1 Introduction

As a consequence of global warming since 20th century (IPCC 2014), extreme weather events such as heatwaves are frequently observed globally (Frich et al. 2004; Schär et al. 2004). Severe heatwaves (e.g. Chicago 1995; Europe 2003; California 2006; China and Russia 2010) impose disastrous impacts over human, natural and industrial systems across the globe (Anderson and Bell 2011; Easterling et al. 2000). For instance, the 2003 European heatwaves killed more than 25,000 deaths (García-Herrera et al. 2010). The destructive impacts of heatwaves gave rise to a large number of researches on its effects and causes (e.g. Black et al. 2004; Feudale and Shukla 2007; Stéfanon et al. 2012). It’s reported that the occurrence of extreme heat waves will increase in the coming years (Meehl and Tebaldi 2004; Russo et al. 2014).

Heatwave events generally last for several consecutive days and exhibit extreme high temperatures. However, no agreement can be reached on the definition of a heatwave, which can be either absolute or relative according to high temperature criteria (Robinson 2001). An absolute heatwave uses a fixed threshold to identify high temperatures, while a relative heatwave use a threshold computed based on the climatology temperature of a station or a grid. Once heatwaves are defined, important information such as the frequency, intensity and duration could be calculated based on the definition, and the changes in the past and possible consequence for the future are investigated (Meehl and Tebaldi 2004; Della-Marta et al. 2007; Kyselý 2010). Robinson (2001) discussed how to decide an appropriate threshold to identify heatwaves in different regions of the United States. Smith et al. (2013) employed 16 definitions for examining spatial patterns and trends of heatwaves in the Unites States. The future changes of heatwaves duration and intensity are quantified by applying two kinds of definitions in Europe and North America (Meehl and Tebaldi 2004). Most of these studies concentrated on the heatwaves of individual sites, considering only the temperatures and durations. However, heatwave events usually swept across a large area in reality. It’s therefore of great essence to look into the spatial extents of the heatwave events, and the spatial extension should also be taken into account when defining a heatwave. An objective identification technique for regional extreme events (OITREE, Ren et al. 2012) has been introduced and applied for identifying regional heatwave events in China (Ding and Qian 2011; Wang et al. 2014). Stéfanon et al. (2012) gave a definition based on the 95th centile of the local temperatures for the regional heat waves over Europe and the Mediterranean region.

Recently, abnormal temperatures and record-breaking heatwaves have been observed in China (Gong et al. 2004; You et al. 2011). Wei and Chen (2011) revealed an abrupt increase of high temperature extremes across China since the mid-1990s. The temporal-spatial variations, controlling mechanisms and future changes of the heatwaves in China are investigated (Shi et al. 2011; Xia et al. 2013; Wang et al. 2016), but most of them focus on the heatwaves of individual sites. In this study, we utilize both absolute and relative thresholds for the DMTs data of 587 stations in China, and then define the absolute and relative regional heatwaves (RHWs-A and RHWs-R) by taking the spatial extent of heatwave events into account. Further, the variability and trends of frequency, duration and intensity of RHWs-A and RHWs-R in past 55 years are analyzed. RHWs-A and RHWs-R are classified into several patterns by cluster analysis (Mo and Ghil 1988; Cheng and Wallace 1993) to obtain the typical distributions of heatwaves in China. In addition, the physical drivers for different heatwaves are examined. It’s widely accepted that persistent highs are fundamental ingredient for heatwaves to sustain (Cassou et al. 2005; Pezza et al. 2012; Perkins 2015). Typically, the persistent anti-cyclonic systems accompanied with high temperatures are coupled with the land surface processes (Perkins 2015). Alfaro et al. (2006) showed that the predictability of daily maximum temperatures is mainly associated with previous (within 1–3 months) soil moisture. Teuling et al. (2010) discussed the contrasting response of forest and grassland energy exchange to heatwaves in Europe, and found that surface heating was twice as high over forest than over grassland, partially explaining the reason for extreme temperatures in August 2003. Therefore, in this study, both the dominant large-scale circulation and land surface hydrological condition behind different heatwave patterns are investigated.

The manuscript is organized as follows: In Sect. 2, we introduce the datasets, the definitions for RHWs-A and RHWs-R and the cluster analysis method. Section 3 gives the preliminary statistical analyses. In Sect. 4, the clustering classification results are presented. The atmospheric circulations and soil moisture patterns associated with different heatwave patterns are investigated in Sect. 5. The conclusions are given in the last Section.

2 Data, heatwave definitions and cluster analysis

2.1 Data

The DMTs of 756 surface observation stations are used to define heatwaves over the period of warm season (May–September) from 1959 to 2013 in China. The datasets provided by the National Meteorological Information Center of the China Meteorological Administration (CMA) have been quality-controlled and homogenized (Li et al. 2004) and widely used in related studies (Ding et al. 2010; Ding and Qian 2011; Wang et al. 2014). Considering the data consistency, stations with more than 20% missing data are eliminated and finally 587 stations remain for subsequent analysis. The distribution of the 587 stations is shown in Fig. 1 (black dots).

Fig. 1
figure 1

Distributions of the 587 observation stations over China (black dots), and 1° × 1° grid boxes (black lines)

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For the large-scale circulation data, the geopotential height is derived from the new Japanese 55-year Reanalysis (JRA-55) at 1.25° × 1.25° resolution (Ebita et al. 2011), provided by Japan Meteorological Agency (JMA). While due to the limitation of long-term soil moisture dataset, the daily surface soil moisture data (0–10 cm below ground layer) is the Gaussian grid dataset from NCEP/DOE AMIP-II reanalysis (R-2, Kanamitsu et al. 2002) and available for every 6 h from 1979 to 2013.

2.2 Heatwave definitions

A regional heatwave event is identified when a hot region last for several consecutive days. And a hot region consists of several hot stations of which the temperatures exceed a given threshold. Comparably a regional heatwave put more emphasis on the spatial extensions. In this study, both absolute and relative thresholds for the DMTs are applied to generate the RHWs-A and RHWs-R respectively. The parameters used for the definitions of RHWs-A and RHWs-R are listed in Table 1 (Stéfanon et al. 2012; Ren et al. 2012; Wang et al. 2014) and described as follows:

Table 1 Details for the two kinds of regional heat waves (RHWs-A and RHWs-R)
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  1. 1.

    Temperature threshold (Td): A hot station is identified when the DMT exceeds the given temperature threshold. For RHWs-A, the fixed value of 35 °C is set as the threshold for each station (Liu et al. 2008). For RHWs-R, the threshold for each calendar at each station is computed as the 90th percentile of a centered 15-day-long time window of DMTs (1959–2013) (Fischer and Schär 2010).

  2. 2.

    Spatial extension: assuming there are totally N neighboring stations around a given hot station i, and the distance between two neighboring stations must be within a fixed distance L. Obviously we can find n hot stations among the N neighboring stations, and the hot station i can be retained as a heatwave station when the ratio of (hot and surrounding) stations.

    $$\frac{n}{N} \geqslant {\alpha},$$

    α is a given threshold. Such a treatment can eliminate the isolated hot stations (Stéfanon et al. 2012). A heatwave region is generated if it contains at least m adjoining heatwave stations. In this study we take L being 250 km, and m being 20 (Wang et al. 2014). Ren et al. (2012) pointed that α should stay between 0.3 and 0.5. We conducted several tests on the effect of different α values, and found out that \({\varvec{\upalpha}}\) than 0.5 leads to sharply reduced heatwaves in Northwestern China with its sparse stations. And we decide that α of 0.4 is proper in our study.

  3. 3.

    Temporal extension: if the heatwave regions have more than 30% overlapping heatwave stations for two consecutive days, they are considered as one single event (Wang et al. 2014). A heat wave event usually last for several consecutive days with no time gap allowed. In this sense, at least three consecutive days are required for the RHWs-A (proposed by the CMA) and four consecutive days are required for the RHWs-R (Stéfanon et al. 2012).

A regional heatwaves can be characterized by its duration (D), extreme high temperature (Im), accumulated high temperature intensity (Is), maximum impacted area (Am), accumulated impacted area (As) and an integrated index Z (Wang et al. 2014). For a specific regional heatwave event i, the above parameters are calculated as follows:

$${I_m}=\mathop {\max }\limits_{k=1,{D_i}} \mathop {(\max ({T_{kn}}))}\limits_{n=1,{J_k}}$$
(1)
$${I_s}=\mathop \sum \limits_{k=1}^{{D_i}} \mathop \sum \limits_{n=1}^{{J_k}} ({T_{kn}} - {T_{kn}}|c)$$
(2)
$${A_m}=\mathop {\max }\limits_{k=1,{D_i}} (Area({S_k}))$$
(3)
$${A_s}=\mathop \sum \limits_{k=1}^{{D_i}} (Area({S_k}))$$
(4)
$${Z}={{e}_{1}}{{I}_{s}}^\% +{{e}_{2}}{{I}_{m}}^\% +{{e}_{3}}{{A}_{s}}^\% +{{e}_{4}}{{A}_{m}}^\% +{{e}_{5}}{{D}^\% }$$
(5)

where Di is the duration of the regional heatwave i; Tkn is the DMT of station n and Jk is the number of heatwave stations in day k; Im means the max DMT during the heat wave process; Tkn|c is the temperature criteria for the heatwave station n in the day k, and the (Tkn − Tkn|c) is the daily intensity for the heatwave station n in the day k. Is means the sum of the daily intensity of all heatwave stations. Sk represents the distributions of all heatwave stations in the day k and Area(Sk) represents the area of all the heatwave stations. To calculate the area, the 587 observation stations are divided into 1° × 1° in latitude and longitude grid boxes (see in the Fig. 1) (Peng et al. 2011). And Area (Sk) is computed as the total area of the boxes, and one box should contain at least one heatwave station.

In addition to the above single indices, an integrated index Z is computed as a function of Im, Is, Am, As and D, so as to represent the integrated characteristic of the regional heatwave. For each heat wave event, Z is computed in following steps:

  1. 1.

    Every index is first normalized using data of 1971–2000 as the baselines, and the normalized indices are represented by Is %, Im %, As %, Am %, and D%.

  2. 2.

    Using the normalized time series of a certain index i (i = 1 to 5), we can get a ratio (R i ) between the sum of top 10th percentiles to the sum of whole time series. We then have R i for five indices of Is %, Im %, As %, Am %, and D%.

  3. 3.

    Coefficient e i is then calculated by dividing R i by the sum of all five ratios (Wang et al. 2014).

2.3 Cluster analysis

The cluster analysis method has been classically used in atmospheric sciences as a way to characterize mid-latitude weather (Mo and Ghil 1988; Cheng and Wallace 1993), including the extreme events. Peng et al. (2011) classified five types of extensive and persistent extreme cold events in China using the cluster analysis. Stéfanon et al. (2012) classified heat waves in Mediterranean into six clusters and indicated that different classes are associated to different physical mechanisms. In order to characterize the existence of typical patterns of heatwaves in China, we conduct the cluster analysis to RHWs-A and RHWs-R.

We firstly produce the event maps. During the heatwave process, an event map can be calculated by averaging the daily intensity of each station (Stéfanon et al. 2012). Distance d between map p and map q is calculated as:

$$d(p,q)=1 - r(p,q)$$
(6)
$$r(p,q)=\frac{{\mathop \sum \nolimits_{i=1}^N {p_i}{q_i}}}{{{{\left( {\mathop \sum \nolimits_{i=1}^N p_i^2} \right)}^{\frac{1}{2}}}{{\left( {\mathop \sum \nolimits_{i=1}^N q_i^2} \right)}^{\frac{1}{2}}}}}$$
(7)

where pi is the average of daily intensity of station i from the map p, and similarly, qi is the average of daily intensity of station j from map q. N is the number of the total stations, namely 587 in this study. A criterion d0 is used to decide the number of clusters, that is, if the distance between maps p and q is smaller than d0, we classify maps p and q into one same cluster. The distance between two clusters is computed as the average of distances between maps of two different clusters. Intra-cluster distance of a cluster is decided as mean distance between maps of the same cluster. The relationships between different clusters can be represented by the form of a “family tree”, as shown in Fig. 7c, d.

The obtained clusters for an appropriate classification should be reproducible, and we then validate the reproducibility according to Cheng and Wallace (1993). The dataset consisting of total event maps was divided into halves 10,000 times by randomly drawing half maps from the original dataset, and subjecting them to cluster analysis above. For each of the preliminary resulting sets of n clusters for the entire dataset, we computed the n*20 correlation matrix R. Each element rij of R is the pattern correlations between one of the n clusters of the entire dataset (denoted by the i subscript) and one of the first 20 clusters of the half subset (denoted by the j subscript). Elements belonging to the ith column of R are the pattern correlations between the ith cluster of the entire dataset and the first 20 clusters of the subset. The degree to which the ith cluster can be reproduced in the subset of data is revealed by selecting the largest pattern correlation among the elements in the ith column. After dividing the dataset into halves 10,000 times, we will have 10,000 best selected pattern correlations for each of the n clusters, and the 10,000 pattern correlations are then averaged as the reproducibility parameter for each of the n clusters. We consider that a cluster is reproducible when reproducibility is above 0.9. Ultimately, only reproducible clusters retain.

3 Results

3.1 Identification of the typical regional heatwave events

There are totally 298 RHWs-A and 374 RHWs-R identified from 1959 to 2013 in China. The temporal correlation of the annual frequency of RHWs-A and RHWs-R is 0.48 and significant at 95% confidence level, which indicates the consistency of interannual variations between the two definitions of heatwaves.

According to the formula (5), it is obvious that the heatwaves of higher intensity, larger impacted area and longer duration are of higher Z-values. Based on the integrated index Z (presented in Fig. 4a), the two top extreme regional heatwave events with the greatest Z-value for the RHWs-A and RHWs-R during the past 55 years are selected to examine the rationality of the two definitions. The most extreme RHW-A lasted from July 2nd to August 11th in 2003, which occupied in most of the southeastern China, with the maximum Z-value up to 14.6. The most extreme RHW-R occurred in the middle and lower reaches of Yangtze River in 2013 lasting from 5th to 18th August, with the maximum Z-value up to 6.4. Table 2 lists the information about the two most severe RHW-A and RHW-R events, including the onset and offset dates, Im, Is, Am, D, the integrated index Z-value and the location.

Table 2 Information about the most severe RHW-A and RHW-R
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Figure 2b presents the evolution of the DMTs of the heatwave stations during the most severe RHW-A (2nd July–11th August, 2003). Due to its long duration of 41 days, the time sequence of 3-day averaged DMTs is constructed and shown. For day k in the heat wave process, there is a daily accumulated intensity Id, computed as (the involved values are same as those introduced in the Sect. 2.2):

Fig. 2
figure 2

a Daily accumulated intensity (Id) and b distributions of DMTs for the most severe RHW-A from 2nd July to 11th August in 2003. The first date of each panel is attached on the bottom left

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$${I_d}=\mathop \sum \limits_{n=1}^{{J_k}} ({T_{kn}} - {T_{kn}}|c)~$$
(8)

Figure 2a shows the variations of Id during 2nd July to 11th August. It’s demonstrated that the heatwave event is dominant in the southeastern China with higher temperatures and larger impacted area from 29th July to 3th August (Fig. 2b), during which its Id reaches the maximum and weakens afterwards (Fig. 2a). The process of this particular heatwave agrees well with the observation in July and August 2003, which led to the hottest summer in record in Shanghai over the past 50 years (Tan et al. 2007).

The evolution of the Id and the DMTs of the most severe RHW-R process is shown in Fig. 3. It can be seen that the RHW-R process influences the middle and lower reaches of Yangtze River (Fig. 3b). During this heatwave episode, the daily variations of impacted area and intensity are evident. The Id reaches the peak on the 11th August (Fig. 3a), with the highest DMT of 42.7 °C. On the other hand, the observed 2013 heatwave in eastern China was recorded as an extremely hot event, which had broken the heat records in the past 141 years. It broke the temperature records in 19 provinces, causing more than 59 billion RMB losses in China (Xia et al. 2013; Sun et al. 2014).

Fig. 3
figure 3

The same as Fig. 2, but for the most severe RHW-R from 5th to 18th in 2013

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Compared with the observations, both absolute and relative thresholds can be applied in describing the spatial distribution and temporal evolution of regional heatwave events in the southern China. For the northwestern regions where are characteristic of intense solar radiation and dry environments, and the eastern China where the northwestern Pacific subtropical high (NWPSH) dominates the summer climate, the DMTs could easily reach 35 °C or even 38 °C therein. However, for the Tibetan Plateau region, the DMTs are normally less than 25 °C during May to September because of the high topography (Ding et al. 2010; You et al. 2011). This indicates the restriction of the absolute threshold of 35 °C, however, the 35 °C is chosen to correspond with the CMA heat warnings, which considers the threats to the human health (Tan et al. 2007). On the other hand, the relative threshold associated with a large percentile of the local weather observation is more physically reasonable to identify the “extreme temperature” events for a region than an absolute threshold such 35 °C.

3.2 Spatio-temporal pattern of regional heatwave climatology

Figure 4 shows the frequency of the integrated index (Z), duration (D), extreme high temperature (Im), accumulated high temperature intensity (Is) and maximum impacted area (Am) for both the RHWs-A and RHWs-R in the past 55 years. The distribution of integrated statistical index indicates higher frequency for small Z values (≤0) while there are only 11 RHWs-A and 3 RHWs-R events with Z values more than 6.0 (Fig. 4a), which means severe RHW events rarely occur. For the individual indices, frequency analysis shows that the duration of RHW is mainly 3–5 days for the RHWs-A and 4–6 days for the RHWs-R. Few RHWs-A and no RHWs-R events can last for more than 20 days (Fig. 4b). The frequency of Im for the RHWs-A reaches the peak value when Im is about 39 and 40 °C for the RHWs-R (Fig. 4c). The frequency distribution of Is is similar to that of the duration that most of the accumulated intensity of RHWs-A/RHWs-R are less than 300 °C, with few severe events exceeding 2100 °C (Fig. 4d). It’s shown that the Am for most of the RHWs-A and RHWs-R are limited less than 1.4 × 106 km2 (Fig. 4e). The results show that most RHWs-A/RHWs-R events are of short lasting, moderate intensity with limited impacted areas, and only few heatwaves are catastrophic.

Fig. 4
figure 4

The frequency distributions of a the integrated index Z, b D, c Im, d Is and e Am for both the RHWs-A and RHWs-R

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The long term variations and trends of annual frequency for RHWs-A and RHWs-R during 1959–2013 are shown in Fig. 5. The frequency of RHWs-A/RHWs-R displays clear interannual and interdecadal variations. For RHWs-A, its frequency depicts a distinct decreased trend before the mid-1980s and increased thereafter with an overall increasing trend of 0.27 times per decade. For the frequency of RHWs-R, it’s also apparently more frequent since 1980s with an average increase of 1.09 times per decade during the past 55 years (Fig. 5b). And the trend is significant at 95% confidence level using a two-tailed Student’s t test. These results are consistent with a signal of warm climate shift in China since the early 1990s (Wei and Chen 2011; Qi and Wang 2012), indicating that both the RHWs-A and the RHWs-R are able to reflect the climate change in the early 1990s, and it supports the consistency of the interannual variations between the two heatwave definitions. Besides, the averaged Z, Is, and D all display similar interannual and interdecadal variations to that of the frequency but insignificant trends.

Fig. 5
figure 5

Variations and trends of the frequency for a RHWs-A and b RHWs-R during 1959 to 2013 in China. The black line represents the 11-values filtered line and the black asterisk denotes the trends above the 95% significance level

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Figure 6 shows the spatial distributions of 55-year averaged frequencies of RHWs-A and RHWs-R in China. It’s noticed that both RHWs-A and RHWs-R are most frequent at the middle valley of the Yangtze River. As shown in Fig. 6a, the averaged frequency from RHW-A is more than 1.0 time in most regions east to 105°E, and the high frequency larger than 2.0 times appears over the southern part of Yellow River. A relative weaker center of RHWs-A frequency appears in the Xinjiang province (the northwest of China), with the center magnitude about 0.5–1.0 times per year. For the RHWs-R events, the averaged frequency is more than 1 times per year over most regions in China, and the high frequency center locates at the middle reaches of Yangtze with the magnitude above 2 times per year. Comparably RHW-R covers more regions, especially in the mid-to-high latitude area of China. As discussed in Sect. 3.1, the spatial differences between RHWs-A and RHWs-R are caused by different climatology in different regions.

Fig. 6
figure 6

Spatial distributions of the averaged frequency for a RHWs-A and b RHWs-R during 1959–2013

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4 Typical heatwave patterns

In this section, we conduct the analysis cluster to the RHWs-A and RHWs-R to characterize the typical patterns of heatwaves in China. To ensure the dissimilarity between different clusters and the similarity among one cluster, the inter-cluster distance (De) should be far enough and the intra-cluster distance (Da) should be close enough. An optimal cluster number requires a large minimum inter-cluster distance (De_min) and a small maximum intra-cluster distance (Da_max), which means a large ratio between the two distances. Therefore, we can preliminarily have the total number of clusters when \(~~\frac{{{D_{e\_min}}}}{{{D_{a\_max}}}}{~}\) reaches the greatest before taking a reproducibility test. For classifications of RHWs-A and RHWs-R, the ratios of \({~}\frac{{{D_{e\_min}}~}}{{{D_{a\_max}}}}~~\) are displayed as the function of the cluster number in Fig. 7a, b. The segments of the “family trees” for RHWs-A and RHWs-B are shown in Fig. 7c, d. Each branch represents a distinct cluster, with the upper value being the cluster size and represented by the number of heatwave maps included in this cluster, and the below value (in the bracket) corresponding to the reproducibility. It can be seen that the ratios of Demin/Damax for RHWs-A as well as RHWs-R reach the greatest values when the numbers of clusters are four and nine. The clusters of reproducibility larger than 0.9 are marked blue in Fig. 7c, d. In the final, three clusters for RHWs-A and seven clusters for RHWs-R are obtained. Their spatial patterns are shown in Figs. 8 and 9.

Fig. 7
figure 7

The ratio of Demin/Damax as a function of the number of clusters for a RHWs-A and b RHWs-R; and a segment of “family tree” for several clustering results for c RHWs-A and d RHWs-R. Each branch in c and d means a distinct cluster, and the upper number represents the number of events in the cluster and the lower number in the bracket is the reproducibility. The reproducible clusters are marked blue

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Fig. 8
figure 8

Spatial patterns of the three clusters of RHWs-A, represented by the averaged daily intensity of all events included in each cluster (units: °C). The number of events in each cluster is listed on the left top of each panel figure (a–c)

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Fig. 9
figure 9

The same as Fig. 8, but for the seven clusters of RHWs-R

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Figure 8 shows the spatial patterns of the three clusters for RHWs-A. For each cluster, its pattern is represented by averaging the entire event maps included in the cluster, with the cluster’s size attached on the left top of the figure. The first cluster is mainly located in the southeast of China, and it contains 224 members (Fig. 8a). The second cluster lies in the middle and lower reaches of Yangtze River with 35 events (Fig. 8b). The third cluster is centered mostly over the northwest China, including 35 events (Fig. 8c). The first cluster is of the greatest size among the three clusters, and accounts for almost 75% of total RHWs-A. It is consistent with the distributions of heatwave frequency that most of the RHWs-A occur over the southeastern China. The third cluster shows the highest averaged daily intensity, followed by the second cluster, and the first one lowest, exhibiting a southward gradient of intensity. The observed fact displays the similar spatial character that the most severe warming takes place in North China (You et al. 2011; Xu et al. 2011).

For RHWs-R, the first cluster locates in the Inner Mongolia, and it groups 50 heatwaves. The second cluster is centered in Tibet Plateau region with 39 events. The third to seventh clusters of RHWs-R located in the middle east of China, southeastern China, a small region of south China, northwestern China and northeastern respectively. The locations of the seven clusters disperse all over the whole China. Similar to the RHWs-A, the averaged daily intensities of northern clusters are higher than that of southern clusters for the RHWs-R. Comparably, the seven clusters of RHWs-R are more uniformly distributed in both space and in size than those of RHWs-A, consistent with the heatwave frequency distributions that RHWs-R are more evenly distributed in China (Fig. 6).

In addition to the reproducibility, the stability of various clusters is another important issue that needs to be addressed. A cluster is considered as stable when it shows little change in size during the consecutive clustering process. As demonstrated in Fig. 7c, the last branch with 4 members and low reproducibility keeps the same size during four clustering steps, while the first cluster is portioned into three sub-clusters at the third step of clustering in the figure (Fig. 7c). Similarly, both the size and reproducibility remain the same for the sixth and seventh clusters of RHWs-R. It therefore can be concluded that some clusters are more stable than others clusters. As for the spatial patterns, the two more stable branches of RHWs-A are located in the northwestern China (Fig. 8c) and northeast region of China (not shown in the figure), and the less stable branches dominate the southeast and lower reaches of Yellow River in China (Fig. 8a, b). The difference between stability of different clusters is probably attributable to different geographical location. Heatwaves in the northwest and northeast part of China are restricted in the limited area, which leads to small spatial distance between them while the heatwaves in southern China spread in a wider region. Therefore it’s easier for heatwaves in the northwest and northeast China to be squeezed into one cluster.

5 Relationships between the heatwave clusters and the upper-level circulations and the soil moisture

5.1 Large scale circulation and soil moisture backgrounds for the typical heatwave patterns

Using cluster analysis, several typical clusters of RHWs-A and RHWs-R are obtained (Figs. 8, 9). To further understand the dominant of the large-scale circulations and local soil moistures for different clusters, the averages and anomalies of 500 hPa geopotential height (referred to H500 in the paper) and the soil moisture anomalies for each cluster are calculated. The averages and anomalies of H500 for three RHWs-A clusters and seven RHWs-R clusters are shown in Figs. 10 and 11. The H500 anomalies are given by removing the average of H500 at the corresponding months during the heatwave events. The black dots show the grid points where the H500 anomalies are statistically significant at 95% confidence level. It’s evident that significant positive anomalous H500 is either covering or adjoining the regions of each cluster of the RHWs-A (Fig. 10). In addition, different clusters are associated with different anticyclone anomalies. The first and third clusters are under the influence of the Northwest Pacific Subtropical High (NWPSH) (Fig. 10a, c). NWSPH plays an important role in summer climate of eastern Asia (Lin et al. 2009; Zhao et al. 2009), as it benefits the air subsidence, reinforces the hot and dry conditions at the surface and thus intensifies heatwaves. The second cluster of RHWs-A is related to the mid-latitude highs. It can be seen that this cluster locates in front of a trough and behind a ridge, favoring the transferring of the hot and dry air from south China to heatwave regions (Fig. 10b). Such mid-latitude high usually occurs over mid-latitude regions and lasts for several days (Pezza et al. 2012), and is responsible for numerous extreme heatwaves over Russian, Europe and North America (Perkins 2015). Similarly, seven clusters of RHWs-R are all associated with the significant positive anomalies of H500 (Fig. 11). The fourth and fifth clusters are susceptible to the NWPSH, and the other clusters are related to the mid-latitude highs.

Fig. 10
figure 10

Composites of H500 (units: m; contour) and H500 anomalies (shading) for the three clusters of RHWs-A (a–c). Statistically significant areas above 95% confidence level are stippled. The black bold line indicates the 5860 m contour

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Fig. 11
figure 11

The same as Fig. 10, but for the seven clusters of RHWs-R

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It has been reported that while persistent circulation anomalies are essential to trigger heatwaves, the coupling with land surface process might be even more important in the maintenance of the heatwaves (Zampieri et al. 2009; Perkins 2015). Soil moisture is the key factor that modulates the exchanges of energy, water between atmosphere and land surface, and plays in important role in affecting regional climate and extremes. The average of soil moisture anomalies of each cluster of RHWs-A and RHWs-R are calculated and shown in Figs. 12 and 13. Considering the short record of soil moisture observation (1979–2013), we focus on the RHWs-A/RHWs-R events since 1979.

Fig. 12
figure 12

The same as Fig. 10 but for the soil moisture anomalies (units: m3 m−3)

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Fig. 13
figure 13

The same as Fig. 11, but for the soil moisture anomalies (units: m3 m−3)

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We notice that significant soil moisture deficiency is present at each cluster location of both RHWs-A and RHWs-R (Figs. 12, 13). This is consistent with the feedback theory between soil moisture, circulation and temperature, which suggests that the lack of soil moisture leads to reduced latent cooling and thereby amplifies the surface temperature anomalies (Fischer et al. 2007; Alexander 2011).

It is concluded that both the RHWs-A and RHWs-R are associated with the anomalous anticyclones accompanied with reduced soil moisture. In particular, RHWs-A and RHWs-R in south part of China are usually influenced by NWPSH, and those in north part of China are usually associated with the classical mid-latitude highs.

5.2 The severe heatwave events in 2003 and 2013

In the following analysis, we choose the most severe RHW-A in 2003 and the most severe RHW-R in 2013 to verify the connections between the heatwaves and the large-scale atmospheric circulations as well as soil moisture anomalies.

The average and anomalies of H500, the soil moisture anomalies and the average of daily intensity during the two severe RHWs are shown in Fig. 14. It is apparent that the 2003 RHW-A is dominated by positive H500 anomalies. And the central region where the mean daily intensity is higher than 2 °C is encircled by the 5880 m contour line with H500 anomaly more than 30 m (Fig. 14a). Meanwhile obvious deficiency of soil moisture exists over the high intensity regions (Fig. 14b). For the 2013 RHW-R, the heatwave is centered at middle and lower reaches of Yangtze River Basin and Yellow River Basin, covered by the positive H500 anomalies up to 30 m (Fig. 14c). Besides, there is obvious soil moisture deficiency over heatwave region as well (Fig. 14d). These results support the above analysis that the upper-level anticyclone and the soil moisture generally co-occur to trigger a heatwave. Additionally, both the two southern heatwave processes are under the control of NWPSH and this severe RHW-A is involved in the first cluster of the RHWs-A and this RHW-R is in the fourth cluster of the RHWs-R.

Fig. 14
figure 14

Composites of daily heat wave intensity (units: °C; black circles), covered by a the H500 (units: m; contour) and H500 anomalies (shading), and b the soil moisture anomalies (units: m3 m−3; shading) for the 2003 RHW-A from 2nd July to 11th August. c, d are same as a and b but for the 2013 RHW-R from 5th August to 18th August. The black bold contour equals to 5880 m

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6 Conclusions

Considering the importance of the spatial extension for an accurate and complete view of a heatwave process, the RHWs-A and RHWs-R are both investigated based on the DMTs of 587 observation stations during the warm season (May–September) from 1959 to 2013 in China.

There are total 298 RHWs-A and 374 RHWs-R events, and few of them are severe and with large impacted area, long duration and high extreme temperatures. The most severe RHW-A affects the southeastern China in July 2003, and lasts for 41 days. The most severe RHW-R occurs in August 2013, influencing the middle and lower reaches of Yangtze River and lasts for 14 days. The two analyzed extreme heatwave events are consistent with the observation in 2003 and 2013, which indicates that both the definitions of RHWs-A and RHWs-R are applicable in the southern China. Because of the various climate regimes in China, the relative threshold that takes the effect of local climatology into account is be more reasonable to identify the regional extreme temperature event. Consequently, the RHWs-A mainly occur at southeastern of China by more than 2.0 times/year and the northwestern area by 0.5–1.0 times/year, while it rarely happens at other regions in China. RHWs-R are more than 1 times per year over most regions of China, and more often occur at the middle reaches of Yangtze with frequency above 2 times per year. Both the RHWs-A and RHWs-R are becoming more frequent since the mid-1980s, which is consistent with a signal of warm climate shift in China since early 1990s (Qi and Wang 2012).

To obtain the typical distributions of heatwaves in China, the cluster analysis is conducted, and three and seven typical clusters of RHWs-A and RHWs-R are identified. The three clusters of RHWs-A cover the southeastern, northwestern China and lower reaches of Yellow River, and most of RHWs-A are grouped in the southeastern cluster. Meanwhile the seven clusters of RHWs-R are uniformly distributed in China, covering the whole China regions. For both the RHWs-A and RHWs-R, heatwave clusters in the northwestern and southeastern China are more stable than other clusters. In addition, the northern clusters show high intensity than that of southern clusters.

The influences of the large scale circulations and soil moisture conditions on the reginal heatwaves are also investigated. For each cluster of RHWs-A/RHWs-R, there is an anomalous high-pressure system centered or adjoining over its domain. Moreover, each cluster is associated with a unique type of anticyclone. For example, the first and third clusters of RHWs-A are under control of NWPSH, which causes air sinking and the surface warming (Gong et al. 2004; Ding et al. 2010). The second cluster of RHWs-A are related to the mid-latitude highs, which prevent the mixture of poleward cooler air with the local warmer air, and thus enhance the building-up of warmness in hot regions. For RHWs-R, the fourth and fifth clusters are controlled by NWPSH, and the other five clusters are related to the mid-latitude highs. Moreover, each cluster of RHWs-A and RHWs-R co-occurs with the large area of soil moisture deficiency. Previous studies revealed that reduced soil moisture leads to reduced latent heat into the atmosphere, inducing a positive feedback between atmospheric heating and further drying of the soil. The combined effects of dry soil moisture conditions and persistent high pressure system are capable to induce more hot summer days (Quesada et al. 2012; Rohini et al. 2016). Other factors such as the sea surface temperature anomalies (SSTAs) and the precipitation anomalies in preceding months could also impose significant influences on the variability of heatwaves (e.g. Arblaster and Alexander 2012; Vautard et al. 2007), which will be issued in our continuous work.