On the Relationship Between the Madden‐Julian Oscillation and the Hadley and Walker Circulations

This study investigates: (i) how the local meridional (Hadley) and zonal (Walker) circulations change in each phase of the Madden‐Julian Oscillation (MJO); and (ii) the effect of enhanced and suppressed MJO‐related convection on the poleward extent of the local Hadley circulations and, thus, the strengths and positions of the subtropical jets. We examine these effects in ERA‐Interim reanalysis by decomposing the vertical mass flux into zonal and meridional components. We show for the first time, that as the envelope of enhanced convection moves eastwards from Africa to the Central Pacific the local Hadley circulation is enhanced. The regional Walker circulation in the Pacific is strengthened when the envelope of active MJO convection is located over the Maritime Continent and weakened when the region of suppressed convection is located there. In regions of anomalous upper‐level divergence the subtropical jet is enhanced. The core of the subtropical jet over Asia shifts eastwards with the progression of the MJO and shifts farther poleward in regions of anomalous upper‐level divergence linked with enhanced convection. The region of either enhanced or suppressed convection over the Maritime Continent strengthens or weakens the local Hadley circulation, producing disturbances in the subtropical jet. These disturbances then force midlatitude Rossby waves that propagate across the Pacific Ocean in both hemispheres.

Overall, we seek to answer the following questions: i) How do the local Hadley and Walker circulations change in each phase of the MJO? ii) How does the MJO affect the poleward extent of the local Hadley circulations, and thus the subtropical jets and midlatitude Rossby wave response, both globally and seasonally? We investigate these questions by objectively decomposing the three-dimensional atmosphere into a pair of orthogonal overturning circulations, that is, local Hadley and local Walker circulations (Schwendike et al., 2014). The sum of the individual circulations equals the original, thereby allowing us to examine regional overturning circulations in an unambiguous way. The method and data used will be described in Section 2. The climatology of precipitation and the local Hadley and Walker circulations in different MJO phases will be shown in Section 3. Section 4 will investigate the influence of the location of the MJO convection on the subtropical jet using the flow decomposition framework. Section 5 will link the MJO and midlatitude Rossby waves. A summary and the conclusions will be given in Section 6. Schwendike et al. (2014) have adapted the ψ-vector method, originally developed by Keyser et al. (1989), to decompose the tropical atmosphere into a pair of orthogonal overturning circulations, satisfying continuity independently in a Cartesian framework in spherical pressure coordinates. This pair of overturning circulations are the local Hadley and Walker circulations, respectively. The method is outlined below and full details can be found in Schwendike et al. (2014).

Data and Method
The meridional overturning circulation at a point or in a plane in the tropics is referred to as the local Hadley circulation, and the zonal overturning circulation at a point or in a plane in the tropics is referred to as the local Walker circulation. Outside of the tropics it is best to think of these circulations mainly as meridionally and zonally overturning circulations.
The vector stream function ψ is defined as where ∇ p is the horizontal gradient operator in isobaric coordinates, μ is a potential function, and ω is the vertical motion.
The vertical motion, ω, can be partitioned uniquely into the zonal and meridional planes according to: where ω λ and ω ϕ are the vertical motion associated with flow in the zonal and meridional planes, ψ λ and ψ ϕ are the stream functions in the zonal and meridional directions, and a is the radius of the Earth. The SCHWENDIKE ET AL.
respectively, where g is the gravitational acceleration.
The adapted version of the ψ-vector method is applied to the European Centre for Medium range Weather Forecasts (ECMWF) ERA-Interim (ERAI) reanalysis data Simmons et al., 2011) with a horizontal resolution of 0.75 degrees for the period 1979 to 2009. Additionally, the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA-RT) 3-hourly data (product 3B42) between 1989 and 2009 with a horizontal resolution of 0.25° is used to examine precipitation anomalies in different phases of the MJO (Huffman et al., 2010). To divide the precipitation and mass flux data into the eight phases of the MJO the real-time multivariate MJO index, RMM, is used (Wheeler & Hendon, 2004). MJO events are selected when the amplitude of the RMM empirical orthogonal functions is one or greater.
We have carried out the same analysis for neutral ENSO phases only by separating the data based on the Southern Oscillation Index (SOI) from the Australian Bureau of Meteorology and chose a threshold of +5 for for La Niña events and −5 for El Niño events. We found that the results remain unchanged. The main difference was that the amplitudes of the fields shown below are higher for neutral ENSO days than when including all days due to the lower number of days in each composite.

Climatology of Hadley and Walker Circulations According to MJO Phase
The rainfall anomalies in different phases of the MJO based on 3-hourly TRMM data are calculated in this section and compared to the response of the local Hadley and local Walker circulations in the respective MJO phase.

Rainfall Anomalies
The eastward propagation of the envelope of enhanced MJO convection, that is, enhanced precipitation, from Africa to the Pacific has been well documented (e.g., Wheeler & Hendon, 2004). To motivate the present study, to remind us of the distribution of regions of enhanced and suppressed convection during different MJO phases, and most importantly to show the link between rainfall and the upward mass flux, we have plotted the TRMM precipitation anomalies in Figures 1 and 2.
The rainfall anomalies between 1989 and 2014 in December, January, February (DJF) are shown for different MJO phases in Figure 1, with every second phase shown for brevity. In Phase 2 of the MJO, the precipitation over the Indian Ocean is increased ( Figure 1a) and the precipitation over the Maritime Continent and the Western Pacific is reduced. A significant precipitation increase also occurs over parts of China and the adjacent ocean. In Phase 4 (Figure 1b), the convection and associated precipitation are located over the Maritime Continent with notable regions of increased precipitation east of the Indian subcontinent, parts of Southeast Asia, along the inter-tropical convergence zone (ITCZ) and the SPCZ. Weaker increases in precipitation also occur along the storm tracks in the Northern Hemisphere. In Phase 6 ( Figure 1c), precipitation is increased east of the Maritime Continent and in the Western Pacific as well as over northern Australia and the SPCZ. The positive precipitation anomaly continues to move eastward until it reaches the Central Pacific Ocean and enhances the SPCZ in Phase 8 ( Figure 1d). In this phase precipitation is reduced over the Maritime Continent.
In June, July, and August (JJA), the eastward movement of enhanced convection is less pronounced, although the changes for the Maritime Continent are distinct ( Figure 2). In Phase 2 (Figure 2a), there is suppressed precipitation over large parts of the Maritime Continent and enhanced precipitation occurs over and south of India as well as large parts of Indonesia. In Phase 4 (Figure 2b), the band of increased precipitation extends farther into the Western Pacific. Precipitation increases also along a band ranging from India to the ITCZ in the Western Pacific. In Phase 6 ( Figure 2c), the anomaly in precipitation is largest in the Western Pacific and north of the Equator, along the ITCZ. Precipitation also increases along the storm tracks in the Southern Hemisphere. In Phase 6, precipitation is reduced over the Central and Eastern Indian Ocean and large parts of Indonesia and Malaysia. Phase 8 (Figure 2d) is characterized by mainly reduced precipitation. Precipitation is enhanced in the Eastern Pacific and over South America.
In most MJO Phases in DJF and JJA, a positive precipitation anomaly occurs on either side of the equator in the Eastern Pacific, potentially indicating a double ITCZ as pointed out in Berry and Reeder (2014). These SCHWENDIKE ET AL.
10.1029/2019JD032117 4 of 28 positive precipitation anomalies disappear or weaken when the active (e.g., Phase 2) or suppressed (e.g., Phase 6) MJO convection is located in the Indian Ocean.

Mass Flux Anomalies
The eastward movement of an envelope of convection and the associated precipitation from Africa to the central Pacific Ocean (Figures 1 and 2) is also reflected in the anomalies of the 500-hPa mass flux. The meridional and zonal mass flux anomalies at 500 hPa during DJF are shown in Figures 3 and 4  from the mean meridional mass flux between 1979 and 2009 at the 95% confidence level. The statistical significance for the anomalies in the remainder of the paper has been calculated in the same manner.
In Phase 2 ( Figure  Moreover, Figure 4 shows that quasi-stationary midlatitude waves occur downstream of the regions of either enhanced or suppressed upward mass flux over the Maritime Continent. The extratropical wave pattern occurs in all MJO phases across most longitudes. Not only does the MJO affect the strength of the local Hadley and Walker circulations, the regions of enhanced and suppressed MJO precipitation are co-located with the origin of a midlatitude wave train as we will show in Section 5. These midlatitude wave trains occur in both hemispheres where they appear to be quasi-stationary relative to the forcing (the MJO) as a propagating wave signal would have been averaged out.
Broadly speaking, a similar pattern of mass flux anomalies and distribution of the divergent part of the wind are also found in JJA, although the details of where the regions of enhanced and weakened mass flux are located are different ( Figures 5 and 6). For instance, in Phase 2 the anomalous upward meridional mass flux is larger over the western Indian Ocean and Malaysia than in the mean ( Figure 5a). Over large parts of Australia, the anomaly is positive, and over Thailand and the South China Sea the anomaly is strongly negative. In Phase 4 ( Figure  When comparing the anomalies of the zonal mass flux for each MJO phase between DJF ( Figure 4) and JJA ( Figure 6), it is apparent that the midlatitude wave trains are more pronounced in the winter hemisphere than in the summer hemisphere. The distribution of mass flux anomalies is relatively similar between JJA and DJF; however, the divergent part of the wind in the zonal direction shows differences.
This analysis shows that the local Hadley circulation strengthens (weakens) by 50% of its climatological mean when it coincides with the envelope of enhanced (suppressed) MJO convection. The absolute changes to the local Walker circulation are similar to those of the local Hadley circulation, but due to being climatologically a factor of two weaker than the local Hadley circulation, the local Walker circulation doubles in strength when the MJO convection is located over the Maritime Continent and is almost completely suppressed when the weakened MJO convection is located over the Maritime Continent.
The large magnitude of these changes to the tropical circulation have consequences that extend well into the midlatitudes. In the following sections, we discuss the changes to the subtropical jet and the midlatitude SCHWENDIKE ET AL.

MJO and the Subtropical Jet
To address how the propagation of the envelope of enhanced and suppressed convection affects the poleward extent of the local Hadley circulations and the subtropical jets we will analyze how the position and the strength of the subtropical jet changes during different phases of the MJO, and we will quantify changes in the jet over selected regions.

Windspeed Anomalies
The subtropical jet is illustrated with the 200-hPa wind speeds larger than 30 m s −1 in Figures 3-6. In DJF, the strongest jet extends from North Africa to Asia with the maximum located between 25 o N and 45°N over Japan and the Western Pacific. A weaker but pronounced jet exists on the southern and eastern flank of North America with the maximum located over the east coast ( Figure 3). The jet in the Southern Hemisphere is weaker, as expected, and extends from South America to Australia. The jets are located at the poleward edges of the descending branch of the local Hadley circulation (see Figure 1 in Schwendike et al. (2014)).
In JJA in the Northern Hemisphere, wind speeds larger than 30 m s −1 only occur over Asia (e.g., Figure 5). In the Southern Hemisphere, a band of wind speeds exceeding 30 m s −1 is located roughly between 25 o S and 50°S. Maxima in wind speed occur east and west of Australia and east of South America.
To illustrate the changes in the subtropical jets in different MJO phases, the differences between the mean windspeed between 1979 and 2009 and the mean windspeed in each MJO phase in DJF and JJA are shown in Figures 7 and 8. In DJF in Phase 2 of the MJO the convection occurs over the Indian Ocean in a region of upper-level divergence ( Figure 7a). North of the region of enhanced convection, at around 30°N, the jet speed is increased by about 8-10 m s −1 . East of this region, where the jet is climatologically strongest, the jet is weakened by about 5-10 m s −1 , an area characterized by convergence over the Maritime Continent. The jet along the storm track over North America and the Atlantic is strengthened by about 3-6 m s −1 .
In Phase 4 (Figure 7b), the wind speed east of the mean maximum of the jet, which is located roughly over Japan, is reduced, and increased west of the region of the maximum. The increase in wind speed to the west of the maximum is consistent with the strong divergent outflow of the convection located over the western part of the Maritime Continent. The region east of the mean jet maximum is characterized by upper tropospheric convergence.
As the envelope of MJO convection moves farther toward the east, the region of increased upper-level wind speed also moves eastward. In Phase 6 (Figure 7c), the wind speed is increased in the region of the mean maximum of the jet, and weakened west of it. In Phase 8 (Figure 7d), the jet is strengthened east of the climatological maximum and weakened west of this region.
In JJA, the same patterns can be seen. In Phase 2 (Figure 8a), the speed of the subtropical jet is increased over South Africa and west of Australia in a region characterized by upper-level divergence. Over southern Australia and east of Australia, the wind speed decreases in a region of upper-level convergence. In Phase 4 (Figure 8b), the wind speed increases farther over the Southern Ocean and extends farther to the east. Similarly, the wind speed decreases over southeastern Australia and at around 30°S east of Australia. In Phase 6 (Figure 8c), when the convection is located over the eastern side of the Maritime Continent, the jet is enhanced and has a maximum over southern Australia. Over South Africa the wind decreases. As the convection moves farther east into the Western Pacific Ocean, the region of increased wind speed also moves eastwards. In Phase 8 (Figure 8d), the jet maximum is located in the South Pacific Ocean. The jet is weakened south of South Africa, the Indian Ocean and parts of Australia.
Comparing the intensity of the winter hemispheric jets between Phases 4, 6 and Phases 8, 2 (Figures 7 and 8) shows that the jet over Australia is stronger between about 90 o E and 150°E in Phase 6 than in Phases 8, 2, when the enhanced convection is located over the Maritime Continent. When the convection is located over the Western Pacific, the jet has a local maximum over the Western Pacific (Figure 8d). A similar behavior occurs for the subtropical jet located over Africa, Asia and the northern Pacific and the jet over North America and the North Atlantic. While we focus here more on the changes in the midlatitudes, it is worth pointing out that there are significant changes in upper-level wind speed in the tropics. These wind speed anomalies are similar to those discussed in Zurita-Gotor (2019), who found that the large-scale eddy momentum transport in the tropics is associated with the correlation between the divergent meridional velocity and the non-divergent zonal SCHWENDIKE ET AL.
10.1029/2019JD032117 13 of 28 velocity. They also pointed out that the Hadley circulation plays the dominant role in the tropical momentum transport.
In summary, the strengthening (weakening) of the jet due to upper-level divergence (convergence) associated with the MJO is strongest in the winter hemisphere. The magnitude of these changes remains similar between Northern and Southern Hemisphere winter.

Changes in the Jet Core Location
The analysis of the wind speed anomalies shows a relationship between the divergent outflow of the convection related to the MJO and the strengthening or weakening of the subtropical jet predominantly in the winter hemisphere when the jet is strongest. Figures 7 and 8 already indicated that there is a shift in the location of the jet core. For instance, the subtropical jet over India is displaced further northwards when the active phase of MJO convection is located over the Indian Ocean. At the same time, the subtropical jet in the southern Indian Ocean is displaced further poleward. To emphasize this relationship, the position of the jet core in both winter hemispheres (i.e., DJF in the Northern Hemisphere and JJA in the Southern Hemisphere) is shown in Figure 9.
When the envelope of active MJO convection is located over India and the Maritime Continent, the jet over Asia is located about 3-5° farther northwards compared to when the envelope of convection is located in the Western Pacific ( Figure 9). The jet maximum over Asia extends by about 10° farther to the East during phases 7, 8, 1 when the active convection is located over the Western and Central Pacific and over eastern Africa. The increase in wind speed and extension to the north is consistent with the strong divergent outflow of the region of enhanced convection.
An eastward shift by about 10° can also be observed for the Southern Hemisphere jet located over Australia during Phases 7, 8, 1 compared to the location of the jet maximum in Phases 4, 5, 6. The jet also extends farther poleward in the Southern Hemisphere when the region of enhanced convection is located over in the Indian Ocean in Phases 4, 5, 6 and slightly poleward when the convection is located in the Central Pacific, but only by about 1-3° (Figure 9).
Our analysis shows that in the winter hemisphere, the jet is shifted polewards in regions of enhanced MJO convection and upper-level divergence, whereas in regions of suppressed convection and upper-level convergence, the location of the jet does not change.

Changes in Jet Core Characteristics Over Different Regions
In this section we consider the impact of the MJO on the jet in winter for three particular regions where this has not previously been studied: the Northwestern Pacific, the Southwestern Pacific and the North Atlantic.
To isolate the changes in the jet maxima with different MJO phases, in Figures 10 and 11 we show the jet core wind speed, the jet width and depth, as well as a measure of the mass transport, which is the product of SCHWENDIKE ET AL. the three fields for three areas, that is, the Northwestern Pacific, the Northern Atlantic and the Southwestern Pacific (the three boxes shown in Figures 10e and 11e).
The jet location was determined by the zero-shear-vorticity line in regions where the wind speed was greater than 20 m s −1 , similar to the definition of the African Easterly jet axes in Berry et al. (2007). Then the line joining algorithm used in Berry et al. (2011) was applied to define the jet core. The jet widths are defined at each point along the jet by using the jet points either side to define a direction and scanning perpendicular to that to find where the wind speed drops to 2/3 of the core value. Likewise, the depth is computed by determining at what level the jet speed at each jet point drops to 2/3 of the core value.
In winter (Figure 10), the variability between MJO phases is high. The jet over the Northwestern Pacific reaches its maximum peak core speed in Phase 6 and its minimum in Phase 1. The peak core speed of the SCHWENDIKE ET AL.
10.1029/2019JD032117 16 of 28 Figure 11. The same as in Figure 10 but for the summer hemispheres. Northwestern Pacific jet in DJF is larger than 100 m s −1 , which makes it the strongest jet of the three. The jet maximum is reached in Phase 7 in the Southwestern Pacific (JJA), and in Phases 1, 2, 3, and 8 over the Atlantic. As the jet core speed increases for the Northern and Southern Pacific jets, the depth of the jet (Figures 10b and 10e) and the mass transport (Figures10d and 10e) increase, but the jet width decreases (Figures 10c and 10e). The jet in the Northern Atlantic (DJF) shows a different behavior: the depth, width and mass transport do not vary coherently with MJO phase. This different behavior of the jet in the North Atlantic might be due to the fact that the anomalies at upper levels due to the MJO convection do not directly reach the North Atlantic. The changes in the subtropical jet in the Pacific are the direct response to tropical heating, but the changes to the jet in the Atlantic are likely due to the remote responses driven by wave propagation.
In summer (Figure 11) over the Northwestern Pacific (JJA), the jet core speed has its maximum with over 36 m s −1 in Phases 3 and 4. The depth of the jet (Figure 11b) remains relatively constant throughout all MJO phases. As the jet maximum increases, the width of the jet decreases (Figure 11c), and the mass transport decreases (Figure 11d). The changes in the jet structure over the Atlantic with MJO phase are different to the Northwestern Pacific. The jet core speed in DJF is largest in Phases 1, 5, 6, and 7 and weakest in Phase 2 ( Figure 11a). The depth of the jet is nearly twice the depth of the jet located over the Northwestern Pacific, and changes only little from phase to phase. The evolution of the width of the jet is very similar to that in the Northwestern Pacific. In accordance to the larger depth of the jet in the North Atlantic is the larger mass transport in this region. The changes in Northern Hemisphere jet wind speed, jet depth and mass transport are distinct between MJO phases. The largest differences occur in the width of the jet. The jet is narrower in Phases 3-5 and wider in the other phases.
In summer over the Southwestern Pacific (DJF), the jet reaches its maximum wind speed in Phase 2 and the peak core speed is smallest in Phase 6. The jet is deeper when the core speed is high, and the jet is widest when the wind speed is lowest. Overall the depth of the jets and the mass transport change relatively little from phase to phase.
To summarize this section, we find that over the Northwestern and Southwestern Pacific, the jet core speed, depth and mass flux increase, while the jet width decreases when the active phase of convection is over the Maritime Continent. The jet in the Northern Atlantic also changes but the behavior is more erratic and does not vary coherently with MJO phase.

MJO and Midlatitude Rossby Waves
Many studies have shown a link between enhanced MJO convection and midlatitude Rossby waves, often by making use of the Rossby wave source and the wave-activity flux. Here, we use these well-established tools, but in contrast to previous studies, we calculate both fields for all MJO phases and for both the Northern and Southern Hemisphere during DJF and JJA. We use these calculations in conjunction with what we found in the previous sections to investigate the role of the divergent part of the wind in perturbing the jet.

Rossby Wave Source
To investigate the downstream impact of the changes in the midlatitude jets due to the enhanced and suppressed convection in the tropics, we calculated the Rossby wave source, S, as defined in Sardeshmukh and Hoskins (1988): where η is the absolute vorticity, D is the divergence of the wind, and v div is the divergent part of the wind.
Additionally, we calculated the wave-activity flux based on Equation 38 in Takaya and Nakamura (2001). The wave-activity flux identifies stationary wave disturbances and indicates where the waves are emitted, refracted, and absorbed. The wave-activity flux is derived from quasi-geostrophic theory and therefore has limitations in the tropics. The two most important properties of the wave-activity flux are that: (i) the convergence and divergence of the wave-activity flux vector can be related to changes in the amplitude of the wave; and (ii) the wave-activity flux shows the instantaneous wave packet propagation of stationary disturbances and the wave-activity flux vector is proportional to the group velocity.
The Rossby wave source and the wave-activity flux (not the anomalies) at 200 hPa in DJF and JJA are shown for Phases 2 (suppressed convection over the Maritime Continent) and 6 (enhanced convection over the Maritime Continent) in Figures 12 and 13. These figures show that disturbances in the jet, initiated from both enhanced upper-level outflow (enhanced convection) and upper-level convergence (suppressed convection), which can be interpreted as a strengthened or weakened local Hadley circulation, can lead to the formation of a quasi-stationary wave pattern along the jet in the Pacific Ocean. This result agrees with Sardeshmukh and Hoskins (1988), who found that the advection of absolute vorticity by the divergent flow in an equatorial region with easterly winds (which do not support Rossby waves) can lead to a Rossby wave source in the subtropical westerlies.
In DJF in Phase 2, the strongest Rossby wave sources occur in the Northern Hemisphere. Broadly speaking, the Rossby wave source over the Pacific is positive along the equatorward flank of the subtropical jet ( Figure 12a)  In DJF in Phase 6 (Figure 12b), when the envelope of enhanced convection is located over the Maritime Continent, the areas of positive and negative Rossby wave source are roughly in the same region as during Phase 2 in both the Northern and Southern Hemisphere. The main differences are that the Rossby wave source is slightly stronger during Phase 6 than during Phase 2.
A similar observation can be made in JJA (Figure 13). The Rossby wave source is strongest in the winter hemisphere, but the differences in the distribution between Phases 2 and 6 are relatively small, aside from the magnitude in Phase 6 being somewhat larger than in Phase 2. One specific difference in JJA, however, is that positive values of the Rossby wave source start only at around 150°E compared to about 115°E during DJF. This displacement to the east is also apparent in the North Atlantic.
The surprising result here is that the mean (not the anomaly) Rossby wave source pattern is very similar regardless of whether the enhanced or suppressed phase of the MJO is located over the Maritime Continent, despite the subtropical jet responding differently in these phases. By examining the wave-activity flux, we will show that the source region for the midlatitude Rossby waves coincides with areas of enhanced upward mass flux, indicating that the Rossby waves form in relation to disturbances in the jet, caused by anomalous upper-level divergent flow of the enhanced or suppressed MJO convection.

Wave-Activity Flux
The arrows in Figures 12 and 13 represent the wave-activity flux. In the Northern Hemisphere, these arrows alternate in direction along the Eurasian jet, marking a stationary wave propagating along a waveguide. In Phase 2 (Figure 12a), the wave-activity flux originates roughly over India, whereas in Phase 6 ( Figure 12b) the wave-activity flux vector originates over Southeast Asia. In both phases, there is a strong convergence of the wave-activity flux at the end of the jet near the west coast of North America.
In the Southern Hemisphere in Phase 2 (Figure 12a), there is enhanced wave-activity flux south of the region of enhanced convection. In Phase 6 (Figure 12b), the wave-activity flux emanates from the poleward extremities of the Maritime Continent near the critical line c p = 0, and converges over southeastern Australia, which has been identified previously as a preferred region for Rossby wave breaking (e.g., Hitchman & Huesmann, 2007;Reeder et al., 2015), and in the southern Pacific.
In JJA in Phase 2 (Figure 13a), a prominent band of wave-activity flux emerges from northern Australia, follows a path to the southwest, before refracting toward the northeast, and converging over South America. A second, but less prominent, band emerges from southern Africa, before refracting and converging over northern Australia. In Phase 6 ( Figure 13b), a pronounced wave-activity flux originates from the poleward extremities of the Maritime Continent, and follows a path to the high Southern Hemisphere latitudes. Again the wave-activity flux converges in the eastern Pacific. This region is not one of the Rossby wave breaking hot spots, but wave breaking does occur there (Hitchman & Huesmann, 2007).
McIntosh and Hendon (2018) have investigated Rossby wave trains in response to the Indian Ocean Dipole (IOD) and have shown that a strong subtropical jet in JJA inhibits the propagation of stationary waves from the tropics into the midlatitudes because the meridional gradient of the absolute vorticity goes to zero on the poleward side of the subtropical jet. The mean easterlies at upper levels in the tropics also provide an unfavorable environment for Rossby wave generation and propagation (Sardeshmukh & Hoskins, 1988).
McIntosh and Hendon (2018) point out that two wave trains occur in the vicinity of Australia in JJA. One wave train is the result of enhanced convection associated with anomalous heating from the IOD and the associated enhanced upper-lever divergence. This evanescent wave train, however, cannot reach the midlatitudes due to the strong subtropical jet and is often refracted back into the tropics. The other wave train is located on the poleward side of the subtropical jet and is related to transient eddies. McIntosh and Hendon (2018) point out that in JJA the combination of both wave trains is typically seen in, for instance, geopotential height anomaly plots. They further argue that in austral spring, when the subtropical jet weakens, Rossby waves can propagate from the subtropics into the midlatitude and that these Rossby waves are forced by the upper-level anomalous divergent wind. The waves trains described in McIntosh and Hendon (2018) for the positive phase of the IOD, where convection is enhanced in the western Indian Ocean and suppressed in the eastern Indian Ocean, emanate from the western Indian Ocean. In contrast, the wave trains in Figure 13 emerge from over South Africa and north of Australia in MJO Phases 2 and 6. Figures 12 and 13 show that the wave-activity flux vectors emerge poleward of the critical line c p = 0 and poleward of the regions of enhanced upward mass flux. These Rossby waves are generated in the midlatitude westerlies and are a direct result of disturbances to the jet, which themselves are caused by changes to the local Hadley circulation as a result of the passing MJO.

Rossby Wave Source and Wave-Activity Flux Anomalies
To further support our conclusion from the previous sections, Figures 14 and 15 show the anomalies of the Rossby wave source and the wave-activity flux from the seasonal mean between 1979 and 2009. The stipples indicate regions where the anomalies are not statistically significant at the 95% confidence level. In DJF in Phase 2 of the MJO, a negative Rossby wave source anomaly is located over Asia and a positive anomaly over most of the North Pacific. A positive Rossby wave source anomaly occurs over the Indian Ocean in the Southern Hemisphere. In the Southwest Pacific the Rossby wave source anomaly is mainly negative. In Phase 6, the signal is almost reversed with a positive anomaly over Asia, a negative anomaly over the Northwest Pacific, a negative anomaly over the Southern Indian Ocean and a positive anomaly over the Western South Pacific.
A similar behavior can be observed during the Southern Hemisphere winter (Figure 15). In JJA in MJO Phase 2 when the convection is located over the Indian Ocean, there is a positive anomaly located in the Southern Indian Ocean and a largely negative anomaly in the Southern West Pacific. In Phase 6, the signal is reversed and the positive Rossby wave source anomaly is located east of Australia near the jet core. The anomalies are weaker in the Northern Hemisphere, where they have the opposite sign. The Rossby wave source anomaly is largely positive over the North Pacific during MJO Phase 2 and largely negative in MJO phase 6.
The largest anomalies in the wave-activity flux overlap with the largest wave-activity flux vectors in Figures 12 and 13 and show that this anomalous wave activity is a result of the disturbances of the subtropical jet due to the MJO convection.

Interaction Between Midlatitude Rossby Waves and the Subtropical Jet
An alternative way to quantify the interaction between the subtropical jet and the midlatitude Rossby waves is to calculate the advection of the potential vorticity (PV) by the divergent part of the wind u χ on the 350-K surface following O'Brien and Reeder (2017) The anomaly patterns in PV advection are similar to those for the Rossby wave source in Figure 12, except they are much less noisy. The anomalies in PV advection in DJF and JJA ( Figure 17) are similar, too. The anomalies are largest close to the jet axis and are stronger in the winter hemisphere than in the summer hemisphere.
O'Brien and Reeder (2017) have argued also that the anomalous divergent part of the wind in the tropics and subtropics leads to the advection of absolute and PV, which in turn leads to the formation of Rossby waves.
Our results are in agreement with those found in Lukens et al. (2017). For the Northern Hemisphere Lukens et al. (2017) have shown that the divergent outflow from the convection associated with the MJO over the western tropical Pacific is the main reason for the impact of the MJO on the midlatitudes in all MJO phases. They further showed that during Phases, 1, 2, 3, 7 the anomalous divergent winds advect absolute vorticity in the subtropics and, in combination with the horizontal convergence in the tropics, this leads to the formation of a cyclonic vorticity anomaly over southeast Asia. This cyclonic anomaly is then advected eastwards toward the central Pacific. In Phases 4, 5, 6, and 7, Lukens et al. (2017)  We have shown that the anomalous upper-level outflow of regional Hadley circulations disturbs in the subtropical jet and that these disturbances are the source for midlatitude Rossby waves. The wave-activity flux shows the propagation of these waves along the midlatitude storm tracks.

Rossby Wave Propagation in the Midlatitudes
The link between changes in the subtropical jet, due to enhanced and suppressed MJO convection and therefore a strengthened or weakened local Hadley circulation, and the downstream propagation of the midlatitude Rossby waves is made even more apparent when looking at the midlatitude wave signal in the Hovmöller plots in Figures 18 and 19. The zonal mass flux anomalies (based on m λ ) and the wave-activity flux are meridionally averaged over 40 o N-60°N and 40 o S-60°S. We show the anomaly of the zonal mass flux from the 31-year mean in each MJO phase as they display the anomalies in the zonal direction, that is, the direction of the midlatitude waves, distinctly. Additionally, the wind speed anomaly from the 31-year wind speed mean averaged over 20 o N-40°N and 20 o S-40°S is shown in contours. The averaging band for the wind speed is chosen to include the maximum of the jet, so as to link the changes in the jet to the stationary Rossby wave pattern. The MJO phase is shown on the abscissa and the ordinate shows the longitude. The fields have been interpolated for plotting to give a sense of the continuity in time.

10.1029/2019JD032117
Broadly speaking, in DJF and JJA the regions of upward and downward mass flux are relatively similar. Bands of upward and downward mass flux, which represent a quasi-stationary wave pattern, propagate eastward with the MJO as the region of enhanced convection moves from East Africa to the Central Pacific. The eastward propagation of the Rossby waves is illustrated by the wave-activity flux vectors.
In the Northern Hemisphere in DJF (Figure 18a), the wave-activity flux has a northeastward direction and is strongest over the Pacific Ocean (roughly between 160°E and 120°W) in Phases 3-8. The wave-activity flux is largest in magnitude in Phases 3, 4, and 8. In Phases 4 and 5 the wave-activity flux vector is directed to the east and the magnitude is also relatively large over North America. The wave-activity flux is, in general, weaker in the Southern Hemisphere (Figure 18b) than the Northern Hemisphere, and is also largest over the Pacific Ocean. Moreover, in both hemispheres, the wind speed anomalies also propagate from west to east with the MJO phase. The wind speed anomalies are largest over the Maritime Continent in all MJO phases and coincide with the largest wave-activity flux vectors.
The bands of anomalous upward and downward mass flux are less coherent in JJA (Figure 19a, b) than in DJF, particularly in the Southern Hemisphere. In the Northern Hemisphere, the largest wave-activity flux occurs in Phases 3 and 8 over the Pacific Ocean. In the Southern Hemisphere, the largest wave-activity flux occurs in Phase 6 and 7. Once again, positive and negative wind speed anomalies move from west to east, with the largest anomalies in the winter hemisphere.
In summary, the anomalous upper-level divergence (convergence) of the region of enhanced (suppressed) convection associated with the MJO leads to changes in the speed and location of the subtropical jet. These disturbances in the jet, along with the advection of absolute vorticity, lead to the formation of a mid-latitude quasi-stationary wave pattern, which changes the propagation characteristics of the Rossby waves.

Summary and Conclusions
We set out to investigate: (i) how the local Hadley and Walker circulations change in each phase of the MJO; and (ii) how the propagation of the envelope of enhanced and suppressed convection affects the poleward extent of the local Hadley circulations and the strength and position of the subtropical jet. We addressed these questions by objectively decomposing the vertical mass flux into zonal and meridional components following the ψ-vector method of Keyser et al. (1989) modiefied by Schwendike et al. (2014). We applied this method to 31 years of ERAI reanalysis data. The advantage of the ψ-vector method is that it allows us to study local Hadley and Walker circulations and their link to the MJO in an unambiguous way.
We have shown, for the first time, that as the envelope of enhanced precipitation moves from Africa to the Central Pacific, the local Hadley circulation is enhanced by about 2 kg m −2 s −1 . The regional Walker circulation in the Pacific is weakened when the suppressed phase of MJO convection is located over the Maritime Continent, and doubles in strength when the active phase of MJO convection occurs over the Maritime Continent. The changes in both local Hadley and Walker circulations are of about the same magnitude. As the local Hadley circulation is climatologically larger than the local Walker circulation (Schwendike et al., 2014), the percentage change in the local Walker circulation is higher than in the local Hadley circulation.
SCHWENDIKE ET AL. Due to the changes in the local Hadley and Walker circulations, the resulting anomalous upper-level divergence (convergence) affects the position and strength of the subtropical jet. The jet is strengthened in regions of upper-level divergence and is weakened in regions of upper-level convergence. Moore et al. (2010) noted that the jet maximum in the Pacific moves with the envelope of enhanced convection, similarly to our results. Over the Indian Ocean, the jet core is displaced farther poleward (equatorward) by the enhanced upper-level divergence (convergence). However, we also find that over India the jet is displaced northwards by about 3-5° and over the Southern Indian Ocean the jet is displaced southwards by about 1-3°. Over the Pacific Ocean, the position of the jet hardly changes.
Additionally, the jets over the Northwestern Pacific, the Southwestern Pacific and the North Atlantic have been characterized in each MJO Phase for the first time. For both jets in the Northwest and Southwest Pacific in winter, the peak jet core speed, the depth of the jet and the mass transport in the jet increase when the active phase of the MJO convection is located over the Maritime Continent. Simultaneously the width of the jet decreases. These four characteristics of the jet also change for the jet in the North Atlantic, but less coherently. This is probably because the anomalous outflow of the either strengthened or weakened local Hadley circulation does not directly reach the North Atlantic. During summer, as expected, the jets in all regions are weaker than in winter due to the weaker meridional temperature contrast, and the changes in jet characteristics are largest for the jet in the Northwest Pacific.
These changes in the strength and location of the jet associated with changes in the local Hadley circulation in different phases of the MJO, lead to disturbances in the jet, which result in quasi-stationary wave patterns that extend into the midlatitudes in both hemispheres and modify the propagation of midlatitude Rossby waves. This wave pattern is strongest in the winter hemisphere. The stationary Rossby wave response to the MJO has been pointed out by a number of previous studies (e.g., Hendon & Salby, 1994;Higgins & Mo, 1997;Kiladis & Weickmann, 1992;Knutson & Weickmann, 1987;Lukens et al., 2017;Matthews et al., 2004).
By calculating the Rossby wave source anomalies globally we have shown that Rossby waves form as a result of disturbances in the midlatitude jet due to either enhanced or suppressed convection over the Maritime Continent. The wave-activity flux vector shows how the Rossby waves then propagate away from the jet into the midlatitudes. The Rossby wave source calculations also show that Rossby waves are generated from both enhanced and suppressed convection in all MJO phases. The calculation of the anomalous advection of the PV by the divergent part of the wind shows regions of interaction between Rossby waves and the subtropical jet.
We have shown, for the first time, that the local Hadley and Walker circulations are regionally enhanced when they overlap with the convectively active phase of the MJO. We have also shown that the anomalous upper-level divergence (convergence) of the local Hadley circulation during enhanced (suppressed) phases of the MJO leads to a northwards shift of the subtropical jet maximum over the continents, and a shift of the jet maximum toward the region of enhanced MJO convection. These disturbances in the jet lead then to the formation of quasi-stationary midlatitude wave trains. This study supports the sometimes questioned view that the MJO plays an important role in the tropics, subtropics and midlatitudes in both hemispheres.

Data Availability Statement
The data used in this analysis were provided by the European Centre for Medium Range Weather Forecasts (http://data-portal.ecmwf.int/data/d/interim_daily/). The TRMM rainfall data were obtained from the National Aeronautics and Space Administration (NASA) and the Goddard Space Flight Centre (https://pmm. nasa.gov/data-access/downloads/trmm). The RMM index data are available from http://www.bom.gov.au/ climate/mjo. The SOI index data are available from http://www.bom.gov.au/climate/current/soi2.shtml.