ABSTRACT

Based on the daily Japanese 55-year Reanalysis (JRA-55) dataset, this study reveals that southern Europe/western Asia (SEWA) and northern China are two large-scale regions that have exhibited consistent interdecadal variations in the frequency of persistent hot events (PHEs). Over the past 58 summers, the period approximately from 1973 to 1996 represents an inactive period for the occurrence of PHEs over the two regions, whereas the antecedent and subsequent periods are active periods. At the subseasonal time scale, the regional PHEs over SEWA are characterized by quasi-stationary wave train anomalies aloft from the northwest Atlantic to Europe, while the regional PHEs over northern China are characterized by quasi-stationary wave train anomalies over the Eurasian continent. The persistence of the quasi-stationary anomalies is associated with the Rossby wave propagation. Moreover, the energy extraction from the basic flow is also favorable for their persistence. Our study reveals that the above typical circulation anomalies for the PHEs over both SEWA and northern China are in phase with the background circulation changes during the two active periods. Thus, the interdecadal changes in background circulation can modulate the frequency of PHEs over the two regions simultaneously. Further analysis reveals that the background circulation changes are closely related to the interdecadal variation in the Silk Road pattern based on their similarities in both spatial pattern and temporal variation. The sea surface temperature over four particular regions seems to facilitate the phase shifts in the Silk Road pattern on the interdecadal time scale.

1. Introduction

Heatwaves contribute to human fatalities and cause widespread economic impacts. For example, a severe heatwave hit eastern Europe in July 2010, and preliminary estimates for Russia indicated that there were 55 000 fatalities, an annual crop loss of ~25%, more than 1 million hectares of burned areas, and a cost of approximately $15 billion (U.S. dollars; Barriopedro et al. 2011). In the summer of 2013, an exceptionally long-lasting heat event of 31 days occurred in eastern China, which resulted in dozens of fatalities (X. Sun et al. 2014). Anthropogenic factors are among the most important contributors to the occurrence of particularly extreme heatwaves in China (Zhou et al. 2014; Y. Sun et al. 2014), Europe (Stott et al. 2004), and the United States (Diffenbaugh and Scherer 2013).

During the last 100-yr period, one interesting phenomenon is that heatwaves have become more frequent, persistent, and intense (Schär et al. 2004; Della-Marta et al. 2007; Ding et al. 2010; Perkins et al. 2012; Wang et al. 2012), which may be associated with both global warming and the amplified variability of air temperature (Schär et al. 2004; Della-Marta et al. 2007). Y. Sun et al. (2014) noticed that the five hottest summers in eastern China have all occurred since 2000, with 2013 representing the hottest year (Sun 2014; Xia et al. 2016). Because heatwaves are more closely related to meteorological disasters and have more direct impacts on society than the average warming climate, people are concerned about how heatwaves will change in a continually warming climate in the future. Based on the outputs from numerical models, numerous studies have demonstrated that heatwaves may occur more frequently in the future (Meehl and Tebaldi 2004; Fischer and Schär 2010; Barriopedro et al. 2011; Wang et al. 2012; Y. Sun et al. 2014), especially in the second half of the twenty-first century. A recent study by Kang and Eltahir (2018) claimed that the North China Plain will suffer from deadly heatwaves at the end of the twenty-first century due to irrigation and climate change based on an ensemble of high-resolution regional climate model simulations.

Although numerous studies have focused on the long-term trend of heatwaves, few studies have discussed interdecadal changes in heatwaves over the Eurasian continent. Ding et al. (2010) focused their research on the changes in heatwaves over China and found that both Xinjiang and East China, which are the two regions with the highest occurrence of heatwaves in China, exhibit a clear interdecadal variation with a rapid increase after the middle 1990s. Xia et al. (2016) explicitly pointed out that in addition to the evident increasing trend, the multidecadal variation in the climate background played an important role in shaping the summer mega-heatwave in 2013 in China. The interdecadal variation over China could also be inferred from early studies on the long-term trend of heatwaves. Zhai and Pan (2003) stated that there is a decreasing trend in the frequency of hot days over China. The use of longer-term data series, however, has shown that positive trends have prevailed over most of China since the late twentieth century (Ding et al. 2010; Wei and Chen 2011; Wang et al. 2012). Such seemingly contradictory results imply that interdecadal variations may exist in heatwaves.

Branstator (2002) and Branstator and Teng (2017) stated that the jet stream can act as a waveguide for the formation of quasi-zonal teleconnection patterns, which are different from quasi-meridional teleconnection patterns (Wallace and Gutzler 1981) formed in the vicinity of a weak meridional gradient of the mean wind. In boreal summer, the waveguide-induced teleconnection patterns are referred to as the Silk Road pattern (SRP) (Lu et al. 2002; Enomoto et al. 2003; Ding and Wang 2005), which occurs along the subtropical jet over the Eurasian continent. Some studies have documented the evident interdecadal variation of the SRP (Chen and Huang 2012; Hong et al. 2017; Wang et al. 2017; Hong et al. 2018), with its phase shifting from positive to negative in the later 1960s and early 1970s and from negative to positive after the mid-1990s. The second shift might have contributed to the asymmetric warming rate over the Eurasian continent (Hong et al. 2017; Wang et al. 2017; Hong et al. 2018) and the rainfall reduction over northeastern Asia (Wang et al. 2017). Moreover, the interdecadal variation in the frequency of large-scale extreme hot days over the middle and lower reaches of the Yangtze River basin is modulated by the SRP (Li and Sun 2017). In addition, an interdecadal variation in the East Asian summer monsoon was documented with two transition points at the end of the 1970s and the early 1990s (Ding et al. 2008; Ding et al. 2009). Some studies (Xoplaki et al. 2003; Trigo et al. 2005; Fischer et al. 2007) mentioned that positive height anomalies are responsible for the formation of hot days by enhancing subsidence, solar heating, and warm advection. Therefore, the main topic of this study is whether consistent interdecadal variations occur in the heatwaves over different regions of Eurasia in accordance with interdecadal circulation changes.

This study will assess whether persistent hot events (PHEs) with a duration of at least 5 days have evident interdecadal variations over the Eurasian continent and discuss the role played by the underlying background circulation changes. Section 2 introduces the reanalysis datasets and methods for detecting PHEs. Section 3 demonstrates that PHEs exhibit a consistent decadal variation over southern Europe/western Asia and northern China. The typical features of circulation anomalies and the associated dynamic features for PHEs over the two regions are shown in section 4. Section 5 shows that the SRP might contribute to interdecadal variations of PHEs, and section 6 further discusses the relationship between the SRP and SST anomalies on the interdecadal time scale. The main conclusions of this study are given in the last section.

2. Data and detection method

a. Data

In this study, we mainly use daily data from the Japanese 55-Year Reanalysis (JRA-55) project conducted by the Japan Meteorological Agency from 1958 to 2015 (Kobayashi et al. 2015). This long-term daily dataset is available on a global longitude–latitude grid with intervals of 1.25°. The geopotential height, wind velocity, and air temperature are the meteorological variables used in this study, which are all measured on isobaric surfaces. The surface air temperature (SAT) at 2 m and surface pressure are also utilized. In section 6, we discuss the role played by the sea surface temperature on interdecadal time scales via the Atlantic multidecadal oscillation (AMO) index (http://climexp.knmi.nl/data/iamo_ersst.dat) and two sea surface temperature (SST) datasets, namely the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) dataset, which has a horizontal resolution of 1° (Rayner et al. 2003), and the monthly mean Extended Reconstructed Sea Surface Temperature (ERSST) dataset version 5, which has a resolution of 2° (Huang et al. 2017).

Since high-frequency eddies may cause large variations in SAT and a PHE may be separated into several episodes due to the high-frequency disturbance, all data are low-pass filtered by the Lanczos filtering procedure to remove the 8-day high-pass-filtered disturbances and isolate the slowly varying component; this is the same method used in our recent study on persistent cold events (Shi et al. 2019). The target season in this study is summer (from 1 June to 31 August). Because the Lanczos filtering procedure can cause data loss at the beginning and end of a data sequence, we extended the summer period from mid-May to mid-September. We also use NCEP–NCAR reanalysis data (Kalnay et al. 1996) to check the sensitivity of the final results of this study and find that qualitative changes have not occurred (not shown). Unless otherwise stated, all the daily fields in the following contexts mean the low-frequency daily fields.

b. Detection method

Many different meteorological variables have been used to define heatwaves or hot days in previous studies, such as the maximum day temperature (Della-Marta et al. 2007; Wei and Chen 2011; Li and Sun 2017), minimum night temperature (Meehl and Tebaldi 2004), daily mean temperature (Gong et al. 2004; Perkins et al. 2012), and humidity (Ding et al. 2010; Fischer and Schär 2010). For simplicity, the present study utilizes the low-frequency daily mean temperature to detect hot events with a duration of at least 5 days.

To sharpen the interdecadal variation signal, the least squares linear trend is estimated for seasonal mean SATs and then removed from the daily SAT at every grid point for the 58 summers. The Mann–Kendall nonparametric test is used to calculate the statistical significance of the monotonic trends. Figure 1 shows that a warming trend is evident over most areas of Eurasia and northern Africa except for central Asia and central eastern China. In fact, central Asia exhibited a significant cooling trend. The weak cooling trend in central eastern China (not significant) corresponds to a local decrease in the heatwave frequency (Zhai and Pan 2003; Ding et al. 2010), which might be associated with the local increasing trend in precipitation during recent decades (Zhu et al. 2011; Li et al. 2017a). For consistency, the long-term linear trends are also removed from other meteorological variables.

Fig. 1.

Linear trends of summertime (June–August) surface air temperature evaluated at every grid point for the period from 1958 to 2015. Units: °C yr−1. The stippling indicates a significant trend at the 0.05 significance level according to the Mann–Kendall nonparametric test.

Fig. 1.

Linear trends of summertime (June–August) surface air temperature evaluated at every grid point for the period from 1958 to 2015. Units: °C yr−1. The stippling indicates a significant trend at the 0.05 significance level according to the Mann–Kendall nonparametric test.

The method for detecting persistent cold events by Shi et al. (2019) is adopted in the present study to detect PHEs, and the following text is derived from there with minor modifications. First, the daily local anomaly of a given variable is defined as its departure from the local daily climatological mean annual cycle. The climatological mean annual cycle for a particular calendar date is defined as the 58-yr mean of the 31-day running mean centered at the corresponding date. The method of defining the local anomaly is the same as in Nakamura and Fukamachi (2004). Daily anomalous SATs are further normalized locally by the standard deviation (STD) of anomalous SATs over 31 days per year × 58 years = 1798 days, where the annual 31-day sequence is centered on that calendar day. Then, PHEs at every grid point are identified if 1) the normalized SAT anomalies are larger than +1.0 STD every day and 2) their durations are longer than 5 days. The peak day for a PHE is defined as the day with the strongest magnitude of the normalized SAT anomalies. Note that the 8-day low-pass filtering does not remove the PHEs that persist for at least 5 days. For a simple harmonic wave, its complete life cycle could be divided evenly into the positive-phase stage and the negative-phase stage. In fact, according to our definition, the 5-day duration of the PHEs (amplitude larger than +1.0 STD, rather than 0.0 STD, for every day) is only part of the positive half period of the simple harmonic wave. Thus, the 8-day low-pass filtering mainly removes the hot events with duration shorter than 4 days. The sensitivity of the results to other threshold values is discussed in the next section.

3. Frequency distribution

The grid-based PHE frequency anomalies over Eurasia at different latitudes are shown in Fig. 2, and these anomalies are obtained by subtracting the 58-yr mean value from the local grid-based PHE frequency. To extract the interdecadal variation, the 11-yr running average is applied in Fig. 2. The second row of Fig. 2 shows the results if the amplitude threshold is set to 1.0 STD. Overall, the grid-based PHEs exhibit evident interdecadal variations over Eurasia. Specifically, over both East Asia (approximately 30°–55°N, 90°–135°E) and southern Europe/western Asia (SEWA) (approximately 30°–55°N, 20°–45°E), the grid-based PHEs occurred frequently from the late 1950s through the early 1970s and became active again after the mid-1990s, with an inactive period between the two active periods. The frequency is higher during the latest active period than during the first active period. Thus, the two regions exhibit a consistent decadal variation in PHE frequency. For central Asia (approximately 45°N, 50°–90°E), the gridded PHEs also show an interdecadal variation but with an active period from approximately the mid-1970s to the mid-1990s and an inactive period after the mid-1990s, thus showing an out-of-phase relationship with its counterpart over East Asia or SEWA. This out-of-phase relationship might be associated with the SRP, which will be discussed in the following sections.

Fig. 2.

Eleven-year running average frequency anomalies of PHEs relative to the 58-yr mean average. Thick black lines indicate the approximate boundaries that separate the periods with relatively high frequencies and relatively low frequencies of PHEs. (from left to right) Frequency anomalies at different latitudes. (from top to bottom) The results based on different amplitude thresholds for detecting the PHEs.

Fig. 2.

Eleven-year running average frequency anomalies of PHEs relative to the 58-yr mean average. Thick black lines indicate the approximate boundaries that separate the periods with relatively high frequencies and relatively low frequencies of PHEs. (from left to right) Frequency anomalies at different latitudes. (from top to bottom) The results based on different amplitude thresholds for detecting the PHEs.

Different amplitude threshold values, such as 0.8 STD or 1.5 STD (the first and third rows in Fig. 2), or different day length thresholds, such as 3 days or 7 days (not shown), for the duration of PHEs did not change the above results essentially. Moreover, we also re-evaluate the results of Fig. 2 after replacing the number of PHEs with the number of hot days that construct the PHEs, and we find that the distribution patterns of the frequency anomalies are quite similar to that in Fig. 2 (not shown). Therefore, at least the frequency represented by the number of the PHEs is consistent with the frequency represented by the number of hot days used to construct the PHEs on interdecadal time scales.

According to the interdecadal variation in the PHE frequency over SEWA and East Asia shown in Fig. 2, the 58-yr period could be roughly divided into three periods: 1958–72, 1973–96, and 1997–2015. Overall, the two regions are featured by the same PHE frequency anomaly sign in each of these three periods. For convenience, these three periods are referred to as the active period, the inactive period, and the reactive period.

To further analyze the spatial distributions, the differences in the mean grid-based PHE frequencies between the two active periods and the inactive period are shown in Fig. 3. Compared with those in the inactive period, the grid-based PHEs during the two active periods show a consistent and significant increase over southern Europe, western Asia, and East Asia but a relatively weak decrease over central Asia and the southwestern Tibetan Plateau. Overall, the alternating signs for the PHE frequency anomalies over midlatitude Eurasia (30°–50°N) are reminiscent of the asymmetric warming over Eurasia (Hong et al. 2017; Wang et al. 2017; Hong et al. 2018). Because of the relatively large spatial scale and the consistent interdecadal increase during the two active periods, SEWA (31.25°–52.5°N, 20°–46.25°E) and northern China (31.25°–42.5°N, 92.5°–117.5°E) are chosen as the two key areas for further study. In fact, the final results do not present qualitative changes if the areas of the two regions are changed slightly.

Fig. 3.

(a) Difference in frequency for PHEs between the active and inactive periods. (b) As in (a), but between the reactive and inactive periods. The contour interval is 0.5. Stippling denotes significance at the 0.05 significance levels, based on a two-tailed Student’s t test. The solid and dashed black rectangles mark the key areas of 31.25°–52.5°N, 20°–46.25°E and 31.25°–42.5°N, 92.5°–117.5°E, respectively, with notable interdecadal variations.

Fig. 3.

(a) Difference in frequency for PHEs between the active and inactive periods. (b) As in (a), but between the reactive and inactive periods. The contour interval is 0.5. Stippling denotes significance at the 0.05 significance levels, based on a two-tailed Student’s t test. The solid and dashed black rectangles mark the key areas of 31.25°–52.5°N, 20°–46.25°E and 31.25°–42.5°N, 92.5°–117.5°E, respectively, with notable interdecadal variations.

The SAT anomalies are further area-averaged over SEWA and northern China individually, and each regional PHE over the two regions is detected accordingly. Table 1 shows the numbers and days of the regional PHE over the two regions. Statistically, 75 regional PHEs with 641 hot days or an average duration of 8.5 days over SEWA and 72 regional PHEs with 532 hot days or an average duration of 7.4 days over northern China are identified for 58 summers. Figure 4 shows the frequency variations of PHEs, which are represented by the numbers of the regional PHEs (Figs. 4a,b) and the numbers of hot days that construct the regional PHEs (Figs. 4c,d). Overall, the two frequencies bear considerable resemblance in their interdecadal variation. Specifically, the 11-yr running mean frequencies of regional PHEs over both SEWA and northern China exceed (fall below) the 58-yr average during the active and reactive (inactive) periods. Note that the frequency of the regional PHEs over SEWA exhibited a slightly longer inactive period and two shorter active periods than that over northern China, with the late 1960s and mid-1990s representing the transition points. Nevertheless, the general consistency of the interdecadal variations in the regional PHEs between the two regions implies that there might be a common underlying mechanism. In fact, the mean frequency of the grid-based PHEs averaged over the two individual regions is also calculated, and the results are similar to that in Figs. 4a and 4b (not shown). Section 5 will show that the SRP may simultaneously modulate the interdecadal variations over the two regions.

Table 1.

Numbers and days of PHEs over SEWA and northern China.

Numbers and days of PHEs over SEWA and northern China.
Numbers and days of PHEs over SEWA and northern China.
Fig. 4.

Frequency of regional PHEs based on the area-average SAT anomalies over (a),(c) SEWA and (b),(d) northern China represented by the rectangles in Fig. 3; shown are (a),(b) number of PHEs and (c),(d) total days of PHEs. The red line is the 11-yr running average, and the blue line is the 58-yr mean.

Fig. 4.

Frequency of regional PHEs based on the area-average SAT anomalies over (a),(c) SEWA and (b),(d) northern China represented by the rectangles in Fig. 3; shown are (a),(b) number of PHEs and (c),(d) total days of PHEs. The red line is the 11-yr running average, and the blue line is the 58-yr mean.

4. Typical features of circulation anomalies

Before showing the interdecadal changes in the background circulation, the composite circulation anomalies of the PHEs at the subseasonal time scale are shown in Fig. 5 (see also Fig. 7). To guarantee the independence of the PHEs from each other in the composite analysis, for every pair of PHEs that occurred in the same year over the same region, the weaker one is omitted if its peak date is not separated by at least 15 days from the others. After excluding those PHEs, 63 PHEs are observed over SEWA and 66 PHEs are observed over northern China, and they are used for the composite analysis. Hereafter, the peak day is used as the reference day and denoted as the day 0 composite for every event, while days −N and N refer to the composite N days before and after the peak day, respectively. Since the geopotential height anomalies generally exhibit a quasi-barotropic structure through the troposphere over midlatitude Eurasia (Hong et al. 2017; Wang et al. 2017), the figures only show the geopotential height anomalies at 300 hPa.

Fig. 5.

Composite evolution of 67 PHEs over SEWA: (left) geopotential height anomalies at 300 hPa and (right) SAT anomalies. (from top to bottom) Days −6, −3, 0, and 3. Contour intervals for geopotential height anomalies and SAT anomalies are 20 gpm and 1°C, respectively. Solid red and dashed blue lines indicate the positive and negative anomalies, respectively. Zero contours are omitted. Shading denotes the statistically significant region at the 0.05 significance level based on the two-tailed Student’s t test. The arrows (m2 s−2) in the right column are the wave activities formulated by Takaya and Nakamura (2001).

Fig. 5.

Composite evolution of 67 PHEs over SEWA: (left) geopotential height anomalies at 300 hPa and (right) SAT anomalies. (from top to bottom) Days −6, −3, 0, and 3. Contour intervals for geopotential height anomalies and SAT anomalies are 20 gpm and 1°C, respectively. Solid red and dashed blue lines indicate the positive and negative anomalies, respectively. Zero contours are omitted. Shading denotes the statistically significant region at the 0.05 significance level based on the two-tailed Student’s t test. The arrows (m2 s−2) in the right column are the wave activities formulated by Takaya and Nakamura (2001).

To explore the dynamic features of the typical circulation anomalies, the wave-activity flux (Takaya and Nakamura 2001) is utilized to represent the stationary Rossby wave propagation associated with regional PHEs. The flux is parallel to the local group velocity of a stationary Rossby wave train in the Wentzel–Kramers–Brillouin sense. In addition, the convergence of the flux corresponds to the accumulation of Rossby wave energy and enhancement of height anomalies, while the divergence contributes to opposite trends.

Moreover, following the work of Kosaka et al. (2009), the local barotropic and baroclinic energy conversions (denoted as CK and CP, respectively) between the typical low-frequency circulation anomalies for the PHEs and the climatological-mean flow are also evaluated briefly. Positive values of CK and CP indicate that kinetic energy (KE) and available potential energy (APE) are extracted from the mean state to the anomalies, respectively. The formulations of CK and CP are as follows:

 
CK=υ2u22(u¯xυ¯y)uυ(υ¯x+u¯y),
(1)
 
CP=fS(υTu¯puTυ¯p)
(2)

In (1) and (2), the stability parameter S=[(RT¯/Cpp)(T¯/p)] and other notations are standard, with prime and overbar indicating the composite anomalies and the corresponding mean state, respectively. Moreover, the efficiencies of the energy conversions are also evaluated as the days τCK = 〈KE〉/〈CK〉, τCP = 〈APE〉/〈CP〉, and τCP+CK = 〈KE + APE〉/〈CK + CP〉. The angle brackets denote the spatial integration over the troposphere (from surface to 100 hPa) of the entire Northern Hemisphere. The spatial integrations exclude the grid points underground, which are eliminated if the values of the pressure levels on which the grid points are distributed are larger than those of the surface pressure. A smaller absolute value of τ corresponds to a higher efficiency of the energy conversion.

a. SEWA

At day −9 (not shown), significant positive height anomalies are formed around Greenland. At day −6 (Fig. 5a), significant negative anomalies appear over the northeastern United States, and the wave-activity fluxes point eastward and converge to the south of Greenland, which is favorable for the southward extension of positive height anomalies over Greenland. On the other hand, Rossby wave packets emanate from the eastern portion of the positive height anomalies and propagate eastward, where they contribute to the formation of downstream negative height anomalies over the northeast Atlantic. At day −3 (Fig. 5b), due to energy dispersion, the center of the positive height anomalies over Greenland moves southward to the northern Atlantic while the upstream negative anomalies are weakened. Meanwhile, consistent with the evident convergence of the flux over the northern Atlantic and southern Europe, the downstream negative height anomalies are enhanced and centered at the United Kingdom and positive height anomalies form over southern Europe. Corresponding to the positive height anomalies centered over southern Europe at day −3, positive SAT anomalies prevail over the region from southern Europe to western Russia with a central amplitude of +2°C (Fig. 5f), indicating the start of the regional PHE.

At day 0 (Fig. 5c), the positive height anomalies over the northern Atlantic are weakened, with the central amplitude reducing to approximately 20 gpm, while the downstream circulation anomalies are gradually amplified and expanded, which is consistent with the arrival of the Rossby wave packets in central Asia. The enhanced and expanded positive height anomalies around SEWA at day 0 are consistent with the enhanced positive SAT anomalies with a central amplitude of +4°C (Fig. 5g).

After day 0, the upstream significant height anomalies over both the northeast Atlantic and western Europe gradually weaken and disappear at day 3 (Fig. 5d). Positive height anomalies over southern Europe still exist but have a reduced central amplitude of approximately 80 gpm. Accordingly, the positive SAT anomalies are still anchored over SEWA with a central amplitude of +3°C. After day 3 (not shown), the positive height anomalies around SEWA are weakened and move eastward. Meanwhile, the SAT anomalies show a similar movement, indicating the decaying stage of the PHEs over SEWA.

From the perspective of energy conversion, the baroclinic energy extraction from the basic flows also contributes to the maintenance of the typical anomaly circulation of the regional PHEs (Fig. 6). Figure 6 shows both the CK and CP vertically integrated from surface to 100 hPa and indicates that the regional PHEs over SEWA not only extract energy from the climatological mean state (positive value, red contours) over some regions but also release the energy into the climatological mean state (negative value, blue contours) over other regions. Integrating the CK and CP over the entire Northern Hemisphere reveals that the CP (right column of Fig. 6) is quite efficient in extracting baroclinic energy from the basic flow. It can replenish the APE of the regional PHEs within 6 days (τCP, indicated in the top-right corner of the panels) before the peak day. However, the CK generally takes more than one month to replenish the KE before the peak day (left column of Fig. 6), which is consistent with the cancellation to a large extent between the positive and negative CK mainly over the Eurasian continent. Considering that the average duration of the PHEs over SEWA is approximately 9 days, the mean total conversion efficiency τCP+CK from day −4 to day 4 is evaluated, and its value is 11.4 days, which is comparable to the mean duration of the PHEs. Thus, the energy extraction from the basic flow, which is dominated by the baroclinic energy extraction, plays a dominant role in maintaining the typical anomaly circulation.

Fig. 6.

(left) Barotropic energy conversion (CK) and (right) baroclinic energy conversion (CP), based on the composite 67 PHEs over SEWA. Both CK and CP are integrated from the surface to the 100-hPa level. Contours are drawn at every ±0.3, ±0.9, ±1.5, … W m−2 for both CK and CP. The value of the conversion efficiency τ is indicated in the top-right corner of the corresponding panel.

Fig. 6.

(left) Barotropic energy conversion (CK) and (right) baroclinic energy conversion (CP), based on the composite 67 PHEs over SEWA. Both CK and CP are integrated from the surface to the 100-hPa level. Contours are drawn at every ±0.3, ±0.9, ±1.5, … W m−2 for both CK and CP. The value of the conversion efficiency τ is indicated in the top-right corner of the corresponding panel.

Therefore, the evolution process of the regional PHEs over SEWA is characterized by quasi-stationary wave train anomalies originating from the northeast Atlantic to SEWA with significant positive height anomalies anchoring over SEWA that are responsible for the local regional PHEs. In addition, the typical circulation anomalies can efficiently extract APE from the basic flows to maintain themselves.

b. Northern China

The regional PHEs over northern China are also characterized by upstream circulation anomalies. At day −6 (Fig. 7a), a dipole pattern for the geopotential height anomalies anchors over the eastern Atlantic. In fact, a dipole pattern emerges from approximately day −9 (not shown), and its northern lobe continually emanates Rossby wave packets downstream, which is favorable for the formation of positive anomalies over Europe at day −6 (Fig. 7a). This situation is similar to that for the regional PHEs over SEWA at day −3 (Fig. 5b) in which the formation of the anticyclonic anomalies centered in Europe is also associated with the eastward propagation of Rossby wave packets. At day −3, in accordance with the Rossby wave energy dispersion, the negative anomalies over the northeast Atlantic disappear and wave train circulation anomalies occur from Europe to eastern Lake Balkhash, indicating the arrival of wave packets in East Asia. Meanwhile, significant SAT anomalies with alternating signs occur over the Eurasian continent, with significant positive SAT anomalies prevailing over northern China.

Fig. 7.

As in Fig. 5, but for the composite evolution of 65 PHEs over northern China.

Fig. 7.

As in Fig. 5, but for the composite evolution of 65 PHEs over northern China.

At day 0, the wave train height anomalies over Eurasia are enhanced except for the positive height anomalies over Europe that shrink to the north, which is consistent with the eastward propagation of Rossby wave packets. Similar to the PHEs over SEWA, the flux generally converges over the western portion of the circulation anomalies but diverges over the eastern portion, which might slow down the eastward movement of the anomalous circulation embedded in the westerlies, thereby contributing to the persistence of the PHEs. Meanwhile, the SAT anomalies over northern China are also enhanced with a central amplitude of approximately 3°C (Fig. 7g).

At day 3 (Fig. 7d), the significant negative height anomalies over central Asia disappear while the positive height anomalies over northern China still persist, which is favorable for the persistence of positive SAT anomalies over northern China. After day 3, both the positive height anomalies and the SAT anomalies over East Asia migrate southward gradually and northern China is no longer under the influence of significant SAT anomalies at approximately day 6 (not shown).

The energy conversion also plays a positive role in maintaining the typical circulation anomalies of the PHEs over northern China (Fig. 8). Compared with its negligible role in the PHEs over SEWA (left column of Fig. 6), the CK becomes important here. The term τCK is 13.2 days at day −6 (Fig. 8a) and gradually reduces to 5.9 days at day 0 (Fig. 8c). At day 3 (Fig. 8d), it becomes negligible at τCK = −1694.7 days due to the almost complete cancellation between the positive and negative CK over the entire Northern Hemisphere. On the other hand, the conversion efficiency τCP is 8.1 days at day −6 (Fig. 8e) and becomes less than 5 days before day −3 (Figs. 8f–h). Clearly, the baroclinic energy conversion is dominant over the barotropic energy conversion. The average duration of the PHEs over northern China is approximately 7 days. Correspondingly, the mean total efficiency τCP+CK is evaluated from day −3 to day 3, and its value is 5.2 days, which is comparable to the 7-day duration of the PHEs over northern China. Therefore, the typical circulation anomalies could be sustained through effectively extracting energy from the basic flow.

Fig. 8.

As in Fig. 6, but for the composite energy conversion of 65 PHEs over northern China.

Fig. 8.

As in Fig. 6, but for the composite energy conversion of 65 PHEs over northern China.

In fact, the typical anomaly circulations of the PHEs over both SEWA (Fig. 5) and northern China (Fig. 7) are generally similar to the SRP or parts of the SRP, except for the circulation anomalies centered in both Europe and central Asia, which are located farther north in the evolution of the PHEs over northern China. Correspondingly, the above results about the energy conversion are consistent with the previous studies in which both the baroclinic (Kosaka et al. 2009; Chen et al. 2013) and barotropic (Sato and Takahashi 2006) energy conversion are important in the formation of the SRP.

Therefore, the regional PHEs over northern China were also characterized by stationary wave train anomalies and by the Rossby wave propagation that emanated from upstream circulation anomalies over the northeast Atlantic. Moreover, the energy extraction from basic flows may also play an important role in shaping the stable wave train anomalies over Eurasia. Under the influence of persistent positive height anomalies over East Asia, northern China tended to experience persistent hot weather.

5. Interdecadal changes in background circulation

As discussed in section 1, both the mean warming and the amplified variability could contribute to the increased frequency of heat waves (Schär et al. 2004; Della-Marta et al. 2007). Fischer and Schär (2010) showed that in the future, the mean warming is responsible for the increased frequency and duration of heatwaves over southern Europe, while the enhanced variability in temperature accounts for the strengthened amplitude of heatwaves farther north. These studies motivate us to explore the roles played by the mean state and the variability in the interdecadal variation of PHE frequency.

Figure 9 shows the probability density function (PDF) of the daily SAT averaged over SEWA and northern China during the three particular periods. On one hand, the PDF patterns are basically stable during the three periods, especially for northern China (Fig. 9b), indicating that the subseasonal variability is not changed much. To verify this point, we evaluate the subseasonal variance of SAT of all summer days for every individual period and further test the significance of the difference during the three periods based on an F test. Due to the autocorrelation of the daily SAT sequence, the effective sample size ne is estimated following Zwiers and von Storch (1995) as nen(1 − r)/(1 + r); n is the length of the original daily sequence and r represents the lag-one autocorrelation coefficient. The results show that the mean subseasonal variance is not changed significantly at the 95% confidence level between either of the two active periods and the inactive period for either of the two regions. On the other hand, almost all SAT values are increased in both active periods (red lines) over both regions evidently compared with that in the inactive period (blue lines). This finding implies that interdecadal variation occurs in the mean state that could contribute to an overall shift in SAT and might modulate the frequency of the PHEs, which will be explored in the following context.

Fig. 9.

Probability distribution functions of the summertime daily SAT averaged over (a) SEWA and (b) northern China during the two active periods (red lines) and one inactive period (blue line). The daily SAT at every grid has been detrended in priority for the whole period from 1958 to 2015.

Fig. 9.

Probability distribution functions of the summertime daily SAT averaged over (a) SEWA and (b) northern China during the two active periods (red lines) and one inactive period (blue line). The daily SAT at every grid has been detrended in priority for the whole period from 1958 to 2015.

As demonstrated in section 4, the regional PHEs are generally associated with positive height anomalies aloft. Thus, the following question arises: Does the background circulation variation facilitate the appearance of the typical circulation anomalies of the regional PHEs? To answer this question, background circulations over the three periods are obtained by averaging the meteorological fields over the corresponding periods individually (Fig. 10). The changes in the background circulation are represented by the differences between the summer mean circulations over different periods. As shown in Fig. 3, the inactive period is treated as the reference period.

Fig. 10.

Difference in the background circulation of summer mean geopotential height (gpm) at 300 hPa (a) between the active period (1958–72) and the inactive period (1973–96) and (b) between the reactive period (1997–2015) and the inactive period (1973–96). (c),(d) As in (a) and (b), respectively, but for SAT (°C). (e)–(h) As in (a)–(d), but all the consecutive hot days of the PHEs are excluded from the summer days. See more details in the text. Contour intervals are 10 gpm for geopotential height and 0.4°C for SAT. Zero contours are omitted in all panels. The solid red and dashed blue lines represent the positive anomalies and negative anomalies, respectively. Shading denotes the statistically significant region at the 0.05 confidence level based on a two-tailed Student’s t test.

Fig. 10.

Difference in the background circulation of summer mean geopotential height (gpm) at 300 hPa (a) between the active period (1958–72) and the inactive period (1973–96) and (b) between the reactive period (1997–2015) and the inactive period (1973–96). (c),(d) As in (a) and (b), respectively, but for SAT (°C). (e)–(h) As in (a)–(d), but all the consecutive hot days of the PHEs are excluded from the summer days. See more details in the text. Contour intervals are 10 gpm for geopotential height and 0.4°C for SAT. Zero contours are omitted in all panels. The solid red and dashed blue lines represent the positive anomalies and negative anomalies, respectively. Shading denotes the statistically significant region at the 0.05 confidence level based on a two-tailed Student’s t test.

Figures 10a and 10c show the circulation differences between the first active period and the inactive period. Evidently, wave train–like anomalies encircle the middle to high latitudes of the Northern Hemisphere (Fig. 10a). Interestingly, the configuration of the decadal circulation changes is basically in phase with the typical circulation anomalies for the regional PHEs over SEWA as shown in Fig. 5, with positive height anomalies over the northwest Atlantic and Europe and negative anomalies over the northeast Atlantic. Downstream of Europe, central Asia and East Asia are under the influence of negative and positive height anomalies (Fig. 10a), respectively, which are also in phase with the typical circulation anomalies for the regional PHEs over northern China shown in Fig. 7. In addition, positive SAT anomalies prevail over Europe/western Asia and East Asia (Fig. 10c). In fact, the abovementioned changes in the background circulation re-emerge when the latest active period is compared with the inactive period (Figs. 10b,d). Therefore, these results imply that the interdecadal variation in the background circulation was favorable for the occurrence of both of regional PHEs over SEWA and those over northern China by enhancing their typical circulation anomalies.

To further check the robustness of the interdecadal difference, we also derive the summer mean components that are independent of the PHEs by excluding all consecutive hot days of the 75 PHEs over SEWA and the 72 PHEs over northern China. There are 358 (26%), 190 (9%), and 553 (32%) hot days excluded from the total summer days for the active period, inactive period, and reactive period, respectively. Based on the independent components, we recalculate the interdecadal differences in the summer mean state between different periods. As shown in the second row of Fig. 10, after excluding all hot days, the interdecadal differences in the summer mean state are still evident, although they are less significant and their magnitudes are reduced to some extent. Specifically, over the Eurasian continent, both active periods are characterized by positive anomalies of geopotential height at 300 hPa to the north of the Black Sea and around Lake Baikal (Figs. 10e,f), which resemble their counterparts if the hot days are not excluded (Figs. 10a,b). Moreover, the anomalous SAT pattern (Figs. 10g,h) is also similar to its counterpart if the hot days are not excluded (Figs. 10c,d). Therefore, the interdecadal differences occur throughout the entire periods and are not limited to the hot days of the PHEs. This finding is consistent with Fig. 9, which reveals an overall shift of the PDF of daily SAT rather than a change in the PDF pattern. In fact, the magnitude of the difference in the background circulation shown in Fig. 10 is comparable to the interannual variability of both the height at 300 hPa and SAT over the Eurasian continent (not shown). Therefore, the interdecadal changes in the background circulation are not weak, and they could simultaneously modulate the interdecadal variations in the regional PHE frequency over SEWA and northern China.

Figure 11 shows the SRP pattern represented by correlation coefficients between the geopotential height anomalies at 300 hPa and the dominant principal component (PC1) of the meridional velocity over 20°–60°N, 30°–130°E. The PC1 is regarded as the SRP index in the following text. The region chosen for the empirical orthogonal function (EOF) analysis is consistent with previous studies (Kosaka et al. 2009; Wang et al. 2017). We also applied the EOF analysis to other regions with slight changes, such as 20°–60°N, 0°–150°E (Hong et al. 2017), and the results showed no qualitative change (not shown). Clearly, the SRP is similar to the decadal changes in the background circulations from the northeast Atlantic to East Asia (Figs. 10a,b). In addition to the above spatial similarity, there are also temporal similarities between the SRP and the interdecadal variation in the mean state during the three periods. As shown in Fig. 11, the SRP showed an evident interdecadal phase shifting, with the early 1970s and mid-1990s representing the phase-transition points (solid blue line), which is confirmed by using several different reanalysis datasets (Wang et al. 2017). The phase-transition points are basically consistent with the partition of the 58 years into the three periods in the present study. Thus, the interdecadal changes in the background circulations are closely related to the interdecadal phase shifts in the SRP.

Fig. 11.

(a) First principal component (PC1) of the summer-mean meridional wind velocity at 200 hPa over the region 20°–60°N, 30°–130°E (blue bars) and the AMO index (red bars). The solid blue and red lines are the 11-yr running average of the PC1 of the summertime meridional wind velocity and the AMO index, respectively. (b) Linear coefficients between the summer-mean geopotential height at 300 hPa and the PC1 of the summer-mean meridional wind velocity at 200 hPa shown by the blue bars in (a). Contour interval is 0.2 in (b). Shading in (b) represents the statistically significant region at the 0.05 significance level based on a two-tailed Student’s t test.

Fig. 11.

(a) First principal component (PC1) of the summer-mean meridional wind velocity at 200 hPa over the region 20°–60°N, 30°–130°E (blue bars) and the AMO index (red bars). The solid blue and red lines are the 11-yr running average of the PC1 of the summertime meridional wind velocity and the AMO index, respectively. (b) Linear coefficients between the summer-mean geopotential height at 300 hPa and the PC1 of the summer-mean meridional wind velocity at 200 hPa shown by the blue bars in (a). Contour interval is 0.2 in (b). Shading in (b) represents the statistically significant region at the 0.05 significance level based on a two-tailed Student’s t test.

In addition to the anomalous centers to the north of the Black Sea and around Lake Baikal, the anomalous center with the opposite sign to the southeast of the Aral Sea is also an important anomalous center for the SRP (Fig. 11b). In fact, such oppositely signed anomalous center to the southeast of the Aral Sea could be discerned in Figs. 10a and 10b, which show the interdecadal negative geopotential height difference occurring at 300 hPa (Figs. 10a,b). However, the magnitude of the difference is relative weak at approximately −10 gpm, which corresponds to the local significant negative SAT difference but at a small spatial scale (Figs. 10c,d). Thus, the SRP might also modulate the frequency of the PHEs over central Asia on an interdecadal time scale and could be responsible for the out-of-phase relationship of the frequency of PHEs over central Asia with its counterpart over East Asia or SEWA as noted in section 3.

6. Discussion of interdecadal SST anomalies

Hong et al. (2017) and Wang et al. (2017) state that the Atlantic multidecadal oscillation (AMO), which has a consistent warming or cooling tendency over the whole Atlantic on a decadal time scale, can facilitate the interdecadal changes in the SRP. The AMO index is shown as red bars in Fig. 11a, and the solid red line represents its 11-yr running mean. Overall, the AMO shifts its phase from negative to positive in approximately the early 1990s on interdecadal time scales, which slightly leads to the decadal change in the SRP in approximately the mid-1990s (solid blue line in Fig. 11a), implying its important role in modulating the SRP phase changes. However, the out-of-phase relationship between the AMO and SRP from the early 1960s to the early 1970s implies that other mechanisms might contribute positively to the interdecadal changes in the SRP.

Figure 12 shows the interdecadal changes in SST derived from the two datasets (i.e., HadISST and ERSST), which consistently show interdecadal warming signals during the two active periods over the mid- and high-latitude oceans except for the Arctic region (Figs. 12a,b,d,e). Thus, in addition to the Atlantic, the significant SST decadal variation over the Mediterranean Sea, Black Sea, and northern Pacific might also be favorable for the decadal changes in the SRP. To explore the long-term variation of the regional SST, we further average the SST anomalies over the four representative areas shown by the fans in Fig. 12. Clearly, Figs. 12c and 12f both show that the SST over all four regions has evident interdecadal variations with two transition points during the 58 summers, which is basically consistent with the SRP and the background circulation changes. Note that the latest transition points for the four regions consistently point to the late 1990s. In contrast, the first transition points for the four regions have a large spread in approximately the late 1960s/early 1970s.

Fig. 12.

Interdecadal changes in SST based on (a)–(c) HadISST and (d)–(f) ERSST, showing (a),(d) differences in the SST between the active period (1958–72) and the inactive period (1973–96), (b),(e) interdecadal changes between the reactive period (1997–2015) and the inactive period (1973–96), and (c),(f) 11-yr running mean of the area-average SST anomalies over the following four particular regions, which are bounded by the fans shown in (a): southwest Atlantic (10°–30°N, −90°–50°E; SW Atl.), northern Atlantic (44°–74°N, −60°–60°E; N Atl.), the Mediterranean Sea and the Black Sea (30°–48°N, 5°W–45°E; MB), and the northern Pacific (10°–30°N, −145°–110°E; N Pac.). Note that (a), (b), (d), and (e) only show the differences significant at the 0.05 confidence level based on a two-tailed Student’s t test.

Fig. 12.

Interdecadal changes in SST based on (a)–(c) HadISST and (d)–(f) ERSST, showing (a),(d) differences in the SST between the active period (1958–72) and the inactive period (1973–96), (b),(e) interdecadal changes between the reactive period (1997–2015) and the inactive period (1973–96), and (c),(f) 11-yr running mean of the area-average SST anomalies over the following four particular regions, which are bounded by the fans shown in (a): southwest Atlantic (10°–30°N, −90°–50°E; SW Atl.), northern Atlantic (44°–74°N, −60°–60°E; N Atl.), the Mediterranean Sea and the Black Sea (30°–48°N, 5°W–45°E; MB), and the northern Pacific (10°–30°N, −145°–110°E; N Pac.). Note that (a), (b), (d), and (e) only show the differences significant at the 0.05 confidence level based on a two-tailed Student’s t test.

Following the work of Wang et al. (2017), the Monte Carlo bootstrapping technique is also used to estimate the summertime PDF of the interdecadal SRP index during the positive and negative phases of the interdecadal mean SST anomalies over the four regions as denoted in Fig. 12. Here, the resampling procedure was repeated 10 000 times. The interdecadal components of both the summer mean SRP index and the summer mean SST anomalies were obtained by the 11-yr running average over the period from 1958 to 2015. Clearly, both datasets showed that the PDFs of the interdecadal SRP index can be separated well from each other during the positive and negative phases of SST anomalies over either of the four regions. According to the 5% and 95% percentiles, which are represented by the dashed lines in Fig. 13, the interdecadal SRP index is significantly different from zero at least at the 95% confidence level during either of the positive or negative phases of the SST anomalies.

Fig. 13.

Probability density functions (PDFs) of the 11-yr running mean SRP index estimated from 10 000 bootstrapped samples in the positive (red) and negative (blue) signs of the 11-yr running mean SST anomalies for the period from 1958 to 2015, based on (a)–(d) HadISST and (e)–(h) ERSST. (from top to bottom) N Pac., MB, N Atl., and SW Atl., respectively, as denoted in Fig. 12. The blue and red vertical dashed lines indicate the 95% percentiles in the negative SST anomalies and 5% percentiles in the positive SST anomalies, respectively.

Fig. 13.

Probability density functions (PDFs) of the 11-yr running mean SRP index estimated from 10 000 bootstrapped samples in the positive (red) and negative (blue) signs of the 11-yr running mean SST anomalies for the period from 1958 to 2015, based on (a)–(d) HadISST and (e)–(h) ERSST. (from top to bottom) N Pac., MB, N Atl., and SW Atl., respectively, as denoted in Fig. 12. The blue and red vertical dashed lines indicate the 95% percentiles in the negative SST anomalies and 5% percentiles in the positive SST anomalies, respectively.

Therefore, from a statistical perspective, the interdecadal variation in the SST anomalies may modulate the interdecadal variation of the SRP. Nevertheless, we are still unclear on the mechanism for the interdecadal connection between the SST over the different regions and the SRP, which deserves further numerical studies.

7. Conclusions

This study identifies PHEs at every grid point over Eurasia using the JRA-55 daily reanalysis dataset. After removing the long-term linear trends from the daily meteorological fields, the results show that SEWA and northern China are two large-scale regions that have exhibited consistent interdecadal variations in PHE frequency over the past 58 summers. The regional PHEs over the two regions occurred at a lower frequency approximately from 1973 to 1996 than the periods immediately before and after. Correspondingly, the three periods are referred to as the active period, the inactive period, and the reactive period.

Based on the composite analysis, the regional PHEs over SEWA are characterized by quasi-stationary wave train anomalies in the upper troposphere from the northwest Atlantic to Europe. As the leading portion of the wave train anomalies, the persistent positive height anomalies over Europe are responsible for the persistence of the positive SAT anomalies over the SEWA. For the regional PHEs over northern China, the quasi-stationary wave train anomalies over the Eurasian continent are also evident with persistent positive height anomalies over East Asia, which are favorable for the persistence of positive SAT anomalies over northern China.

The persistence of quasi-stationary wave train anomalies is explored via both the Rossby wave propagation and the energy conversion with the basic flow. The Rossby wave packets that emanate continually from the upstream region are favorable for the persistence of the anomalous circulation. Moreover, from the perspective of energy conversion, the quasi-stationary wave train anomalies associated with the PHEs over northern China could be efficiently maintained via energy extraction from the basic flow, including the baroclinic and the barotropic energy extraction, while their counterparts over SEWA are efficiently sustained only by baroclinic energy extraction.

Our study reveals that changes in the background circulation can modulate the frequency of regional PHEs over SEWA and northern China simultaneously. This finding occurs because the interdecadal changes in the background circulation between the two active periods and the inactive period resemble the typical circulation patterns at the subseasonal time scale for the regional PHEs. In other words, the mean states in the two active periods have changed to facilitate the occurrence of the typical circulation anomalies of the PHEs. Further analysis reveals that the background circulation changes are closely related to the interdecadal variation in the SRP due to their similar spatial patterns and temporal variations. From a statistical perspective, the SST anomalies over the northern Pacific, Mediterranean Sea, Black Sea, northern Atlantic, and southwest Atlantic could facilitate variations in the background circulation on interdecadal time scales.

The present study mainly focuses on interdecadal variations in the frequency of PHEs or days. In fact, many other aspects of hot days also have long-term variations. Previous studies have shown increasing trends in heatwave intensity, frequency, and duration over the last several decades based on observation data (Perkins et al. 2012; Li et al. 2017b) and even over the next century based on numerical model results (Fischer and Schär 2010; Meehl and Tebaldi 2004; Y. Sun et al. 2014). Therefore, whether the SRP could modulate the amplitude or duration of PHEs over the Eurasian continent on interdecadal time scales is worthy of further investigation.

Acknowledgments

This work is supported jointly by the National Key R&D Program of China (Grant 2016YFA0600702), the Chinese Natural Science Foundation (41575057), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the funding of Jiangsu innovation and entrepreneurship team. The NCAR Command Language (NCL) was used for performing calculations and drawing the plots.

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