The synergistic effect of the summer NAO and northwest pacific SST on extreme heat events in the central–eastern China

Extreme heat events happen frequently in East Asia, and may cause great damage to the ecosystem and society. The synergistic effect of the summer positive North Atlantic Oscillation (pNAO) and positive northwest Pacific (pNWP) sea surface temperature anomaly (SSTA) on the interannual variability of the extreme heat events in the central–eastern China (CEC) is investigated in this study. The two factors act synergistically in strengthening the extreme heat events in the CEC via a series of atmospheric bridges, and the CEC is likely to experience a hotter summer when both the summer pNAO and pNWP SSTA occur. The pNWP SSTA increases the strength of pNAO via the eastward propagating Rossby wave from the western Pacific. The enhanced pNAO induces a stronger eastward Rossby wave propagation across the Eurasian continent, and leads to a strong anomalous anticyclone over the CEC. The significantly increased atmosphere thickness increases the air temperature of the layer, and favors the extreme heat events in the CEC. Besides, the pNWP SSTA also has adjacent effect on the atmospheric circulation over the CEC, which could lead to a positive geopotential height anomaly. Therefore, the summer pNAO and pNWP SSTA act synergistically in influencing the atmospheric circulation over the CEC, and thereby significantly increase the extreme heat events in the CEC.


Introduction
Under the background of global warming, extreme heat events happen more frequently than before, and the intensity of extreme heat events sees an increase in recent decades (Meehl and Tebaldi 2004;Perkins 2015;Fragkoulidis et al. 2018;Kornhuber et al. 2019). In the summer of 2022, China experienced record-breaking extreme heat events, and many stations in the Eastern and central-western China recorded the highest daily temperature in the history of the record. The frequent occurrence of extreme heat events which are often accompanied by drought and desertification has great impacts on the ecosystems, crop production and even humankind health (Alessandro and de Garín 2003;Bastos et al. 2014;Russo et al. 2015;Horton et al. 2016;Deng et al. 2018). The central-eastern China (CEC) is among the most heavily populated area, which is also the economic center in China, and the increase of extreme heat events may lead to huge negative impacts on the economy and society in this region (Sun et al. 2014;You et al. 2017).
The extreme heat events in the CEC have received a lot of attentions across many research fields in recent years, and it is of great importance to investigate the climatic mechanisms behind the extreme heat events in the CEC (e.g. Tan et al. 2007;Wu et al. 2012;Peng 2014). The extreme heat events can be caused by various factors, and the most common large-scale atmospheric circulation responsible for the extreme heat events is the anomalous anticyclone, which 1 3 could reduce the cloud cover and increase the solar radiation (Black et al. 2004;Gershunov et al. 2009;Chen and Lu 2015;Lu and Chen 2016), and the atmosphere thickness change related to the anomalous atmospheric circulation can significantly influence the intensity and frequency of the extreme temperature events . Gong et al. (2004) found that the anomalous high in the 500-hPa level is able to cause high temperature events in the CEC. Ding and Ke (2015) examined the extreme heat events in 2003 and 2013, and discovered that the extreme heat events in the eastern China could be related with the westward extended subtropical high with stronger intensity. Chen and Lu (2015) categorized the synoptic circulation related to the extreme heat events in the CEC into three patterns, and the most typical pattern is characterized by an anomalous anticyclone over the CEC.
The North Atlantic oscillation (NAO) is one of the most important atmospheric patterns, and it is the dominant mode of atmospheric circulation variability over the North Atlantic (Wallace and Gutzler 1981;Hurrell 1995;Li and Wang 2003). Previous studies found that the summer NAO is able to have impacts on the atmospheric circulation over East Asia via Rossby wave (Watanabe 2004;Chen et al. 2005;Zuo et al. 2015;Li and Ruan 2018). Xie et al. (2019) suggested that the NAO is able to modulate the surface air temperature over the East Asia on the decadal time scale via teleconnection, and the CEC is the most influenced region. The NAO is also found to influence air temperature and the resultant crop production in China through the upper-level Rossby wave (Sun et al. 2008;Zhou et al. 2013). Sun (2012) highlighted the effect of the summer NAO on the extreme heat events in the CEC, and the eastward propagated Rossby wave acts as the bridge between them.
The regional anomalous atmospheric circulation associated with the extreme heat events can also be modulated by many factors from the relatively adjacent regions. Many studies found that the decreased snow cover in the Tibetan Plateau could cause anomalous high pressure over the CEC, thus favors the extreme heat events (Sun et al. 2014;Wu et al. 2012). Deng et al. (2018) investigated the cause of the strong extreme heat event in southern China in 2018, and they discovered that the delayed South China Sea summer monsoon is the reason for it. Chen et al. (2016) found that the anomalous anticyclone caused by the boreal summer intraseasonal oscillation over the western Pacific can lead to heat waves in China. Zhu et al. (2012) highlighted the influence of the weakened East Asian summer monsoon on the extreme heat events. Hu et al. (2012) found that the late summer extreme heat events in the southern China can be affected by the Indian Ocean SST.
The northwestern Pacific (NWP) sea surface temperature (SST) is also an important adjacent factor influencing the climate in China. The NWP SST anomaly (SSTA) has important influence on the atmospheric circulation around China (e.g. Liu et al. 2006;Frankignoul et al. 2011;Matsumura et al. 2016). The NWP SST variability may influence the precipitation in the CEC by modulating the vapor transport (Li 2008;Li and Luo 2014). Previous studies suggested that the summer heat waves in the CEC could be caused by the NWP SSTA, since the NWP SST may force the anomalous atmospheric circulation over China (Chen and Zhou 2018;Sparrow et al. 2018). Huang et al. (2010) found that the NWP SST, which is near the eastern China, is able to modulate the summer extreme heat events in the CEC, and the positive NWP SSTA favors the increase of extreme heat events.
Since both the summer NAO and NWP SST may affect the variability of air temperature in the CEC respectively, we want to know that whether they have a combined effect on the interannual variability of the summer extreme heat events in the CEC. A new method was put forward by Li et al. (2019a) to determine the climatic synergistic effect of multiple factors, and this method was extensively used in previous studies. An et al. (2021) found that the Pacific and Atlantic SST could modulate the strength of circumglobal teleconnection and further influence the air temperature over the Mongolian Plateau. Sun and Li (2022) revealed that the wintertime precipitation over southeastern China and the Kuroshio Current in the East China Sea will be greatly enhanced if the El Niño and the positive phase of the North Pacific Oscillation both occur. Wang et al. (2022) explored the synergistic effect of the preceding winter positive phase of Northern Hemisphere Annular Mode and the spring negative phase of the tropical North Atlantic SST on weakening the spring extreme cold events in the mid-high latitudes of East Asia. Tang et al. (2022) revealed that the El Niño and negative phase of the NAO may lead to the significantly increased precipitation over the southeastern United States. Investigating of synergistic effect of the two factors may have great importance, since compared with single factor happening, the synergistic effect results in much greater amplitudes of the extreme events when two factors cooccur, which may cause more damage to the society and ecosystem. Thus, in this paper, we will focus on the synergistic effect of the summer NAO and NWP SST.
The remainder of this paper is organized as follows. The datasets and methodology are introduced in Sect. 2. Section 3 describes the characters of the synergistic effect of the summer positive NAO (pNAO) and positive NWP (pNWP) SSTA on the extreme heat events in the CEC. Section 4 presents the regional atmospheric circulation which is responsible for the extreme heat events in the CEC. Section 5 further explores the mechanisms of the synergistic effect. Finally, the summary and discussion are presented in Sect. 6. Table 1 lists all the datasets which are used in the study. The observational SST dataset is the HadISST1 (version 1.1) which is provided by the Met Office Hadley Center, and it has a horizontal resolution of a 1° latitude × 1° longitude and covers the period between January 1870 and July 2022 (Rayner et al. 2003). The HadEX3 dataset is employed to provide the gridded extreme temperature indices, and the dataset is provided by the Met Office Hadley Center covers the period 1901-2018 with a 1.25° latitude × 1.875° longitude grid (Dunn et al. 2020). The TXx, TNx, TX90p and TN90p indices are used in the dataset, and they represent the monthly highest value of the daily maximum temperature, monthly highest value of the daily minimum temperature, percentage of time when the daily maximum temperature is higher than the 90th percentile, and percentage of time when the daily minimum temperature is higher than the 90th percentile, respectively. The intensity and frequency of extreme heat events can be accurately represented by these indices (Dunn et al. 2020). The global surface air temperature time series of the HadCRUT4 dataset by the Met Office Hadley Center, which covers the period between January 1850 to January 2021 (Morice et al. 2012), is used to remove the global warming signal from all variables. The geopotential height, winds and sea level pressure (SLP) data are obtained from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis dataset, which covers the period from 1948 to August 2022 on a 2.5° latitude × 2.5° longitude mesh (Kalnay et al. 1996).

Data
The HadEX3 dataset ends in 2018, and has some missing data over East Asia before 1960. Therefore, the period 1961 − 2018 is used in this study.

Statistical methods
In this paper, summer is defined as June − July − August, and the two-tailed Student's t test is employed to determine statistical significance.
The synergistic effect diagnostic method used in this study is put forward by Li et al. (2019a). This method is able to determine the existence of synergistic effect statistically. Assuming there are two forcing factors F 1 and F 2 , and each of the factors can be divided into positive, negative, and neutral phases. If we choose the positive phase of each factor, the conditions of the two factors will be represented as F + 1 and F + 2 , representatively. F + 1 ⊕ F + 2 denotes the cases with the cooccurrence of F + 1 and F + 2 , and the cases are termed as joint events F + 1 ⊕ F + 2 . F + 1 �F + 2 indicates the cases when F + 1 occurs without F + 2 , and the cases are termed as single F + 1 events. F + 2 �F + 1 represents the cases when F + 2 occurs without F + 1 , and the cases are termed as single F + 2 events. Assuming the response T is investigated in the study, we can compare the difference between different events to determine whether there is a synergistic effect. If the |T| of F + 1 ⊕ F + 2 is greater than the maximum of the |T| of F + 1 �F + 2 and F + 2 �F + 1 , it denotes that there is a synergistic effect of F + 1 and F + 2 on T. However, if the |T| of F + 1 ⊕ F + 2 is smaller than the minimum of the |T| of F + 1 �F + 2 and F + 2 �F + 1 , it indicates that there is an antagonistic effect of F + 1 and F + 2 . Finally, if the |T| of F + 1 ⊕ F + 2 is between the |T| of F + 1 �F + 2 and F + 2 �F + 1 , it indicates that there is no combined effect of F + 1 and F + 2 . By using this synergistic diagnostic method, the existence of the synergistic effect of two factors can be determined.
The statistical significance of the synergistic effect is assessed by using the bootstrapping method (Deser et al. 2017(Deser et al. , 2018. 1000 bootstrapped composites are formed based on joint events summer pNAO ⊕ pNWP, single summer pNAO events and single summer pNWP SSTA events. The bootstrapping method is used to test the difference between the joint events and single events by examining the distribution of 0 between the 10th and 95th percentiles. When 0 lies outside this area, the synergistic effect is significant. However, when 0 lies inside this area, the synergistic effect is insignificant. The NAO index is calculated by the difference in the normalized regionally zonal-averaged SLP over the North Atlantic (80°W-30°E) between 35°N and 65°N according to Li and Wang (2003). All variables in the study are linearly detrended by removing the trends related to global warming in the global SAT time series of the HadCRUT4.

Dynamic analysis methods
The Rossby wave ray tracing theory in a horizontally nonuniform basic flow is performed to trace the trajectory of the stationary Rossby wave train and characterize the pathway of the impact of the NAO and NWP Li et al. 2015Li et al. , 2019bLi et al. , 2021Zhao et al. 2015Zhao et al. , 2019. The previous studies showed that the dispersion relationship of the Rossby wave frequency and wavenumber in a horizontally non-uniform flow can be written as (Karoly 1983;Li and Nathan 1997;Li and Li 2012;Li et al. 2015;Zhao et al. 2015Zhao et al. , 2019: where is the wave frequency; k and l are the zonal and meridional wavenumbers, respectively; u M , v M = (u, v)∕cos is the Mercator projection of zonal and meridional winds; is the latitude; q = ∇ 2 M ∕ cos 2 + f represents the absolute vorticity of the background; and q x and q y are the zonal and meridional gradients of q . Let K = √ k 2 + l 2 represent the total wavenumber, and the zonal and meridional components of the group velocity take the form: The background flow changes along the ray, thus the wavenumbers determined by the kinematic wave theory can be written as (Whitham 1960): where d g dt = t + u g x + v g y is the material derivative moving with the group velocity. According to Eqs. 4 and 5, the zonal and meridional wavenumbers change along the wave ray, which differs from the theory by Hoskins and Karoly (1981). Equations 2-5 are the wave ray tracing equation set. Therefore, the initial local meridional wave number l is determined by using Eq. (1) once the initial position and zonal wavenumber k are given. Then, the wave ray tracing equation set is able to obtain the corresponding wave ray trajectory. The integration is terminated when the local meridional wavelength is less than 1000 km in the largescale Rossby wave.
The wave activity flux proposed by Takaya and Nakamura (2001) is also used in this study to identify the Rossby wave propagation, and the horizontal wave activity flux is calculated as the formula below: in this equation, ′ indicates the perturbation stream function; U = (u, v) denotes the climatological mean wind velocity horizontal flow; p represents the pressure that is normalized by 1000 hPa; and a is the Earth's radium.
In order to study the effect of the anomalous atmospheric circulation on the air temperature anomaly, the perturbation hypsometric equation proposed by Li et al. (2021) is used: in this equation, ⟨T⟩ ′ is the anomaly of the mean temperature of the layer, ΔZ � is the atmospheric thickness anomaly between two pressure surfaces p 1 and p 2 , g 0 is the gravitational acceleration, and R is the gas constant of dry air. It can be seen from the Eq. (7) that the perturbation mean air temperature of the atmospheric layer is proportional to the perturbation atmospheric thickness bounded by isobaric surfaces. Thus the atmospheric thickness anomaly can represent the perturbation mean air temperature of the atmospheric layer. The perturbation hypsometric equation is used to identify the effect of the upper-level atmospheric circulation anomaly on the air temperature variation.
We use a dry version of the linear baroclinic model (LBM) to investigate the influence of NAO and NWP SSTA on the atmospheric circulation. The LBM consists of primitive equations linearized of a summer climatology obtained from the NCEP-NCAR reanalysis dataset, and adopts a T21 horizontal resolution and 20 vertical levels using the sigma coordinate system. A further detailed description of the LBM can be found in Watanabe and Kimoto (2000). The model is integrated for 35 days, and it takes about 20 days for the model to achieve a steady atmospheric circulation. The averaged result of days 26-35 is used in this study. Figure 1 shows the correlation maps between the summer NAO and extreme temperature indices in East Asia. Even though there are different extreme temperature indices, the significantly correlated area in China is always found in the CEC. The NAO shows a significantly positive correlation with the extreme heat events in the CEC, and it implies that the summer maximum daily temperature is higher than the climatology ( Fig. 1c and d) and occurrence of hot days is more frequent when the summer pNAO happens ( Fig. 1a and b). In other words, the occurrence of the summer pNAO is likely to be accompanied by the strengthened extreme heat events in the CEC (Sun 2012;Xie et al. 2019). Based on the results in Fig. 1, the region (25°-40°N, 110°-125°E) in the CEC is selected as the research area in this study. Figure 2 further shows the time series of the summer area-averaged extreme heat indices in the CEC, and the pNAO years are marked on them. To include more cases, we use 0.6 standard deviations for the NAO index to select pNAO years (years with black dots in Fig. 2). It is clear that not every pNAO year exhibits strengthened extreme heat events in the CEC. Some pNAO years correspond to the significantly strengthened extreme heat events in the CEC (e.g. 1961CEC (e.g. , 1967CEC (e.g. and 2013, while the slightly increased or even weakened extreme heat events occur in some pNAO years. This result could imply that there may be some factors Firstly, we want to know whether there is difference between the pNAO strength in the years with strong (red bars with black dots in Fig. 2a or b) and weak (blue bars with black dots in Fig. 2a or 2b) extreme heat events. The pNAO years with strong and weak extreme heat events are also shown in Table S1. Figure 3a shows the NAO anomalies for the pNAO years with strong and weak extreme heat events, and the difference between them. It is obvious that the strength of the pNAO in the strong extreme heat events years is much greater than that in the weak extreme heat events years, and the difference between them is significant at the 95% confidence level based on the Student t-test. This result implies that the extreme heat events in the CEC have a stronger response to a strengthened pNAO. Next, we aim to explore the factors leading to an increased extreme heat events response in the CEC. Figure 3b shows the composite difference of the SSTA between the pNAO years with strong and weak extreme heat events. It is clear that there is a large area exhibiting significantly positive anomaly over the NWP, which means that there is a stronger pNWP SSTA in the pNAO years with strong extreme heat events in the CEC. We further select the domain (20°-40°N, 130°-180°E) to quantify the NWP SST variation, and Fig. 3c further displays the NWP SSTA for the different pNAO years with strong and weak extreme heat events and the difference between them. It can be clearly seen that there is a strong pNWP SSTA in the pNAO years with strong extreme heat events. However, as for the years with weak extreme heat events, there is not such a significantly positive SSTA over the NWP. The  Fig. 3 a The NAO anomalies for the pNAO years with strong (the red bar) and weak (the blue bar) extreme heat events, and the green bar represents the difference between them. b Composite difference of the SSTA (°C) between the pNAO years with strengthened and weak-ened extreme heat events. Dotted areas indicate significant values at the 95% confidence level based on the Student t test. The yellow box represents the NWP. c As in (a), but for the NWP SSTA (°C) difference between the them is also significant at the 95% confidence level based on the Student t-test. The above results imply that it could be the pNWP SSTA that leads to a stronger pNAO strength, which further yields a stronger extreme heat event response in the CEC. Figure 4 further shows the correlation maps between the summer global SSTA and area-averaged extreme temperature indices in the CEC. There are many large areas showing significant correlation with the extreme temperature indices, including the NWP. The significantly correlated area in the NWP is relatively stable for different extreme heat indices, and the NWP is close to the research area and may have adjacent effect on the extreme heat events in the CEC. The NWP SST is positively correlated to the TN90p and TX90p in Fig. 4a and b, which implies that the occurrence of warm NWP SST is likely to be accompanied by the increased extreme heat event frequency (Huang et al. 2010). And the positive correlation between the NWP SST and TXx (TNx) in Fig. 4c, d indicates that the daily temperature is higher than normal when the NWP gets warmer. The above results in Figs. 3 and 4 imply that the NWP SSTA could be another important factor influencing the variation of extreme heat events in the CEC.

The synergistic effect of the summer NAO and NWP SST
Based on the above results, the pNAO and pNWP SSTA are both related to the increased extreme heat events in CEC. Therefore, we further investigated the combined effect of these two factors on the summer extreme heat events in the CEC. To include more cases in this study, we use 0.6 standard deviations to determine the occurrence of the pNAO or pNWP SSTA event. Table 2 lists the numbers and years of the joint events of the summer pNAO and summer pNWP SSTA (pNAO ⊕ pNWP), single summer pNAO events and single summer pNWP SSTA events. As is shown in the Table 2, there are 24 cases in total. Among the 24 cases, 6 cases are the joint events summer pNAO ⊕ pNWP, 9 cases are the single summer pNAO events, and the rest 9 cases are single summer pNWP SSTA events.   1961, 1967, 1994, 2001, 2013, 2017 1970, 1973, 1979, 1983, 1984, 1988, 1990, 1996, 2002 1964, 1971, 1975, 1978, 1991, 1998, 1999, 2000, 2004 After dividing into different kinds of cases, the three greatest TX90p anomalies in Fig. 5a are all joint events summer pNAO ⊕ pNWP, which implies there are greater extreme heat index magnitudes for joint events summer pNAO ⊕ pNWP. Besides, all the joint events summer pNAO ⊕ pNWP are positive TX90p or TXx anomalies, which demonstrates that the same-sign rate of joint events summer pNAO ⊕ pNWP is far greater that of the other two kinds of single events. Similar results could be found in TN90p and TNx, 5 in 6 joint events summer pNAO ⊕ pNWP are positive, and the only left are weak negative. This result indicates a greater probability of strengthened extreme heat events when the two factors both happen. The averaged TX90p, TXx, TN90p and TNx anomaly values for joint events summer pNAO ⊕ pNWP are 6.83, 0.66, 7.24 and 0.38 respectively, which are much larger (up to 10 times) than those for the single summer pNAO events (-2.07, -0.23, -1.72 and -0.13) and single summer pNWP SSTA events (0.81, 0.06, 0.94 and 0.17). It is shown in Fig. 3a that there are greatly strengthened extreme heat events when pNAO is stronger. To further confirm whether the stronger pNAO happens in the joint events summer pNAO ⊕ pNWP, we compare the NAO anomalies for different events in Fig. 5e. It is clear that the NAO shows a much greater positive anomaly in the joint events summer pNAO ⊕ pNWP than that in the single summer pNAO events. Besides, after removing the NWP signal from the time series of the NAO index by the linear regression, the positive pNAO anomaly in the joint events years is much smaller. This result implies that pNWP SST could strengthen the pNAO, which means that pNWP SST is favorable for a greater pNAO anomaly. The above results manifest that there is a strong synergistic effect of the summer pNAO and pNWP SSTA, and the cooccurrence of the two factors leads to a higher daily temperature and increased hot day frequency. In other words, there will be more likely to be strengthened extreme heat events in the CEC when both of the two factors occur. Figure 6 further shows the composite maps of summer extreme temperature indices for different events. In the joint events summer pNAO ⊕ pNWP (Fig. 6a, d, g and j), we can clearly see that the extreme heat indices exhibit significantly positive anomalies in the CEC, and the area with the synergistic effect of the summer pNAO and pNWP SSTA could cover 20° to 40 °N, 90 °E to the eastern China. Although  (25°-40°N, 110°-125°E). The green, grey and yellow dots represent the joint events of summer pNAO and pNWP SSTA (pNAO ⊕ pNWP), single summer pNAO events and single summer pNWP SSTA events respectively. e The NAO anomalies for the joint events summer pNAO ⊕ pNWP (green), single summer pNAO events (grey) and joint events years after removing the NWP signal (magenta), respectively there may be some different mechanisms which works for TXx and TNx (Lobell et al. 2007;Yeh et al. 2021), the synergistic effect for the four indices is all evident in the CEC, which further highlights the robustness of the synergistic effect on the extreme heat events. It is also worth noting that the synergistic effect of the two factors is significant in most region of the CEC based on the bootstrapping method. The center of the positive anomaly lies in the eastern China, and extends to the central China, covering the region which the NAO is significantly correlated with. However, the anomalous extreme heat events in the CEC for the single summer pNAO events and summer pNWP SSTA events are insignificant (the second and third rows in Fig. 6). By comparing the spatial patterns of the extreme heat indices anomalies in the joint events summer pNAO⊕pNWP with those in the single summer pNAO events and summer pNWP SSTA events, we can clearly see that there is a significant synergistic effect of the summer pNAO and pNWP SSTA on strengthening the extreme heat events in the CEC.
The above results show that there is a significant synergistic effect of the summer pNAO and pNWP SSTA on strengthening the extreme heat events in the CEC, and a stronger pNAO will happen if the pNWP SSTA occurs.
Thus, questions are raised: does the synergistic effect arise from the strengthening of the pNAO in the joint events summer pNAO⊕pNWP, and what role does the pNWP SSTA play in the strengthening of the pNAO in the joint events summer pNAO⊕pNWP?

The atmospheric circulations in different events
To further determine the difference of the atmospheric circulations between three kinds of events, Fig. 7a, b and c show the composite maps of the summer 500-hPa geopotential height and 850-hPa winds in the East Asia for different events. As shown in Fig. 7a, there is a strong anomalous anticyclone over the eastern China, with strong southerlies in the CEC, and the center of the anticyclone locates between the Shandong Peninsular and Korean Peninsula. The anomalous southerlies in the west side of the anticyclone bring the warm air to the CEC, which is favorable for the increase of air temperature. Besides, the anomalous anticyclone can also hider the southern movement of the cold air to the CEC from the northern area. However, for the single summer pNAO events and single summer pNWP SSTA events, there is not significant atmospheric circulation anomaly over most of the East Asia ( Fig. 7b and c). It is worth noting that the two factors show a significant synergistic effect on the anomalous anticyclone in East Asia (Fig. 7a), which means the two factors may influence the extreme heat events by acting synergistically on the atmospheric circulation in the joint events summer pNAO ⊕ pNWP. According to the previous study , the atmosphere thickness is vital to the air temperature change, and the change of atmosphere thickness comes from the aforementioned perturbation of the upper-level atmospheric circulation, thus we further compare the atmosphere thickness in three kinds of events. Figure 7d, e and f display the composite maps of the summer 500 − 1000 hPa atmosphere thickness in the East Asia for different events. It is clear that there is a large area showing a positive atmosphere thickness anomaly in the CEC, and the two factors have a significant synergistic effect of the increased atmosphere thickness, which means that the positive atmosphere thickness anomaly is much stronger when both of the summer pNAO and pNWP SSTA occur (Fig. 7d). The correlation coefficient between the atmospheric thickness and air temperature over the CEC is 0.74, while the correlation coefficients between the air temperature and TXx, TNx, TX90p and TN90p are 0.68, 0.74, 0.71 and 0.74, respectively, and they are all statistically significant at the 99% confidence level based on the Student t-test. This result implies that the significantly increased atmosphere thickness leads to the air temperature increase in the atmospheric layer , which further favors the extreme heat events in the CEC. However, there is not significant atmosphere thickness anomaly over the CEC during the single summer pNAO events or single summer pNWP SSTA events ( Fig. 7e and f).
By comparing different events in Fig. 7, it can be found that the anomalous anticyclone with the significantly positive atmosphere thickness anomaly occurs over the CEC in the joint events summer pNAO ⊕ pNWP. The positive atmosphere thickness anomaly in the joint events summer pNAO ⊕ pNWP is much greater than that in the two kinds of single events, leading to the higher air temperature of the atmosphere layer in the joint events summer pNAO ⊕ pNWP. Therefore, the extreme heat events are far stronger in the joint events summer pNAO ⊕ pNWP, and the CEC is more likely to experience a hot summer.

The mechanism of the synergistic effect
The above results show that the summer pNAO and pNWP SSTA have a synergistic effect on the atmospheric circulation over the East Asia, and the significantly increased atmosphere thickness over the CEC contributes to the strengthened extreme heat events. Why is there such a great difference in the atmospheric circulation over East Asia between the joint events summer pNAO ⊕ pNWP and two kinds of single events? We mean to explore this question in this section.
To compare the Rossby wave propagation in different events, T-N wave activity flux is used, and it is a useful way to check the propagation of Rossby wave (Takaya and Nakamura 2001). Figure 8 shows the composite map of summer 500-hPa T-N wave activity flux and anomalous QG stream function for the joint events summer pNAO ⊕ pNWP, single summer pNAO events and all summer pNWP SSTA events. Previous studies have shown that the NAO is able to influence the atmospheric circulation in East Asia via Rossby wave (Watanabe 2004;Chen et al. 2005;Zuo et al. 2015;Li and Ruan 2018), and we further compare the difference of Rossby wave propagation in different events. As shown in Fig. 8a, it is clear that there is obvious easterly propagating Rossby wave from the Atlantic to the East Asia, and the easterly propagation of the Rossby wave is strong over the whole Eurasian continent. Therefore, it can lead to a strong atmospheric circulation response in the East Asia. Although there is easterly Rossby wave propagation from the Atlantic in the single summer pNAO events, the easterly Rossby wave propagation over the east side of the Eurasian continent is quite weak, which denotes the atmospheric circulation response in the East Asia is much weaker in the single summer pNAO events (Fig. 8b). The results in Fig. 5e indicate that the NAO has a much stronger positive anomaly when the pNWP SSTA occurs. Thus, a stronger pNAO leads to the enhanced Rossby wave propagation in the joint events summer pNAO ⊕ pNWP, and results in the significant atmospheric circulation response in the East Asia. How does the pNWP SSTA influence the strength of pNAO? As is shown in Fig. 8c, there is obvious easterly propagating Rossby wave from the western Pacific to the Atlantic in all the pNWP SSTA events, which indicates that pNWP SSTA may influence the atmospheric circulation over the Atlantic, and further lead to a pNAO-like atmospheric response, which can increase the pNAO strength. The above results show that, the pNWP SSTA could lead to a strengthened pNAO via the easterly propagating Rossby wave from the western Pacific, and the resultant stronger pNAO in the joint events summer pNAO ⊕ pNWP may lead to a stronger easterly Rossby wave propagation over the Eurasian continent. Thus, there is a significantly atmospheric circulation response over East Asia in the joint events summer pNAO ⊕ pNWP (Fig. 7a and 8a).
To further confirm the change of Rossby wave propagation from the Atlantic, the Rossby wave ray is compared Li et al. 2015Li et al. , 2019bLi et al. , 2021andZhao et al. 2015, 2019). Figure 9 shows the summer stationary Rossby wave trajectories in the horizontally nonuniform flow for different events. As shown in Fig. 9a and b, there is more Rossby wave energy propagating towards the east side of the Eurasian continent, and the Rossby wave is more concentrated over the CEC in the joint events summer pNAO ⊕ pNWP when the wave source is set around the southern activity center of the NAO (35°-45°N, 45°-70°W). The similar result can be found in Fig. 9c and d, which also demonstrates that there is much more easterly propagating Rossby wave energy in the east side of the Eurasian continent when the wave source is set around the northern activity center of the NAO (55°-65°N, 10°-50°W). The above results further confirm the finding in the results of T-N wave activity flux, which is that there is more Rossby wave propagating easterly over the Eurasian continent, leading to a stronger atmospheric circulation response over the east side of the Eurasian continent in the joint events summer pNAO ⊕ pNWP.
To further confirm the influence of the pNWP SSTA on the pNAO, we further use the LBM and carry three experiments. In the first experiment (EXP1), the heating source Fig. 8 The composite map of summer 500-hPa T-N wave activity flux (m 2 s −2 ; vectors) and anomalous QG stream function (10 6 m 2 s −1 ; shaded) for (a) the joint events of summer pNAO and summer pNWP SSTA (pNAO ⊕ pNWP), b single summer pNAO events and c all summer pNWP SSTA events is set in the domain 30°-50°N, 0°-60°W with a 4 K day −1 heating peaking at 0.7 sigma level, and the heating sink is set in the domain 60°-80°N, 0°-60°W with a − 6 K day −1 heating peaking at 0.6 sigma level, which mimics the pNAO situation. In the second experiment (EXP2), the heating source is set in the domain 20°-40°N, 130°-180°E with a 4 K day −1 heating peaking at 0.4 sigma level, which mimics the heating effect of the pNWP SSTA. The third experiment (EXP3) is a combination of EXP1 and EXP2, which includes all the heating effects of pNAO and pNWP. Figure 10 shows the steady 500 hPa geopotential height response in the three experiments. As shown in Fig. 10a, there is a positive geopotential height anomaly response over the CEC, indicating that the NAO is able to influence the atmospheric circulation Fig. 9 Summer stationary Rossby wave trajectories in the horizontally nonuniform flow (blue curves) with zonal wavenumber k = 4 for a and c the joint events of summer pNAO and summer pNWP SSTA (pNAO ⊕ pNWP), b and d single summer pNAO events. The black dots denote the Rossby wave source which is set in the south-ern activity center of NAO in a and b, and northern activity center of NAO in c and d. The shaded area is the climatological mean 500 hPa zonal wind (m s −1 ). The Rossby wave ray tracing is calculated by adopting the approach by Li and Li (2012), Li et al. (2015;2019b; and Zhao et al. (2015) and induce an anomalous anticyclone in this area. This result is consistent with the T-N wave activity flux and Rossby wave ray results. As shown in Fig. 10b, the heating effect of the NWP can induce the pNAO-like atmospheric response over the Atlantic, which means that the pNAO is likely to be strengthened when the pNWP SSTA occurs. This result may explain why the NAO shows greater positive anomaly in the joint events summer pNAO ⊕ pNWP than that in the single summer pNAO events (Fig. 5e). The pNAO-like atmospheric response to the heating effect over the NWP also confirms the T-N wave activity flux result of all the pNWP SSTA events (Fig. 8c). Besides, there is also a positive geopotential height anomaly response to the heating over the NWP in the CEC, which denotes that the pNWP SSTA has adjacent effect to the atmospheric circulation in the CEC, and it also favors the increase of geopotential height in the CEC (Fig. 10b). It is clear that both the heating effects of pNAO and pNWP could lead to a stronger positive anomalous geopotential height response over the eastern China, which highlights the synergistic effect of the two factors (Fig. 10c). The above LBM results confirm the effects of the pNAO and pNWP SSTA on the atmospheric circulation over the CEC and the effect of the pNWP SSTA on strengthening the pNAO. Thus, the NAO has a greater positive anomaly and a stronger atmospheric circulation response occurs over the CEC in the joint events summer pNAO ⊕ pNWP. Fig. 10 Steady 500-hPa geopotential height response (gpm) to a the NAO, b NWP and c both of the NAO and NWP heating in the LBM. The red and blue contours (unit: K day −1 , contour interval: 1 K day −1 ) indicate the heating source and heating sink respectively. The black crossed areas indicate the composite differences between EXP3 and EXP1, as well as EXP3 and EXP2, are both significant at the 95% confidence level based on the Student t test. The white dotted areas in c indicate the synergistic effect of the NAO and NWP heating effect 6 Summary and discussion In this paper, we investigate the synergistic effect of the summer pNAO and pNWP SSTA on the extreme heat events in the CEC, and find that the extreme heat events are significantly strengthened when the two factors occur, which means the cooccurrence of the two factors may lead the CEC to experience a hot summer. Figure 11 shows the process of the synergistic effect of the summer pNAO and pNWP SSTA on the extreme heat events in the CEC. The summer pNWP SSTA may increase the strength of summer pNAO via the atmospheric bridge, leading to a strengthened summer pNAO. There is eastward propagating Rossby wave from the western Pacific to the Atlantic, and the LBM confirms that the heating effect over the NWP can induce a pNAO-like atmospheric response over the Atlantic. Thus, there is a stronger summer pNAO. And the summer pNAO may influence the atmospheric circulation around the CEC via another atmospheric bridge which is the eastward propagating Rossby wave from the Atlantic. As the pNAO is much stronger when the pNWP SSTA occurs, the Rossby wave propagation over the Eurasian continent is stronger in the joint events summer pNAO ⊕ pNWP, which induces an anomalous anticyclone in the eastern China. The southerlies in the west side of the anomalous anticyclone bring the warm air to the CEC, and the significantly increased atmosphere thickness in the CEC induces the increase in the air temperature of the atmospheric layer, which favors the strengthened extreme heat events in the CEC. Besides, the pNWP SSTA also has adjacent effect on the atmospheric circulation over the CEC, there is a positive geopotential height anomaly response over the CEC to the heating effect over the NWP. Therefore, the summer pNAO and pNWP SSTA have a synergistic effect on the extreme heat events in the CEC, and the summer extreme heat events are significantly strengthened.
There are strong extreme heat events in China during the 2022 summer, and many regions in China suffer recordbreaking high temperature. It is worth noting that there are also the pNAO and pNWP SSTA happening in the summer of 2022 (figures not shown), which indicates that the extreme heat events in China may be partially resulted by the synergistic effect of the two factors, and it is of vital importance to pay more attention to the synergistic effect of the two factors in the weather forecast. However, besides the CEC, the western part of China also suffers extreme heat events in 2022 summer, especially for the Sichuan and Chongqing, and these areas are out of our investigated area. This implies that there may be other factors also contributing to the 2022 summer extreme heat events in China, especially in the western China, although the summer pNAO and Here, we only show the result based on 0.6 standards deviations. However, the synergistic effect of summer pNAO and pNWP SSTA is also evident under other thresholds, which highlights the robustness of the synergistic effect (Fig. S1). Besides, the greater the threshold is, the stronger the synergistic effect will be. However, a relatively great threshold could lead to relatively small sample sizes. Thus, we use the threshold of 0.6 standard deviations in the manuscript. It is also worth noting that we only discuss the synergistic effect of the summer pNAO and pNWP SSTA, there might be other factors having synergistic effect with the two factors. Besides the NWP, there are other places showing significant correlation with the extreme heat events in the CEC (Fig. 4), and they may also have the potential to influence the extreme heat events in the CEC synergistically, which needs further research. There are also some places in Fig. 3b which shows significant difference in different pNAO years with strong and weak extreme heat events, implying that they may contribute to the change in the response of the extreme heat events in the CEC, and they may also lead to a synergistic effect, which needs more detailed research. Furthermore, the synergistic effect of multiple factors is also worth investigating, but it requires the data covering a much longer time period to provide enough sample sizes.