHWN and AHWP in ERA5 were more obvious than those in the observations, whereas the downward trends of the ACWN and ACWP in ERA5 were weaker than those of the observations. This may be because ERA5 slightly underestimated Tmax and overestimated Tmin, which in turn led to the strengthening of the upward trends of heat waves and the weakening of the downward trends of cold waves.
The spatial characteristics of the AHWN in the observations (Fig. 12a) and in the ERA5 (Fig. 12b) were similar (approximately 4.6 to 5 times/year), and both showed that the AHWN in the southern part of the basin was slightly greater than that in the northern part of the basin. As shown in Fig. 12c, the AHWP presented the opposite spatial pattern of the AHWN, and the AHWP in the northern part of the basin was greater than that in the southern part of the basin. The spatial pattern of the AHWP from ERA5 (Fig. 12d) was similar to the observed value, but the specific AHWP value was slightly smaller. Although the AHWN in the southern part of the GRB was slightly greater, the duration (AHWP) in the northern part of the basin was relatively long, resulting in a high AHWMI in the northern part of the basin. The spatial pattern of the ACWN (Fig. 12e) from the observations was similar to that from ERA5 (Fig. 12f), but the specific ACWN value was slightly larger than that of ERA5. In general, the spatial characteristics of the ACWN were similar to those of the AHWN (relatively high values in the south), but the specific ACWN values were smaller than those of the AHWN, indicating that the number of cold waves in the GRB was less than that of humid heat waves. Unlike the AHWP patterns, the ACWP showed relatively high values in the southern parts of the basin in both the observations (Fig. 12g) and ERA5 (Fig. 12h) datasets. The relatively high ACWN and ACWP values in the southern parts of the basin resulted in relatively high ACWMI values, indicating the relatively high severity of cold waves in the southern parts of the basin.
3.3 The characteristics of humid heat and cold waves at different grades
We extracted the AHWMI and ACWMI values of all the heat and cold waves for all the stations/ grids in the GRB from 1961 to 2018 to draw cumulative probability density curves using the empirical cumulative density function (CDF). As shown in Fig. 13, the CDF curves of the AHWMI in the observations and ERA5 were relatively consistent, and the CDF curves of the ACWMI in the observations and ERA5 basically coincided. We divided the heat and cold waves into their respective four magnitude grades. The grades of heat waves (Fig. 13a) include mild (0 < AHWMI ≤ 12), moderate (12 < AHWMI ≤ 17.5), severe (17.5 < AHWMI ≤ 25.5), and extreme (AHWMI > 25.5). The grades of cold waves (Fig. 13b) also include mild (0 < ACWMI ≤ 7), moderate (7 < ACWMI ≤ 11.2), severe (11.2 < ACWMI ≤ 17.2), and extreme (ACWMI > 17.2). The cumulative probabilities corresponding to the AHWMI (ACWMI) values of 12 (7), 17.5 (11.2), and 25 (17.2) were in turn 0.5, 0.75, and 0.9, respectively, representing the conditions of half, most, and almost all of the heat (cold) waves, respectively. The occurrences of mild, moderate, severe, and extreme heat (cold) waves corresponded to probabilities of 50–100%, 25–50%, 10–25%, and < 10%, respectively.
ERA5 can reasonably reflect the annual variations of heat wave frequencies at different grades (Fig. 14). Mild events showed slight upward trends in both the observations and ERA5 from 1961 to 2018 (Fig. 14a). As shown in Fig. 14b, the moderate events showed a significant upward trend in the ERA5, and the increasing rate (0.091 events/decade) in ERA5 was about two times that of the observations. The ability of ERA5 to simulate the frequencies of moderate events (r = 0.73, RB = − 1.59%, and DISO = 0.412) was higher than in the other three grades. The increasing rate of severe events in ERA5 was 0.096 events/decade, which was obviously greater than in the observations (Fig. 14c). Extreme heat wave events showed a slight upward trend in observations but a slight downward trend in ERA5 (Fig. 14d). In general, except for the extreme grade, ERA5 showed larger upward trends in the heat wave frequencies than the observations.
Unlike annual changes in heat wave frequencies at the four grades, the cold waves of all grades showed decreasing trends both in the observations and ERA5 from 1961 to 2018 (Fig. 15). As shown in Fig. 15a, mild events showed a significant downward trend in observations (–0.175 events/decade) and a slight downward trend in ERA5. Moderate events in both the observations and ERA5 showed significant downward trends, with rates of − 0.093 events/decade and − 0.09 events/decade, respectively (Fig. 15b). Severe events declined at a rate of − 0.105 events/decade in the observed dataset and − 0.071 events/decade in the ERA5 dataset (Fig. 15c). As shown in Fig. 15d, extreme events in the observations and ERA5 declined significantly at very similar rates (–0.113 events/decade in observations and − 0.11 events/decade in ERA5). In general, the ability of ERA5 to simulate annual changes in cold waves at all the grades was greater than its ability to simulate heat waves. As the grade increased, the downward trend of the cold waves became more obvious. The decreasing trends of cold wave frequencies at all the grades in ERA5 were weaker than those in the observations.
Under various grades of heat wave conditions, Tmax and RH showed obvious negative correlations (Fig. 16a), indicating that higher temperatures tended to produce lower RH values. The higher the grade of the heat waves, the faster the Tmax increased as the RH declined. The relationships between Tmax and RH at various grades of heat waves in the ERA5 was similar to those in the observations (Fig. 16b). It was evident that the correlation between warming and drying was robust in the GRB. Thus, there is a positive feedback mechanism between hot and dry conditions. After replacing the Tmax with the ATc under heat wave conditions, the relationship between the ATc and RH differed from that of the Tmax in the GRB, and ATc increased slightly along with the RH under mild and moderate heat wave conditions in the observations (Fig. 16c). There was a more pronounced upward ATc trend as the RH increased in ERA5 (Fig. 16d). This suggested that a relatively high RH increased the ATc, which in turn amplified the severity of the heat waves.
Under cold wave conditions, Tmin increased along with RH (Fig. 17a). The greater the cold waves grade, the slower the Tmin increase along with the RH. Similarly, a positive correlation between Tmin and RH also existed in ERA5 (Fig. 17b), and the increase of Tmin along with RH was smaller in ERA5 than in the observations. When using ATc (Tmin) instead of Tmin, the ATc increased along with the RH under mild cold wave conditions, but the ATc decreased as the RH increased under extreme cold wave conditions (Fig. 17c). Under the extreme cold wave conditions, the ATc of ERA5 showed a more obvious downward trend as the RH increased (Fig. 17d). This proved that under extreme cold wave conditions, a relatively high RH reduced the ATc, which in turn amplified the severity of the cold waves.
We explored the characteristics of Tmax, ATc (Tmax), RH, and heat wave days under different grades (AHWMI) of heat waves (Fig. 18). As the grade increased, the corresponding average Tmax increased (Fig. 18a). The specific values of Tmax from ERA5 were smaller than those from the observations, and its box range was also larger than those of the observations. As shown in Fig. 18b, average values of ATc also increased as the grade increased. The ATc values during each grade of heat wave were obviously larger than the Tmax values, which proved again that the RH amplified the ATc. The ATc from ERA5 was significantly smaller than that from the observations, which was caused by the smaller RH from ERA5 compared with the observations (Fig. 18c). The RH in both observations and ERA5 tended to decrease as heat wave grade increased. The duration of mild heat waves was approximately 3.5 days, whereas the extreme heat wave days increased to about 13.5 days (Fig. 18d).
As shown in Fig. 19a, with the increase in the cold wave grade, the corresponding average Tmin decreased. ERA5 overestimated the average values of Tmin under cold wave conditions, and its box range was also slightly smaller than that of the observations. With the increase in the cold wave grade, the average values of the ATc also decreased (Fig. 19b). The ATc values in each grade of cold waves were slightly lower than the Tmin values, which indicated that RH reduced the ATc. The ATc from ERA5 was obviously greater than from the observations, which was caused by the higher Tmin and the smaller RH values in the ERA5 dataset compared with the observed dataset. The RH in the observations and ERA5 did not present significant decreasing or increasing trends as the cold wave grade increased (Fig. 19c). As the cold wave grade increased, the number of cold wave days increased rapidly (Fig. 19d), especially from the severe (around 8.5 days) to the extreme (around 15 days) grade. The average duration of an extreme cold wave was approximately 1.5 days longer in the ERA5 dataset than in the observed dataset.
3.4 Typical cases of 2014 heat waves and 1969 cold waves
We calculated the annual differences between the AHWMI and HWMI from 1961 to 2018 in the observed and ERA5 datasets, respectively, and selected the year with the largest difference as a typical year for humid heat waves. The year with the largest difference between AHWMI and HWMI in both the observations and ERA5 was 2014. We extracted the start and end dates of heat waves based on the maximum AHWMI values during the 2014 period. Most of the stations (Fig. 20a) and grids (Fig. 20b) occurred after July 6, 2014, and there were two concentrated occurrence dates (around July 16 and 27). Most stations (Fig. 20c) and grids (Fig. 20d) had end dates before August 12, 2014, and there were also two concentrated occurrence dates (roughly July 23 and August 12). Therefore, we selected July 6–August 12 as the temporal span of the typical humid heat wave in terms of the whole GRB. For cold waves, the year with the largest difference between the ACWMI and CWMI in observations was 1969, and it had the second largest difference in ERA5. We selected 1969 as a typical humid cold year, and extracted the start and end dates based on the maximum ACWMI values during 1969. The majority of stations (Fig. 20e) and grids (Fig. 20f) occurred after February 14, 1969. Most of the stations (Fig. 20g) and grids (Fig. 20h) had end dates before March 3, 1969. Therefore, we adopted February 14–March 3, 1969 as a typical humid cold wave in the GRB.
The mean Tmax of the 2014 humid heat wave was 34.89°C in the observations (Fig. 21a) and 33.99°C in the ERA5 (Fig. 21b), corresponding to return periods of 3.9 and 3.6 years using GEV-fit. The mean RH of the 2014 humid heat wave was 78.48% in the observations (Fig. 21c) and 78.11% in the ERA5 (Fig. 21d), corresponding to return periods of 3.9 and 4.4 years. If only Tmax was considered for the heat wave magnitude, then the return periods were 4.4 years in the observations (Fig. 21e) and 3.9 years in the ERA5 (Fig. 21f). However, if the effects of Tmax and RH on heat wave magnitude (HWMI) were considered together, then the return periods of heat wave magnitude (AHWMI) increased substantially, reaching 47.6 years in observations (Fig. 21g) and 769 years in ERA5 (Fig. 21h). Higher RH values significantly magnified the severity of heat waves. This also indicated that the simultaneous occurrence of two non-extreme events may lead to compound extremes that have significant impacts. ERA5 reasonably reflected the specific values of Tmax, RH, HWMI, and their corresponding return periods for the 2014 humid heat wave. Although the AHWMI simulated by ERA5 was 6% lower than the observations during the 2014 humid heat wave period, it over-amplified the severity of the heatwave (resulting in an apparently excessively long return period using the ERA5 dataset).
The mean Tmin of the 1969 humid cold wave was 2.75°C for the observations (Fig. 22a) and 3.04°C in the ERA5 (Fig. 22b), corresponding to return periods of 30.1 and 35.2 years using GEV-fit. The mean RH of the 1969 humid cold wave was 89.52% in the observations (Fig. 22c) and 88.46% in the ERA5 (Fig. 22d), corresponding to return periods of 38 and 25.8 years. If only Tmin was considered for the cold wave magnitude (CWMI), then the return periods were 29.8 years in the observations (Fig. 22e) and 34.4 years in the ERA5 (Fig. 22f), which were more consistent with the return periods of Tmin. However, if combination of Tmin and RH on cold wave severity were considered, then the return periods of the cold wave magnitude (ACWMI) increased to 53.2 years in observations (Fig. 22g) and 63.7 years in ERA5 (Fig. 22h). The ability of RH to amplify the severity of cold waves was far less than that of heat waves in the GRB. This may be because the specific average Tmin was not particularly low (generally around 0°C) during the cold waves in the GRB. ERA5 was more capable of simulating cold waves than heat waves, especially when the magnitude incorporated the RH.