Revisiting the East Asian summer monsoon structure: a combined effect of condensational heating and synoptic eddy activities

The East Asian summer monsoon (EASM) is a unique regional monsoon in the extratropics involving not only tropical but midlatitude processes. Most of the previous studies identified the role of condensational heating which is largely relevant to the tropical moisture transport in determining the dynamical structure of EASM. However, how midlatitude synoptic eddy activities can affect the EASM structure has not been well recognized. With dynamical diagnoses, this study revisits the EASM structure by emphasizing the roles of feedbacks of condensational heating versus synoptic eddy activities. As EASM is characterized by a grand low-level low with strong humid southerly flows extending from the tropics to the northeastern Asia, its vertical structure is found to have a dramatic meridional difference bounded at around 35.5°N. In the southern domain, EASM features a meridional overturning cell and a baroclinic structure with an upper-level high versus a lower-level low in geopotential height, which are primarily controlled by substantial condensational heating due to abundant monsoon precipitation. However, in the northern domain, EASM exhibits an equivalent barotropic structure with an upper-level low versus a lower-level low. Such a unique structure results from a combined effect of feedbacks of condensational heating and synoptic eddy activities, in which the upper-level low is dominated by the synoptic eddy dynamical feedback while the lower-level low is induced by the both feedbacks. The role of the midlatitude synoptic eddy activities in shaping the EASM structure proposed in this study provides a new perspective for understanding the formation and variation of EASM.


Introduction
The East Asian summer monsoon (EASM) is a distinctive regional component of the grand Asian summer monsoon system which features a prominent seasonal reversal of prevailing winds and an abrupt change from dry to wet climate (Ramage 1971;Tao and Chen 1987;Lau 1992;Ding 1994;Webster et al. 1998;Lau et al. 2000;Li and Zeng 2003). Substantial variation of EASM can cause weather and climate disasters in the densely populated East Asia He et al. 2007;Ding et al. 2008;Chang et al. 2012;Li et al. 2016;Zhou et al. 2018).
Like the South Asian summer monsoon, another component of the Asian summer monsoon system, the EASM flows mainly come from tropical regions. However, EASM cannot be just considered as the eastward and northward extension of the South Asian summer monsoon (Zhu et al. 1986;Tao and Chen 1987;Lau et al. 2000;Ding and Chan 2005;Huang et al. 2017). EASM can bring abundant moisture and rainfall by intense low-level southerlies from the tropics towards midlatitudes (Ding 1994;Lau et al. 2000;Wang and Lin 2002;Wang et al. 2004;Jiang and Wang 2005;He et al. 2007). Meanwhile, EASM is also closely related to the midlatitude circulation systems. The EASM rain belt is intimately associated with the frontal zone where the northward warm-moist flow meets the cold-dry air from the mid-high latitudes. Thereby, in addition to the tropical and subtropical circulation systems such as the monsoonal trough and the subtropical high, the mid-high latitude troughs and ridges that can affect the thermal and dynamical conditions of EASM should also be considered in the complete EASM system (Ding and Chan 2005;He et al. 2007;Ding et al. 2018). Given those natures, Wang and Lin (2002) defined the EASM domain within 20°-45°N and 110°-140°E, a region mostly in the extratropics, distinguishing it from the South China Sea summer monsoon. And even, Molnar et al. (2010) insisted that EASM should be defined as a frontal system rather than a "monsoon" in terms of its distinctly extratropical natures. No matter what way of the identification, it comes to an agreement that EASM is extremely complicated for its hybrid natures.
To understand the complex natures of EASM, great efforts have been made to investigate the formation mechanisms responsible for EASM. Most of the previous studies identified the roles of various thermal processes in the EASM formation, in which the seasonal variation of solar radiation (Halley 1686;Zhao and Wang 2014) and the thermal contrast between land and ocean (Luo and Yanai 1983;Li and Yanai 1996;Sun et al. 2001;Qi et al. 2008) are widely believed to be two fundamental thermal factors. The elevated sensible heating by the Tibetan Plateau is proposed to be another factor for the monsoon formation (Yeh 1982;Ueda and Yasunari 1998;Yanai and Wu 2006;Wu et al. 2007Wu et al. , 2012Wu et al. , 2015Molnar et al. 2010;Liu et al. 2012;Qiu 2013;Ma et al. 2014). Besides, the deep condensational heating generated from the latent heat release of monsoonal rainfall dominates the diabatic heating over East Asia and feedbacks onto the EASM itself. The feedback of condensational heating is not only in favor of the South China Sea summer monsoon onset (Liu et al. 2002;Wen et al. 2004), but also contributes to the amplification and maintenance of the EASM circulation (Li and Luo 1988;He et al. 1989;Jin et al. 2013). Based on numerical experiments, Jin et al. (2013) confirmed that the condensational heating feedback caused by monsoon rainfall acts to largely enhance low-level flows of the EASM and essentially determine its baroclinic vertical structure and meridional cell, once the solar radiation and the inhomogeneity of the Earth's surface induce low-level monsoon flows over East Asia by enhancing land-sea thermal contrast.
However, as the EASM flows march northward into the midlatitudes, EASM exhibits some midlatitude characteristics (Tao and Chen 1987;Zhang and Tao 1998;Wu 2002;Ding and Chan 2005). The midlatitude circulation favors the vigorous genesis of synoptic eddies which can feedback onto the mean flow through redistributing momentum and heat (Holopainen et al. 1982;Lau and Oort 1982;Lau and Holopainen 1984;Luo 2005). Various studies pointed out the importance of synoptic eddy feedback onto the seasonal-mean atmospheric circulation anomalies (Hoskins 1983;Nakamura et al. 2002;Chen et al. 2013;Leung and Zhou 2015;Fang and Yang 2016). Although synoptic eddy activities are relatively weak in boreal summer, there is increasing evidence showing significant impacts of synoptic eddy activities on EASM and associated climate anomalies. For example, active synoptic eddies at mid-high latitudes tend to enhance the rainfall in the Yangtze-Huaihe River basin by inducing more southward invasion of cold air (Tan 2008;Dong et al. 2006). Synoptic-scale geopotential height anomalies in the upper troposphere and temperature anomalies in the mid-lower troposphere are the early signals for the summer low-temperature events in northeastern China (Qian and Jiang 2014). Anomalous synoptic eddy activities in boreal summer can induce the anomalous southerlies over eastern China (Park et al. 2015), the interannual meridional displacement of the East Asian subtropical jet (Xiang and Yang 2012), and the decadal changes of EASM around the early 1990s (Chen et al. 2016).
Since the warm and humid southerlies of EASM can meet the cold and dry northerlies, that is the front genesis, in the midlatitudes, the atmospheric baroclinicity enhances, favoring synoptic eddy activities. Whether and how the synoptic eddy can feedback onto EASM have not been well explored before. In this study, we try to revisit the EASM structure in which the roles of feedbacks of condensational heating versus synoptic eddy activities are particularly identified through dynamical diagnoses in terms of the seasonal-mean quasi-geostrophic potential vorticity equation. The rest of paper is organized as follows. Section 2 describes the data and methods used. Section 3 presents a complete picture of the EASM structure. Sections 4 and 5 explore the roles of feedbacks of condensational heating and synoptic eddy activities in the EASM structure, respectively. The final section is devoted to conclusions and discussion.

Data
The 6 hourly circulation variables including geopotential height, temperature, winds, and vertical velocity are obtained from the Japanese 55 year Reanalysis (JRA-55) dataset conducted by the Japan Meteorological Agency (Kobayashi et al. 2015). The reanalysis dataset comprises 23 vertical levels between 1000 to 200 hPa with a fine horizontal resolution of 1.25° × 1.25°. Additionally, the components of diabatic heating due to longwave radiation, solar radiation, large-scale condensation, convective condensation, and vertical diffusion are derived from the JRA-55 dataset. The global daily precipitation dataset with a horizontal resolution of 0.5° × 0.5° is part of product suite from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center Unified Precipitation Project (Xie et al. 2007). The daily large-scale and convective precipitation rate data is taken from the Climate Forecast System Reanalysis (CFSR) reanalysis dataset with a spatial resolution of 0.5° × 0.5° provided by the National Centers for Environmental Prediction (NCEP) (Saha et al. 2010). All the variables and their derivatives are averaged for summer (June, July and August) with a time span for 1980-2021. In addition, to isolate the regional characteristics of EASM, the regional departure circulations over the East Asian domain are extracted through removing globally zonal means.

Methods
In the extratropics, the seasonal-mean atmospheric state is approximately governed by the quasi-geostrophic potential vorticity (QGPV) equation (Lau and Holopainen 1984;Fang and Yang 2016) which is written as, where the overbar denotes the seasonal mean, Φ is the geopotential, ⇀ V h the horizontal wind vector, T the air temperature, f the ambient vorticity, R the gas constant for dry air, and 1 the static stability parameter which varies only with altitude ( 1 = − ⋅ ln ∕ p , is the geopotenial temperature and the reciprocal of atmospheric density). Q d is the seasonal-mean diabatic heating due to longwave radiation, shortwave radiation, large-scale condensation, convective condensation, and vertical diffusion. Q eddy and F eddy are the seasonal-mean heating and vorticity forcing, respectively, induced by transient eddy activities, which are expressed as, where the prime denotes the 2-10 d synoptic disturbances obtained with a Lanczos filter (Duchon 1979) in this study. and are the vertical velocity and the relative vorticity, respectively. Obviously, Q eddy and F eddy are determined by the convergences of synoptic eddy heat and vorticity fluxes, respectively.
To identify the effects of diabatic heating and synoptic eddy forcing on the mean flow, Eq. (1) can be re-written as, where the left-hand side of Eq. (4) represents the tendency of QGPV with a three-dimensional linear operator acting on the tendency of geopotential. On the right-hand side, there are three forcing terms producing atmospheric potential vorticity, which are the diabatic heating forcing term ( F 1 ), the synoptic eddy heating forcing term ( F 2 ), and the synoptic eddy vorticity forcing term ( F 3 ). There are also three vorticity advection terms associated with atmospheric internal processes, which are the relative vorticity advection ( A 1 ), the ambient vorticity advection ( A 2 ), and the stretching vorticity advection ( A 3 ). For the climatological state of the atmospheric circulation, the tendency of QGPV is nearly zero and thus the vorticity advection terms can be considered as an adjustment to or a balance with the vorticity production terms. The seasonal-mean geopotential tendencies produced by those terms on the right-hand side of Eq. (4) can be numerically solved with the three-dimensional linear operator on the left-hand side of Eq. (4) by the successive overrelaxation (SOR) method with the boundary conditions referred to Lau and Holopainen (1984). Therefore, the roles of diabatic heating and synoptic eddy forcing in the EASM structure can be examined through analyzing these tendencies.
Synoptic eddy activities are closely related to the low-level atmospheric baroclinicity (Simmons and Hoskins 1978; Hoskins and James 2014), which is represented approximately by the maximum Eady growth rate BI (Lindzen and Farrell 1980;Hoskins and Valdes 1990). It is defined as is the Brunt-Väisälä frequency. Synoptic eddy activities can be characterized with the eddy available potential energy (EAPE) and the eddy kinetic energy (EKE), which are defined as EAPE = (C p )(T � 2 )∕2 a n d EKE = (u �2 + v �2 )∕2 , r e s p e c t i v e l y, w h e r e = −R∕(pC p )(p 0 ∕p) R∕C p ( ∕ p) −1 is an inverse measure of the background stratification (Lorenz 1955), C p is the specific heat capacity of dry air at the constant pressure, and p 0 = 1000hPa is the mean sea level pressure. (4) 3 Three-dimensional structure of EASM Figure 1 demonstrates climatological horizontal distributions of summertime precipitation rate and winds. The monsoonal circulation over East Asia exhibits a distinct seasonal reversal, characterized by prevailing low-level winds changing from wintertime northerlies to summertime southerlies (vectors in Fig. 1a). In boreal summer, the westerlies and the southwesterlies originating from the tropics converge with the southeasterlies originating from the northwestern Pacific and then they turn northward together over the South China Sea. The development of monsoonal southerlies is followed by a northward shift of rain belt, producing abundant precipitation over China, Korea, southern-central Japan, and even northeastern Asia (Fig. 1a). Previous studies argued that the subtropical high over the North Pacific plays a key role in the formation and maintenance of monsoonal southerlies (Kodama 1992;Zhou et al. 2009;Wang et al. 2013). After removing the globally zonal means, a grand cyclonic circulation deviation naturally occurs, replacing the wintertime anticyclone over the East Asian continent at the low levels ( Fig. 1b). The regional monsoonal low represents the localized feature of EASM, and it is natural to believe that the strong monsoonal southerlies are not only related to the North Pacific subtropical high but also closely connected with the grand monsoonal low over the East Asian continent (Fig. 1b). Upon the grand low-level monsoonal low (Fig. 2a), there is an obvious meridional difference in the upper-level circulation. The monsoonal low in the southern domain is overlain by a high deviation at the upper level with anticyclonic circulation centered over the Tibetan Plateau, while in the northern domain the low deviation with cyclonic circulation extends into the upper troposphere (Fig. 2b). This upperlevel low deviation in the northern domain superimposed on the basic westerlies has not been well recognized before. It is noted that the location of the upper-level seasonal-mean low deviation is consistent with that of the northern stationary eddy cyclone circulation over East Asia identified by Sun et al. (2018).
The meridional difference of circulation in vertical configuration is further identified in detail with the latitude-height section of geopotential height along 105°-135°E (shading in Fig. 3a). The geopotential height south of 35.5°N is characterized by a clear baroclinic vertical structure with a negative deviation at the lower level and a positive deviation at the upper level. However, the geopotential height between 35.5°-50°N features an equivalent barotropic vertical structure with a low deviation throughout the troposphere. It is also observed that the geopotential height appears to be equivalent barotropic with a high deviation north of 50°N. Resultantly, only upper-level westerly deviations centered at 35.5°N and the equivalent barotropic easterly deviations centered at 50°N are found (contours in Fig. 3a), in terms of the geostrophic balance relation. The centers of the westerly and easterly deviations separating the different vertical structures of geopotential heights are roughly located at 35.5°N and 50.5°N, respectively. The meridional difference in the thermal field is also clear. Regional warm air almost occupies the whole troposphere with the mid-level warm center at 300 hPa in the southern domain, while the warm air is nearby the surface in the northern domain (Fig. 3b), which is constrained by the static equilibrium relationship between geopotential height and temperature.
Regarding the latitude-altitude circulation, it can be seen that the southerly deviation at the lower level is overlaid by the northerly deviation at the upper troposphere and the significant ascending flows control the whole troposphere, forming a grand overturning cell over the East Asian sector south of 35.5°N (Fig. 3c, e, f). The low-level southerlies converge first in the tropical monsoon region forming ascending flows in the tropics, and then converge in the southern domain of EASM forming new significant ascending flows at around 30°N. The flows originating from the ascending flow centered at 30°N join in the high-level divergent flows backing to the Southern Hemisphere, contributing to the grand monsoon cell (Fig. 3e, f). This three-dimensional circulation structure over the East Asian sector south of 35.5°N accords well with the thermal adaption theory that highlights that the positive vertical shear of meridional flows is proportional to the ascending movement (Wu andLiu 2000, 2003;Liu et al. 2001;Wu et al. 2007). However, the vertical motions are complicated in the northern domain of EASM. The ascending motion is accompanied with the barotropic southerly deviations to the east, while the descending motion and the barotropic northerly deviations occur to the west of 120°E (Fig. 3c, d). The overturning cell is very weak and appears in the western part at the mid-lower troposphere with the flows sinking in a region located over 35°-45°N (Fig. 3e). The low-level southerlies march northward and converge in the northern domain of EASM, forming significant ascending flows at around 42.5°-50°N to the east of 120°E. It is noted that the ascending flows north of 35°N do not go back to the tropics but turn to the high latitudes at the high-levels (Fig. 3f). Obviously, the latitude-altitude circulation structure in the northern domain of EASM is different from that in the southern domain and cannot be described by the thermal adaption theory (Wu andLiu 2000, 2003;Liu et al. 2001;Wu et al. 2007).
The observational fact that a transition zone between large-scale and convective precipitations just appears at about 34°N is another evidence for the meridional difference in the dynamics of the circulations over the southern and northern EASM regions. The summertime precipitation in the southern domain is mainly attributed to the convection that is a rapid, efficient, and vigorous overturning of the atmosphere required to neutralize an unstable vertical distribution of moist static energy (Houze 1997), while in the northern domain, the precipitation is dominated by the stratiform clouds in relatively stable layers in which the ascending motions are generated by large-scale lifting (Fig. 4).
Overall, the above revisit on the three-dimensional structure of EASM suggests that the complete EASM regime is complicated, featuring two different vertical structures bounded at around 35.5°N in the meridional direction, although there exists a grand monsoonal low near the surface in the whole domain. One is the baroclinic structure with an upper-level high versus a lower-level low in the southern domain. The other is the equivalent barotropic structure with a low extending into the entire troposphere in the northern domain. The baroclinic vertical structure with opposite signs at the upper versus lower levels in the southern domain is widely considered as the traditional monsoonal feature and has been proved to be attributed to the role of condensational heating (Liu et al. 2001;Jin et al. 2013). The barotropic vertical structure over northern East Asia implies the effect of midlatitude dynamics in which the detailed dynamical processes have not been well recognized. The mechanism responsible for the vertical structure in the northern domain is particularly explored and presented in the next sections. As illustrated in Fig. 5a, the diabatic heating warms up almost entire tropospheric air column (except some layers below 850 hPa equatorward of 40°N) with centers at about 400 hPa in the tropics, the subtropics, and the midlatitudes. As EASM brings out abundant water vapor and consequently generates substantial latent heat release, the condensational heating considerably dominates total diabatic heating in boreal summer along the East Asia sector, especially in the southern EASM domain (Fig. 5a, c). In the northern domain the diabatic heating is much weaker and presents two heating centers, in which one is in the boundary layer attributed to the land surface sensible heat flux (Fig. 5d) and the other is in the mid-troposphere due to the latent heat release (Fig. 5c). Over all the EASM region, the contribution of the radiative heating to total diabatic heating is much weaker than the other two heating components (Fig. 5b).
In terms of Eq. (4), the diabatic heating centered at 400 hPa tends to produce a positive (negative) potential  Latitude-altitude sections of the deviations from globally zonal means of climatological a diabatic heating rate (K·day −1 ) and their components due to b radiative heating rate, c condensation heat-ing rate, and d vertical diffusion heating rate, averaged within 105°-135°E in boreal summer for 1980-2021 vorticity source, consequently exciting a negative (positive) geopotential tendency below (above) 400 hPa, which is supported by the numerically-solved results of geopotential tendency (Figs. 6 and 7). The baroclinic atmospheric response with a negative (positive) geopotential tendency below (above) 400 hPa is induced by the diabatic heating forcing at the middle layers, coinciding well with the observed baroclinic vertical structure of geopotential height in the southern EASM domain. Thus, it can be concluded that the diabatic heating forcing that mainly comes from the latent heat release determines the steady baroclinic vertical structure in the southern EASM domain once EASM is initially driven. This thermodynamic relationship agrees well with the result by Jin et al (2013).
In the northern domain, there are two heating centers which can both produce a positive (negative) potential vorticity below (above) the centers. However, the eventual result presents a baroclinic atmospheric response with a negative geopotential tendency below versus a positive geopotential tendency upon 500 hPa (Figs. 6 and 7). The low response induced by the local diabatic heating is relatively weak and confined at the lower troposphere, while the diabatic heating-induced high response exists in the upper troposphere ( Figs. 6 and 7), which contradicts the observed equivalent barotropic structure with an upper-level low upon a lowerlevel low (shading in Fig. 3a). In other words, if the role of diabatic heating is only considered, the vertical structure of EASM in the northern domain should also be baroclinic, with an upper-level high versus a lower-level low in geopotential height, like that in the southern domain. Obviously, the feedback of diabatic heating-only cannot explain observed equivalent barotropic structure north of 35.5°N over the EASM region.

Role of feedback of synoptic eddy activities in EASM structure
As the synoptic eddies are vigorous in the midlatitudes, they can act as a forcing to maintain the time-mean flow through generating potential vorticity sources, as the diabatic heating does (Holopainen et al. 1982;Lau and Oort 1982;Lau and Holopainen 1984). On the right-hand side of Eq. (4), there are two forcing terms associated with synoptic eddy activities: the synoptic eddy heating forcing term ( F 2 ) and the synoptic eddy vorticity forcing term ( F 3 ). The former is proportional to the vertical gradient of the synoptic eddy heating, while the latter is determined by the divergence of synoptic eddy vorticity flux. Clearly, synoptic eddy activities can affect the mean atmospheric state by redistributing heat and vorticity.

Features of synoptic eddy activities
In climatology, the summertime westerly has a maximum in the upper troposphere at around 40°N, showing a typical feature of the subtropical westerly jet stream over Asia (Fig. 8a). Due to large vertical wind shear and meridional temperature gradient associated with the jet, considerable extratropical baroclinicity involves in EASM. The maximum Eady growth ratte BI (Lindzen and Farrell 1980) measuring the baroclinicity has a maximum around and north of 40°N over northern East Asia (Fig. 8a), indicating genesis of the synoptic eddies there. Consistent with the large low -level atmospheric baroclinicity, the eddy available potential energy (EAPE) maximizes in the mid-lower troposphere around 40°N over northern East Asia (Fig. 8b). With the development and eastward movement of the generated synoptic eddies, high cyclone frequency and large eddy kinetic energy (EKE) downstream occur in the upper troposphere (Fig. 8c, d). The eddy activities tend to affect the mean atmospheric state via redistributing heat and momentum through eddy heat flux ( v ′ T ′ ) and eddy momentum flux Fig. 6 Latitude-altitude sections of the deviations from globally zonal means of a the climatological diabatic heating forcing term ( F 1 ) (shaded, 10 −11 s −2 ) versus the geopotential height (contours, dagpm) and b the geopotential tendencies induced by the diabatic heating forcing (shaded, 10 −3 m 2 ·s −3 ) versus the geopotential height (contours, dagpm), averaged within 105°-135°E in boreal summer for 1980-2021. Note that the contours in (b) are the same as in (a) ( u ′ v ′ ). The eddy heat flux is poleward, crossing the jet and maximizing around 40 o N (Fig. 8e), which tends to produce a cooling (warming) effect on the upper troposphere south (north) of the jet axis. Meanwhile, the eddy momentum flux is poleward (equatorward) south (north) of the jet axis (Fig. 8f), with the strongest poleward momentum flux occurring at around 30°-40°N. Such an eddy momentum flux pattern favors an acceleration of the mean westerly at around 40°-50°N via the convergence of eddy momentum fluxes.

Feedback of synoptic eddy activities
In agreement with the horizontal distribution of synoptic eddy heat flux at 300 hPa (Fig. 8e), the latitude-altitude section of the seasonal mean synoptic eddy heating forcing Q eddy shows the cooling (heating) south (north) of around 40°N throughout the mid-upper troposphere (Fig. 9a). In terms of Eq. (4), the synoptic eddy heating forcing term ( F 2 ) is proportional to vertical gradient of Q eddy . Positive (negative) vertical gradient of Q eddy is the source of the positive (negative) potential vorticity (PV). Over the subtropical region (30°-40°N), a significant middletropospheric cooling centered at around 400 hPa is dominant (Fig. 9a). Such a cooling tends to cause a negative (positive) PV tendency in the lower (upper) troposphere (Fig. 9b). After solving the seasonal-mean geopotential tendency induced by the synoptic eddy heating forcing, a baroclinic vertical structure of the atmospheric response is obtained and manifested with positive geopotential tendency at the low level versus the negative at the upper level (Fig. 9c). Such a vertical structure is opposite to that induced by the seasonal-mean diabatic heating, especially over the latitudes of 30°-40°N (Figs. 6b, 9c). The horizontal distribution of the geopotential tendency induced by synoptic eddy heating forcing as seen in Fig. 10 further suggests that the cooling by the synoptic eddy heat transport yields a baroclinic vertical structure with a high-level decreased versus a low-level increased geopotential over the most of East Asian continent. Thus, the role of synoptic eddy heating forcing partly offsets that of diabatic heat forcing in the seasonal-mean structure of EASM. The synoptic eddy activities also influence the atmospheric state by redistributing vorticity. Over East Asia, the local synoptic eddy vorticity flux convergence produces a positive PV source at around 20°-35°N and 40°-55°N throughout the troposphere with large values above 400 hPa (Fig. 11a). In terms of Eq. (4), the synoptic eddy vorticity forcing is also one of the PV sources for the seasonalmean atmosphere. Accordingly, numerical solution shows that the synoptic eddy vorticity forcing induces the negative geopotential tendency with an equivalent barotropic structure (maximized at the upper level) over the two zones (20°-35°N and 40°-55°N) (Fig. 11b). Although the negative geopotential tendency induced by the synoptic eddy vorticity forcing can also be partly offset by the positive geopotential  tendency induced by diabatic heating forcing at upper levels, the equivalent barotropic negative geopotential tendency accords well with the observed equivalent barotropic low deviation in the northern EASM domain (Figs. 11b, 12).
Both the diabatic heating and the synoptic eddy vorticity forcing contribute to the equivalent barotropic low deviation at low levels in the northern EASM domain. At upper levels, the synoptic eddy vorticity forcing plays a major role in the formation of observed low deviation. However, if carefully checking Figs. 11 and 12, we notice that the positive PV source and the negative geopotential tendency induced by the synoptic eddy vorticity forcing centered at around 47.5°N obviously shift northward by about 5 latitudes and somewhat westward, when compared with the observed low deviation. This shift can be interpreted in terms of the balance relation between the vorticity production (synoptic eddy vorticity forcing) and advection terms. As seen in Fig. 13, three types of advection processes, as introduced in the method in Sect. 2, are involved in the response to the synoptic eddy vorticity forcing. One is the relative vorticity produced by the synoptic eddy vorticity forcing advected by the globally zonal where U is the globally zonal mean zonal winds and Φ t,Feddy is the geopotential tendency induced by the synoptic eddy vorticity forcing. It is seen in Fig. 13a that this advection process tends to make the negative geopotential tendency by the synoptic eddy vorticity forcing shift eastward and southward. Another is the advection of the basic zonal flow on the stretching vorti- Like the first advection process, the stretching vorticity-related advection also contributes to the eastward and southward shift of the geopotential tendency induced by the synoptic eddy vorticity forcing (Fig. 13c). Specifically, the eastward shifting is attributed to the decreasing of the perturbed relative vorticity and stretching vorticity by the synoptic eddy vorticity forcing with longitude. The southward shifting is due to the inhomogeneity of the globally zonal mean zonal flow in the meridional direction with the center at around 43 o N, which is just located south of the center of the negative tendency induced by the synoptic eddy vorticity forcing. The last is the ambient vorticity advected by the meridional flows induced by the synoptic eddy vorticity forcing, − f Φ t,Feddy x . With the geostrophic relationship, the negative geopotential tendency by the synoptic eddy vorticity forcing corresponds to a southerly tendency in the east and a northerly tendency in the west, thus yielding the southward and northward transports of the ambient vorticity, respectively. This advection process leads to a westward shift of the initial produced low deviation (Fig. 13b). In general, the shifting of the location of the low deviation in the equilibrium state from that induced by the synoptic eddy vorticity forcing is mainly attributed to the advection of the produced relative vorticity and stretching vorticity by the globally zonal mean flow (Fig. 13a, c, d). Therefore, different from the dynamics for tropical circulation in the southern EASM domain that the vorticity changes induced by the diabatic heating are mainly balanced with the Fig. 9 Latitude-altitude sections of the deviations from globally zonal means of climatological a synoptic eddy heating Q eddy (shaded, K·day −1 ), b synoptic eddy heating forcing term ( F 2 ) (shaded, 10 -11 s −2 ), and c the geopotential tendencies induced by the synoptic eddy heating forcing (shaded, 10 −4 m 2 ·s −3 ), averaged within 105°-135°E in boreal summer for 1980-2021. The geopotential height deviations are presented in contours in (a-c) meridional advection of the ambient vorticity, the midlatitude circulation in the northern EASM domain is mainly subjected to the QGPV dynamics that the vorticity tendency induced by the synoptic eddy vorticity forcing is balanced with the advection of the relative vorticity and stretching vorticity by the globally zonal mean flow.

Conclusions and discussion
A revisit on the three-dimension circulation structure of EASM suggests that upon the grand low-level monsoonal low with strong humid southerly flows extending from the tropics to Northeast Asia, there exists a dramatic meridional difference in the vertical structure of EASM bounded at around 35.5°N. In the southern domain south of 35.5°N, EASM features a meridional overturning cell and a baroclinic vertical structure with an upper-level high versus a lower-level low in geopotential height. However, in the northern domain north of 35.5°N, EASM exhibits an equivalent barotropic structure with an upper-level low versus a lower-level low. And the vertical circulation is featured by the ascending (descending) motion with barotropic southerlies (northerlies) east (west) of 120°E over northeastern Asia. Such differences in the three-dimensional structures imply some different dynamics in the two domains.
To understand the formation of the different vertical structures of EASM, we explored the feedbacks of diabatic heating and synoptic eddy activities by diagnosing the QGPV equation, a useful tool for identifying the Fig. 10 As in Fig. 7, but for a the geopotential tendencies (shaded, 10 −4 m 2 ·s −3 ) induced by climatological synoptic eddy heating forcing term ( F 2 ) versus the climatological geopotential height (contours, dagpm) Fig. 11 As in Fig. 6, but for a the synoptic eddy voriticity forcing ( F 3 ) (shaded, 10 −11 s −2 ) and b the geopotential tendencies (shaded, 10 −4 m 2 ·s −3 ) induced by the synoptic eddy voriticity forcing seasonal-mean atmospheric response to the forcing. The baroclinic monsoonal circulation in the southern domain of EASM is dynamically determined by diabatic heating, especially condensational heating. Specifically, the midtropospheric diabatic heating tends to induce the baroclinic circulation response characterized by positive PV and negative geopotential tendency at the low level versus negative PV and positive geopotential tendency at the upper level. Through the advection of meridional wind on the ambient vorticity, the circulation response to the diabatic heating tends to shift westward, and then, in the equilibrium state, the southerly wind prevails at the lower level and the northerly wind prevails at the upper level. Thereby, a local meridional overturning cell dominates over the southern EASM region and then joins in the tropical monsoonal circulation south of 20°N.
However, in the northern domain of EASM, if the effect of diabatic heating is only considered, a regional high should prevail above the monsoonal low and the low is only confined to the lower troposphere. This response is clearly inconsistent with the observational fact, so the role of the synoptic eddy forcing in the formation of the observed equivalent-barotropic low pressure should be considered. In fact, over the northern EASM region, there exist vigorous synoptic eddy activities during summer. The synoptic eddy heat flux diverges over the south of 40°N, yielding a cooling in the middle tropospher, and consequently inducing a distinct baroclinic structure with an upper-level low and a lower-level high tendency. The structure of the atmospheric response induced by the synoptic eddy heating forcing is just opposite to that induced by the diabatic heating forcing, suggesting that the mid-tropospheric cooling by the synoptic eddy heat forcing partly offsets the diabatic heating forcing. Most importantly, the synoptic eddy vorticity forcing tends to produce a negative geopotential tendency centered at the upper layers with a barotropic vertical structure. Although the center of the initial atmospheric response induced by the synoptic eddy vorticity forcing lies northwest to the observed barotropic low over northeastern Asia, due to the adjustment of the relative vorticity and stretching vorticity advected by the globally zonal mean zonal flow, the initial atmospheric geopotential tendency induced by the synoptic eddy vorticity forcing shifts southeastward and eventually coincides with the observed regional barotropic low. Combined with the effect of the diabatic heating on the lowlevel flow, there exists a distinct vertical structure of regional low centered roughly at 42.5°N with deep southerlies and upward motion in the east and deep northerlies and downward motion in the west in the northern domain.
In summary, we conclude that in the complete EASM regime, the feedbacks of diabatic heating and synoptic eddy forcing are both important for the formation of EASM structure. The vertical circulation structure over the southern EASM region is mainly determined by the impact of the diabatic heating, especially the condensational heating. However, the vertical structure over the northern EASM region is attributed to the combined effect of the feedbacks of diabatic heating and synoptic eddy activities, in which the role of synoptic eddy vorticity forcing in the mid-upper troposphere is dominant.  Fig. 7, but for the geopotential tendencies (shaded, 10 −4 m 2 ·s −3 ) induced by the climatological synoptic eddy voriticity forcing ( F 3 ) versus the climatological geopotential height (contours, dagpm) The role of synoptic eddy forcing in the formation of the boreal summer low-level low over the northern EASM region was noticed by Lin and Bueh (2021). Although their result shows that the effect of synoptic eddy forcing is negligible for the formation of the northern East Asian low based on a linear baroclinic model with simplified physical processes and omitted nonlinear interactions, Lin and Bueh (2021) has already realized some limits on their study and recognized the underestimation of the effect of synoptic eddy forcing. This underestimation could due to that the coarse-resolution reanalysis cannot resolve synoptic eddies sufficiently (Sang et al. 2021). Therefore, even though the feedback of synoptic eddy activities is somewhat weaker than that of diabatic heating in quantity, we still believe that the synoptic eddy dynamical feedback works in the formation of the EASM structure in the northern domain.
The role of the midlatitude synoptic eddy activities in shaping the EASM structure gives us a new insight into understanding the formation and variation of EASM from the perspective of wave-mean flow interaction. This study only focused on the synoptic eddy feedback on the boreal summer mean state of the East Asian monsoon system. How Fig. 13 Horizontal distributions of the advections (shaded, 10 −16 s −3 ) at 300 hPa in boreal summer for 1980-2021 for a the relative vorticity produced by the synoptic eddy vorticity forcing advected by the globally zonal mean flow, b the ambient vorticity advected by the meridional flows induced by the synoptic eddy vorticity forcing, c the stretching vorticity produced by the synoptic eddy vorticity forcing advected by the globally zonal mean flow, and d the sum of a-c. The climatological geopotential height deviations at 300 hPa no more than 0 dagpm are contoured in black and the geopotential tendencies no more than − 2 × 10 -4 m 2 ·s −3 induced by the synoptic eddy vorticity forcing are contoured in red the synoptic eddy feedback can affect the seasonal evolution, interannual and even other timescale variabilities of EASM are still an open question, which need further investigation to improve our understanding and prediction of EASM and its variabilities.