The increasing concurrences of heatwaves and droughts in the context of global warming have attracted much attention from the scientific community given their devastating social and environmental impacts. In this study, the effects of heatwaves in each adjacent week of flash drought onset on the intensification rate of soil moisture were quantified through a meta-Gaussian-based conditional probability model. Results showed that both heatwaves and flash droughts have become more frequent since the middle of the 1990s. For the seasonal distributions, except for the southwestern region where flash droughts lagged behind heatwaves, there was a good synchronization between the two climate extremes. Strong correlations between heatwaves and flash droughts were found in the northeastern, northern, and southwestern regions. Heatwaves with varied timing of emergence behave differently on the formation of flash droughts, along with significant regional differences. Short-term impending hot conditions were crucial for the breakout of flash droughts, especially for the week when flash droughts were initiated, the emergence of heatwaves was likely to increase the intensification rate of soil moisture by 20% compared to those with no heatwaves in their development stage.

  • The composite patterns of concurrent heatwaves and flash droughts are investigated.

  • Conditional probability is adopted to quantify the effect of heatwaves on drought.

  • Heatwaves increase the intensification rate of drought events by about 20%.

In the context of global warming, recent years have witnessed growing frequencies of dry and hot events which brought great threats to the ecological environment and human society (Yuan et al. 2015; Naumann et al. 2018; Seneviratne et al. 2021). In addition to the occurrence of each isolated climate extremes alone, the probability of concurrent multiple extremes (e.g., droughts and heatwaves) also increases as a result of globally rising temperatures (AghaKouchak et al. 2014; Ridder et al. 2020; Hao 2022). Numerous observational and modeling studies have shown the enhanced trends of such compound events both in severity and magnitude in many regions around the world (Hao et al. 2018; Zscheischler et al. 2018; Manning et al. 2019; Alizadeh et al. 2020; Geirinhas et al. 2021; Mukherjee & Mishra 2021).

Reasons for the chain process of cascaded climate extremes are complicated, which involve both atmospheric dynamics mechanisms and land–atmosphere feedbacks. For instance, large-scale atmospheric circulation and sea surface temperature anomalies are commonly recognized as the early diagnostic signals for the initiation of droughts and heatwaves (Zhou et al. 2019). Atmospheric blocking which induces significant precipitation and temperature anomalies (Sousa et al. 2017; Lenggenhager & Martius 2019; Zhu et al. 2021) creates favorable weather conditions for the occurrence of heatwaves and drought. Meanwhile, its effects can be spatially variable given the location of blocks occurring in different geographical regions (Röthlisberger & Martius 2019). In addition to synoptic circulation anomalies, local and remote land–atmosphere feedbacks also play a vital role in the simultaneous occurrences of hot and dry extremes, as well as for the intensification of both extremes. For instance, based on observations and atmospheric general circulation model products, the co-variability of temperature and precipitation has been investigated both at global and regional scales with negative correlations detected over land (e.g., Trenberth & Shea 2005; Koster et al. 2009). Soil moisture also strongly modulates near-surface heat and aridity deficits through soil moisture-temperature coupling and soil-precipitation coupling (Seneviratne et al. 2010; Schumacher et al. 2022). The linkages between droughts and heatwaves are still under study, in particular, the influences of heatwaves on the formation of flash droughts have rarely been discussed.

In the absence of a universal definition, flash drought typically refers to a drought with sudden onset and rapid rate of intensification (RI). Given the close relation between hot conditions and flash droughts, the temperature has been adopted by previous studies in their ways of defining and identifying flash drought events. For instance, Mo & Lettenmaier (2015) considered the anomalies of temperature both in precipitation deficits driven and heatwave driven flash droughts, and explicitly illustrated the role of high temperatures in the latter type which leads to evapotranspiration increases and therefore decreases of soil moisture. In addition, the temperature was also implicitly incorporated in some monitoring indices (e.g., the evaporative stress index) for flash drought prediction and forecasting purposes (Otkin et al. 2014; Lorenz et al. 2021). Focused on the physical drivers of flash drought, several studies analyzed the impacts of antecedent meteorological conditions on the depletion of soil moisture (Ford & Labosier 2017; Qing et al. 2022). However, the specific role of hot extremes on flash droughts, with varied timing of emergence during the drying process, is still unclear.

The aim of this study, therefore, is to evaluate to what extent the drying process may be accelerated under heatwaves before and during the onset of flash drought. Investigations were conducted over China on the basis of reanalysis of soil moisture products and temperature observational data. The effects of heatwaves on flash drought were quantified by using both multi-regression model and conditional probability model. The remainder of this paper is organized as follows: Section 2 describes the data used in this study, and the methods for quantifying the effects of heatwaves. Section 3 presents the results, Section 4 discusses the findings, with conclusions drawn at the end.

Data

ERA-Interim is a global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECWMF; https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/). Following a sequential data assimilation scheme, the ERA-Interim reanalysis uses available observations combined with prior information to produce a forecasting and estimates physical parameters such as precipitation and soil moisture as well (Dee et al. 2011). The soil moisture data from ERA-Interim were employed to identify drought conditions in China. Daily soil moisture estimations of four layers (0–7 cm, 7–28 cm, 28–100 cm, 100–289 cm) are provided at a spatial resolution of 0.75° and are updated on a monthly basis. Other optional interpolated data with different spatial resolutions are also available. In this study, records of the top three layers at 0.25° spatial resolution from 1979 to 2018 were collected, and they were converted into volumetric moisture contents at a depth of 1 m in units of m3/m3. To eliminate the seasonality impact, original daily series were aggregated into weekly values, then converted into soil moisture percentile for every 52 weeks.

The daily maximum temperature was employed to identify heatwaves. Records of 756 meteorological stations evenly distributed in China were obtained from the National Meteorological Science Data Center (http://data.cma.cn/), covering a temporal span from 1961 to 2016. This dataset is released with strict quality control, and is recommended as a priority option for analyzing climate extremes in China. To match the spatial resolution of soil moisture data, the site-based observations were interpolated to gridded data at a spatial resolution of 0.25° by using the Kriging method, as its interpolation accuracy is higher than other interpolation methods such as ordinary nearest neighbor and inverse distance weighting (Lin et al. 2002; Chen et al. 2010).

Methods

Heatwaves identification

Heatwaves broadly refer to periods of days with anomalously warmer temperatures than normal. The variables related to measuring such extreme hot weather can be maximum, minimum or apparent temperature. The critical threshold for representing the normal condition can be fixed thresholds or percentiles, and the warm spell of heatwaves can be consecutive days or cumulative counts of single days above a predetermined threshold (Perkins et al. 2012). All these constitute the diversity of heatwave definitions. This study focused on the impacts of heatwaves on soil moisture depletion, and the extreme hot condition in the daytime is more important for revealing such heat effects. Therefore, the daily maximum temperature (Tmax), combined with the relative thresholds was employed for identifying heatwaves given the vast territory of the research domain. Following the common methodological definition, heatwave periods of at least three consecutive days are detected when anomalies of maximum temperature exceed the 90th percentile of Tmax for each calendar day. The 90th percentile is derived from the probability density function computed by using the maximum temperature data averaged on a 15-day moving window during the 30-year (1961–1990) climatological period. The thresholds were calculated for each grid cell separately, which allows for comparative analysis between grids in different regions.

Flash drought identification

In the absence of a universal definition, flash drought is frequently characterized by a sudden onset and rapid intensification which has distinguished features from traditionally slowly evolving droughts. Definitions focusing on the rapid soil drying process have been mostly used in previous research (e.g., Hunt et al. 2014; Ford & Labosier 2017; Osman et al. 2021). Following this notion, a quantitative method of measuring the intensification rate was employed to identify flash drought events. According to Otkin et al. (2018), there are two key requirements to recognize a flash drought. One refers to the events that should actually fall into drought and also contain some periods of soil moisture conditions approaching the critical level of vegetation moisture stress. This can be controlled by two thresholds associated with soil moisture percentiles, i.e., the upper limits of 40th percentile and the lower limits of 20th percentile, respectively (Svoboda et al. 2002; Liu et al. 2020a). To eliminate the seasonality effect, soil moisture percentiles were estimated separately for each week. Thirteen candidate theoretical probability distributions (including BETA, GAMMA, LOGIST (LOG), Loglog (LLG), Generalized extreme value (GEV), Weibull (WBL), Exponential distribution (EXP), Generalized pareto (GP), NAKAGAMI (NAKA), Birnbaum-Saunders(BIRN), Normal distribution (NORM), RAY, and RICI) were employed to fit soil moisture series, and the optimal distribution was chosen as the one that can pass the Kolmogorov–Smirnov test at the 95% significance level, along with the minimum root-mean-square error (RMSE).

The other refers to the rapid intensification process to classify the event as a flash drought. For this purpose, a quantitative method for measuring the RI was introduced:
(1)
where T1 is the onset time of flash drought, which is defined as the first week that the soil moisture percentile falls below the 40th percentile during the drought process. Tb is the termination of rapid intensification, manifested as the inflection point that soil moisture changes from rapid decline to smooth fluctuation. We search the optimal polynomial function by increasing the order of the polynomial until the deterministic coefficient R2 is greater than 0.95. The termination point can be extracted when the first derivative of the optimal polynomial equals to zero in calculus. A flash drought is recognized when RImean is no more than −6.5 percentile per week (Liu et al. 2020b).

Multivariate linear regression

The multivariate linear regression is an effective statistical method to model the relationship between a dependent variable and explanatory variables. In this study, RI can be simulated through the linear regression model by using the information of heatwave occurrences in adjacent weeks of drought onset (i.e., the time periods taken into account range between 7 weeks prior to drought onset (T0−7) and 7 weeks after drought onset (T0+7)). For each week, RIi can be modeled by:
(2)
(3)
where RI is the rate of intensification, H is the proportion of heatwave days in the week, w0 is the constant, wi (i = 1, ……, n) is the weighting coefficients of the linear regression model, represents the estimation error, and n is the number of input parameters.

Conditional probability

Developed by Sklar (1959), copulas are functions that link univariate distribution functions to form multivariate distribution functions. The merit of using copulas to construct multivariate distributions is that copulas can separate the dependence effects from the marginal distribution effects. Construction of multivariate distribution is thus reduced to study the relations among the correlated random variables if marginal distributions are given (e.g., Chen et al. 2011; Grimaldi & Serinaldi 2011; Hao et al. 2016). The books of Nelsen (2006) introduce a copula theory in detail. Shiau (2006) first applied copulas to drought research to investigate the link between drought severity and duration. Hao et al. (2019, 2020) established the cumulative probability of compound dry-hot events based on copulas and quantified the potential severity of dry-heat events. Vergni et al. (2020) used a copula function to explore the effects of climate and irrigation strategies on the distribution of agricultural drought characteristics. Menna et al. (2022) constructed a joint distribution function based on precipitation and soil data to analyze drought risk in the upper reaches of the Tekeze River basin. In this study, the conditional form based on the copula concept was employed to quantify the specific role of heatwaves on flash drought. As shown in Figure 1, the conditional joint distribution was established at weekly scales, and the proportion of heatwave days in 1 week (denoted as xi, varying between 0 and 1) was introduced so as to match the temporal scale of flash droughts. Supposing the vector Y represents the intensification rate of drought events, and for each drought event, we consider heatwaves that occurred 7 weeks before and after the onset time of a drought event, and they were denoted as the explanatory vector X = [xt0–7, … , xt0, … , xt0+7]. For constructing the joint probability distribution of variables X and Y with the marginal distributions F(X) and G(Y), the meta-Gaussian copula was chosen given its flexibility in modeling both negative and positive dependence structures, and the efficiency in handling high dimensions. Define Z1 = N−1(F(X)) and Z2 = N−1(G(Y)), variables X and Y were converted into normally distributed variables Z1 and Z2. The meta-Gaussian-based joint distribution can be expressed as:
(4)
where N represents the joint normal distribution function; μ and are the mean and covariance matrix; N−1 is the inverse of the standard normal distribution function. Accordingly, the explicitly analytical expression of the conditional distribution of Y given X can be expressed as (Wilks 2011):
(5)
where μY|X and ΣY|X represent the mean, and covariance matrix of the conditional probability distribution, respectively, and they can be derived from:
(6)
(7)
where μX and μY are the means of X and Y; ∑xx, ∑xy, ∑yx, and ∑yy are the covariance matrix of X and Y.
Figure 1

Framework of copula-based analysis for estimating the intensification rate of soil moisture conditioned on heatwaves in adjacent weeks under varying scenarios.

Figure 1

Framework of copula-based analysis for estimating the intensification rate of soil moisture conditioned on heatwaves in adjacent weeks under varying scenarios.

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To obtain the best estimation of y, a random sampling procedure was performed with 1,000 uniformly distributed random numbers over the interval (0,1] generated for week ti, while the proportion of heatwaves in other weeks was set to zero. In other words, 1,000 estimated values of y would be generated through the conditional probability distribution function, and the mean value was considered as the best estimate of y. The intensification rate (RIi) of soil moisture conditioned on the joint behaviors of heatwaves in adjacent weeks can be expressed as:
(8)
To measure the role of heatwaves in week ti on soil moisture intensification comparing to the condition that non-heatwaves occur during the drought development stage, the increasing ratio (IR) of soil moisture depletion was introduced:
(9)
where RI denotes the estimated intensification rate under the condition of no heatwaves in adjacent weeks (i.e., from t−7 to t7). Positive values of IRi suggest heatwaves in week ti accelerate the depletion of soil moisture, while negative values indicate the inhibition effects on the drying of soil moisture.

Spatial and temporal distribution of heatwaves and flash droughts

Following the identification methods of climate extremes, statistics of heatwaves and flash droughts in China during 1961–2016 were extracted. As shown in Figure 2(a), heatwaves hit southwest China and southeast coastal areas more frequently than other regions. In contrast, the occurrences of heatwaves were generally lower in the northwest, eastern parts of the northeast, and the Huaihe River basin. As for the temporal patterns of heatwave days (Figure 2(b)), both annual and decadal means suggest a decreasing trend from 1960 to 1980s. Then heatwave days significantly increased and reached up to 30 days per year in the 2010s, implying the enhanced persistence of heatwaves in the context of global warming. Likewise, the frequencies of flash drought occurrences were high in south China and low in northwest regions (Figure 2(c)). Meanwhile, north China and northeast regions also suffered more flash droughts during the past 56 years. Given the high frequencies of heatwaves and flash droughts in south China, concurrent climate extremes are more likely to occur in this region. According to the serial proportion of flash drought areas nationwide (Figure 2(d)), the decadal means follow a similar pattern as that of heatwave days with continuous increments since 1990s. However, such sustained expansions in flash drought areas were not seen for the annual series, where a downward tendency was apparent during the recent 10 years. The reason for the different temporal features between heatwaves and flash droughts lies in that in addition to temperature, the drought condition indicated by soil moisture essentially reflects the comprehensive moisture status, where water-related variables such as precipitation also influence drought trends.
Figure 2

Spatiotemporal distributions of heatwaves and flash droughts in China during 1961–2016. (a) Spatial distribution of heatwave frequencies, (b) annual and decadal mean values of heatwave days, (c) spatial distribution of flash drought frequencies, and (d) annual and decadal means of the proportion of flash drought area.

Figure 2

Spatiotemporal distributions of heatwaves and flash droughts in China during 1961–2016. (a) Spatial distribution of heatwave frequencies, (b) annual and decadal mean values of heatwave days, (c) spatial distribution of flash drought frequencies, and (d) annual and decadal means of the proportion of flash drought area.

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Figure 3 presents the weekly distributions of heatwaves and flash droughts occurrences in four regions of China (cases in the northwest region were not shown given the low frequencies of these two climate extremes) during 1961–2016. It can be seen that both heatwaves and flash droughts exhibited high occurrences in growing seasons (approximately from the 20th week to the 40th week), indicating the likelihood of concurrent hot and dry extremes during these periods. As for regional patterns, the northeastern and northern regions generally presented a similar pattern, where the peak of heatwave occurrences emerged in June, which was 3–5 weeks ahead of flash droughts. Then the frequencies of heatwaves decreased to ∼5%, and there were virtually no heatwaves in late autumn and winter (non-growing seasons). For the southwest region, asynchronous variations were apparent between the curves of these two climate extremes. Different from the multi-peak shapes of heatwaves, significant hysteresis was found for flash drought with its peak emerged in October. In contrast to the patterns in the southwest region, the highest frequency values of heatwaves in the southeast region emerged in September, which was two months later than that of flash droughts. This suggests persistent high temperature days would not necessarily increase the likelihood of drought occurrences in humid areas, while the condition of water-related variables is also crucial for the formation of drought.
Figure 3

Weekly distributions of heatwave (HW) and flash drought (FD) occurrences (i.e., the ratio of heatwave/flash drought events in each week to annual average heatwave/flash drought events) in four regions of China during 1961–2016.

Figure 3

Weekly distributions of heatwave (HW) and flash drought (FD) occurrences (i.e., the ratio of heatwave/flash drought events in each week to annual average heatwave/flash drought events) in four regions of China during 1961–2016.

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Variation of soil moisture in response to heatwaves

Heatwaves characterized by persistent high temperatures can increase evapotranspiration, which has the potential to accelerate the depletion of soil moisture. Taking the case of the Beijing site as an example, the daily soil moisture series during the dry spells between two adjacent precipitation events in summer were extracted, and they were divided into two categories, i.e., under heatwaves and non-heatwave occurred during the selected time intervals. As shown in Figure 4(a), although both categories presented consecutive reduction since the termination of preceding precipitation (i.e., t1 in Figure 4(a)), there exists a significant difference regarding the decline rate, where soil moisture under heatwaves decreased more rapidly than in non-heatwave days. To further investigate the behaviors of soil moisture in different regions, the average changes in soil moisture during heatwave days from 1979 to 2016 were analyzed. As shown in Figure 4(b), most regions in China presented positive changes in soil moisture, with particularly higher values in the northeastern, northern, eastern, and southwestern regions, implying the potential drying effects of heatwaves on the soil layer in these areas. For arid regions such as Inner Mongolia and Xinjiang, such warming effects were generally minor with variation values close to 0. Cases in the Qinghai–Tibet Plateau were the exception, where negative values were observed. This may be related to the specific frozen soil cover in this region. Heatwaves characterized by rising temperatures promote the melting of permafrost, as a result, more water would be released to recharge the soil layer, leading to increments of soil moisture in a short time period.
Figure 4

Variations of soil moisture in response to heatwaves: (a) depletion curves of soil moisture during the dry spells between two adjacent precipitation events (t1 represents the first day after the termination of precipitation events) in summer. Light red shadows represent the cases during heatwaves and light blue shadows for non-heatwave days. Blue and red solid lines represent the mean scores of soil moisture. Data were from the grid cell where the Beijing city is located. (b) Average changes of soil moisture in response to heatwaves from 1979 to 2016. Negative values indicate increments of soil moisture during heatwaves, while positive values represent the reduction of soil moisture during heatwaves. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2023.022.

Figure 4

Variations of soil moisture in response to heatwaves: (a) depletion curves of soil moisture during the dry spells between two adjacent precipitation events (t1 represents the first day after the termination of precipitation events) in summer. Light red shadows represent the cases during heatwaves and light blue shadows for non-heatwave days. Blue and red solid lines represent the mean scores of soil moisture. Data were from the grid cell where the Beijing city is located. (b) Average changes of soil moisture in response to heatwaves from 1979 to 2016. Negative values indicate increments of soil moisture during heatwaves, while positive values represent the reduction of soil moisture during heatwaves. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2023.022.

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To further investigate the linkage between heatwaves and flash droughts, the correlation between the two climate extremes was analyzed, shown in Figure 5. Specifically, the persistence of heatwave conditions represented by the proportion of heatwave days in adjacent weeks (15 weeks were considered with 7 weeks before and after flash drought onset) of the initiation of flash drought, and the intensification rate of soil moisture was introduced for correlation analysis. Higher values of correlation coefficients (CC) indicate the positive effects of heatwaves on the decline of soil moisture. As shown in Figure 5, except for the northwestern region (correlation analysis was not conducted given the insufficient samples of flash droughts in this region), the majority of areas in China suggested positive correlations, with the values of CC ranging between 0.4 and 0.9. Spatially, a strong correlation was found in the northeastern, Huang-Huai-Hai Plain, and the southwestern regions, with the CC values above 0.7. This also indicates the higher likelihood of concurrent climate extremes in these regions than in other districts.
Figure 5

Correlation between the intensification rate of soil moisture and the proportion of heatwave days in adjacent weeks of flash droughts. Areas with insufficient samples or the correlation failed to pass the significance test were marked blank.

Figure 5

Correlation between the intensification rate of soil moisture and the proportion of heatwave days in adjacent weeks of flash droughts. Areas with insufficient samples or the correlation failed to pass the significance test were marked blank.

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Quantify the role of heatwaves on flash droughts

To investigate the specific role of high temperatures with varied timing of emergence on flash droughts, the multivariate regression model was employed to establish the relationship between heatwaves in 15 adjacent weeks of flash drought onset and the intensification rate of soil moisture. As shown in Figure 6, the weighting coefficients transited between positive and negative values at different time intervals, along with significant regional differences. Taking the case of the northeastern region as an example, due to the spatial heterogeneity of soil moisture, there exists considerable heterogeneity for the effects of heatwaves given the wide ranges of the weighting coefficients between the 75th and 25th quantiles. On average, positive weighting coefficients were apparent from weeks T0−2 to T0, with the highest value emerged in T0 (i.e., exactly the week when flash drought initiated), implying the promotion effects of hot conditions at these time intervals for accelerating the decline of soil moisture. Then the weighting coefficients fell into negative values from T0+1 to T0+4, and turned to positive again after 5 weeks of the flash drought initiated (Figure 6(a)). Patterns in the northern region were similar to the northeastern region from T0−7 to T0, while for weeks after the initiation of flash drought, the weighting coefficients decreased but on average sustained positive (Figure 6(b)). As for the eastern region (Figure 6(c)), only heatwaves during T0−2 to T0 may have a promotion effect with positive weighting coefficients observed. In a different manner, heatwaves in seven preceding weeks all presented positive values in the southwestern region, but maintained negative after flash drought was initiated (Figure 6(d)).
Figure 6

Weighting coefficients of heatwave days in each adjacent week derived from the multivariate regression model in each region. T0 represents the week when flash drought initiates. The blue shadows show the 75th and 25th quantiles of the weighting coefficients in the region.

Figure 6

Weighting coefficients of heatwave days in each adjacent week derived from the multivariate regression model in each region. T0 represents the week when flash drought initiates. The blue shadows show the 75th and 25th quantiles of the weighting coefficients in the region.

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In addition, the meta-Gaussian model was also employed to what extent the drying process may be accelerated under heatwaves with varied timing of emergence. For constructing the conditional probability model between heatwaves and flash droughts, 13 candidate theoretical probability distributions were employed to fit the marginal distributions of the intensification rate of soil moisture and proportion of heatwave days, respectively. The optimal probability distribution was chosen when the minimum value of RMSE between the empirical and estimated theoretical probabilities was obtained. For the intensification rate of soil moisture, the marginal distribution was determined based on 50,000 samples randomly selected from 500,000 drought events (the sum of all historical drought events in 15,691 grid cells) over China. As shown in Figure 7(a), the RMSE values for 13 candidate theoretical probability distributions over China varied between 0.007 and 0.2 m3/m3, with the best performances for LLG, GEV, and GAMMA. In terms of regional performances (Figure 7(b)), the LLG outperformed other theoretical probability distributions with lower RMSE values in northeast, north, and eastern regions than in the southwestern region. Following a similar selection process of the optimal theoretical probability distribution, Figure 8 exhibits the results for the proportion of heatwave days. With RMSE value of 0.024 m3/m3, the GP performed best over China, followed by GAMMA and LOG. Regionally, the GP presented the best fit results with overall lower RMSE values in the northern and southwest regions.
Figure 7

(a) Comparisons between empirical and theoretical probabilities for the intensification rate of soil moisture over China. (b) Root mean square errors for 13 candidate probability distributions in four major flash drought-affected regions.

Figure 7

(a) Comparisons between empirical and theoretical probabilities for the intensification rate of soil moisture over China. (b) Root mean square errors for 13 candidate probability distributions in four major flash drought-affected regions.

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Figure 8

As in Figure 7 but for the proportion of heatwave days.

Figure 8

As in Figure 7 but for the proportion of heatwave days.

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Based on the established meta-Gaussian model, the probability of intensification rate of soil moisture conditioned on varied proportions of heatwaves in adjacent weeks of the initiation of flash drought can be derived. Figure 9 shows the increasing ratio of RI by heatwaves compared to the condition with no heatwaves during flash droughts. Overall, patterns of the positive effects of heatwaves in four regions were generally inconsistent with the results derived from the multivariate regression model (Figure 6). In addition, the likelihood of boosted intensification ratio for each week can also be quantified through the conditional model. From a probabilistic perspective, all four regions showed that heatwaves emerged exactly in the week when flash drought initiated (T0) were most likely to exert positive effects on the decline of soil moisture, with the increasing ratio values ranging between 0 and 60% at the 90% confidence interval, and the most probable increasing ratio of 20%. For other time intervals, the likelihood of increasing ratio was no more than 10%, along with significant regional differences. In the northeastern region, heatwaves at T0−1, T0+5, T0+6, and T0+7 exhibited positive impacts by accelerating the RI by 10% (Figure 9(a)). With comparable increasing ratios, intermittent positive signals (i.e., T0−5, T0−3, and T0−1) were found for the preceding weeks in the northern region, besides, heatwaves at T0+1 also presented positive effects (Figure 9(b)). Similar to the results from the multivariate regression model (Figure 6(c)), the conditional probability derived results in the eastern region also indicated long effects of heatwaves, with positive roles from T0−2 to T0+7 (Figure 9(c)). For the southwestern region, significant distinctions were found among heatwaves before (i.e., from T0−7 to T0−1) and after (i.e., from T0+1 to T0+7) the initiation of flash drought, where the positive values virtually covered from T0−7 to T0 with the increasing ratios by 5 ∼ 10% (Figure 9(d)).
Figure 9

Increasing ratio of the intensification rate of soil moisture by heatwaves in adjacent weeks of the initiation of flash droughts in four regions. The orange areas represent heatwaves that promote the intensification rate of soil moisture, while the grey areas represent negative effects. The red dots and solid lines for each probability distribution curve show the most probable, and 90% confidence intervals of the increasing ratio values. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2023.022.

Figure 9

Increasing ratio of the intensification rate of soil moisture by heatwaves in adjacent weeks of the initiation of flash droughts in four regions. The orange areas represent heatwaves that promote the intensification rate of soil moisture, while the grey areas represent negative effects. The red dots and solid lines for each probability distribution curve show the most probable, and 90% confidence intervals of the increasing ratio values. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2023.022.

Close modal

Recent studies mostly focused on concurrent climate extremes such as heatwaves and droughts (e.g., Alizadeh et al. 2020; Mukherjee & Mishra 2021; Hao 2022), while limited attention has been paid to the relation between heatwaves and flash droughts. As a new drought type increasingly discussed in the recent 20 years, flash drought is characterized by the sudden onset and rapid intensification, and their relation with hot conditions may be different from traditional slowly-evolving droughts. Trenberth et al. (2014) stated that the increased warming due to climate change may exacerbate the drying process in a quicker and more intense manner. Such reinforcements from the heating condition were also observed in this study. According to Figure 4, it is found that soil moisture under heatwaves decreased more rapidly than in non-heatwave days, meanwhile, the decrement of soil moisture varied over different regions. To investigate the specific roles of heatwaves with the varied timing of emergence, we used two models, i.e., the multivariate regression model and the meta-Gaussian copula model, to quantify such effects. From Figures 6 and 9 we can see that both models revealed similar quantitative results, where heatwaves occurred exactly in the week when flash drought initiated had the strongest forces, and the intensification rate of soil moisture was likely to be accelerated by 20% according to the meta-Gaussian model. This highlights the importance of short-term impending hot conditions for the breakout of flash drought.

Cases in other weeks were complicated, along with significant regional differences. For instance, the positive effects of heatwaves for the southern region covered seven complete preceding weeks. However, for other regions in China, such positive effects of heatwaves were manifested as intermittent signals, combined with negative values at certain intervals. The reasons for the negative values are complicated. From Figure 9 we can see that most negative values before the 2-week lead were close to zero, indicating a weak correlation of heatwaves with flash drought onset. Ford & Labosier (2017) analyzed meteorological conditions at four pentads prior to flash drought onset, and also found a gradually enhanced correlation from 4-pentad to 1-pentad lead. In other words, flash droughts are more relevant to short (no more than 2-week lead) periods of hot conditions in most regions. Besides, negative effects were also found for weeks after the flash drought was initiated. This may be related to the transition between energy-limited and water-limited conditions as a result of persistent reduction of soil moisture under heatwaves. Vegetation also influences the drying process by controlling the rate of evapotranspiration (e.g., Zhang & Zhang 2019; Yin et al. 2021). Liu et al. (2022) found that under water-stressed conditions, vegetation may alleviate droughts, and such alleviating effects differ among different vegetation types. This may in part explain the negative roles of heatwaves in restraining the depletion of soil moisture, and the varied timing of such negative effects of heatwaves after flash droughts initiated in different regions (Figure 9). In the context of global warming, drastic climate change poses great challenges to global security and sustainable development, accelerating the rate of interregional hydrological cycles, leading to significant global extreme events such as droughts or heatwaves (Bian et al. 2022; Sun et al. 2023). Droughts may trigger or exacerbate heatwaves through the effect on surface fluxes, which in turn generate positive feedback to droughts by increasing evaporative demand or reducing precipitation (Tilloy et al. 2019). From the standpoint of land–atmosphere feedback, the potential role of land–atmosphere feedback is in increasing the frequency of compound dry and hot extreme events under climate change (Zscheischler & Seneviratne 2017). The prevailing view is that heatwaves caused by global warming may not cause droughts to occur, but they may make existing droughts faster and more severe (Trenberth et al. 2014). In addition, a modest positive drought-heat effect has been found using the numerical experiments with the Weather Research and Forecasting (WRF) model; however, the evidence of drought-heat-drought-coupled feedback was still lacking (Osman et al. 2022).

The major findings of this study are given as follows: Both heatwaves and flash droughts became more frequent since the middle of the 1990s, and spatially higher frequencies of heatwaves (20–45%) and flash droughts (10–15%) were found in southern China, with low frequencies for both climate extremes in the northwestern region. For the seasonal distributions, except for the southwestern region where flash droughts lagged behind heatwaves, there was a good synchronization between the two climate extremes. Strong correlations between the heatwave days and the intensification rate of soil moisture were found in the northeastern, northern, and southwestern regions, with the values of CC above 0.7. Consistent quantitative results from the multivariate regression model and meta-Gaussian model suggest that short-term impending hot conditions were crucial for the breakout of flash drought, especially for the week when flash drought initiated, the intensification rate of soil moisture under heatwaves was likely to increase by 20% comparing to those with no heatwaves in their development stage. Meanwhile, heatwaves with varied timing of emergence behaved differently on the formation of flash drought, and the persistence of positive effects for accelerating soil moisture decline also differs over different regions. The results highlighted the necessity of recognizing the composite patterns of concurrent heatwaves and flash droughts, which is essential for objective assessment of compound events, and drought adaptation and management strategies.

X.Z. carried out the analyses, prepared the figures and wrote the manuscript. Y.L. prepared the figures and designed the paper. Y.Z. wrote the manuscript and supervised the formulation of this manuscript. Q.M. and G.P. supervised the formulation of this manuscript. Y.Q. and H.Y. prepared the data. All authors discussed the results and contributed to the final paper.

This research has been supported by the National Natural Science Foundation of China (grant nos 41901037, 42171021, and 42071040), the National Natural Science Foundation of Jiangsu Province, China (grant no. BK20220145), and the Central Guidance for Local Science and Technology Development fund projects, under Grant no. 2021ZY0027.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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