The multi-center tracking algorithm employed in this study follows the approach of , which builds upon the single-vortex detection method of . To locate centers of the ASMA, we use three variables taken directly or computed from reanalysis datasets: zonal wind (u), Montgomery stream function (MSF = cpT + Φ, where T is temperature, Φ is geopotential, and cp is the specific heat at constant pressure), and relative vorticity (ζ).

The first step involves identifying the zonal-wind ridgeline (u = 0) within the designated spatial domain (15–45° N, 0–180° E) at each 6-hourly analysis snapshot. This approach is motivated by the observation that the zero-zonal wind contour is nearly zonal within the ASMA . We apply a marching squares algorithm to identify the u = 0 isopleth, which systematically partitions the wind field into grid cells (squares) and employs a divide-and-conquer strategy to determine the exact intersection points where the flow transitions from easterly to westerly .

A schematic illustration of the method used to identify vortex centers is provided in Fig. . Each potential anticyclonic vortex center corresponds to a local maximum in MSF along the u = 0 contour (bold black line). Because the u = 0 isopleths do not align perfectly with the discrete reanalysis grid, the location of the contour and the values of MSF along it are determined using linear interpolation between the two nearest grid points in the meridional direction. For instance, the value of MSF at the blue open circle would be linearly interpolated from the adjacent poleward and equatorward grid points (the closest red dot and the blue dot, respectively). MSF values along the contour are treated as a function of path distance si, computed as the cumulative great-circle arc length from a reference point on the contour. Local maxima of MSF along the ridgeline are required to be unique within a span of length 2Δs around si (si ± Δs), where Δs is a half-angle search window. Following , we set the central angle of the great-circle arc to Δa = Δs/Re = 7.5°, where Re is the average radius of the Earth. The distance Δs thus also defines the minimum allowable separation between adjacent peaks (candidate vortex centers) along the ridgeline. To exclude “spurious centers” arising from small-scale noise or localized features, we apply three filtering criteria:

Vorticity sign. The relative vorticity ζ at the identified center and its four nearest grid points (blue crosses) must be anticyclonic (i.e. ζ < 0 in the Northern Hemisphere).

The final step in the algorithm is to track the movement and duration of each vortex center over time. To do this, we repeat the same vortex-tracking analysis at 6-hourly intervals. A vortex is classified as “persistent” (long-lasting) if two conditions are met. First, the vortex center must move no more than 10° along the Earth's surface (measured as great-circle distance) between one time step and the next. Second, the vortex must remain visible (continuous) for at least four time steps (i.e. > 18 h total). Any identified vortices that do not meet these conditions are designated as “transient” (short-lived) vortices . All tracking procedures are performed using u, MSF, and ζ on the 370 K isentropic surface.

To quantify the multi-center structure, zonal propagation, and intensification of the ASMA on isentropic surfaces, we develop a combined diagnostic based on MSF, PV, and PV tendency. Each quantity plays a distinct and complementary role in the evolution of the upper-level anticyclone. MSF provides a dynamically consistent field for identifying anticyclonic centers on isentropic surfaces. Analogous to geopotential on pressure surfaces, MSF defines streamlines of geostrophic wind on isentropic surfaces. However, unlike geopotential, MSF incorporates local thermal contributions in addition to column-thickness dynamical contributions. MSF is used to identify and track multiple ASMA centers along the zero zonal-wind contour simultaneously, following the approach of as outlined above. This component enables objective identification of persistent and transient anticyclonic modes.

We use PV to evaluate the strength and coherence of each vortex. PV is especially advantageous in the UTLS because it is conserved for adiabatic and frictionless flow, and thus provides a valuable physical tracer of vortex evolution . First, we define the isentropic mass density σ (the inverse of static stability) as: 1σ=-1g∂p∂θ. where g is the gravitational acceleration and p is pressure. Building on the momentum and continuity equations on isentropic surfaces , we use PV to diagnose the boundaries, area, and strength of each anticyclonic vortex. Under a hydrostatic and small-slope approximation, the simplified Ertel's PV is defined as: 2PV=ζθ+fσ=-gζθ+f∂θ∂p where ζθ is the relative vorticity perpendicular to the isentropic surface and f is the planetary vorticity .

Although instantaneous PV fields can effectively describe the structure of the ASMA, including sub-vortices, they cannot directly distinguish changes driven by intensification from those driven by propagation. To address this, we analyze the PV tendency, which explicitly quantifies the processes responsible for changes in PV over time. Assuming friction is negligible for the large-scale UTLS flow, the PV tendency is approximated as the sum of dynamic (advective) and thermodynamic (diabatic) terms: 3∂PV∂t=-u∂PV∂x-v∂PV∂y-θ˙∂PV∂θ+Qθ where θ˙ is the (diabatic) vertical velocity in potential temperature coordinates and Qθ represents the PV tendency from total diabatic heating (including both radiative and non-radiative processes). Keeping only the vertical component of the diabatic source term, we have: 4Qθ≡PV∂θ˙∂θ To further clarify the drivers of ASMA variability, we decompose the flow into a time-mean zonal-mean background flow (φ‾) and a perturbation flow (φ′), such that φ(x,y,p,t) = φ(y,p)‾ + φ′(x,y,p,t) . The PV tendency equation can then be expanded to highlight variations in intensification: 5∂PV∂t=∂PV′∂t≈-u‾∂PV′∂x-u′∂PV′∂x-v∂PV‾∂y+∂PV′∂y-θ˙∂PV‾∂θ+∂PV′∂θ+PV‾+PV′∂θ˙∂θ Here, -u‾∂PV′/∂x represents the advection of the PV perturbation by the background zonal flow (referred to as “mean zonal advection”), while -v∂PV‾/∂y corresponds to the meridional advection of background PV (“meridional mean advection”). The terms -u′∂PV′/∂x and -v∂PV′/∂y are collectively referred to as “nonlinear horizontal advection”, with -θ˙∂PV/∂θ representing total diabatic vertical advection . Among the variables, only u and PV are split into a time-mean background and a perturbation component (i.e. v′ = v and θ˙′ = θ˙). This is tantamount to defining the background state as the time-mean tropical easterly jet and subtropical westerly jet, averaged zonally across the ASMA and separated by the zonally-oriented u = 0 ridgeline. The zonal advection of mean PV, -u∂PV‾/∂x, vanishes because the background PV field is defined to be zonally uniform along the ridgeline (i.e. ∂PV‾/∂x = 0).

We adopt potential temperature as the vertical coordinate for analysis due to its advantages for studying upper-tropospheric dynamics, particularly those related to PV . Isentropic surfaces, which are defined as surfaces of constant potential temperature θ, are intrinsically aligned with adiabatic air parcel motion. This alignment simplifies interpretation of PV evolution because PV is conserved under adiabatic, frictionless conditions, making it easier to track air mass movement and isolate the key dynamical and thermodynamic mechanisms driving ASMA variability. In addition, this coordinate system simplifies the vertical term, as the adiabatic component of vertical motion is wrapped into the horizontal advective terms. The local rate of change of PV on the 370 K isentropic surface is thus governed primarily by horizontal advective transport of PV, modified by diabatic transport and diluted by diabatic vertical convergence, as expressed in Eq. ().

One key uncertainty concerns the assumption of frictionless flow, as convective momentum transport, gravity wave drag, and shear-flow instability could all modify the flow near the monsoon tropopause. Assimilation effects on winds and temperatures can also be locally large in reanalyses, especially in the vicinity of complex topography such as the Tibetan Plateau e.g.. However, these effects are often tied to topography, and are therefore difficult to interpret and potentially confounding in a vortex-relative framework such as the one adopted here. We center our analysis around the model-generated diabatic heating terms to better attribute these contributions and their consistency across reanalyses, and defer a more complete accounting of assimilation effects and parameterized momentum sources and sinks to future work.

Montgomery stream function (MSF), relative vorticity, and zonal wind are used to identify and track multiple vortex centers within the ASMA over the domain 0–180° E and 15–45° N during the period 2000–2020. Figure  shows an illustrative example of vortex identification on the 370 K isentropic surface using the method described in Sect. . Figure  highlights the dynamical consistency among potential vorticity (PV; Fig. a), relative vorticity (ζ; Fig. b), and MSF and zonal wind (u; Fig. c). Vortex centers are identified at locations where MSF reaches a local maximum along the u = 0 ridgeline. These vortices are likewise characterized by negative relative vorticity (ζ < 0) and small values of PV. The typical number and frequency of ASMA vortex centers from May to August are shown in Fig.  for JRA-3Q, with results for other reanalyses shown in Fig. S1 of the Supplement. The most frequent centroid locations are consistent across the three reanalysis products, with JRA-3Q and ERA5 agreeing particularly well (Fig. S1; see also Fig. ). The longitude–frequency distribution (Fig. ) shows three distinct modes: an “Iranian Plateau” (IP) mode near 50° E, a “Tibetan Plateau” (TP) mode near 90° E, and a “Western Pacific” (WP) mode at 135–150° E, in agreement with previous studies . These modes correspond to the Iranian, Tibetan, and Bonin (Ogasawara) highs . The Bonin High (BH) is the closed anticyclonic system corresponding to the Western Pacific mode of the ASMA, with its center located near the Bonin Islands in the Northwest Pacific. The TP and WP modes are often collectively associated with the South Asian High, while the IP and TP modes exhibit clear spatial interaction e.g.. Moreover, part of the WP mode, which occurs mainly later in the monsoon season, can be linked to eastward eddy shedding. As shown by , the occurrence frequencies of the IP and TP modes are concentrated within 25–35° N and 45–100° E. also highlighted a broad region of frequent vortex occurrence associated with the Bonin High (BH) over 120–180° E, where vortices are generally weaker than those defining the IP and TP modes. Overall, the vortex tracking results presented here are consistent with previous studies in both spatial distribution and frequency characteristics.

To gain a better understanding of ASMA variability, particularly the pronounced trimodal structure from May to September, Hovmöller diagrams are constructed to illustrate the spatiotemporal evolution of vortex centers. These diagrams depict the densities of longitudinal and latitudinal positions of anticyclonic vortices within the ASMA as a function of time of year. The trimodal structure comprising the IP, TP, and BH modes is clearly evident in Fig. a–c. The longitudinal ranges of the vortex centers are well defined, with climatological centers for the IP, TP, and BH modes located at approximately 45–65, 85–100, and 135–145° E longitude, respectively. The relative prevalence of these three centers likewise shows a clear seasonal evolution, with the TP center dominant during May, IP from mid-June to mid-July, and a shift back to predominantly TP centers as the BH emerges in August and September. The ASMA exhibits a clear latitudinal evolution of vortex centers as well, with a northward migration of vortex density in early boreal summer followed by a southward migration later in the season. The northernmost position of approximately 40° N is reached between 15 July and 14 August. This behavior is likewise consistent with previous findings . Persistent vortices account for more than 65 % of identified vortex centers in ERA5 and JRA-3Q, while transient vortices occur much less frequently (Table S1 in the Supplement).

Figure shows four examples of anticyclone evolution during May–September of the years 2000, 2005, 2010, 2015, and 2020. The panels show PV fields on the 370 K isentropic surface, with color shading ranging from 0 to 2 PVU. Low-PV structures in JRA-3Q are highly consistent with the locations of the identified anticyclone centers. Many anticyclonic features show evidence of westward propagation, although some features propagate eastward, especially in the early and late monsoon, and periods of long-lasting quasi-stationary centers are also evident (e.g. August 2020). Tails extending toward both the eastern and western boundaries indicate eddy shedding events . There remains no universally accepted quantitative threshold for defining eddy shedding in the ASMA, as it involves gradual vortex splitting, detachment, and westward/eastward propagation that is inherently continuous and difficult to discretize objectively. We therefore mark only a handful of typical, visually clear cases to illustrate eddy shedding behavior in Fig. , rather than attempting to label every event. The Western Pacific sector lies within the southward-flowing, eastward flank of the anticyclone, where high-PV air from the extratropical lowermost stratosphere is often advected toward lower latitudes. This southward mean advection contributes to the enhanced PV there . Although vortex motion is predominantly zonal (east–west), many vortices also experience meridional (north–south) displacements during their life cycles (not shown).

Figure 6 shows vertical cross-sections for each term in Eq. (). The extents are defined as ±30° in longitude and ±15° in latitude relative to the center of the vortex. A dipolar structure of positive and negative PV tendencies is evident in both the horizontal advection terms (Fig. a–b). In the composite mean, zonal PV advection exhibits a positive tendency to the west and a negative tendency to the east of the vortex center above 300 hPa, while meridional advection is positive to the east and negative to the west as opposed to dipolar pattern thus largely cancel when the horizontal advection terms are summed together (Fig. c) and they yield a tripolar structure. The net time tendency of PV (Fig. d) shows a similar pattern but with smaller amplitude. The dipole patten features positive tendencies peaking immediately west of the vortex center, flanked by negative tendencies on both east and west, although the negative tendencies to the west are considerably farther from the vortex center. Focusing on the tendencies close to the vortex center, the sum of horizontal advection terms exhibits a dipolar structure (Fig. c) with positive values to the west and negative values to the east of the vortex center. Physically, this pattern corresponds to eastward propagation of the anticyclonic vortex in which positive PV tendencies erode the low-PV anomaly on the western flank, while negative PV tendencies reinforce it on the eastern flank, causing the entire vortex core to move eastward over time.

The dipolar signature is driven primarily by horizontal advection and accounts for the zonal translation of the vortex. When diabatic source terms are incorporated, the total PV tendency develops a characteristic tripolar structure (Fig. d). This dipolar structure arises from the superposition of two physically distinct processes, an advective east–west dipole that governs zonal propagation, and a central monopole that modulates vortex intensification. The flanking dipolar components, dominated by net horizontal advection, set the speed and direction of vortex movement. The central component, driven mainly by diabatic heating and its vertical gradient, modulates the overall strength of the low-PV core without displacing its horizontal position. A negative central tendency strengthens the anticyclone, while a positive central tendency weakens it.

Diabatic heating plays an influential role in setting the PV tendency and is essential for anticyclonic vortex development. The vertical structure of diabatic heating is defined by a balance between latent heating and radiative cooling below about 360 K and dominated by radiative heating above this level. Figure  illustrates the distribution of diabatic heating around the identified anticyclonic vortices. On average, the identified vortices show strong deep convective heating collocated with the vortex center and below the eastern flank of the vortex, with much weaker heating below the western part of the vortex. Radiative heating in the upper levels also peaks near the center of the vortex, especially in ERA5 (Fig. a2). Strong radiative cooling in the lower levels compensates much of the positive anomaly in convective heating below 360 K, creating a band of negative net heating around 355–360 K that extends downward to 350 K in the western part of the vortex (Fig. c).

The contributions of diabatic heating to vortex evolution can be separated into two terms. The first of these corresponds to diabatic vertical advection, as shown in Fig.  (the horizontal distribution on the 370 K isentropic surface is provided in Fig. S3). In this term, the diabatic heating distributions shown in Fig.  operate on the partial derivative of PV with respect to potential temperature. PV increases with height, with a local minimum at the vortex center that is strongest in ERA5 and weakest in MERRA-2 (Fig. S2). As a result, upward vertical velocities tend to reduce PV and downward vertical velocities tend to increase PV. The net effect is a vertical dipole centered just below 360 K, with positive tendencies below and negative tendencies above this level. Whereas the qualitative structure is set primarily by the distribution of radiative heating, latent heating acts to shift the zero line downward. Further investigation shows that the positive tendency associated with latent heating near the vortex center results from collocation of the largest positive latent heating with a local reversal of the vertical gradient of PV.

Figure  shows PV tendencies induced by the vertical divergence of different diabatic heating components: radiative heating (Qrad), latent (QLH; JRA-3Q and MERRA-2) or non-radiative heating (Qnon; ERA5), and total diabatic heating (Q). The vertical divergence of radiative heating produces a strong positive tendency at these altitudes (Fig. a), primarily contributed by the increase in background radiative heating with increasing height (Fig. a). These tendencies indicate that the vertical structure of radiative heating in the UTLS, where tropospheric radiative cooling transitions to stratospheric radiative heating, generally acts to spin down the monsoon anticyclone through the diabatic source term. Beyond this general tendency, the spatial structure of radiative heating effects around the vortex center shows a stronger positive tendency in the eastern part of the vortex and a weaker positive tendency near the center of the vortex: the spin-down effect is less pronounced near the center of active anticyclonic vortices. Examination of Fig. , which shows that the composite mean vertical gradient of θ˙ is largest near the vortex center, indicates that this local minimum primarily reflects the local minimum in PV. By contrast to radiative heating, the decrease in latent heating with increasing height near the tops of deep convective clouds produces negative PV tendencies (Fig. b). These negative tendencies show two peaks. The first is located near the center of the vortex, where it supplements the weaker positive radiative tendencies noted above. The second is located in the eastern sector of the vortex, where it offsets at least part of the stronger positive radiative tendencies. The net effect of the vertical divergence of diabatic heating (Fig. c) is to spin down the negative PV anomaly at higher altitudes, with stronger effects near the edges of the vortex and weaker effects near the center. The three reanalyses show large differences in the vertical locations of these effects and their relative magnitudes. Whereas positive tendencies in JRA-3Q peak near 360 K, positive tendencies in ERA5 and MERRA-2 increase with increasing height. Moreover, both ERA5 and MERRA-2 show negative tendencies in the lower part of this vertical range extending eastward from the vortex center. These differences may be explained by stronger anvil cloud radiative effects in ERA5 and MERRA-2 , which weakens the vertical gradient of radiative heating by producing positive longwave heating effects below the anvil and negative effects above the anvil (Fig. a). Like the earlier JRA-55 reanalysis, JRA-3Q produces very little prognostic cloud ice at these altitudes . Meanwhile, the gradient in diabatic source tendencies in MERRA-2 is larger than those based on the other two reanalyses, owing to larger values of PV throughout this altitude range (Fig. S2).

Figures  and  show latitude–longitude distributions of the diabatic source term on the 350 and 370 K levels based on JRA-3Q (equivalent distributions based on ERA5 and MERRA2 are shown in Figs. S5 and S6). Results are shown separately for vortices associated with the IP, TP, and BH modes of the ASMA. Radiative heating (Fig. a–c) produces strong positive PV tendencies to the north of the vortex core at 350 K, indicating an increase in radiative heating with increasing potential temperature acting to increase PV and weaken the vortex. By contrast, latent or non-radiative heating (Fig. d–f) generates strong negative PV tendencies south of the vortex center. The associated reduction in PV enhances the anticyclonic vorticity and contributes to vortex intensification or propagation. The total diabatic heating (bottom row), which combines both radiative and latent effects, shows a net negative PV tendency along the southern flank the vortex and opposing effects along the northern flank. The orientation of this dipole between positive and negative tendencies differs between vortices associated with the IP, TP, and BH modes, primarily owing to differences in the latent heating component. Whereas the latent heating intensification is located in the southeast for the IP mode, it is located in the south for the TP mode, and mainly to the southwest of the vortex center for the BH mode. Meanwhile, positive tendencies wrap around the western flank of IP-mode vortices and the eastern flank of BH-mode vortices. These distributions of the diabatic source term will tend to pull vortices in all modes back toward the southern flank of the central ASMA, where the convective core of the monsoon is located, and inhibit their propagation away from this center. We note that these distributions are composite means over many vortex centers; the tendencies associated with individual vortices may differ.

The dipole patterns shown in Fig.  are weaker on the 370 K level, as shown in Fig. . This difference largely results from a redistribution of the positive tendencies due to radiative heating and a weakening of the negative tendencies due to latent heating. In particular, positive tendencies due to radiative heating at 370 K are weakest within the anticyclonic vortices and strongest toward the convective core of the monsoon. Although the net effect of both terms is to weaken the vortices, the total positive tendencies are weakest from the center toward the southeast for IP-mode vortices and from the center toward the southwest for TP-mode vortices (with a second local minimum in the far southeast). The distribution associated with BH-mode vortices has a more complex structure, with minima to the north and southeast, relatively strong positive tendencies near the vortex center, and stronger positive tendencies to the east and west.

On average, diabatic heating exerts a southward pull on anticyclonic vortices at 370 K, with both latent heating and radiative processes contributing to this tendency. However, the magnitude of the diabatic heating term is small relative to that of horizontal advection, particularly north of the vortex center (Fig. ; equivalent results based on ERA5 and MERRA2 are shown in Figs. S7 and S8). Vertical advection produces a net negative tendency at 370 K, which is located above the level of zero net radiative heating (Fig. a). This advection thus represents a supply of low-PV air from lower altitudes. The combined effects of vertical advection, horizontal advection, and total diabatic heating produce a tripolar structure associated with the anticyclone (Fig. g–i). The three poles of this structure include a predominantly advective dipole along the northern flank of the vortex, characterized by strong negative tendencies to the northeast of the vortex center and positive tendencies to the northwest, and a more monopolar distribution that straddles the vortex center in the south. Warm, moist air with low values of PV is transported upward to the southeast of the vortex and then westward along the southern flank. These two effects combine to produce the predominantly negative net tendencies at latitudes south of the vortex center, which we refer to as the monopole (Fig. g–i). Meanwhile, the background zonal flow (i.e. the subtropical westerly jet) imports relatively high values of PV from upstream of the vortex and exports relatively low values downstream, explaining the dipole along the northern flank (see also Fig. a).

The PV tendency equation provides a useful framework for examining how vortices within the ASMA evolve over time. To better quantify the contributions of each term to intensification and propagation, we take the PV tendencies inside the boxes marked in Fig.  to represent vortex development. Propagation is taken to be defined by the dipole situated along the northern flank of the composite vortex, as represented by the red and blue boxes: 6q˙prop=q˙propW-q˙propE where q˙propW is the average tendency in the red (western) box and q˙propE is the average tendency in the blue (eastern) box. By this definition, a positive value of q˙prop indicates an eastward propagation tendency. The locations of the western and eastern boxes for each mode are listed in Table . Intensification (q˙int) is taken to be defined by the monopole straddling the vortex center, defined as the average tendency within the purple boxes outlined in Fig.  (-10 to +10° relative longitude and -10 to +5° relative latitude). The same ranges in relative longitude and latitude are used to define q˙int for all three vortex modes.

The diabatic term Qθ (Eq. ) is often important for understanding vortex intensification. By analyzing the PV tendency on 370 K, we can directly isolate and quantify the impacts of latent heat release (i.e. convective heating) and radiative heating on the time evolution of PV in each of the three modes relative to those of other processes. The rapid decrease in convective heating with height below the 370 K surface creates a negative PV tendency on that surface (Fig. ), directly linking convective processes to large-scale dynamics. This negative tendency is supplemented by upward advection of low PV, especially above 360 K (Fig. c), but opposed by the increase in radiative heating with increasing height (Fig. a). The total diabatic heating term (-θ˙∂PV/∂θ + Qθ) features local minima consistent with deep convection near the vortex core (Fig. d–f), especially for vortices in the TP and BH modes (Fig. a–c). This negative PV tendency reduces radiative spin-down of the anticyclonic circulation, while horizontal PV advection (Fig. d–f) introduces the northern dipole pattern.

Contributions from each term in Eq. () to anticyclone intensification are shown in Fig. . A larger positive PV tendency corresponds to a weakening of the anticyclone, whereas negative PV tendencies indicate strengthening. The PV tendency decomposition highlights the common dynamics underlying the maintenance of different ASMA modes, as well as key differences across modes and among reanalysis products. Across all modes, the net advective contributions are small, with substantial compensation among the terms, although the extent of cross-term compensation varies among the different modes. For the IP mode, background zonal advection contributes to weakening anticyclonic vortices, consistent with the location of this mode in the western part of the anticyclone. For the BH mode, nonlinear advective contributions act to weaken vortices, consistent with the location of this mode near the eastern flank of the anticyclone, where the subtropical westerly jet exit region and the tropical easterly jet entrance region create a critical zone that hosts frequent wave breaking. For the TP mode, advective contributions to the intensification monopole are weak, consistent with its location near the center of the climatological ASMA . By contrast, diabatic contributions to vortex intensification are larger for the TP mode than for the other two modes. Latent heating and diabatic vertical advection act to strengthen vortices in this mode, whereas radiative heating typically acts to weaken it. The composite-mean balance of these terms varies substantially across the three reanalyses: strengthening in ERA5, weakening in MERRA-2, and near-zero net tendencies in JRA-3Q. Both radiative and non-radiative heating contribute to these differences. The results show greater consistency across the reanalyses for the IP mode, where the latent heating source is weak and the net tendency is dominated by radiative damping offset by diabatic ascent. BH mode vortices are weakly damped in ERA5, moderately damped in JRA-3Q, and strongly damped in MERRA-2. The weaker damping in ERA5 derives from meridional advection-induced strengthening supplementing latent heating and diabatic ascent, while the stronger damping in MERRA-2 is due to greater radiative heating-induced spin-down. Indeed, radiative damping is considerably stronger in MERRA-2 than in the other reanalyses for all three modes, leading to stronger overall vortex damping via net q˙int and its total diabatic component in this reanalysis.

Figure  shows contributions from each term in Eq. () to anticyclone propagation (q˙prop), as defined in Eq. (). Total tendencies are eastward (positive) due to the dominant contributions of zonal advection, indicating the critical influence of the subtropical westerly jet in advecting individual vortices eastward relative to the surface. The balance of all other terms is dominated by meridional advection, which offsets the eastward contribution of the zonal background flow. This contribution indicates that, despite moving eastward on average relative to the surface, the vortices in all three modes typically move westward relative to the background flow due primarily to the meridional advection of potential vorticity, the dominant term governing Rossby wave propagation. Other contributions are negligible by comparison. Both the eastward contribution from mean zonal advection and the westward contribution from meridional advection are considerably weaker in MERRA-2 than in the other two reanalyses, whereas ERA5 and JRA-3Q show close agreement in these primary terms. Inter-reanalysis differences in the overall magnitude of q˙prop are explained to close approximation by differences in perturbation zonal advection, particularly the stronger eastward propagation tendency of BH-mode vortices in MERRA-2 and the weaker eastward propagation tendency of TP-mode vortices in ERA5.