Diversity of the tropical easterly jet’s core location

The upper-tropospheric tropical easterly jet (TEJ) is one of the most important systems in modulating the Asian summer monsoon rainfall. In addition to the intensity variability that has been extensively studied, the TEJ’s core experiences remarkable changes in the zonal and meridional directions. The TEJ can be identified as three locational patterns using the cluster analysis: the east, northwest, and southwest modes. The frequencies of the three locational modes exhibit discernable changes on the monthly and the interannual-decadal time scales. While the anomalous zonal divergent circulation with the convergent/divergent center over the tropical Indian Ocean (IO) determines the zonal location of the TEJ’s core, the meridional temperature gradient between the Eurasian continent and the tropical IO distinguishes the meridional location of the TEJ’s core. It reflects the fundamental role of the large-scale east-west and north-south thermal contrasts in the movement of the TEJ’s core location. The variability of the TEJ’s core location has distinct impacts on the summer monsoon precipitation via redistributing the upper-level divergence and modulating the monsoon meridional circulation, especially in South, Southeast, and East Asia. In conjunction with the thermal effect of the Tibetan Plateau, the meridional shift of the TEJ’s core can affect the precipitation along the south slope of the Tibetan Plateau. These findings highlight the cause of the diversified TEJ’s core location and the significant impacts on the summer monsoon rainfall.


Introduction
In boreal summer, a strong easterly stream is found in the upper troposphere in the tropics, which is the so-called tropical easterly jet (TEJ) (Koteswaram 1958).It is a large-scale geostrophic jet stream extending from the tropical western Pacific westward to the tropical eastern Atlantic, with the peak easterly wind speed greater than 20 m s −1 over the tropical Indian Ocean (IO) (figure 1(a)).The formation of the TEJ originates from the gigantic thermal contrast between the Asian landmass and the IO and the elevated heating of the Tibetan Plateau (Koteswaram 1958).It is one of the most prominent components of the Asian and African summer monsoon systems (Krishnamurti and Bhalme 1976) and exhibits obvious changes in the wind intensity and the spatial location (Huang et al 2020).
Most of the previous research focused on the variability of the TEJ's intensity from the intraseasonal and interannual time scales to the long-term trend (Chen and Yen 1991, Sathiyamoorthy 2005, Sathiyamoorthy et al 2007, Roja Raman et al 2009, Sreekala et al 2014, Sharma et al 2024), which can be attributed mainly to the tropical sea surface temperature (SST) anomalies and the latent heat released by the tropical convection through the modulation on the tropical divergent circulation and the meridional temperature gradient (MTG) (Ramesh et al 1996, Pattanaik and Satyan 2000, Sathiyamoorthy et al 2007, Abish et al 2013, Nithya et al 2017, Huang et al 2019, 2021).It has been well demonstrated that the change in the TEJ's intensity plays an important role in summer monsoon rainfalls in the Afro-Asian region (Hulme and Tosdevin 1989, Nicholson 2008, Fontaine et al 2011, Rai and Dimri 2017, Lemburg et al 2019), tropical cyclone activities in the North IO and western North Pacific (Rao et al 2004, 2008, Zhan et al 2022a, 2022b), the atmospheric wave and disturbance (Sasi et al 2000, Ramkumar et al 2010) as well as the northward propagation of the boreal summer intraseasonal oscillation (Jiang et al 2004, Drbohlav andWang 2005).
The variability of the TEJ's core location has received less attention.Earlier studies noticed the seasonal evolution of the TEJ's core location, which exhibits a northwestward movement in June and a southeastward retreat in September, concurrent with the onset and withdrawal of the Asian summer monsoon, respectively (Koteswaram 1958, Ding et al 1988).During the Indian summer monsoon season, the TEJ tends to locate southward in the active spell but northward in the break spell (Sathiyamoorthy et al 2007).Lu and Ding (1989) first examined the interannual location of the TEJ's axis and identified five patterns (i.e.western, middle, eastern, twobranch, and multi-core) with a coarse data resolution (5 • longitude × 5 • latitude) and a limited analysis period (1968)(1969)(1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980).The advent of high-resolution reanalysis data provides opportunities to elaborate the spatial structure of the TEJ, especially its core location.For example, Rao and Srinivasan (2016) showed that the TEJ's core obtained from the National Centers for Environmental Prediction (NCEP) reanalysis data with a 2.5 • × 2.5 • resolution is located westward by ∼20 • in July 1988 relative to 2002.Based on the fifth generation of the European Centre for Medium-Range Weather Forecasts (ERA5) atmospheric reanalysis data with a horizontal resolution of 2.5 • × 2.5 • , Ye et al (2023) suggested an interannual longitudinal oscillation of the TEJ's core, which is most evident in June than July and August.They used the principal component of the second empirical orthogonal function (EOF) mode of the upperlevel zonal wind to depict the longitudinal oscillation of the TEJ's core and found it independent of the change in the intensity and the latitude of the TEJ's core.Recently, Liu et al (2024) recognized obvious latitudinal movements of the TEJ's core in both June and July using the 1 • × 1 • data resolution.They further pointed out a close relationship between the longitudinal and latitudinal variations of the TEJ's core in July and thus proposed a northwest-southeast locational index.It is clear from the literature that the zonal and meridional variations of the TEJ's core location would differ from month to month, which may be an obstacle to the application of a unified locational index.An objective investigation of the TEJ's core location diversity is essential for gaining a comprehensive understanding of the locational variation of the TEJ's core and the related mechanism.Rao and Srinivasan (2016), Ye et al (2023), andLiu et al (2024) achieved a consensus that the diabatic heating associated with the convective activity in South Asia results in the change in the TEJ's core location through affecting the zonal divergent circulation, but the influence of the MTG, a critical factor for the genesis of the TEJ, is less mentioned.Yet how the MTG contributes to the locational variation of the TEJ's core remains unclear.
In this study, we utilized an objective cluster analysis to distinguish the locational modes of the TEJ's core and examine their spatiotemporal characteristics.We attempted to unravel the possible causes of the TEJ's core location diversity and the impact on the summer monsoon precipitation.The results are expected to advance our knowledge of the TEJ's variability and offer valuable insights into the dynamical mechanism of the Asian summer monsoon variability.

Data and method
The monthly mean variables used in the present study are derived from the ERA5 reanalysis data with a horizontal resolution of 1 • × 1 • (Hersbach et al 2020), including the three-dimension wind fields, geopotential height, temperature, total precipitation, surface fluxes, and the radiation.The column-integrated heat source/sink (Q 1 ) is calculated following Yanai et al (1973).The monthly mean SST data is obtained from the Met Office Hadley Centre Sea Ice and SST (HadISST1) datasets (Rayner et al 2003).The analysis focuses on June, July, August, and September when the TEJ dominates the tropical IO from 1979 to 2023, and the TEJ in each month is considered as an individual case so there are 180 TEJ cases in total (45 years × 4 months).The anomaly is calculated as the deviation from the average across the 180 cases.The student's t test is used for the statistical significance.
The K-means cluster analysis (Kaufman and Rousseeuw 1990) is applied to objectively classify the locational patterns of the TEJ.First, a threshold of 1 m s −1 surrounding the peak easterly wind (U peak ) is used to detect the jet's core zone.A larger threshold would lead to a poorer representation of the TEJ's core (figure not shown).Then the value of 1 is assigned to the grid points within the core zone and the value of 0 outside the zone to eliminate the influence of the wind speed.The calculation is as follows: where U represents the 200 hPa zonal wind at each grid point.The 180 arrays of X within the region of 10 • S-20 • N, 30 • -110 • E are finally input into the Kmeans algorithm.'Cosine' is adopted to measure the distance between each cluster member and the corresponding cluster centroid.The 180 TEJ cases can be optimally classified as three clusters.Thirty-one out of 180 members with a silhouette value (a proxy to assess the skill of the cluster) less than 0.1 are considered poorly matched to the corresponding cluster centroid and excluded from this study.Additionally, four 'outliers' are removed as their corresponding grid points of U peak are visibly inconsistent with the cluster centroid (figure S1).Finally, there remain 145 TEJ cases in the three clusters (figure S2), which will be analyzed in the following study.

Diversity of the TEJ's core location
The location of the TEJ's core oscillates strikingly in both zonal and meridional directions (dots in figure 1(a)).The longitudinal frequency exhibits a bimodal distribution, indicating two preferable locations of the TEJ's core in the zonal direction.About 56% of the cores appear to the east of 75 The K-means cluster analysis classifies the TEJ's core locations into three optimal clusters.Figures 1(d)-(l) show the composite structure of the TEJ and the frequency distribution of the TEJ's core location in each cluster.The first cluster exhibits the TEJ's core located to the east of 75 • E and concentrated around Sri Lanka (averagely at 79 • E, 7 • N) (figures 1(d)-(f)).The TEJ's cores in the other two clusters appear to the west of 75 • E, but they are distinguished by the meridional displacement.The TEJ's core at a higher latitude is located to the east of Somali (averagely at 58 • E, 11 • N) (figures 1(g)-(i)), whilst the TEJ's core at a lower latitude is centered over the equatorial central-western IO (averagely at 64 • E, 4 • N) (figures 1(j)-(l)).Therefore, the three clusters are referred to as the east mode, the northwest mode, and the southwest mode, respectively, according to their relative locations.The U peak of the three location modes (−24.2 m s −1 , −24.6 m s −1 , and −23.9 m s −1 ) is nearly identical to the climatological mean (−24.0 m s −1 ), suggesting the independence between the location and the intensity variabilities of the TEJ's core.
The three locational modes account for approximately 42%, 21%, and 17% of the total TEJ cases, respectively.However, the frequency of each mode differs from month to month (figure 2(a)).The occurrence frequency among the east (29%), the northwest (20%), and the southwest modes (22%) are comparable in June, whereas the east mode (64%) is most predominant in August.The TEJ's core location in July primarily exhibits a change between the east and the northwest modes, coherent with the northwest-southeast shift of the TEJ's core suggested by Liu et al (2024).In September, the considerable frequency of the east and the southwest modes may imply a southwest-northeast movement of the TEJ's core.
The frequency of the northwest mode experiences a remarkable decline from the 1980s to 2010s, but the southwest mode increases dramatically, concurrent with the slight increase of the east mode (figures 2(b)-(d)).The number of the northwest mode in the 2010s is only 5, with a reduction of 61% compared to that in the 1980s (13).In contrast, the number of the southwest mode in the 2010s ( 11) is almost four times that in the 1980s (3).It should be noted that the total frequency of the northwest and the southwest modes is approximately equal to that of the east mode in each decade except the 2000s.It can be inferred that the TEJ's core tends to oscillate in the northwestsoutheast direction in the 1980s but in the southwestnortheast direction in the 2010s, illustrating a regime shift in the interannual oscillation of the TEJ's core location.It may be attributed to the strengthening trend of the easterly wind in the southern part of the TEJ throughout June to September (figure S3), which may stem from the arrest of the declining MTG between the Tibetan Plateau and the tropical IO (Sharma et al 2024), the lower stratospheric ozone recovery (Venkat Ratnam et al 2013), and the intensified Walker circulation in recent decades (England et al 2014).
The structural differences among the three modes are further examined.The eastward and the westward shifts of the TEJ's core regardless of the latitudinal displacement show different easterly wind distributions near the equator.The southern-branch easterly jet over the Maritime Continent (MC) (Flohn 1964, Zhan et al 2022b) gets intensified as illustrated by the eastward expansion of the −12 m s −1 isotach for the eastward-shift core (figure 1(d)), whereas it retreats westward for the westward-shift core (figures 1(g) and (j)).Meanwhile, the extent of the TEJ over the equatorial western IO shrinks eastward (expands westward) as the TEJ's core moves eastward (westward).
While the TEJ structure in the off-equator region remains unchanged for the east mode compared to the climatology, it exhibits apparent differences between the northwest and the southwest modes (figures 1(g) and (j)).First, for the northwest mode, the northern-branch easterly jet along 20 • N is stronger than normal as reflected by the northeastward bulge of the isotaches over the northern South China Sea and the western North Pacific, whereas it weakens slightly for the southwest mode.Second, the intensification and expansion of the easterly wind in the outflow region over West Africa is obvious for the northwest mode relative to the reduction for the southwest mode.Third, the north edge of the −12 m s −1 isotach intrudes northward from 20 • N to 22 • N for the northwest mode, whereas it displaces southward slightly for the southwest mode.In short, the change in the TEJ's core location is more than a local phenomenon; it is tightly associated with the structural change of the entire TEJ.

Possible causes of the TEJ's core location diversity
The movement of the TEJ's core is closely linked to the inhomogeneous distribution of the zonal wind anomaly.The anomalous westerly over the tropical western IO and the anomalous easterly over the MC jointly shift the TEJ's core eastward (figure 3(a)).Conversely, the opposite signs of these wind anomalies lead to the TEJ's core shifting westward (figures 3(d) and (g)).Furthermore, the easterly anomaly dominating the northern flank of the TEJ from West Africa to the western North Pacific is responsible for the northwest mode (figure 3(d)), while the westerly anomaly there results in the southwest mode (figure 3(g)).Intriguingly, no significant wind anomalies appear in the subtropical region for the east mode (figure 3(a)).These zonal wind anomalies are important for distinguishing the locational modes of the TEJ's core and accounting for the different TEJ structures among the three modes.
The reversal of the anomalous zonal wind over the tropical western IO and the MC indicates the potential influence of the anomalous zonal divergent circulation.The eastward-shift TEJ's core is collocated with the upper-level convergent anomaly over the tropical IO, as shown by the positive 200 hPa velocity potential (VP) anomaly, whereas the upperlevel divergent anomaly is prominent for both the  1981-1990, 1991-2000, 2001-2010, and 2011-2020   northwest and the southwest modes (figures 3(b), (e) and (h)).The anomalous convergent/divergent center over the tropical IO also connotes the eastward/westward movement of the upward branch of the Pacific Walker circulation corresponding to the zonal shift of the TEJ's core (figure S4(a)), which is different from the intimate linkage between the intensity of both the TEJ and the Walker circulation (Chen and Yen 1993, Huang et al 2019).Accordingly, the divergent zonal wind anomalies are opposite over the tropical western IO and the MC, explaining the zonal feature of the zonal wind anomalies.
The anomalous zonal winds along 20 • N arise from the mid-to-upper-level temperature anomaly over the Eurasian continent.For the northwest mode, the Eurasian continent is controlled by the warming anomaly in the mid-to-upper level and the increased geopotential height anomaly (figure 3(f)), yielding a strengthened South Asia High (figure S4(b)).The poleward temperature gradient is thus intensified, accelerating the easterly wind to its south according to the thermal wind relationship.The warming anomaly, however, is displaced by the cooling and decreased geopotential height signals for the southwest mode (figure 3(i)), which would reduce the South Asian High and the poleward temperature gradient.As a result, the zonal-elongated westerly anomalies emerge and push the TEJ's core southward.It is worth noting that the composite temperature and geopotential height anomalies are too feeble to influence the east mode (figure 3(c)).
The relationship between the locational variation of the TEJ's core and the zonal divergent circulation and the MTG anomalies is further explored in figure 4. The area-averaged upper-level VP anomaly over 10 • S-25 • N, 50 • -100 • E, which represents the convergent/divergent center of the anomalous zonal divergent circulation, shows a significant correlation with the longitudinal location of the TEJ's core (r = 0.55, p < 0.01).The MTG anomaly, calculated by the mid-to-upper-level temperature difference between the Eurasian continent and the tropical IO, exhibits a positive correlation with the latitudinal location of the TEJ's core (r = 0.33, p < 0.01).Excluding the east mode would increase this correlation coefficient to 0.53 (p < 0.01), suggesting a more influential role of the MTG between the northwest and the southwest modes.In short, the anomalous zonal divergent circulation with the divergent/convergent center over the tropical IO likely determines the longitudinal location of the TEJ's core, while the mid-to-upper-level thermal contrast between the Eurasian continent and the tropical IO is possibly responsible for the latitudinal location of the TEJ's core.
Questions naturally arise about how the zonal divergent circulation and the MTG anomalies are generated.Figure 5 shows the column-integrated heat source (Q 1 ) and the surface temperature associated with the three modes.The upper-level convergent (divergent) anomaly over the tropical IO is induced by the anomalous diabatic cooling (heating) associated with the suppressed (enhanced) convection locally for the east (northwest/southwest) mode.Further analysis shows that the diabatic heat source/sink in the tropical IO may be traced to the local or remote SST anomalies.Whilst the basin-wide cooling in the IO may suppress the convective activity and the resultant diabatic cooling for the east mode (figure 5(c)), the tropical IO warming anomaly may promote convection in situ for the southwest mode (figure 5(i)).Meanwhile, the SST anomaly in the tropical northeastern (eastern) Pacific helps maintain the anomalous zonal divergent circulation between the tropical IO and the tropical Pacific by inducing the positive (negative) Q 1 and the upper-level divergent (convergent) anomaly in situ for the east (southwest) mode.For the northwest mode (figure 5(f)), the zonal dipole distribution of the SST anomaly in the tropical IO may not fully explain the large-scale positive Q 1 in South Asia; instead, the remote SST anomaly in the subtropical North Atlantic could facilitate the zonal divergent circulation between the tropical Atlantic and the tropical IO via suppressing the convection and the diabatic heating there.
Though strong SST anomalies are found in the mid-latitude northern oceans for the east and the northwest modes, they are contrary to the midlatitude atmospheric temperature anomalies.The large-scale atmospheric temperature anomalies over the Eurasian continent are more coherent with the Q 1 and the land surface temperature anomalies (figures 5(d)-(i)), which show a significant increase for the northwest mode but a decrease for the southwest mode and are mainly caused by the change in the net shortwave radiation (figure S5).It can be concluded that the east-west and the north-south thermal contrasts can jointly result in the movement of the TEJ's core by triggering the zonal divergent circulation and the MTG anomalies.

Impacts on the summer monsoon precipitation
The relationship between the TEJ's core location and the summer monsoon precipitation and the related physical processes are further explored in this section.Comparing the east mode with the northwest/southwest mode, opposite precipitation anomalies are found in South Asia, Southeast Asia, the South China Sea, and the western North Pacific (red rectangles in figure 6).Specifically, the precipitation decreases by about 20% (the ratio of the anomaly to the mean) in southern India, the eastern Arabian Sea, and the southern Bay of Bengal for the eastward shift of the TEJ's core, whereas the precipitation increases by about 18% (13%) these regions for the northwestward (southwestward) shift of the TEJ's core.The largest precipitation anomaly takes place along the west coast of India due to the orographic effect of the western Ghats and the low-level moisture transport (figure S6).In the inflow region, the precipitation anomaly exhibits a north-south seesaw distribution, which is characterized by a negative (positive) anomaly in the MC and a positive (negative) anomaly in the South China Sea and the western North Pacific for the east (northwest/southwest) mode.
Previous studies have demonstrated that the spatial structure of the TEJ can distribute the upperlevel divergence field and trigger the secondary circulation, ultimately favoring the precipitation to occur in the north (south) of the inflow (outflow) region (figures 7(a)-( c)) (Flohn 1964, Uccellini and Johnson 1979, Webster and Fasullo 2003).In South Asia, the eastward shift of the TEJ's core leads to the anomalous upper-level convergence (figure 7(d)) due to the zonal difference of the anomalous zonal wind (figure S7), facilitating the mid-level descent anomaly between 10 • -20 • N (figure 7(e)), whereas the divergence and the ascent anomalies occur for the northwest and the southwest modes (figures 7(g)-(k)).In the MC and the western North Pacific, the dipole precipitation anomaly is contributed by the meridional dipole pattern in the divergence field aloft, which is closely linked to the intensity of the southern-branch easterly jet.The southern-branch easterly jet is accelerated for the east mode (figure 1(d)), which can produce the ageostrophic northerly anomaly according to the zonal momentum equation ( dug dt = fv a , the subscripts g and a denote the geostrophic and the ageostrophic components, respectively), facilitating the anomalous divergence and ascending air at about 20 • N and the anomalous convergence and descending air near the equator (figures 7(d) and (f)).Converse situations are found for the northwest/southwest mode with a decelerated southernbranch easterly jet (figures 7(g)-(l)).Additionally, the positive precipitation anomaly is stronger and extends westward for the southwest mode relative to the northwest mode, which may result from the southward displacement of the upper-level divergent anomaly over the IO (figures 3(g) and (h)) as well as the lower-level moisture convergence (figure S6).
The major differences in the precipitation between the northwest and the southwest modes are found in northern India, the south slope of Tibetan Plateau, West Africa as well as northern China (blue rectangles in figure 6), where the anomalous precipitation associated with the east mode is relatively weak or insignificant.The precipitation tends to increase (decrease) to the north of 20 • N over the Indian subcontinent and has a significantly large amplitude along the south slope of the Tibetan Plateau corresponding to the northwest (southwest) mode, which results from the easterly (westerly) anomalies along the northern flank of the TEJ through the alteration of the background easterly vertical shear.The easterly (westerly) anomalies also imply a northward (southward) displacement of the subtropical westerly jet located at 40 • N (figure S4(b)), which is shown to provoke the precipitation in central and northern India (Chowdary et al 2022).Besides, the Tibetan Plateau is covered by the increased diabatic heating for the northwest mode (figure 5(d)), which can deflect the low-level water vapor belt northward to the south slope of the Tibetan Plateau (figure S6) and strengthen the northern branch of the South Asian summer monsoon north to 20 • N (Wu et al 2012(Wu et al , 2015)).Conversely, the decreased diabatic heating over the Tibetan Plateau corresponding to the southwest mode would weaken the upward branch and inhibit the precipitation along the south slope of the Tibetan Plateau.It implies a potential role of the TEJ's core location in the Tibetan Plateau-monsoon feature, which received less attention before.
In East Asia, significantly enhanced precipitation occurs in northern China, South Korea, and southern Japan where the subtropical Meiyu front is active in the boreal summer for the northwest mode.It may be fostered by the strengthened northernbranch jet along 20 • N for the northwest mode, which favors the anomalous secondary circulation with the upward air in the north and the downward air in the south (figure 7(i)).In addition, the precipitation anomaly manifests a meridional dipole pattern between 5 • N and 10 • N in West Africa, especially for the southwest mode, which is concurrent with the upper-level divergence anomaly in situ (figure 7(j)).The southwestward shift of the TEJ's core is in conjunction with the southward shift of the African easterly jet (figure S8), which can jointly prompt a southward displacement of the tropical rain belt and bring rainfall to the Guinea Coast (Nicholson 2008(Nicholson , 2009)).

Summary and discussion
The present study classified the location of the TEJ's core into the east mode (centered over Sri Lanka), the northwest mode (centered to the east of Somali), and the southwest mode (centered over the equatorial central-western IO) by using the K-means cluster analysis.Each locational mode shows distinct features in the spatial structure of the TEJ.The difference in the monthly frequency implies that the seasonal mean result would yield an obscure representation of the locational variation of the TEJ's core.On the interannual-to-decadal time scale, the southwest mode emerges more frequently in the 2010s relative to the 1980s, along with the less frequent northwest mode.
The causes of the TEJ's core location diversity stem from the influence of the zonal divergent circulation and the MTG between the Eurasian continent and the tropical IO.The anomalous zonal divergent circulation with the convergent center over the tropical IO can lead to the occurrence of the east mode.In the presence of the divergent center over the tropical IO, the strengthened poleward temperature gradient would yield the appearance of the northwest mode, whilst the weakened gradient favors the formation of the southwest mode.These two important factors can be attributed to the zonal thermal contrast between the IO and other ocean basins and the meridional land-sea thermal contrast.
Furthermore, the locational change in the TEJ's core plays a significant role in the summer monsoon precipitation via redistributing the upper-level divergence field and stimulating the secondary circulation, especially in South, Southeast, and East Asia.In conjunction with the thermal effect of the Tibetan Plateau and the Africa easterly jet, the change in the TEJ's core location can influence the precipitation in the south edge of the Tibetan Plateau and West Africa.
The present study sheds light on the cause and influence of the TEJ's core locational diversity.We acknowledged that the conclusions in the present study are based on statistical analysis, which may limit the thorough understanding of the causal relationship between the TEJ's core location and other phenomena.Future research using numerical experiments is necessary to delineate the root cause of the TEJ's core location.In addition, whether the stateof-the-art climate model can capture the locational variation of the TEJ's core remains unclear.It calls for more investigations on assessing the model fidelity of simulating the TEJ's core location diversity and projecting the future change of the TEJ's core location, which may provide implications to advance the knowledge of the monsoon variability under climate change.

Figure 1 .
Figure 1.Composite of 200 hPa easterly wind (shaded; m s −1 ) (left column), the longitudinal-frequency (middle column) and the latitudinal-frequency distributions (right column) of the peak easterly wind for (a)-(c) all TEJ cases, (d)-(f) the east mode, (g)-(i) the northwest mode and (j)-(l) the southwest mode.The −12 m s −1 isotach is outlined in white for the average across all TEJ cases and in black for the average within each locational mode.The gray dashed line indicates the elevation of 1500 m.The yellow dots denote the location of the peak easterly wind of each TEJ case.The number and the corresponding percentage of each locational mode are shown in the top-right corner in (d), (g), (j).The mean longitude and latitude are shown in the top-right corner of the middle and the right columns, respectively.

Figure 2 .
Figure 2. (a) Monthly frequency distribution of each TEJ locational mode.The percentage of each mode in the corresponding month are shown on the top of the columns.Yearly frequency distribution of (b) the east mode, (c) the northwest mode, and (d) the southwest mode.The frequencies in1981-1990, 1991-2000, 2001-2010, and 2011-2020  are shown in the parentheses.
Figure 2. (a) Monthly frequency distribution of each TEJ locational mode.The percentage of each mode in the corresponding month are shown on the top of the columns.Yearly frequency distribution of (b) the east mode, (c) the northwest mode, and (d) the southwest mode.The frequencies in1981-1990, 1991-2000, 2001-2010, and 2011-2020  are shown in the parentheses.

Figure 4 .
Figure 4. Scatter diagram of (a) meridional temperature gradient (MTG; • C) and velocity potential (VP; 10 6 s −1 ), (b) VP and longitude of the TEJ's core, (c) latitude of the TEJ's core and MTG.The MTG is calculated as the difference in the 500-200 hPa temperature between 30 • -45 • N, 40 • -100 • E, and 0 • -15 • N, 40 • -100 • E (rectangle boxes shown in figure 3(c)).The VP is calculated as the area-averaged 200 hPa VP over 10 • S-25 • N, 50 • -100 • E (rectangle box shown in figure 3(b)).The cross symbols denote the averaged value in the corresponding mode.The solid lines in (b)-(c) show the linear regression and the correlation coefficients are shown in the top-right corner.The dashed line in (c) shows the linear regression within the northwest and the southwest modes and their correlation coefficients are shown in the bottom-right corner.

Figure 6 .
Figure6.Anomaly of the precipitation (shaded; mm day −1 ) for (a) the east mode, (b) the northwest mode, and (c) the southwest mode.The structure of the TEJ is shown by using the 0, −12, and −22 m s −1 isotaches.The oblique lines denote significance at the 90% confidence level.The red rectangles mark the region influenced by the zonal movement of the TEJ's core while the blue rectangles mark the region associated with the meridional movement of the TEJ's core.

Figure 7 .
Figure 7. Horizontal divergence (shaded; 10 −6 s −1 ) and horizontal winds (m s −1 ) at 200 hPa (left column), latitude-level cross section of meridional wind and p-coordinate vertical velocity averaged along 70 • -90 • E (middle column) and along 110 • -130 • E (right column) for (a)-(c) the climatological mean, (d)-(f) the east mode, (g)-(i) the northwest mode, and (j)-(l) the southwest mode.The structure of the TEJ is shown by using the 0, −12, and −22 m s −1 isotaches in the left column and by using the −5, −10, and −15 m s −1 isotaches in the middle and right columns.The oblique lines denote significance at the 90% confidence level.Only the vectors significant at the 90% confidence level are shown.