The severity of heat and cold waves amplified by high relative humidity in humid subtropical basins: a case study in the Gan River Basin, China

High relative humidity (RH) and temperature extremes can occur simultaneously and persist for periods of time, resulting in serious harm to human health, especially in humid regions. Here, in the case of the Gan River Basin, we used air temperature and RH from the observed and ERA5 reanalysis datasets to construct the apparent temperature and investigate the characteristics of heat and cold waves. Heat waves showed the increasing trends from 1961 to 2018 (particularly from 1997 to 2018), whereas during the same period, cold waves showed the significant decreasing trends. In general, ERA5 reasonably reflected the spatiotemporal characteristics of heat and cold waves, and the ability to simulate cold waves was slightly greater than that of heat waves. The amplifying effect of high RH on heat waves was significantly greater than on cold waves. The increasing rates of heat waves in ERA5 at the mild, moderate, and severe grades were slightly greater than the observations. Cold waves at various grades showed significant downward trends, and the decreasing rates of cold waves in the observations were slightly greater than those in ERA5. Using an analysis of the return period (occurrence probability), traditional univariate risk assessment methods based on maximum or minimum temperature may substantially underestimate the risk of extreme events, such as the 2014 heat wave and the 1969 cold wave, because the effects of RH were ignored.


Introduction
Extreme high or low temperatures can cause serious harm to human health (Qian et al. 2018;Gaitán et al. 2019;Smid et al. 2019;Deen et al. 2021;Ha et al. 2022). Apparent temperature usually describes the human-perceived temperature ("feels-like" equivalent temperature), which is affected not only by air temperature, but also by relative humidity (RH), wind speed, and solar radiation (Fischerand Knutti 2013;Wang et al. 2019c;Di Napoli et al. 2021). Under very humid hot environmental conditions, it is difficult for the human body to achieve a cooling effect through perspiration, resulting in a high apparent temperature, which in turn causes human discomfort and even increases mortality rates (Mora et al. 2017;Wang et al. 2019a). The deadly heat threshold decreases as RH increases, which is consistent with other heat-stress assessments (Buzan et al. 2015;Mora et al. 2017). The apparent temperature can decrease along with RH under high air temperature conditions. Therefore, humid heat events are more likely to result in human thermal stress than dry heat events at the same high air temperature conditions (Wouters et al. 2022). In the monsoon regions of southeastern China, humid heat events are more likely to occur than dry heat events (Ding and Ke 2015;Fang et al. 2020). For example, after a severe flood event (extreme precipitation caused by the long Meiyu Period) in the Yangtze River Basin in the summer of 2020 (Qiao et al. 2021), a subtropical high affected the region and the temperature increased. Sufficient moisture provides strong evaporation, which maintains a high RH, resulting in humid heat waves. Humid heat events are closely correlated with the novel compound extremes, namely sequential flood-hot extremes (Wang et al. 2019b;Liao et al. 2021). In winter, cold waves pass through the humid regions of southern China, resulting in severe cooling and even precipitation (Zhang et al. 2011;Qian et al. 2014;Zheng et al. 2022). The humid cold environmental conditions are no less harmful to human health than humid hot weather. Currently, there are far fewer studies on humid cold events than heat events.
Commonly used apparent temperature indices that combine RH and air temperature include the following: heat index (Steadman 1979;Russo et al. 2017), apparent temperature for shaded conditions (Steadman 1984;Matthews 2018), and the wet-bulb globe temperature (Willettand Sherwood 2012;Fischer and Knutti 2013;Heo et al. 2019). The above three apparent temperature indices can reasonably reflect the amplifying thermal effects of RH under hot conditions, but they do not reflect the amplifying cold effects of RH under low-temperature conditions. Previous studies on heat and cold waves have been mostly based on a single air temperature variable (Liu et al. 2015;Johnson et al. 2018;Gaitán et al. 2019;Xie et al. 2020), which may underestimate the severity of heat and cold waves in humid regions owing to the high RH. Therefore, it is necessary to apply an apparent temperature index, which integrates air temperature and RH, and can reasonably reflect the severity of humid heat and cold events (RH can aggravate the severity of these events). The identification of heat and cold waves using this apparent temperature index will help increase awareness regarding the public health-related harm caused by these extreme events.
To measure the severity of heat waves, the excess heat factor and occurrence probability methods are generally used (Nairn et al. 2015;Russo et al. 2015;Wang et al. 2020). Similarly, the severity of cold waves can also be calculated using the excess cold factor (e.g., daily minimum temperature below 5th or 10th percentile of the minimum temperature series) and the probability of occurrence (Liu et al. 2015;Qian et al. 2018;Gaitán et al. 2019;Zhang et al. 2021c). Currently, severity (magnitude) indices of humid heat events are relatively limited, but there are two schemes: excess heat factor based on apparent temperatures (Russo et al. 2017) and cumulative values of simultaneous temperature and RH above certain thresholds under heat wave conditions (Ge et al. 2021). At present, there is still a lack of research on humid heat events at different grades (severity levels) that are based on their magnitude. There are far fewer studies on cold wave magnitude indices than those of heat waves, as well as on the spatiotemporal characteristics of humid cold waves at different grades. Exploring the variations in humid heat and cold waves at different grades will increase our understanding of the possible mechanisms responsible for humid heat and cold extremes.
ERA5 is the new fifth-generation reanalysis dataset released by the European Centre for Medium Range Weather Forecasts (ECMWF), which integrated multiple data sources (e.g., model outputs and observations) using the 4D-Var assimilation method (Hersbach et al. 2020). This reanalysis dataset contains a large number of hydrometeorological variables with a high spatiotemporal resolution. The ERA5 dataset has been widely applied in hydrometeorological investigations and evaluations worldwide (Senatore et al. 2020;Chinita et al. 2021;Jiang et al. 2021;Owen et al. 2021;Zhang et al. 2021b), especially in areas with sparse observation stations. Currently, the ERA5 dataset is divided into two parts based on the time span: 1950-1978 (preliminary back extension) and from 1979 onward (final release plus timely updates). At present, the assessment of apparent temperature in ERA5 is limited (Di Napoli et al. 2021), especially for humid heat and cold waves. Assessing the capability of ERA5 to identify humid heat and cold waves will help in the adoption of human health-related scientific measures to mitigate the threats caused by humid heat and cold waves.
In this study, we used the Gan River Basin (GRB) as a case to explore the characteristics of humid heat and cold waves under different grades and quantify the amplifying magnitude of RH on heat and cold waves based on the observed and ERA5 datasets. The primary goals of this study included: (1) evaluating the accuracy of ERA5 data in monitoring humid heat and cold waves; (2) investigating the rationality of different apparent temperatures to identify humid heat and cold events; (3) exploring the characteristics of humid heat and cold waves, especially the changes under different grades; and (4) quantifying the amplifying magnitude of RH on heat and cold waves by assessing typically cases. Determining the role of RH in heat and cold waves will provide a basis for mitigating potential losses and harm to human health as a result of humid heat and cold events in humid regions.

Study area
The GRB is located within the south-central parts of the Poyang Lake (the largest freshwater lake in China) Basin (Fig. 1a), with an area of 80,948 km 2 that is controlled by the Waizhou hydrological station (outlet). The GRB receives approximately 678 × 10 8 m 3 of annual streamflow on average, representing the largest sub-basin both in area (51%) and runoff (50%) of the Poyang Lake Basin (Zhang et al. 2021d). The topography of the GRB is relatively high in the south and low in the north. The GRB belongs to a subtropical humid monsoon climate zone, with annual mean precipitation and temperature values of 1600.1 mm and 18.2 °C, respectively (Zhang et al. 2017). The maximum temperature 1 3 (T max ) and minimum temperature (T min ) in the GRB increase and decrease during the first and second halves of the calendar year, respectively (Fig. 1b). The temperature typically reaches its peak in July (T max of 34 °C and T min of 24.7 °C) and falls to its lowest level in January (T max of 11.2 °C and T min of 3.5 °C). The average RH in each month is stable at 75.9-82.8% (Fig. 1c), typically reaching a maximum value in March (82.8%) and a minimum value in July (75.9%). The averages of annual T max , T min , and RH in the basin were 23.2 °C, 14.7 °C, and 79.4% during 1961-2018.

Data
Daily meteorological observations including T max , T min , and RH during 1961-2018 were provided by the National Meteorological Information Centre of the China Meteorological Administration (http:// data. cma. cn/). These observations were subjected to quality control and homogeneity assessments before release. We removed the meteorological stations having more than 0.15% (i.e., 31 days) missing daily values during 1961-2018 to ensure the integrity and continuity of the data series (e.g., the same station has the same time series of T max , T min , and RH). The missing values (≤ 0.15%) for any station were interpolated with values from its neighboring stations on the same day. In total, 47 meteorological stations ( Fig. 1) were finally selected across the GRB from 1961 to 2018.
In this study, the ERA5 reanalysis dataset (air temperature at 2 m above surface of land and RH at 1000 hPa) spanning 1961-2018 was obtained from the fifth-generation ECMWF atmospheric reanalysis of the global climate (Hersbach et al. 2020), with a spatial resolution of 0.25° and hourly temporal resolution. Because daily datasets of the meteorological observations are 20:00-20:00 UTC + 8 in China (e.g., the daily mean temperature of February 20, 2022, is the average of the timesteps 20:00-20:00 UTC + 8 of the February 19-20, 2022, and the precipitation is the accumulated value of this period), we strictly matched the time period of the ERA5 data to the time period of the meteorological observation data. The average value of 24-h RH values (ERA5) in a given day (20:00 − 20:00 UTC + 8) was regarded as the RH of that day. The maximum and minimum values of 24-h temperature values (ERA5) in a given day were regarded as the T max and T min of that day, respectively. The number of ERA5 grids in the GRB is 121 (Fig. 1), which is much greater than the number of meteorological stations.

Evaluation indices
In this study, five commonly used indices were applied to quantitatively compare the ERA5 data against meteorological observations. These five indices were mean bias (Bias), relative bias (RB), correlation coefficient (r), root-mean-square error (RMSE), and the distance between the indices of simulation and observation (DISO) (Yang et al. 2016;Hu et al. 2019;Zhang et al. 2021b;Zhou et al. 2021). The zero values of Bias, RB, and RMSE indicated that the simulations were equivalent to the observations. DISO is a comprehensive index that combines r, Bias, and RMSE based on the distance between the simulated and observed values in a three-dimension coordinate system. The closer the DISO value is to zero, the closer the simulated value is to the observed value. The formulas for these five indices are as follows: where S i and O i represent the simulations (i.e., ERA5) and observations at each time step i (e.g., daily or annual). n is the number of time steps. S and O represent the average values of simulations and observations during the study period. NB is Bias divided by the O . NRMSE is RMSE divided by the O . A small difference in O can cause a large difference in DISO when O is very close to zero; consequently, DISO is invalid when O equals zero (Zhang et al. 2021b;Zhou et al. 2021), such as standardized sequences with mean zero. (1)

Apparent temperatures
In this study, we applied four kinds of apparent temperatures (combined with RH and air temperature) to explore the characteristics of humid heat and cold waves in the GRB. The first apparent temperature index in China (ATc) is an empirical formula proposed by Zhu et al. (2020) based on air temperature and RH, as follows: where the unit of ATc is °C. T and RH represent the air temperature ( °C) and relative humidity (0-100). Equation (6) should satisfy the condition RH > 0.13 × T 2 − 13.5 × T + 363 and T > 30 °C; otherwise, the formula of the ATc is as follows: The second apparent temperature index is the heat index (HI) from the US National Weather Service (https:// www. wpc. ncep. noaa. gov/ html/ heati ndex_ equat ion. shtml), as follows: where the unit of HI is ℉. Thus, it needed to be converted into °C for comparisons in this study (℉ = 32 + 1.8 × • C ). T and RH represent air temperature (℉) and relative humidity (0-100), respectively. If RH < 13% and air temperature is between 80 and 112℉ (i.e., 26.7 to 44.4 °C), then the following adjustment shown in Eq. (9) is subtracted from Eq. (8).
When HI < 80℉, a simpler formula is applied to calculate HI values: The third apparent temperature in the world (ATw) was proposed by Steadman (1984), as follows: where the unit of ATw is °C. T, e, and V represent air temperature (°C), vapor pressure (hPa), and wind speed (m/s), respectively. This study mainly focused on humid heat and cold events, and it did not consider the effects of wind speed on apparent temperature. Thus, the constant V = 1 m/s was used in this study. The e is generally a function of T and RH (WMO 2008), as follows: where T and RH represent air temperature (°C) and relative humidity (0-100).
The fourth apparent temperature refers to the simplified wet-bulb globe temperature (WBGT) (Willett and Sherwood 2012;Fischer and Knutti 2013), as follows: where the unit of WBGT is °C. T and e denote air temperature (°C) and vapor pressure (hPa). The e is also calculated using Eq. (13).
As shown in Fig. 2, both ATc and HI can reflect a nonlinear increase along with the increase in RH, and they are relatively consistent. Both ATw and WBGT can reflect the increase linearly along with the increase in RH. The increase in the WBGT per humidity unit was greater than that of ATw under high air temperature conditions. Below a certain low temperature, the ATc showed a nonlinear decrease as the RH increased, whereas the other three kinds of apparent temperatures did not decrease as the RH increased. Below a certain low temperature, the HI and ATc were slightly lower than the air temperature regardless of the RH. Under the certain high-temperature conditions, the ATc increased nonlinearly along with the increase in RH, and under the certain low-temperature conditions, the ATc decreased nonlinearly as the RH increased. Therefore, ATc reasonably represented the characteristics of humid heat and cold events.

Definitions of heat and cold waves
A hot day is generally defined as a T max greater than the 90th or 95th percentile during the specific period (Russo et al. 2015;Wang et al. 2017;Zhang et al. 2020), and a cold day is generally represented by a threshold where T min is less than the 10th or 5th percentile during the specific period (Piticar et al. 2018;Gaitán et al. 2019;Zhang et al. 2021c). The percentile threshold was computed from the local daily climatology data during 1961-2018. After considering the climate characteristics of the GRB, we defined a heat wave as an event lasting at least three consecutive hot days (ATc T max > 90th percentile) and a cold wave as an event lasting at least three consecutive cold days (ATc T min < 10th percentile).
We used the heat wave magnitude index (HWMI) to quantify the severity of heat wave events in different regions of the GRB. The HWMI formula in this study is similar to that of Russo et al. (2015), as follows: where T max(i) represents the T max of the day i in a heat wave event at a given station or grid. T max25th and T max75th represent the 25th and 75th percentiles of the daily T max time series of the given station or grid during 1961 − 2018. T max(i) was greater than the 90th percentile value of T max , and n ≥ 3. The calculation of apparent HWMI (AHWMI) is similar to the HWMI, but it was necessary to replace T max(i) with the apparent T max on day i during a given heat wave event. The cold wave magnitude index (CWMI) was calculated as follows: where T min(i) represents the T min of the day i in a cold wave event at a given station or grid. T min25th and T min75th represent the 25th and 75th percentiles of the daily T min time series of Changes in the a ATc, b HI, c ATw, and d WBGT for each air temperature at different relative humidity levels. The contour lines from bottom to top are the apparent temperature changes under the air temperature conditions of − 20 to 40 °C (interval of 5 °C). The red, green, and blue lines represent apparent temperature changes at 35 °C, 20 °C, and − 5 °C air temperatures, respectively the given station or grid during 1961-2018. T min(i) was less than the 10th percentile value of T min , and n ≥ 3. The calculation of apparent CWMI (ACWMI) is similar to the CWMI, but it was necessary to replace T min(i) with the apparent T min on day i during a given cold wave event.

Generalized extreme value distribution
The generalized extreme value distribution (GEV) has been widely applied to analyze the return period (risk) of hydrometeorological extremes (Xia et al. 2012;Whan et al. 2015;Ragno et al. 2019), especially for heat-related extreme events Shin et al. 2020). The cumulative distribution of the GEV can be written as follows: where and represent location and scale parameters. represents the shape parameter that defines the tail behavior of the distribution (i.e., Gumbel: =0, Fréchet: >0, and Weibull: <0). The parameters , , and were determined using the maximum-likelihood estimation method (negative log-likelihood function). The values (return level) with return period T derived from the GEV were expressed as follows: where Q p represents the value with return period T year. The , , and parameters were defined as in Eq. (17).

Apparent temperature characteristics
A brief ERA5 assessment of T max , T min , and RH is generally required for reproducing humid heat and wet cold events. On the daily scale, the ERA5 can accurately reflect T max characteristics (Fig. 3a), with a high r (0.997) and low Bias (− 0.61 °C), RB (− 2.6%, slightly underestimated), RMSE (0.952 °C), and DISO (0.049) values. The simulated effect Fig. 3 Scatter plots of daily a T max , b T min , and c RH from the ERA5 against the observations averaged GRB during 1961−2018 1 3 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 T min (Fig. 3b) was similar to that of the T max , 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 T max , T min , and RH in the GRB. We extracted the average daily apparent temperatures based on T max and T min 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 T max , we focused on the right curves. As shown in Fig. 4a, the kurtosis of apparent temperatures was smaller than the T max values. Apparent temperature curves extended to the right side more obviously, especially those of the ATc and HI. This implied that the RH amplified 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 T min , we emphasized the left curves. As shown in Fig. 4c, the kurtosis of apparent temperatures (except for WBGT) was smaller than the T min values. The curves of the apparent temperatures at low temperatures, except for those of the WBGT, were distributed more to the left than the T min values. The difference between apparent temperature and T min on the left side at a low temperature was not as large as that between apparent temperature and T max on the right side at a high temperature. This indicated that the RH amplified the severity of a high temperature more than a low temperature in the GRB. The ERA5 simulated apparent temperature based on T min 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 T max > 90th percentile threshold, T max and RH showed an obvious negative correlation, indicating that warm drying was robust in the GRB under high-temperature conditions. Apparent temperatures based on T max were higher than T max 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 apparent temperatures reproduced by ERA5 were lower than those of the observations. The relationships between apparent temperatures and their RH values under conditions of T max > 95th percentiles (Fig. 5c,d) were similar to those under conditions of T max > 90th percentiles. The increments (slopes) Fig. 5 Scatter plots of apparent temperatures and corresponding RH values at the T max > 90th percentile threshold in the a observed and b ERA5 datasets, and the apparent temperatures and corresponding RH values at the T max > 95th percentile threshold using the c observed and d ERA5 datasets per year averaged over the GRB during 1961 − 2018 of apparent temperatures with RH values were generally larger for T max > 95th than T max > 90th percentile thresholds. For example, the slope value of ATc was 0.413 for observations and 0.378 for ERA5 at the T max > 95th percentile threshold, which were higher than those at the T max > 90th percentile threshold (0.279 for observations and 0.294 for ERA5).
Under conditions of T min < 10th (Fig. 6a, b) and < 5th (Fig. 6c, d) percentile thresholds, the T min 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 T min < 5th percentile threshold (− 0.134 for observations and − 0.121 for ERA5) were slightly greater than those at the T min < 10th percentile threshold (− 0.122 for observations and − 0.108 for ERA5). The characteristics of apparent temperatures based on T min 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. Fig. 6 The same as Fig. 5, but for the T min < 10th and 5th percentile thresholds

Temporal and spatial characteristics of humid heat and cold waves
We extracted heat waves using the 90th percentile threshold of the ATc (T max ) 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 AHWMI values in the southern regions of the basin showed significant upward trends, indicating that the risks of humid heat waves in these regions increased. The spatial patterns of the HWMI and AHWMI values were roughly similar (Fig. 8b), but the AHWMI values and their upward trend values were approximately twice those of Fig. 7 Annual variations in the AHWMI and the corresponding HWMI values for the a observed and b ERA5 datasets per year averaged over the GRB from 1961 to 2018. Scatter plots of c the AHWMI and d the corresponding HWMI of ERA5 against the observed datasets the corresponding HWMI values, suggesting that a high RH can significantly amplify the severity of heat waves in the GRB. The AHWMI (Fig. 8c) and HWMI (Fig. 8d) values for ERA5 were lower than the observed values in the northern parts of the basin. The spatial patterns of AHWMI and HWMI values in ERA5 were also roughly similar (e.g., the stations with significant upward trends were concentrated in the southern parts of the basin), but the magnitudes and upward trend values of the AHWMI were also approximately twice Fig. 8 Spatial patterns (annual mean and trends) of a the AHWMI and b the corresponding HWMI of the observed dataset, and spatial patterns of c the AHWMI and d the corresponding HWMI of the ERA5 dataset during 1961-2018. Upward and downward triangles denote increasing and decreasing trends, respectively; black solid triangles represent linear trends reaching the 0.05 significance level those of the HWMI. Although the values of AHWMI and HWMI in ERA5 were smaller than those of the observed dataset due to the slight underestimations of T max and RH, ERA5 reasonably simulated the AHWMI and HWMI spatial features.
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 large magnitudes of the humid cold waves in the southern parts of the basin were attributed to the high RH. The spatial distribution of the annual mean CWMI was similar to that of the ACWMI, but the magnitude values slightly decreased (Fig. 10b). This indicated that the RH slightly magnified the severity of the cold wave event because the specific T min of the GRB was not too low (the average T min in January was 3.5℃). The ACWMI and CWMI showed significant downward trends in almost Fig. 9 Annual variations in the ACWMI and the corresponding CWMI for the a observed and b ERA5 datasets per year averaged over the GRB from 1961 to 2018. Scatter plots of c the ACWMI and d the corresponding CWMI of ERA5 against the observed dataset the entire basin, and the decreasing rates were basically consistent. The decreases in ACWMI and CWMI were relatively large in the northern parts of the basin. The spatial patterns of the ACWMI (Fig. 10c) and CWMI (Fig. 10d) of ERA5 were similar to those of the observations. The ACWMI and CWMI in ERA5 showed significant decreasing trends in the whole basin, and the decreasing rates were slightly less than the observed values. 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 (T max ) heat waves (AHWN), annual sum of participating heat wave days (AHWP), annual number of ATc (T min ) 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 T max and overestimated T min , 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 patterns of the annual mean 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. In both observed and ERA5 datasets, AHWN showed upward trends in most parts of the basin, especially in the southern parts (> 0.3 events/decade). As shown in Fig. 12c, the annual mean 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 annual mean of the AHWP from ERA5 (Fig. 12d) was similar to the observed value, but the specific AHWP value was slightly smaller. For the observed dataset, AHWP and AHWN were similar and mainly showed upward trends. For the ERA5 dataset, AHWP and AHWN also mainly showed upward trends, and the number of grids in AHWN increased significantly more than in AHWP. 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 patterns of the annual mean ACWN values (Fig. 12e) from the observations were similar to those of ERA5 (Fig. 12f), but the specific ACWN values were slightly larger than those 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 humid cold waves in the GRB was less than that of humid heat waves. Both in the observed and ERA5 datasets, ACWN showed significant downward trends in most parts of the basin, and the decreasing rates in the observed dataset were slightly greater than those in the ERA5 dataset. Unlike the AHWP patterns, the ACWP showed relatively high values in the southern parts of the basin in both the observed (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. Both in the observed and ERA5 datasets, ACWP basically showed significant downward trends in the whole basin, and the decreasing rates in the observed dataset Upward and downward triangles denote increasing and decreasing trends, respectively; black solid triangles represent linear trends reaching the 0.05 significance level were slightly greater than those in the ERA5 dataset, especially in the northern parts of the basin.

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 or 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 25.5 (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 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, T max 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 T max increased as the RH declined. The relationships between T max and RH at various grades of heat waves in ERA5 were 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 T max with the ATc (T max ) under heat wave conditions, the relationship between the ATc and RH differed from that of the T max 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, T min increased along with RH (Fig. 17a). The greater the cold waves grade, the slower the T min increase along with the RH. Similarly, a positive correlation between T min and RH also existed in ERA5 (Fig. 17b), and the increase of T min along with RH was smaller in ERA5 than in the observations. When using ATc (T min ) instead of T min , 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 a relatively low ATc, which in turn amplified the severity of the cold waves.
We explored the characteristics of T max , ATc (T max ), RH, and heat wave days under different grades (AHWMI) of heat waves (Fig. 18). As the grade increased, the corresponding average T max increased (Fig. 18a). The specific values of T max 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 T max 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 T min decreased. ERA5 overestimated the average values of T min 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 T min 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 T min 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.

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, 2014, 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 T max 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 T max 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 T max 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 nonextreme events may lead to compound extremes that have significant impacts. ERA5 reasonably reflected the specific values of T max, 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 T min 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 T min 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 T min . However, if combination of T min and RH on cold wave severity was 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 T min 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.

Discussion
High RH and temperature extremes can occur simultaneously in the monsoon regions (humid regions) of southern China (Ding and Ke 2015;Russo et al. 2017;Wang et al. 2019a), which results in the human body feel hotter (colder), thereby increasing morbidity and even mortality rates. The human body is general not sensitive to humidity at approximately 18 °C, and there is little difference in the "feels-like" equivalent temperature at various humidity levels. When the air temperature is greater than 4 °C or less than 22 °C, the air temperature is consistent with the ATc at an RH of approximately 65% (Fig. 2a). However, the ATc increases nonlinearly along with the RH at high air temperatures, and the ATc decreases nonlinearly as the RH increases at low air temperatures. Some other commonly used apparent temperature indices including HI, ATw, and WBGT mainly reflect humid heat characteristics (Steadman 1984;Fischerand Knutti 2013;Russo et al. 2017;Matthews 2018;Wang et al. 2019c), which cannot reflect the decrease in apparent temperature as the RH increases under low-temperature conditions. Therefore, the ATc can reasonably reflect the impacts of humid heat and cold events on human health.
The ERA5 dataset slightly underestimated T max and RH, and slightly overestimated T min in the GRB, and these results were similar to those of previous studies (Li 2020;Zhang et al. 2021a, b). The effect of ERA5 in simulating temperature was slightly better when RH was included because of the correlation between RH and precipitation. The ability of 1 3 ERA5 to simulate precipitation is generally weaker than its ability to simulate air temperature (Huai et al. 2021;Jiang et al. 2021;Zhang et al. 2021b). In addition, the 1000 hPa RH used in this study and the near-surface observations of the GRB have some altitude errors, which can also cause the RH simulation effect to be weaker than that of air temperature. Under high-temperature conditions, air temperature and RH were negatively correlated in the GRB, indicating that drier conditions amplify the warming effect. This may be due to excessive energy being converted into sensible heat instead of being evaporated as latent heat under dry conditions (Chiang et al. 2018). The amplifying effects of RH on ATc and HI were more obvious at high air temperatures in the GRB. At low temperatures, air temperature and RH were positively correlated, which may be because the specific heat capacity of wet air is greater than that of dry air, and the cooling rate is slower than that of dry air. HI, ATw, and WGBT did not show decreases as RH increased under low-temperature conditions, but the ATc did. Therefore, this confirmed that ATc can better reflect the ability of the RH to amplify the severity of heat and cold events in both observed and ERA5 datasets.
This study extracted heat and cold waves based on the ATc (T max and T min ) data series. Annual changes in the AHWMI and the corresponding HWMI were relatively similar, with overall upward trends in the observations and ERA5, especially from 1997 to 2018. This was more consistent with the results of Zhang et al. (2017), which may be attributed to the obvious increase in T max after 1997. The average of the AHWMI was approximately twice that of the corresponding HWMI, which was consistent with the results obtained by Russo et al. (2017) based on the HI index. The AHWMI and HWMI values simulated by ERA5 were smaller than the observations, which may be caused by the underestimation of T max and RH values by ERA5. Annual changes in ACWMI and the corresponding CWMI were relatively consistent, and both showed significant downward trends in the observations and ERA5. The ACWMI was slightly greater than the corresponding CWMI, implying that RH slightly amplified the severity of the cold waves. The humid heat waves in the GRB showed an upward trend, whereas the humid cold waves presented a downward trend from 1961 to 2018 (Fig. 23).
The increasing trends of heatwaves in ERA5 were more obvious than in the observations, especially for severe grade. The downward trends of cold waves in ERA5 were slightly weaker than in the observations, especially for mild grade. Thus, ERA5 captured the warming signal better than the cold signal (Zhang et al. 2021b;Yang et al. 2022), and the increase in T min was generally greater than that of T max . With the increase in the heat wave grade, the mean value of T max increased, and the negative correlation between T max and RH was strengthened in the GRB. This indicated that RH decreased under sustained high temperatures, and Chiang et al. (2018) obtained similar results in which Fig. 23 Schematic diagram of humid heat and cold waves over the GRB long-persisting low RH and vapor pressure deficit amplify warming, because the available energy is expressed as sensible heat instead of being evaporated as latent heat. The combination of low RH and high temperature is prone to produce compound droughts and heat waves, which can adversely affect the environment, society, and human health (Sutanto et al. 2020;Zscheischler and Fischer 2020;Zhang et al. 2021b).
Although heat waves accelerate evaporation and cause RH declines, relatively high RH levels remain in humid regions (e.g., the GRB), and this generates high apparent temperatures (i.e., ATc), which in turn amplifies the severity of heat waves. Fischer and Knutti (2013) also demonstrated the similar conclusion in which large degrees of warming in dry regions (becoming even drier) and lesser degrees of warming in humid regions (remaining humid) produce the same responses in apparent temperature owing to the nonlinearity in its definition. Under cold wave conditions, the air temperature can increase along with the RH in the GRB. This reflects that the air temperature at a high RH is generally warmer than the dry air temperature under low-temperature conditions (Zhang et al. 2011). With the strengthening of cold wave severity, the increasing rate of the air temperature slowed slightly as the RH increased in the GRB. In fact, under high RH and low-temperature conditions, the human body feels colder because the cold water vapor penetrates protective clothing and more easily condenses on the skin, allowing it to absorb more heat from the body. With the increase in cold wave severity, the apparent temperature (i.e., ATc) decreased more rapidly as the RH increased, especially in the ERA5 dataset.
Traditionally, a return period is used to assess the risk (occurrence probability) of an extreme event (Aghakouchak et al. 2015). We hypothesize that the occurrence probabilities of the 2014 heat wave (HWMI) and the 1969 cold wave (CWMI) extracted based on a univariate air temperature (T max or T min ) were underestimated because the RH effects were ignored. The HWMI return period of the 2014 humid heat wave in the observed dataset was 4.4 years, while the AHWMI return period was as high as 47.6 years, indicating that RH amplified the severity of this heat wave by a factor of nearly 10. The CWMI return period of the 1969 humid cold wave was 29.8 years in the observed dataset, while the return period of the ACWMI was about twice that of the CWMI, suggesting that RH clearly magnified the severity of this cold wave. The amplifying effect of RH on heat waves was significantly greater than on cold waves. This may be because that the GRB is located in southern China, which has a subtropical humid monsoon climate. The average T max in summer is approximately 30-35 °C, and the RH is more likely to significantly amplify the severity of heat waves. The average T min in winter is around 0-5 °C, and RH has difficulty amplifying the severity of cold waves to a great degree. The HWMI (CWMI) of the ERA5 was close to that of the observations, while the AHWMI (ACWMI) was significantly higher than that of the observations. Thus, ERA5 may overestimate the amplifying effect of RH on the severity levels of heat and cold waves.
An in-depth understanding of the mechanisms of humid heat and cold events provides a scientific basis for providing early warning measures, especially in humid regions with dense populations undergoing rapid economic growth in southern China. The T max and specific RH have a strong linear relationship, particularly in southern China during summer. Thus, simultaneous occurrences of high temperatures and high HR can occur (Wang et al. 2019a). Humid heat events are generally caused by low-latitude water vapor and heat anomalies brought by subtropical highs (Ge et al. 2021). The GRB is affected by the East Asian summer monsoon season. Generally, there is more precipitation from April to June (i.e., rainy season) over the GRB (Zhang et al. 2015), which can increase the RH. After middle and late June, the basin is controlled by a subtropical high, the temperature increases rapidly, sufficient moisture allows for evaporation, and the RH remains relatively high, which easily leads to serious humid heat waves. In winter, more northerly winds (cold air) caused by strong East Asian winter monsoons penetrate southern China (e.g., the GRB), resulting in the rapid cooling of this region. The decrease in air temperature can lead to a decrease in the saturated water vapor pressure, which in turn increases the RH and eventually leads to humid cold waves.

Conclusions
In humid hot (cold) weather, a comparatively high RH can lead to a relatively high (low) apparent temperature, which in turn produces humid heat (cold) waves that are seriously harmful to human health. We used the GRB (humid basin) as a case to investigate the characteristics of humid heat (cold) waves from 1961 to 2018 based on the ATc index in the observed and ERA5 datasets. Using typical cases (the 2014 humid heat wave and the 1969 humid cold wave), this study demonstrated that a high RH can significantly amplify the severity of humid heat (cold) waves. Our main conclusions can be summarized as follows: (1) ERA5 can accurately simulate the daily T max , T min , and RH, and then it can accurately predict the apparent temperatures (i.e., ATc, HI, ATw, and WBGT) in the GRB. ATc can reasonably reflected the "extra heat (cold)" effect of a high RH under high (low)temperature conditions for human perception. Therefore, the humid heat and cold waves were reasonably identified by the ATc data series.
(2) Heat waves showed increasing trends from 1961 to 2018 (especially from 1997 to 2018), whereas cold waves showed significant decreasing trends. The AHWMI was approximately twice that of the corresponding HWMI, and the ACWMI was slightly greater than the corresponding CWMI, indicating that a high RH amplified the severity of heat waves more significantly than cold waves. ERA5 accurately reflected the spatiotemporal patterns of heat and cold waves, and the ability to simulate cold waves was greater than that of heat waves in the GRB. (3) The increasing rates of heat waves in ERA5 at the mild, moderate, and severe grades were slightly greater than the observations, especially for severe grade. Cold waves at various grades showed downward trends in both observations and ERA5, and the downward trends in ERA5 were slightly weaker than in the observations. (4) Through return period analysis of the 2014 humid heat wave and the 1969 humid cold wave based on GEV-fit, we found that the heat (cold) wave severity based on univariate air temperature was severely underestimated owing to RH being ignored. In the GRB, the severity of humid heat waves was significantly underestimated to a greater degree than that of humid cold waves, especially for ERA5 datasets.