We first examine the variability of the SAH, SMJ, and AMO on the interdecadal timescale using four reanalysis datasets from 1958 to 2010 for JRA-55, 1948–2010 for NCEP/NCAR, and 1900–2010 for 20CRv3 and ERA-20c. Following previous studies (Wei et al., 2014, 2015), the dominant modes of the 200-hPa geopotential height anomalies over (15°–40°N; 20°–130°E), where the main body of the SAH is generally located, extracted by the EOF technique are usually used to examine the SAH variation. Figure 1 shows the first EOF (EOF1) modes and the corresponding principal component (PC1) time series of the summer 200-hPa geopotential height anomalies from four reanalysis datasets. Spatial patterns of the EOF1 show same-sign geopotential height anomalies over the considered area and seem obviously consistent in four reanalysis datasets (Figures 1A,C,E,G). The EOF1s of the JRA-55, NCEP/NCAR, 20CRv3, and ERA-20c account for 58%, 57.3%, 65.6%, and 59% of the total variances, respectively. The correlation coefficients between the PC1 and the normalized SAHI index are calculated in Table 2 for the different datasets. The two time series are highly consistent with each other in four datasets with all of the correlation coefficients exceeding 0.8. Thus, the EOF1 represents the variation of the SAH strength.

Before any analysis is performed, the consistency of the SAH and SMJ strength variabilities represented by the different datasets is checked by calculating the correlation coefficients of the PC1 and SMJI time series among the datasets (Table 3). Almost all of the correlation coefficients exceed the 95% confidence level based on two-tailed Student’s t-test, except for the correlation coefficients of the SMJI index between the NCEP/NCAR and 20CRv3 dataset. The SAH strength variability in the ERA-20c dataset is highly consistent with that in the JRA-55 and 20CRv3 datasets, with all the correlation coefficients on the order of 0.75 or higher during their overlapping periods. In contrast, the SMJ strength variability is less consistent among the different datasets with only the correlation coefficients between the ERA-20c and JRA-55 datasets for the period of 1958–2010 exceeding 0.7. Therefore, the ERA-20c datasets during the period of 1900–2010 is used throughout this study except where otherwise stated explicitly. As evidenced by Figures 1B,D,F,H, the remarkable interdecadal variabilities of the SAH and SMJ strength are clearly seen by PC1 and SMJI time series. Except for the 20CRv3 dataset, almost all of the correlation coefficients between the 9-year running averaged component of the PC1 and those of the SMJI in the different datasets are on the order of 0.6, exceeding the 99% confidence level. The time series of the SMJI on the interdecadal timescale is in phase with that of the PC1 as shown by the 9-year running averaged component of the PC1 and SMJI. Our previous work also verified the positive correlation between SMJ strength and South Asian High on interdecadal timescale, when the SMJ strength is weak (strong), the summertime South Asian High is also weak (strong) and retreats westward (advances eastward) (Shi et al., 2017). As revealed by previous studies, the synchronous variability of the SAH and SMJ strength could be achieved via the upper-level tropical easterly jet across the Indian subcontinent (Ashfaq et al., 2009; Hu et al., 2010; Ren et al., 2014; Shi et al., 2017). A stronger summer SAH changes the upper-level wind circulations and leads to the anomalous easterly flow over the south of the SAH location (represents a stronger upper-level tropical easterly jet). Thus, anomalous lower-level westerly flow over the Arabian Sea occurs via the meridional circulation of the ISM and leads to a strengthening of the SMJ.

The AMO is one of the two leading modes of the internally generated interdecadal variability of the climate system (the other is the Interdecadal Pacific Oscillation) (Liu, 2012). It has considerable impacts on the summer monsoon system. As previous studies investigated, the AMO-related SSTAs show a basin-wide warming/cooling in the North Atlantic, with tropical and extratropical branches centered over the tropical North Atlantic and Labrador Sea, respectively (e.g., Sutton and Hodson, 2005; Gastineau and Frankignoul, 2015). Figures 2B–I show regressions of the interdecadal SST component onto the interdecadal component of the SMJI and PC1 in summer from the different datasets. The AMO-like regression SST patterns are seen from the northern Atlantic Ocean in the JRA-55, 20CRv3, and ERA-20c datasets. In contrast, the AMO-like SSTAs are much weaker in the NCEP/NCAR dataset than those in the other datasets. This analysis reveals a positive correlation of the AMO with the SAHI and SMJI in an interdecadal timescale. A remarkable feature of the AMO index in the latest 100 years is that the AMO has experienced three cold–warm phase turnings, with the turning points in near mid-1920s, 1960s, and mid-1990s (Figure 2A). Comparing Figures 1F,H and Figure 2A, it is easy to find that these three indices (PC1, SMJI, and AMO) evolve almost synchronously on multidecadal timescales, with the two AMO cold phases (AMO−) for a period of 59 years (1900–1925 and 1963–1995) corresponding to the weak phases for the SAH and SMJ, and the two warm AMO phases (AMO+) for 52 years (1926–1962 and 1996–2010) corresponding to the strong phases for the SAH and SMJ.

In the following, we further conduct a composite analysis of the summer 925-hPa wind anomalies, 200-hPa geopotential height anomalies, and zonal mean meridional wind anomalies below 500 hPa along equator for AMO− years (1900–1925 and 1963–1995) and AMO+ years (1926–1962 and 1996–2010). The blue and pink solid contours in Figure 3 represent the composited ridge lines (i.e., 12,500- or 12,400-gpm contours of the 200-hPa geopotential height) of the summer SAH for the AMO− and AMO+ years, respectively. Figures 3E,F show that significant northwesterly/southeasterly anomalies appear over the western Indian Ocean between 0° and 25°S for AMO−/AMO+ years in the ERA-20c dataset, indicating marked weakening/strengthening of the SMJ in the AMO cold/warm phase. This is also announced by northerly/southerly wind anomalies for the AMO−/AMO+ phase from the ERA-20c dataset at 40°E below 600 hPa, which is the domain region of the SMJ, with its maximum center occurring between 800 and 700 hPa (Figures 4C,D). The significant northerly/southerly anomalies from the Arabian Sea to the Southern Indian Ocean are also seen from the 925–hPa wind anomalies composite of the 20Rv3 dataset (Figures 3A,B). The northerly/southerly wind anomalies exceeding 90% confidence level for AMO−/AMO+ phase in the 20CRv3 dataset are also found at 50°E below 800 hPa. Furthermore, associated with the AMO cold/warm phase, large-scale negative/positive geopotential height anomalies at 200 hPa are seen from Figures 3C,D,G,H with significant values over Northeast Asia and the Mediterranean Sea and extending from the Arabian Peninsula to the Bay of Bengal. In comparison, the significant height anomaly area from the 20CRv3 dataset, which extends from the Northern Africa to the northwestern Pacific Ocean is substantially larger than that from the ERA-20c dataset. The above evidences indicate that when the AMO is in the cold (warm) phase, the summer SAH tends to weaken and shrink (intensify and expand) as revealed by the composited ridge lines and the composites of the SAH intensity and area calculated in Table 4. The quantitative analyses in Table 4 clearly show that the differences of the SAH area and intensity between the warm and cold AMO phases from both 20CRv3 and ERA-20c datasets are significant and exceed the 95% confidence level.

To investigate the effects of the AMO phases on the intensity of the SAH and SMJ on the interdecadal timescale, a composite analysis is performed on the lower and upper atmospheric circulations for the AMO− and AMO+ periods. Figure 5 illustrates the composites of the SSTAs over the northern Atlantic Ocean and SLP anomalies in summer during the AMO− and AMO+ periods for the ERA-20c dataset during the period of 1900–2010. In the AMO− phase, the negative SSTAs are clearly seen over nearly the whole northern Atlantic Ocean region. Two significant value branches centered over the tropical North Atlantic and Labrador Sea. However, remarkable positive SLP anomalies are located near 20°N and 60°N of the Atlantic Ocean, as well as around the west of the Arabian Peninsula. Clearly, the large-scale negative SLP anomalies appear in Northeast Asia. In the AMO+ phase, the result is well similar to that in the AMO− but with the opposite sign. The tropical and extratropical branches of the SSTAs are coinciding with the location of the SLP anomalies over the northern Atlantic Ocean. It seems that the cold/warm Atlantic Ocean SSTAs could promote/reduce SLP anomalies over the tropical and extratropical Atlantic Ocean because of the atmospheric instability. Significantly, the SLP anomalies around the west of the Arabian Peninsula weaken/enhance the SLP gradient between the tropical Indian Ocean and the continent to its northwest, which will mainly contribute to the decreased/reinforced SMJ strength on the interdecadal timescale as shown in Figures 3E,F.

Along the Asian westerly jet, there is a wave train-like teleconnection pattern zonally propagating from Europe to East Asia. This pattern is referred to as the SRP, which is similar to the CGT over the Eurasian continent (e.g., Ding and Wang, 2005; Hong et al., 2018). The SRP, the leading mode of the upper tropospheric meridional wind anomalies in summer (e.g., Hong and Lu, 2016; Kosaka et al., 2009; Sato and Takahashi, 2006; Cen et al., 2020), indicates both a remarkable interannual component and a considerable decadal component (e.g., Enomoto et al., 2003; Lu et al., 2002; Sato and Takahashi, 2006; Hong et al., 2018; Wang et al., 2017; Lin et al., 2016). The temporal evolution in the interdecadal component of the SRP was found to be synchronous with that in the AMO. Based on sensitivity experiments driven by the specified AMO-related SSTAs in the North Atlantic using five AGCMs, Lin et al. (2016) suggested that ID-CGT pattern should be excited, at least partially, by the AMO-related SSTAs. To confirm this, Figures 6A,B illustrate composites of the summer 200-hPa meridional wind anomalies and the summer horizontal wave activity flux during the AMO− and AMO+ phases for 1900–2010. The wind anomalies appear as a clear wave-like pattern characterized by alternate southerly and northerly anomalies along the Asian westerly jet (the blue solid contours in Figure 6). The midlatitude wave train is consistent with the interdecadal component of SRP as announced by various previous studies (e.g., Chen and Huang, 2012; Hong and Lu, 2016; Kosaka et al., 2009; Lu et al., 2002; Sato and Takahashi, 2006; Yasui and Watanabe, 2010). For the AMO− period, southerly anomalies are centered over the tropical North Atlantic, Labrador Sea, Caspian Sea, and northeast Asian and northerly anomalies around the East Europe, North Africa, Lake Belga, and east of the Okhotsk Sea (Figure 6A). The wave activity flux (Takaya and Nakamura 2001) associated with the AMO− phase emanates from Europe, enters the Asian jet stream near the Caspian Sea, and points continuously eastward toward East Asia along the jet stream, confirming that the wave-like pattern is a Rossby wave train. For the AMO+ period, locations and amplitudes of the anomalous centers tend to be similar but with the opposite phase (Figure 6B). To further confirm whether this AMO-related wave-like pattern is similar to the interdecadal SRP, we then compare the regression of the interdecadal component of the summer 200-hPa meridional wind and horizontal wave activity flux anomalies onto the interdecadal component of the summer AMO and SRP indices in Figures 6C,D. Clearly, the alternate southerly and northerly anomalous centers along the Asian westerly jet are essentially consistent in Figures 6C,D, except for the anomalies over the northern Atlantic Ocean. Both regressions of the horizontal wave activity flux anomalies in Figures 6C,D are propagating from East Asian to Europe along the jet stream, which reveals the warm AMO phase corresponding to the negative phase of the SRP. Similar results are obtained by Wang et al. (2017), and they also suggest that the positive (negative) phase of the AMO significantly facilitates the occurrence of a negative (positive) phase of the interdecadal SRP (e.g., figure 9B and figures 11A,B of Wang et al., 2017). The spatial similarity coefficient between the regression of the interdecadal 200-hPa meridional wind onto the AMO index (Figure 6C) and that onto the SRP index (Figure 6D) in the main SRP region (30°–60°N, 30°–130°E) is as high as 0.72, indicating that the AMO-related wave-like pattern is a SRP-like wave train.

Figure 7 is the same as Figure 6, but for the summer 200-hPa geopotential height anomalies (departures from zonal means), 200-hPa relative vorticity anomalies, and horizontal wave-activity flux anomalies. In the AMO− phase, a well-organized wave train between 30°N and 60°N propagates along the Asian westerly jet (the blue solid contours in Figure 7) with positive geopotential height/negative relative vorticity anomalies over the northern Atlantic Ocean and east of the Caspian Sea and negative geopotential height/positive relative vorticity anomalies over the Mediterranean Sea, Arabian Peninsula–Iranian Plateau, and Northeast Asia (Figures 7A,C). These positive and negative anomalies are consistent with the 200-hPa meridional wind anomalies shown in Figure 6A. Actually, this atmospheric wave train originated from the extratropical Atlantic Ocean, which can be confirmed by the wave activity flux (Figure 7A). This suggests that in virtue of the strong barotropic instability at the jet exit region over the North Atlantic during the AMO− phase, an anomalous high can be triggered over the extratropical Atlantic Ocean, followed by alternatively positive and negative anomalies further downstream. The consistent positive anomalies over the extratropical Atlantic Ocean and negative anomalies over Northeast Asia in SLP with those in 200-hPa geopotential height reveal a barotropic structure. The barotropic property of the Rossby wave train on interdecadal timescale as suggested by previous studies (Luo et al., 2011; Lin et al., 2016; Hong et al., 2018) also can be revealed by the zonal mean height/relative vorticity from 30°W to 120°E in Figure 8. The barotropy of the cyclonic/anticyclonic centers between 0° and 30°E in the AMO−/AMO+ phase is relatively weak in the geopotential height field (Figures 8A,B), but it is strong and significant in the relative vorticity field (Figures 8C,D). As suggested by Hoskins et al. (1977), the relative vorticity has some advantages over geopotential height in representing the two-dimensional propagation of Rossby waves.

As indicated by the wave activity flux, the interdecadal SRP-like wave train excited by the cold SST anomalies over the extratropical Atlantic Ocean propagates poleward across Europe and then to the equator across Northeast Asia. Specifically, the negative 200-hPa geopotential height/positive 200-hPa relative vorticity anomalies from the Mediterranean Sea to the Arabian Peninsula corresponding to the positive SLP anomalies around the west of the Arabian Peninsula indicate a strong baroclinicity of the local atmospheric circulation, which is favorable to the weakening of the SAH and SMJ. Meanwhile, the strong and significant anomalies over the northwest Pacific Ocean in the geopotential height field (departure from zonal mean) are relatively weak and insignificant in the original geopotential height (Figures 3G,H) and relative vorticity fields (Figures 7C,D), which suggests that the weakening or strengthening of the summer SAH mainly rely on the low/high anomaly from the Arabian Peninsula to the Bay of Bengal (Figures 3G,H). In the AMO+ phase, a similar Rossby wave train pattern propagating from the North Atlantic across Northeast Asia is visible (Figures 7B,D), but with a quite opposite phase. The above result indicates that a propagating Rossby wave train associated with the AMO−/AMO+ phase leads to reduced/enhanced SAH via the anomalous Arabian Peninsula–Iranian Plateau low/high along with its path, and consequently a weakening/strengthening of the SMJ through the weakened/enhanced pressure gradient between the tropical Indian Ocean and the continent, which is caused by the baroclinic structure of the local atmospheric circulation over the Arabian Peninsula–Iranian Plateau (Figures 5C,D).

By now, we have clearly demonstrated the modification of AMO-related SSTAs on the interdecadal variabilities of the SAH and SMJ intensities through the propagation of the interdecadal SRP-like wave train excited by the extratropical heating branch. As diagnosed in Figures 5A,B, the tropical heating branch related to the AMO phase cannot be ignored, but how it can exert influence on the interdecadal variabilities of SAH and SMJ intensities is still unclear. To investigate the tropical atmospheric response to AMO-related SST anomalies, we conducted a composite analysis of SAT anomalies, equivalent potential temperature (EPT) anomalies at 1,000 hPa, and tropospheric temperature anomalies (average between 850 and 200 hPa) in summer during the AMO− and AMO+ periods (Figure 9). For the summer SAT, significant negative temperature anomalies exist over the tropical and extratropical North Atlantic, as well as the northern African continent and Central Siberia area in AMO−, but there are obvious positive anomalies over these domains in the AMO+. The response of the EPT anomalies at 1,000 hPa is the same as that of the SAT, but with the significant value around the Central Siberia area, which expands southward to the tropical Indian Ocean, which is a result of the Matsunuo–Gill response of the tropical atmosphere. For the tropospheric temperature (average between 850 and 200 hPa), the temperature response exhibits a Matsunuo–Gill-like pattern with uniform negative/positive values zonally extending to the entire tropical region in the AMO−/AMO+ phase. Qian et al. (2002) pointed out that the center of the SAH has the heat preference property, which is usually located over or moving toward an area with larger heating rates. Huang et al. (2011) also indicated that tropical tropospheric temperature variation is closely related to geopotential height anomalies at the upper troposphere and variation of the SAH in terms of both intensity and spatial location. The tropospheric warming over the tropical Indian Ocean is favorable for a positive height anomaly in the south of the SAH location in summer, which results in the strengthening and southward shifting of the SAH. According to the barometric equation, the negative/positive AMO-related tropical SSTAs cool/warm the tropospheric temperature in the south of the SAH location and then lower/elevate the height above it, which is favorable for the weakening/strengthening and northward/southward expansion of the SAH.

Besides, pronounced anomalies are found around the western Atlantic Ocean, northeast Asia, Mediterranean Sea, and Arabian Peninsula, which mainly result from the interdecadal SRP-like wave train triggered by the extratropical AMO-related SST anomalies. Among them, the significant negative/positive temperature anomalies from the Mediterranean Sea to the Arabian Peninsula could decrease/increase meridional gradient of the tropospheric temperature between the tropical Indian Ocean and its north continent. The increased meridional gradient anomalies of the tropospheric temperature over the tropical Indian Ocean associated with the AMO+ could enhance the SMJ. This mechanism coincides with previous works (Goswami et al., 2006; Feng and Hu, 2008; Li et al., 2008; Luo et al., 2011), which viewed that the ISM may be enhanced by the AMO through the increased meridional gradient of the tropospheric temperature between the Indian subcontinent and tropical Indian Ocean. To provide more evidence, the composite of the meridional mean (30°–80°E) air temperature anomalies in summer during the AMO− and AMO+ periods is investigated in Figures 10A,B. In AMO−, remarkably significant negative values between 20°N and 30°N could extend to nearly 200 hPa, which reduces the meridional gradient of the tropospheric temperature between the tropical Indian Ocean and its north continent, as well as consequently weaken the SMJ intensity. The result in the AMO+ phase is exactly opposite to that in AMO−, with stronger positive anomalies at 20°N–30°N from the surface to the upper layer, which mainly contribute to the strengthened SMJ.

Next, how can the AMO-related SSTAs or SAT anomalies over the tropical Atlantic Ocean influence the tropical tropospheric temperature anomalies? Many studies viewed that the moist adjustment process was very important for the tropospheric warming in the tropical atmosphere (Emanuel et al., 1994; Su et al., 2003; Su and Neelin, 2003). As verified by Xie et al. (2009), SST warming in the tropical Indian Ocean could warm the overlying atmospheric column through modifying the EPT and moist static energy in the atmospheric boundary layer, with a Matsunuo–Gill response of the tropospheric temperature anomalies located over the Indian Ocean. A qualitatively similar response of the tropical tropospheric temperature anomalies to the AMO-related SSTAs over tropical North Atlantic is seen from Figures 9E,F. Response of the tropospheric temperature to SSTAs in the tropical North Atlantic Ocean exhibits an obvious Matsunuo–Gill-like pattern with the large-scale approximate uniform anomalies covering the whole tropical region. This is also revealed by the zonal mean (0°–30°N) EPT anomalies composed during the AMO− and AMO+ periods in Figures 10C,D. In AMO−, the significant negative EPT anomalies can extend from the surface to more than 200 hPa over the tropical Atlantic Ocean (between 80°W and 30°W). An approximate uniform variation of the EPT anomalies from the lower to upper level is also seen between 30° and 90°E. These reveal that the EPT change in the atmospheric boundary layer (seen from Figures 9C,D) induced by AMO-related SSTAs is an important pathway through which the lower atmospheric heat can be transferred to the upper layer, modifying the tropospheric thermal variation. In the AMO+, the result is similar to that in AMO−, but with an opposite sign. In brief, the AMO-related tropical SST cooling (warming) induces negative (positive) EPT variation in the atmospheric boundary layer, modulates air temperature of the overlying atmosphere, and further cools (heats) the atmospheric column.

To better understand the AMO modulation on the interdecadal variabilities of the summer SAH and SMJ intensities via the tropical atmospheric response, we further focus on the composites of the 500-hPa omega anomalies, divergent wind, and velocity potential anomalies at 1,000 and 200 hPa in summer for the AMO− and AMO+ phases (Figure 11). As for the 500-hPa omega anomalies, significant AMO− phase-related subsiding anomalies are found over the northern tropical North Atlantic, southern Sahel, central tropical Indian Ocean, and central East Asia where the reverse signal of vertical velocity can be seen for the AMO+ (Figures 11A,B). Among them, the descending motion anomaly over northern tropical North Atlantic and central East Asia in Figure 11A is mainly associated with a southward shift and weakening of the climatological Intertropical Convergence Zone (ITCZ), which is in accordance with previous results (e.g., Zhang and Delworth, 2006; Luo et al., 2011), while pronounced descending motion anomalies over the southern Sahel of Figure 11A are suggestive of a decreasing Sahel summer rainfall as investigated by Zhang and Delworth (2006). In particular, subsidence motion anomalies over the central tropical Indian Ocean (Figure 11A) correspond to a basin-wide divergence in the lower troposphere and convergence in the upper troposphere over the tropical Indian Ocean during the AMO− period (Figures 11C,E). The tropical Indian Ocean divergence associated with the AMO− phase in the lower troposphere leads to the weakened SMJ, and the tropical Indian Ocean convergence for the AMO− phase in the upper troposphere is favorable for the decrease and northward displacement of SAH. Here, the extratropical divergence/convergence over the North Atlantic in the lower/upper troposphere is produced by the extratropical North Atlantic heating, and the tropical divergence/convergence extending from North Atlantic to the tropical Indian Ocean in the lower/upper troposphere is suggestive of a Matsunuo–Gill-like pattern trigged by tropical North Atlantic heating in agreement with our above result. For the AMO+ phase, the result is quite opposite, which is conducive to the strengthening of the SMJ and SAH in summer (Figures 11B,D,F).