Zonal wave 3 pattern in the Southern Hemisphere generated by tropical convection

A distinctive feature of the Southern Hemisphere extratropical atmospheric circulation is the quasi-stationary zonal wave 3 pattern. This pattern is present in both the mean atmospheric circulation and its variability on daily, seasonal and interannual timescales. While the zonal wave 3 pattern has substantial impacts on meridional heat transport and Antarctic sea ice extent, the reason for its existence remains uncertain, although it has long been assumed to be linked to the presence of three major landmasses in the Southern Hemisphere extratropics. Here we use an atmospheric general circulation model to show that the stationary zonal wave 3 pattern is instead driven by zonally asymmetric deep convection in the tropics, with little influence from extratropical orography or landmasses. Localized regions of deep convection in the tropics form a local Hadley cell, which in turn creates a wave source in the subtropics that excites a poleward- and eastward-propagating wave train, forming quasi-stationary waves in the Southern Hemisphere high latitudes. Our findings suggest that changes in tropical deep convection, either due to natural variability or climate change, fundamentally control the zonal wave 3 pattern, with implications for southern high-latitude climate, ocean circulation and sea ice. The zonal wave 3 circulation pattern in the Southern Hemisphere is driven by tropical convection, according to results from an atmospheric general circulation model.

T he quasi-stationary zonal wave 3 (ZW3) pattern is a prominent feature in the Southern Hemisphere (SH) extratropical circulation, with impacts on Antarctic sea ice 1,2 , meridional heat and momentum transport 3 and CO 2 uptake 4 . The ZW3 pattern is evident in the time mean but exhibits seasonal variations in location, with small longitudinal movement (~20° longitude) between autumn and winter 3 and substantial variability in both amplitude and phase at submonthly to monthly timescales 5,6 . Previous studies have suggested that the quasi-stationary ZW3 pattern is linked to the land-ocean distribution in the SH mid-latitudes, in particular the presence of three separated landmasses and three ocean basins 2,3,7-10 . This conjecture seems plausible given the presence of the annual mean ZW3 surface pressure ridges on or near the southern flank of the three continents and troughs in the three ocean basins between them 3,7 . However, a similar stationary ZW3 pattern is also present in the Northern Hemisphere (NH) extratropics 11 , where there is no obvious three-fold symmetry in the land-ocean distribution. Therefore, the mechanisms responsible for the generation of this stationary ZW3 pattern in the SH extratropics require further examination.
Planetary wave activity in the SH extratropics is dominated by the presence of stationary zonal wave 1 (ZW1) and ZW3 at submonthly to interannual timescales 5,6 . It has been suggested that ZW1 is maintained by the Rossby wave activity forced both from lower latitudes [12][13][14][15][16] and from the high orography of Antarctica 15,17,18 . ZW3 is a prominent feature in geopotential height and wind fields and dominates the zonally asymmetric extratropical circulation at submonthly 19,20 , seasonal 21 and interannual timescales 22,23 . ZW3 also plays an important role in wintertime SH blocking events 24 and has been suggested to be the most persistent mode of SH eddy circulation 25 . The magnitude of the ZW3 pattern is at a maximum near 55° S and explains ~8% of variance in empirical orthogonal function (EOF) analysis of monthly geopotential height south of 20° S (ref. 3 ) and more than 45% of the variance in monthly meridional wind fields at 55° S (ref. 23 ).
ZW3 also plays an important role in the variability of meridional heat and momentum transport 3 , with a substantial impact on Antarctic sea ice and SH extratropical climate 1,2 . The ZW3 pattern is evident in regression patterns of winds, sea level pressure and geopotential height onto the Southern Annular Mode (SAM) index, with the SAM representing the leading mode of climate variability in the SH on monthly to interannual timescales (Fig. 1a). The ZW3 pattern is also a prominent feature in the projected future mean sea level pressure (MSLP) changes in the SH extratropics (Fig. 1b). In recent years, extremes in the ZW3 strength have been linked to the unprecedented 2015-2016 Antarctic sea ice decline [26][27][28] and the SH blocking highs 29 . Given the importance of ZW3 for Antarctic and SH climate, it is important to understand the generation and maintenance of this persistent atmospheric pattern. While the presence of this pattern in the SH has been previously linked to the land-ocean distribution in the extratropics 2,3,7-10 , there has been no previous modelling work that substantiates this explanation. In this study, we undertake a series of sensitivity experiments using an atmospheric general circulation model subject to different landocean configurations to uncover the mechanisms responsible for generating a stationary ZW3 pattern in the SH extratropics.

Experimental setup
We use the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM v1.2.2), which was part of the Coupled Model Intercomparison Project 5 (CMIP5). All model simulations have interactive atmospheric and land model components that are forced with prescribed sea surface temperatures (SST) and sea ice. The control model experiment includes globally realistic landmasses and orography as well as climatologically and geographically varying SST forcing. A series of simulations is configured with different land-ocean and SST configurations to examine the mechanisms that generate the stationary ZW3 in the SH extratropics (Methods), building up in complexity from a simple aquaplanet simulation with zonally uniform SST forcing. The subsequent experiments then include additional tropical, extratropical and polar landmasses and orography relative to the control experiment.
The control simulation captures the overall pattern of the observed 30 ZW3 (Extended Data Fig. 1a,b). However, the magnitude of the modelled ZW3 is weaker than that estimated from observations. This is a common problem with CMIP-type simulations, which systematically underestimate the amplitude of ZW3 in the SH (ref. 1 ). Comparison across different Atmospheric Model Intercomparison Project (AMIP) simulations of CMIP5 models shows that the CESM model simulates both the amplitude and phase of ZW3 reasonably well compared to other similar model ensembles (Extended Data Fig. 1c).

ZW3 response to landmass configurations
Fourier analysis is used to separate the wave activity associated with each zonal wavenumber across the experimental set. Stationary waves are defined as the time mean component of each wave. Therefore, by definition, a purely random wave (having different phases at different time steps) will have zero stationary wave component. In order to build our understanding of the factors important for ZW3, we first analyse the aquaplanet simulation (Methods). Using monthly averaged data, only waves with zonal wavenumbers k ≤ 5 are present (higher wavenumbers are only important at submonthly timescales). Wave 5 dominates the 300 hPa meridional wind fields north of ~50° S, with maximum strength between 30° S and 40° S (Extended Data Fig. 2a), consistent with previous studies [31][32][33][34] . These waves are believed to be trapped within the jet stream and maintained by baroclinic energy conversion 34 . However, waves in the aquaplanet simulation are not phase locked; that is, they possess random phases over time ( Fig. 2a and Extended Data Fig. 3). Indeed, the lack of zonal asymmetry in the aquaplanet should preclude any phase locking of the waves. However, a weak phase locking can be seen. This likely relates to the finite radiation time step used in the model, which creates asymmetries because of the sun warming the same locations after a certain fixed interval of time, leading to small zonal asymmetries in solar heating. The resulting time mean ZW3 signal is, however, more than an order of magnitude smaller than the signals found in subsequent experiments.
To understand the role of SH landmasses in creating and maintaining a phase-locked ZW3 pattern, we next add a single flat (at sea level) landmass to the aquaplanet configuration ( Fig. 2b and Methods). We choose South America among the three landmasses of the SH mid-latitudes as it extends the furthest south, has a tropical extension and also exhibits the highest topography (that is, the Andes). The wave energy in this simulation shifts to lower wavenumbers compared to the aquaplanet simulation (Extended Data Fig. 2a) with ZW1 and ZW3 now dominating and very little energy at wavenumbers 4 and above (Extended Data Fig. 2b). A clear stationary (phase-locked) ZW3 is now apparent, with an amplitude comparable to the control simulation, although the phase is different (Fig. 2b). This suggests that a single landmass in the SH can generate a phase-locked ZW3 pattern. Longer waves (that is, ZW1 and zonal wave 2) are also phase locked in this simulation (Extended Data Fig. 4).
To examine whether the meridional location of the landmass is important in generating a stationary ZW3 structure, two additional simulations are investigated, one with only the tropical part of the South American landmass and another with only the extratropical South American land (Fig. 2c,d and Methods). These simulations reveal that a stationary ZW3 pattern is only present in the tropical landmass simulation (with amplitude and phase almost identical to the simulation with all of South America present; Fig. 2c); conversely, in the mid-latitude-only simulation, the wave phase is  almost random (only a weak stationary ZW3 is present, with similar phase and amplitude to the aquaplanet experiment; Fig. 2a,d). These simulations show that while a landmass in the extratropics plays only a weak role in generating a stationary ZW3 pattern, a single landmass in the tropics is sufficient to generate a large-amplitude stationary ZW3.
In the above experiments, the landmasses were all added without orography (that is, flat landmasses at sea level). To examine whether the presence of three landmasses in the SH extratropics can generate a phase-locked ZW3 in a more realistic configuration, we next examine a simulation in which three extratropical landmasses are all present with realistic orography (that is, South America, Africa and Australia, added south of 20° S; Fig. 2e). Mountains are known to play an important role in creating phase-locked zonal waves in the NH extratropics, particularly due to the presence of the Rockies and the Plateau of Tibet 35 . Even though there are fewer high orographic features in the SH, the Andes are as high as 2,900 metres south of 20° S in the model and may play a role in phase locking the waves, such as the wavenumber 3 pattern. Yet in this simulation with added extratropical landmasses and orography, there is no enhanced stationary ZW3 over and above that seen in the aquaplanet (Fig. 2e): the ZW3 signal possesses a random phase in time (that is, it is not stationary). The model resolution precludes orography of the Andes that precisely matches the real world (2,900 m in the model compared to 3,400 m in reality). However, recent studies 36 have found that biases in the Andes elevation in models have little effect on the wave activity in the SH. This indicates that the presence of SH extratropical landmasses (including orography) does not play an important role in generating the phase-locked ZW3 pattern in the SH extratropics; the Andes have too narrow a longitudinal range to generate a strong stationary wave as compared to their NH counterparts, where the mountains are higher and have much larger zonal extent. This finding is in contrast to the hypothesis put forward in previous studies 2,3,7-10 .
ZW3 is also phase locked in other experiments we tested with tropical landmasses added elsewhere (for example, Africa, the maritime continent), with the resulting phases and amplitudes differing across these simulations compared to the tropical South America simulation (Extended Data Fig. 5). We hypothesize that the tropical-extratropical teleconnection relates to deep adiabatic heating in the tropics that can be generated by any of the landmasses and also by warm tropical SSTs. This will be examined further in the next section.
Finally, while Antarctica is known to generate a stationary ZW1 in the SH extratropics 15,17,18 , it is not thought to generate a stationary ZW3 pattern in the SH extratropics 37   an additional experiment wherein we added Antarctica with orography to the aquaplanet configuration (Extended Data Fig. 6). This experiment shows a stationary ZW1 but no stationary ZW3 pattern (Extended Data Fig. 6).

Mechanism to generate stationary ZW3
We now elucidate how a localized zonal asymmetry in the tropics generates a stationary ZW3 pattern in the extratropics. We begin by examining the tropical South America experiment in more detail. The presence of land in the tropics provides a low-level perturbation to the otherwise zonally uniform flow and results in convergence at the surface over the landmass. This low-level convergence causes convective heating in the atmosphere (Extended Data Fig. 7a) that results in enhanced upward motion (Fig. 3a) and divergence with an associated anticyclonic vorticity anomaly at upper levels (Fig. 3b). The response in the lower troposphere is similar to a Gill-type response 38 for a heat source in the tropics with two cyclonic circulations present on either side of the Equator (Fig. 3c). The lower-level perturbation is mostly confined to near the heating source and has a weaker response in the extratropics; however, this is not the case in the upper troposphere, where strong perturbations extend farther into the SH extratropics (Fig. 3b,c). The source (landmass) is present in the tropics where the mean flow is easterly. However, Rossby waves need westerly flow to propagate. This gap is bridged by the divergence in the upper-tropospheric flow in the tropics, which results in sinking motion in the subtropics, forming a local Hadley cell (Fig. 3a). This results in upper-level convergence in the subtropics that then acts as a Rossby wave source because of the presence of westerlies in the subtropics 13 . In the upper troposphere (at 300 hPa), a wave train is set up poleward and eastward of the source region (Fig. 3b). This is similar to the wave train dynamics described by Hoskins and Karoly 12 for a subtropical heating source and by Trenberth et al. 13 for a tropical heating source. These eastward-and poleward-propagating waves (Extended Data Fig. 7b) reflect from the high latitudes where the meridional gradient of absolute vorticity approaches zero and then decay in the tropics where the zonal wind is zero 12 . The lowest wavenumbers (k ≤ 3) have the strongest meridional group velocities so can propagate further poleward 12,13 before being reflected back to the tropics (Fig. 3b). The response is basically a dispersive Rossby wave train with each wavenumber following a different ray path 12 . The lowest wavenumber (ZW1) therefore travels the furthest poleward, followed by progressively higher wavenumbers, which then create stationary zonal waves in the SH extratropics (Extended Data Fig. 8). The stationary wavenumber (K s ) profile in the SH (Extended Data Fig. 8) suggests that wavenumber 3 is the dominant wavenumber in the SH extratropical region (between 50° S and 65° S), which explains why ZW3 dominates in this latitude band. This wave train structure has been observed in previous studies using simple barotropic and baroclinic models with prescribed diabatic heating anomalies 12,13 . However, here we use a more sophisticated atmospheric general circulation model that is known to simulate realistic atmospheric stationary waves 9,39 . These poleward-moving wave trains are absent in all simulations we consider unless a source of zonal asymmetry in the deep convection is present in the tropics. Without any tropical zonal asymmetry, there are no upper-level changes to initiate a poleward-propagating Rossby wave train (Extended Data Fig. 9). This is likely due to the lack of deep convection in mid-latitudes 12 (Extended Data Fig. 9a). While a low-level perturbation (heating) is balanced by strong vertical advection in the tropics, in the mid-latitudes, it is balanced by horizontal advection of cold air from polar latitudes near the surface 40 .
Changing the location and extent of the landmass in the tropics experiments in turn changes the location and extent of maximum deep convection-and hence the location of the Rossby wave source in the subtropics-which in turn changes the phase of the ZW3 pattern in the SH extratropics (Extended Data Fig. 5). In other words, the phase of the ZW3 pattern is dependent on the longitudinal location of the Rossby wave source in the tropics. The combined effect is, however, non-linear; that is, the amplitude of the combined ZW3 for all three individual tropical landmass cases is different from that of the full tropical landmass simulation (Extended Data Fig. 5).
While the above experiments use an idealized landmass to provide a tropical source of heating, the strongest tropical heating actually occurs over the Indo-Pacific warm pool and therefore acts as the strongest source of deep convection in the tropics (refer to vertical velocity in the control simulation, Extended Data Fig. 10a). An additional experiment was carried out that had a realistic tropical configuration with landmasses and climatological SSTs between 10° S and 10° N and zonally uniform setup elsewhere ( Fig. 2f and Methods). A clear stationary ZW3 pattern was found in this simulation (Fig. 2f) with a similar magnitude to the control run, including higher amplitude than the previous simulations that included just tropical landmasses. This suggests that convection over the Indo-Pacific warm pool plays a strong role in generating the stationary ZW3 in the SH extratropics. We note that a wave train also propagates into the NH in this simulation and thus may play a role in ZW3 formation (Fig. 2f), although the higher and more extensive Tibetan Plateau and Rockies may also be important 35 . Small differences in ZW3 in this simulation as compared to the control simulation are expected because the mean circulation in this simulation is slightly different from the control because of the absence of realistic extratropical landmasses, and the refractive effects on the waves are determined by the mean atmospheric circulation (Extended Data Fig. 8).
The mechanism generating a ZW3 pattern is represented in a schematic shown in Fig. 4 and Supplementary Video 1. Deep convection in the tropics forms a local Hadley cell that subsides over the subtropics where the westerlies are present. The localized upper-level convergence generated because of the local Hadley cell generates a Rossby wave source in the subtropics. Rossby waves with strong meridional group velocities then move poleward and eastward from the subtropics and create phase-locked stationary zonal waves in the SH extratropics. In addition to ZW3, the other low-frequency waves that dominate the wave spectrum (that is, ZW1 and zonal wave 2) are also phase locked in simulations with a tropical source of deep convection.

implications for ZW3 variability and future changes
Our work suggests that the Indo-Pacific warm pool plays a major role in generating a stationary ZW3. Indeed, a clear wave train is found to be propagating poleward and eastward from the Indo-Pacific warm pool in the control simulation (Extended Data   Fig. 10b). In addition, other sources of convection in the tropics are also likely to be important (Extended Data Fig. 10). These sources vary in time, either because of changes in natural variability both at shorter timescales (for example, the Madden Julian Oscillation and monsoon variability) and at longer timescales (for example, El Niño Southern Oscillation or the Indian Ocean Dipole) or because of climate change 39,41 .
ZW3 also exhibits strong variability at submonthly and seasonal timescales, with stronger ZW3 found during austral fall and winter and weaker ZW3 in spring and early summer 6 . Appearance of a ZW3 pattern is strongly dependent on not only tropical deep convection but also the background atmospheric circulation. Comparing AMIP (with prescribed observed SST and sea ice) and CMIP5 (with internal model-generated SST and sea ice) ensembles (Extended Data Fig. 1c,d) reveals a similar spread in the bias in both ZW3 magnitude and phase. Factors other than SST differences must therefore be important. Indeed, wave propagation from the tropics to the extratropics is affected by both the convective patterns simulated by each model and the refractive effects related to the background circulation (Extended Data Fig. 8).
Future changes in the ZW3 pattern will be primarily dependent on changes in (1) tropical SST warming and (2) changes in the atmospheric circulation in the SH. However, future warming of tropical SST is expected to weaken the tropical-extratropical teleconnections because of the projected weakening in tropical convective circulation 39 . Warming of tropical SST is projected to result in amplified upper-tropospheric tropical warming, which leads to an increase in the static stability 39,41 . Increased static stability results in weaker vertical motions in response to tropical convection, which would lead to weaker tropical-extratropical teleconnections. Westerly winds in the SH extratropics are also projected to intensify with global warming 42 . Stationary wave theory implies that wavenumber scales inversely with the strength of the zonal flow, which therefore suggests a decrease in wavenumber in the future. While this is a simple assessment of expected future changes in the ZW3 pattern under global warming, uncertainties remain. For example, changes in the tropical wave source resulting from possible reorganization of convection in the tropics 43 and a projected poleward shift in the zonal winds in the SH extratropics 42 may also play a role in driving future changes in the ZW3 pattern. This has important implications for climate variability and climate change in the region.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41561-021-00811-3. shows streamfunction and wave propagation in the SA-tropics simulation. Shading in panel b) represents streamfunction at 300 hPa calculated from the perturbation zonal and meridional velocities (zonal mean removed) and vectors represent wave activity flux for the SA-tropics simulation. Fig. 10 | Vertical Velocity, Perturbation vorticity and eddy geopotential height for control (ctRL) simulation. Panel a) shows vertical velocity at 300 hPa (Pa/sec). Panels b) and c) represent the perturbation vorticity (units are W, where W = 7.29 × 10-5 rad/sec, is rotational rate of earth) at 300 hPa and 850 hPa respectively. Panels d) and e) represent eddy geopotential height corresponding to wavenumber 3 (shading, in meters) at 300 hPa and 850 hPa respectively.