a. Model setup

We use an aquaplanet version of Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model 2.1 (AM2.1; Anderson et al. 2004; Delworth et al. 2006) coupled with a motionless mixed layer ocean that allows thermodynamic atmosphere–ocean interactions. The horizontal resolution of the model is 2° latitude × 2.5° longitude, and the vertical resolution of the model is 24 levels. There is no seasonal cycle, a fixed surface albedo (i.e., no sea ice or snow feedback), and steady insolation is applied, varying only with latitude so that it provides the present-day Earth’s annual mean insolation at all times. The insolation is computed based on an obliquity of 23.5°.

b. Experimental design

A set of experiments is performed with prescribed extratropical thermal forcing and varying mixed layer depth. The extratropical thermal forcing is applied between 50° and 80°S by directly adding a source of heat into the oceanic mixed layer energy budget equation, as specified analytically in Eq. (2.1) below and Fig. 1a. Unlike Kang et al. (2008) and Kang et al. (2009), we only prescribe forcing in one hemisphere, allowing us to track the evolution of heating originated from one location. This forcing is representative of ocean heat uptake or ocean heat release in a changing climate, or changes in other components that would affect net radiation at the surface, such as sea ice, aerosol, and clouds. The equation of the imposed heating, denoted H, is

$\{\begin{array}{c}H=-A\sin \left(\frac{\varphi +50°}{30°}\pi \right),\mathrm{for}-80°<\varphi <-50°,\\ H=0,\mathrm{otherwise},\end{array}$(2.1)

where A sets the maximum strength of the forcing (W m⁻²) and ϕ is latitude in degrees. To obtain significant transient responses with limited ensemble members, we select a relatively large value of A, 60 W m⁻², so that a total of 2.12 PW is added to the mixed layer. The imposed hemispherically asymmetric forcing is about half of the range of Earth’s seasonal cycle. Indeed, the single cross-equatorial cell in the equilibrium response (Fig. 1c) implies that our findings may offer insights for understanding seasonal cycle transition, while not changing insolation in the tropics directly and focusing on the extratropical influence. The strong forcing, however, does raise the question of relevance of our results to climate change signals, the latter which tends to be a lot smaller in magnitude. We have performed other cases with A being 30 or 10 W m⁻², and the equilibrium responses are qualitatively similar, albeit smaller in magnitude.

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Equilibrium responses of surface temperature, precipitation, and atmospheric circulations. (a) Latitudinal distribution of imposed forcing H (W m⁻²). (b) The zonal mean SST in all heating cases. (c) Anomalous zonal wind (shaded; m s⁻¹), anomalous meridional mass streamfunction [green contours; contour interval (CI) = 10¹¹ kg s⁻¹] in equilibrium in MLD200 case, and climatological zonal wind (black contours; CI = 15 m s⁻¹, zero contour omitted and negative dashed), and climatological E-P fluxes (vectors; m² s⁻²). (d) As in (b), but for precipitation.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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To investigate the role of SST in setting the response time scales, we perform cases with mixed layer depths of 50 m (MLD50), 100 m (MLD100), and 200 m (MLD200). Since the magnitudes of the initial midlatitude temperature and wind responses depend on mixed layer depth, we set the same mixed layer depth in the forced region to 200 m in all experiments and only alter the mixed layer depth elsewhere. The unrealistically deep mixed layer depths (i.e., 200 m) outside the forced region allow us to cleanly separate the processes solely related to atmospheric dynamics and those involving air–sea interactions. We have additionally performed a case with observed zonal mean annual mean mixed layer depth, which amounts to about 35 m in the tropics (25°S–25°N). The proposed two-stage responses can be also found in the case with observed mixed layer depth, with the response time scales being similar to the case with 50-m mixed layer depth.

The control case with 50-m mixed layer depth and no prescribed forcing is run for 36 years. The 60 ensemble members of MLD200 cases are run for 3 years and 5 of them are extended to 48 years, reaching equilibrium around year 10. The MLD100/50 experiments are also run for 3 years, but only 30 ensemble members are run.

c. Indices

The Southern Hemisphere Hadley cell index φ_SH is defined to be the averaged mass streamfunction between 15° and 25°S at 700 hPa, measuring the strength of the extreme of the Hadley circulation in the Southern Hemisphere. The cross-equatorial Hadley cell index φ_EQ is calculated by averaging the mass streamfunction between 5°S and 5°N at 700 hPa. The altitude 700 hPa is chosen because the maximum of mass streamfunction appears in this altitude in the control climate.

Another index that is representative of the behavior of Hadley circulation is the energy flux equator, the latitude where the vertical column integrated zonal mean energy transport $⟨\overline{\upsilon m}⟩$vanishes (Kang et al. 2018).

Previous studies suggested that the boundary layer cross-equatorial flow, as well as the anomalous cross-equatorial Hadley cell, are driven by cross-equatorial SST gradients (Lindzen and Nigam 1987; Chang et al. 2000; Chiang and Bitz 2005; Cvijanovic and Chiang 2013). Here we define the interhemispheric asymmetric SST index (Δ_SST) as the SST difference between 0°–10°S and 0°–10°N to measure the interhemispheric SST asymmetry in the deep tropical region.

a. Equilibrium responses

We first present the equilibrium responses, calculated by averaging the last 30 years of each simulation. For all figures in this paper, only signals that are statistically significant are shown. The anomalous warming is most apparent at the heating location and extends to the tropics, shifting the ITCZ southward (Figs. 1b,d). The imposed heating decreases the meridional temperature gradient of the southern subtropics and weakens the subtropical jet in the Southern Hemisphere (defined as the latitude of the zonal wind maximum of the entire tropics, which is located around 200 hPa) (Fig. 1c). In the Northern Hemisphere, surface temperature decreases slightly in the subtropics and is nearly unchanged in extratropics. The northern subtropical jet is strengthened. The temperature, precipitation, and circulation responses in Fig. 1 are nearly identical in the cases with different mixed layer depth. Increasing mixed layer depth has little influence on the equilibrium responses, consistent with Kang et al. (2008). In the next two sections, we take MLD200 case as an example to demonstrate the equilibrium responses in the momentum and the energetic perspectives.

1) Equilibrium responses in the momentum perspective

In the control case, the eddy momentum flux convergence peaks at around 40°N and 40°S (blue shading in Fig. 2a; see also the climatological E-P flux in Fig. 1c), where the eddy-driven jets located (defined as the latitudes of maximum zonal wind at 850 hPa). In the subtropics, the eddy stress, the horizontal eddy momentum flux divergence [$S\equiv \left(1/a{\cos }^2\vartheta \right)\left(\partial /\partial \vartheta \right)\left({\cos }^2\vartheta \overline{u^{\prime }{\upsilon }^{\prime }}\right)$], is balanced by meridional advection of absolute vorticity in the upper branch of the Hadley cell, with the poleward flows in the upper branches collocated with positive S [Fig. 2a; refer to Eq. (1.1) for the momentum balance].

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Equilibrium responses of circulation and momentum fluxes. Zonal mean of S (shaded; m s⁻²) and mass streamfunction (green contours; with CI = 10¹¹ kg s⁻¹; solid for positive and dashed for negative, and gray contours for zero) in (a) the control case and (b) the MLD200 case, and (c) the anomalies (the MLD200 case minus control). Note that S in the control case is plotted as black contours (with CI = 10⁻⁵ m s⁻²; zero contours omitted and negative dashed) in (c) for reference.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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The steady-state responses of circulation and momentum fluxes in our experiments are consistent with previous studies demonstrating the influence of eddies on Hadley cell via varying insolation (Bordoni and Schneider 2008; Schneider and Bordoni 2008; Bordoni and Schneider 2010), interannual variability (Caballero 2007), or on the spread of GCMs’ climatological biases (Caballero 2008). In subtropics, the variations in eddy stress are accompanied by variations in Hadley cell strength. When imposing heating in the southern extratropics, eddy stress and Hadley cells weaken in the southern tropics and strengthen in the northern tropics (cf. Figs. 2a and 2b or see Fig. 2c for anomalies).

2) Equilibrium responses in the energetic perspective

Driven by the uneven distribution of insolation, the atmosphere transports energy poleward in both hemispheres in the control case (black line in Fig. 3a). In extratropics, eddies transport both DSE and moisture poleward. In most of the tropics, the mean meridional overturning circulation plays the main role of transporting energy away from ITCZ, with the poleward DSE transport in the upper troposphere outweighing the equatorward moisture transport near the surface (red and blue lines in Fig. 3a).

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Equilibrium responses of energy transports. Northward atmospheric energy transports (PW) in (a) the control case and (b) the MLD200 case, and (c) anomalies (the MLD200 case minus control), with total MSE transport in black, contribution from DSE in red, contribution from moisture in blue. Note that the ranges of the y axes are different between (a), (b), and (c).

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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The equilibrium responses of energy fluxes in Figs. 3b and 3c are consistent with previous modeling studies with various extratropical forcings (Kang et al. 2008, 2009; Swann et al. 2011; Hwang et al. 2013; Chiang and Friedman 2012; Schneider et al. 2014) and can be understood via the energetic framework. In a stable atmosphere, the total atmospheric energy transport (or MSE transport) is in the same direction as the DSE transport but in the opposite direction to moisture transport. Responding to the imposed heating in the Southern Hemisphere, the Hadley cell transports excessive energy to the Northern Hemisphere. Both the energy flux equator and the ITCZ shift southward (Figs. 1d and 3b).

b. Transient responses

Figure 4 shows the evolution of SST and circulation in all three experiments during the first three years after imposing the time-invariant extratropical forcing. To allow a direct comparison with the steady-state responses in Fig. 1, time slices of year 9 of the experiments when the system approaches equilibrium are plotted in the same format (in the right columns). The propagation speed of the anomalous warming depends on latitudes, with the subtropical region (~20°S) warming faster than the surrounded latitudes. The dependency of propagation speed on latitudes suggests atmospheric circulation (instead of diffusive processes) playing a critical role in the teleconnection between the tropics and extratropics. Two distinct stages of the tropical meridional mass streamfunction responses are observed: a weakening centering at around 20°S occurring at around month 4 for all three experiments and an anomalous cross-equatorial cell develops later. We define the start time of the first stage as the day when the change of the strength of the southern cell (δφ_SH) becomes detectable.¹ The day of the anomalous cross-equatorial cell (δφ_EQ) first becomes significant marks the start time of stage 2. As shown in Fig. 5, the time scale for observing statistically significant weakening of the southern cell (stage 1) is independent of mixed layer depth, whereas the time scale for developing a statistically significant anomalous cross-equatorial cell (stage 2) increases with mixed layer depth. Once developed, the anomalous cross-equatorial cell strengthens throughout the simulations and dominate the equilibrium responses.

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Time series of zonal mean meridional mass streamfunction and SST. Anomalous zonal mean meridional mass streamfunction at 700 hPa (shaded; kg s⁻¹) and SST (gray contours; CI = 0.3°C; zero contours omitted and negative dashed) in cases with (a) MLD200, (b) MLD100, and (c) MLD50. The vertical gray solid lines mark the start times of stages 1 and 2. The horizontal red lines indicate the northern edge of imposed forcing. The right column shows the near-equilibrium responses.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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The start time of stages 1 (cross) and 2 (asterisk) in MLD200, MLD100, and MLD50 cases.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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In the following two sections, we take the MLD200 case as an example to demonstrate that the two distinct stages of the tropical circulation responses are driven by different mechanisms. The southern subtropical responses in the first stage can be interpreted by the momentum perspective, and the deep tropical responses in the second stage are mostly consistent with the energetic perspective.

1) Transient responses from the momentum perspective

Figure 6a shows the time series of anomalous eddy momentum divergence (i.e., anomalous eddy stress δS) and the product of Coriolis parameter and anomalous upper-level meridional wind $\delta f\overline{\upsilon }$. Poleward of 15°, where the local Rossby number ($\mathrm{Ro}\equiv -\overline{\zeta }/f$) is smaller than 0.4, variations of eddy momentum flux divergence δS are mostly balanced by anomalous zonal-mean meridional advection of planetary vorticity $\delta f\overline{\upsilon }$ [see Eq. (1.1)]. For example, at stage 1, anomalous positive eddy stress (red color centering around 45°S) is balanced by anomalously positive planetary vorticity advection $\delta f\overline{\upsilon }$ (solid contours), and anomalous negative eddy stress (blue color centering around 25°S) is balanced by anomalously negative planetary vorticity advection $\delta f\overline{\upsilon }$ (dashed contours). The Coriolis parameter f is negative in the Southern Hemisphere, so anomalously negative planetary vorticity advection (i.e., negative $\delta f\overline{\upsilon }$) in the southern subtropics is consistent with reduced northerly wind in the upper levels and the weakened (more positive) southern Hadley cell (Fig. 6b). After entering stage 2 and throughout the whole simulation, any variation of Hadley cell strength (demonstrated as $\delta f\overline{\upsilon }$ in Fig. 6a) poleward of 15° is always accompanied by a variation of eddy stress $\overline{\delta S}$ with the same sign.

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Time series of stage-1-associated responses in MLD200 case. Anomalous zonal mean (a) daily S (shaded; m s⁻²) and daily fυ (blue contours with CI = 5 × 10⁻⁶ s⁻²; zero contour omitted and negative dashed) in the upper atmosphere (above 700 hPa), (b) daily Southern Hemisphere Hadley cell (φ_SH; kg s⁻¹), (c) daily S above 700 hPa and between 15° and 25°S (m s⁻²), and (d) daily surface wind speed between 15° and 25°S (m s⁻¹). The vertical solid lines mark the start times of stages 1 and 2. The right column shows the near-equilibrium responses. In (a), the horizontal red line indicates the northern edge of imposed forcing and the horizontal gray lines mark the latitude of 0.4 local Rossby number. The thick black lines in (b)–(d) indicate the ensemble mean, with each ensemble in gray. Note that in (c) the ranges of the y axes are different between the left and right panel. The time series are smoothed by 15-day running mean to remove high-frequency internal variability.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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The momentum balance does not indicate a causal relationship. Through imposing idealized forcing confined in the extratropics and investigating the transient evolutions of the responses in experiments with varying mixed layer depth, we attribute the initial weakening of the southern Hadley cell φ_SH in stage 1 to reduced eddy momentum flux divergence $\overline{S}$ in the subtropics. The imposed surface heating at 50°–80°S could lead to a reduction of $\overline{S}$ in the southern subtropics via a baroclinic and a barotropic process [see Shaw et al. (2019) and the appendix for more detailed description of the two processes]. Further analyses show the baroclinic process dominates: Both the stability near the surface and the meridional temperature gradient decrease at the equatorward side of the imposed heating, reducing eddy heat flux in the climatological baroclinic zone (around 45°S). Associated with the reduction of eddy source, poleward eddy momentum flux and its divergence $\overline{S}$ in the subtropics also decrease (Fig. A1).

Although the equilibrium responses of momentum fluxes in subtropics discussed in section 3a(1) fulfill the momentum balance between Hadley cell strength φ_SH and eddy stress $\overline{S}$, our investigation of the transient evolutions suggests that the equilibrium responses are distinct from the stage-1 eddy-momentum driven response in terms of latitudinal positions and strengths (cf. the equilibrium responses on the right column to the stage-1 responses on the left in Fig. 6). Moreover, there is a noticeable recovery stage in between. We defer the interpretations of the recovery stage, which involve interactions among SST, eddy stress $\overline{S}$, and Hadley cell strength, to the end of section 3b(3).

Note that the signal-to-noise ratios of these eddy-driven responses are small. After applying a 15-day running mean to remove high-frequency internal variability in individual ensemble members, the spread of anomalous eddy stress $\overline{\delta S}$ across ensemble members still reaches 1.3 × 10⁻⁵ m s⁻², which is larger than the y axis in Fig. 6c. The spread of anomalous southern Hadley cell strength among ensemble members is also much larger compared with the change in ensemble mean. While we are able to demonstrate the existence of stage 1 using 60 ensemble members, identifying the time scale of stage 1 is not possible for individual ensemble members. It remains an open question as to how the eddy-driven mechanism discussed above plays a role in individual realizations. When accessing the spread across the ensemble members, there is a statistically significant positive correlation (R = 0.6) between anomalous eddy stress $\overline{\delta S}$ and anomalous Hadley cell strength δφ_SH at the time the ensemble-mean responses enter stage 1, indicating that the two factors are dominating the momentum balance at this stage.

2) Transient responses from the energetic perspective

For the MLD200 case, there is no significant change in energy transport and meridional mass streamfunction in the deep tropics before month 13. The development of the cross-equatorial cell at the second stage is tightly linked with the anomalous interhemispheric SST gradient in the tropics (δ_ΔSST). When the anomalous interhemispheric SST gradient in the tropics δ_ΔSST becomes significant (at month 13), the anomalous mass streamfunction develops and the energy flux equator shifts southward (Figs. 7b,c). There is an approximate 3-month lag between the cross-equatorial cell and the shift of the energy flux equator. Further analysis shows a close linkage between the energy flux equator, the cross-equatorial MSE transport, and the ITCZ. The three variables all lag the anomalous mass streamfunction δφ_EQ by three months for the MLD200 setting (quantitative analyses not shown, but precipitation and energy flux equator responses are plotted in Figs. 7a and 7d). Once they all become statistically significant, the southward shift of the energy flux equator and the anomalous cross-equatorial cell are consistent with the energetic framework.

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Time series of stage-2-associated responses in MLD200 case. Anomalous zonal mean (a) northward MSE transport (shaded; PW), SST (gray contours with CI = 0.3°C; zero contours omitted and negative dashed), and anomalous precipitation (contour = 1, 2, 4, 8, 16 mm day⁻¹; positive purple and negative green), (b) daily cross-equatorial Hadley cell index (φ_EQ; kg s⁻¹), (c) daily interhemispheric asymmetric SST index (Δ_SST; °C), and (d) energy flux equator (EFE; °). The vertical solid lines mark the start times of stages 1 and 2. The right column shows the near-equilibrium responses. The horizontal red line in (a) indicates the northern edge of imposed forcing. The thick black lines in (b)–(d) indicate the ensemble mean, with each ensemble in light gray. Note that in (b)–(d) the ranges of the y axes are different between the left and right panels. The time series of daily data are smoothed by the 15-day running mean to remove high-frequency internal variability.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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Our transient analysis suggests that it is only when the southern tropical SST heats sufficiently and the ITCZ shifts that the extratropical energy supply can be exported to the other hemisphere across the equator (Cvijanovic and Chiang 2013). With a deeper mixed layer, it takes longer for the SST to adjust, causing stage-2 responses to emerge with a larger lag (Fig. 5). The SST gradients drive the anomalous cross-equatorial cell, and the MSE transport adjust accordingly. Wei and Bordoni (2018) and Wei and Bordoni (2020) also emphasize a crucial role of SST gradient, reporting the migration of ITCZ lagging the variation of energy flux equator during the climatological seasonal cycle. In our stage-2 responses, both the changes in cross-equatorial cell and the meridional mean circulation component of the cross-equatorial MSE transport occur at the time when the anomalous interhemispheric SST gradient δ_ΔSST becomes statistically significant. The 3-month lag between the energy flux equator and the anomalous interhemispheric SST gradient is explained by the eddy component of the MSE transport.²

Note that the signal-to-noise ratio of the anomalous cross-equatorial streamfunction in stage 2 is larger than that of the anomalous southern cell strength in stage 1 (Fig. 6b). While the time scale of developing a cross-equatorial cell cannot be accurately quantified in a single ensemble, the characteristics of the anomalous cross-equatorial cell are detectable for all ensemble members. There is a statistically significant positive correlation (R = 0.8) between the anomalous interhemispheric asymmetric SST index δ_ΔSST and the strength of anomalous cross-equatorial cell δφ_EQ at the time the ensemble mean response entering stage 2, supporting the crucial role of SST gradient. The anomalous interhemispheric SST gradient δ_ΔSST, the strength of anomalous cross-equatorial Hadley cell δφ_EQ, and the cross-equatorial MSE transport all strengthen with a constant rate before approaching the new equilibrium state (not shown). The equilibrium state in the right columns in Fig. 7 could simply be interpreted as a fully developed response of stage 2.

3) Connecting the two stages: The role of wind–evaporation–SST feedback

In this section, we discuss how the weakening of southern Hadley cell in stage 1 may lead to the cross-equatorial cell in stage 2 via the wind–evaporation–SST feedback.

Through careful inspection of the transient evolution (Fig. 7) and comparison among the three experiments of different mixed layer depth (Fig. 5), the time scale for developing the cross-equatorial cell appears to be tightly linked with the interhemispheric SST gradient. Following Xie et al. (2010), Jia and Wu (2013), and Hwang et al. (2017), we combine the mixed layer energy budget and the linearized version of the aerodynamic bulk formula of latent heat flux,

$\rho c_{p}H\frac{\partial T}{\partial t}=\delta \mathrm{SW}+\delta \mathrm{LW}+\delta L{H}_{\mathrm{wind}}+\delta L{H}_{\mathrm{SST}}+\delta L{H}_{\mathrm{RH}}+\delta L{H}_{dT}+\delta \mathrm{SH},$

to analyze the surface energy budget in Southern Hemisphere subtropics to explore factors influencing SST. In this equation, ρ is the density of seawater, c_p is the specific heat of seawater, H is mixed layer depth, T is the mixed layer temperature (equal to the SST), and the symbols δ on the right-hand side denote anomalies, calculated as the difference of the heating experiment (at the month of interest) and the control experiment. Also, δSW is anomalous net downward shortwave radiation, δLW is anomalous net downward longwave radiation, δSH is anomalous sensible heat flux, and δLH_wind, δLH_SST, δLH_RH, and δLH_dT, respectively, are anomalous latent heat flux associated with changes in surface wind speed, SST, relative humidity, and the stability of the boundary layer (the difference between surface temperature and 2-m air temperature).

Figure 8a suggests that changes in latent heat flux related to changes in wind speed δLH_wind is the main factor contributing to the heating tendency in southern tropics. This role of wind speed suggests a link between the momentum-driven stage 1 and the energetic related stage 2. We hypothesize that weakening of eddy stress $\overline{S}$ in stage 1 could lead to the cross-equatorial Hadley cell through the following four steps, illustrated in Fig. 9: 1) The reduction of $\overline{S}$ at the edge of the southern cell is balanced by the reduced planetary vorticity advection due to reduced poleward flow at the upper branch. 2) To satisfy momentum balance in the subtropics, the reduction of $\overline{S}$ aloft must be balanced by the reduction of friction at the surface, requiring weakened surface easterlies. Consistently, by mass continuity, the meridional component of surface wind weakens with the weaker poleward flow in the upper branch. The weakened southeasterly surface wind results in decreasing evaporation. 3) Reduced evaporation at the surface leads to increasing SST in the southern tropics, driving the cross-equatorial Hadley cell. 4) As the cross-equatorial Hadley cell strengthens, the upper branch transports energy northward. The cross-equatorial Hadley cell also leads to a subtle increase in surface wind speed and evaporation in the northern tropics, which further enhances the interhemispheric SST gradient and the cross-equatorial Hadley cell. In this view, the anomalous eddy stress $\delta \overline{S}$ in the upper troposphere, anomalous Hadley cell in southern subtropics, and reduced evaporation are connected, supporting the hypothesis linking the momentum and the energetic perspective via the wind–evaporation–SST feedback.

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WES feedback. (a) Mixed layer energy budget attribution in southern tropical region (between the equator and the southern edge of the Hadley cell in the SH; 27°S) during the stage 1 period. The error bars mark the one standard deviation departure from the ensemble mean of each variable. Also shown are anomalous (b) surface latent heat flux due to wind change (W m⁻²) and (c) surface shortwave flux (W m⁻²) in the SH tropical region. The vertical dashed lines in (b) and (c) mark the start times of stages 1 and 2, respectively. The right column shows the near-equilibrium responses. The thick black lines in (b) and (c) indicate the ensemble mean, with each ensemble in light gray.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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Schematic diagram of the two-stage response. (top) The anomalous mass streamfunction at 700 hPa (shaded; power of 10 kg s⁻¹), anomalous S over 700 hPa (light blue contours; CI = 10⁻⁶ m s⁻²), and northward DSE transport anomaly (brown contours; CI = 0.5 PW). (bottom) The latent heat anomaly due to wind change (shaded; W m⁻²), SST anomaly (yellow contours; CI = 0.3 K), and northward moisture transport anomaly (brown contours; energy equivalent; CI = 0.5 PW; zero and positive are omitted). The blue and orange contours in the vertical panels show the anomalous mass streamfunction in two stages respectively (CI = 3 × 10⁹ and 2.4 × 10¹⁰ kg s⁻¹ at left and right, respectively).

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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The large ensemble spreads in Figs. 8a and 6b make us question if the linkage between stage 1 and stage 2 described above explains the transition in individual ensemble members. While we cannot exclude the possibility of other mechanisms triggering the development of the cross-equatorial cell in individual ensemble members, an evaluation across the ensemble members supports our hypothesis. At the start time of stage 2 defined from the ensemble mean, 56 out of 60 ensemble members simulate the anomalous cross-equatorial cell in the deep tropics. Among these 56 ensemble members, all but two exhibit an anomalously weak southern Hadley cell and surface wind speed in the southern subtropics. The two exceptions that do not exhibit weakening of the southern Hadley cell despite having developed a cross-equatorial Hadley cell anomaly had previously exhibited an extended period with a weakened southern Hadley cell. This suggest that while it is difficult to pinpoint the onset of stage 1 in and individual integration, it appears that if the southern Hadley cell weakens over some suitable integration period, it may be enough to initiate stage 2.

A closer examination reveals that, before the anomalous cross-equatorial cell fully develops and the southern Hadley cell almost diminishes, there is an intermediate stage when the eddy stress $\overline{S}$ and the Hadley cell in the southern subtropics recover in the ensemble mean time series [see Fig. 6, as described in section 3b(1)]. We suspect this intermediate stage can be explained by the feedback among the SST gradient, the eddy stress, and the Hadley cell strength in the subtropics. The wind–evaporation–SST feedback discussed in the previous paragraph is strongest at around 25°S. As a result, SST in the region warms more rapidly than other latitudes, leading to an increasing meridional SST gradient on the polar side and decreasing meridional SST gradient on the equatorward side (Fig. 4). The increasing SST gradient on the polar side is accompanied by increasing eddy heat and momentum fluxes (not shown), and the eddy stress $\overline{S}$ and the southern Hadley cell thus restrengthen (Figs. 6b,c). The restrengthening reduces the wind–evaporation–SST feedback and the anomalously positive meridional SST gradient eventually diminishes. The duration of the recovery stage increases with the mixed layer depth (Fig. 4), supporting the role of SST.

a. Stage 1: The Hadley cell in the forced hemisphere weakens

Surface temperature in the forced region increases after the surface heating in the Southern Hemisphere high latitudes is imposed. The imposed high-latitude heating decreases meridional temperature gradient and boundary layer stability in midlatitudes and subtropics, leading to a reduction of both eddy heat flux and momentum flux (Fig. 10c). The southern cell thus weakens to balance the reduction of eddy momentum flux divergence in the subtropics (Fig. 10a). The anomalous Hadley circulation is limited to the Southern Hemisphere in this stage, and there is very little change in tropical SST and precipitation (Fig. 10g). While the idea of extratropical eddy influencing the strength of Hadley cell is not new, the causal relationship is clearer in our simulations compared with previous studies. For studies investigating seasonal cycles (i.e., Bordoni and Schneider 2010), the insolation in the tropics varies; therefore, it is difficult to identify the root cause for variation of local Rossby number and thus the abrupt transition of the monsoon circulations. Similarly, the positive correlation between Hadley cell strength and eddy stress demonstrated in Caballero (2008) among a group of global climate models does not indicate a causal relationship. In our simulations, the imposed extratropical forcing is the root cause of all of the responses. In addition, the time scale for stage 1 responses is independent of mixed layer depth (Fig. 5), supporting the interpretation that this stage being controlled by atmospheric momentum flux changes.

b. Stage 2: Cross-equatorial Hadley cell responses

The reduction of eddy momentum flux divergence in stage 1 also leads to decreasing easterly trades at the surface (Fig. 10e), reducing evaporation and resulting in warmer SST in the SH subtropics. Once the anomalous warming propagates to the deep tropics and the interhemispheric temperature gradient becomes significant, an anomalous cross-equatorial cell develops and the tropical precipitation shifts southward (Figs. 10b,f,h). The cross-equatorial cell is confined in the deep tropics, where angular momentum is nearly constant. Once developed, the anomalous cross-equatorial cell is an order of magnitude stronger than the anomalous Hadley circulation in stage 1. The larger signal-to-noise ratio in the second stage may explain why the energetic framework has more support in the literature than the momentum perspective. The equilibrium responses are qualitatively similar to the responses in stage 2. The momentum balance of the equilibrium responses can be explained by the momentum advection of the cross-equatorial Hadley cell: the Hadley cell and the eddy stress weaken in southern tropics and strengthen in northern tropics. The response time scale of the anomalous cross-equatorial cell is roughly proportional to mixed layer depth (Fig. 5), suggesting the critical roles of air–sea interactions and boundary layer processes in triggering the cross-equatorial cell. The necessity of using the thermodynamic perspective to explain the anomalous Hadley cell strength in the deep tropics is consistent with Singh et al. (2017). Comparing two idealized simulations with and without large-scale eddies suggests that the upper-layer eddy momentum flux may affect boundary layer entropy (and thus the strength of Hadley cell) by inducing a low-level frictional flow that reduces the ability of the Hadley cell to transport heat poleward.

The particular model configuration employed in our study was key to revealing the complex transient evolutions of the extratropical-to-tropical teleconnection. This is unlike the tropical-to-extratropical teleconnection, whose pathway and time scale could be understood via anomalous stationary planetary wave propagation generated from Rossby wave sources resulting from convective changes in the tropical Pacific (Wallace and Gutzler 1981; Hoskins and Karoly 1981). Once developed, the planetary-scale stationary wave patterns are steady, unless there are variations in background wind. The two-stage transient evolution of the tropical responses to extratropical thermal forcings reported in our study might be less relevant for a single tropical weather event triggered by extratropical perturbation. They could, however, be crucial for understanding the decadal variabilities or the transient evolution of anthropogenically forced climate change in the tropics. For transient climate responses (i.e., 1% increase CO₂ or standard RCP forcing scenarios), it is likely that mechanisms with various time scales all play a role in shaping the forced responses.

Our experimental setup and a large number of ensemble members allow us to reveal the two-stage mechanisms operating in the interannual time scale that are not represented in simplified models with fixed SST (or relaxing toward an equilibrium SST), while isolating the roles of stationary waves and ocean dynamics. A more careful and systematic evaluation of the magnitudes and time scales of various mechanisms through a hierarchy of numerical models of the atmosphere–ocean–land system is important to obtain a full picture understanding of extratropical influences on tropical climate. Some open questions that can be addressed using models with different complexity include the following:

1. The influence of seasonality: Eddies are stronger in the winter hemisphere. However, the influence of eddy momentum flux may be more apparent for the weak summer Hadley cell in the subtropics, where the Rossby number is small and the Hadley cell is closer to an eddy-driven regime [Eq. (1.1); Kang and Lu 2012]. It is yet to be explored how the time scales for the two stages would vary in simulations with seasonally varying insolation.

2. The influence of zonal asymmetry: In our zonally symmetric aquaplanet model, the surface boundary is covered by a uniform mixed layer ocean. The eddy–mean flow interactions may be damped by the large thermal inertia of the mixed layer ocean, as the mean circulation is strongly constrained by SST. In a more realistic configuration, the small heat capacity of landmasses and the shallow mixed layer depth in the eastern oceanic basins may allow stronger feedback between eddy momentum flux and regional mean circulations, which then strengthen the responses in the momentum-driven stage (stage 1). In addition, including zonal asymmetry also induces zonal variations of storm tracks and eddy momentum flux, allowing eddies to affect local Hadley cell. The wind–evaporation–SST mechanism may be more concentrated in the eastern basins, where the climatological trades are more organized and the mixed layer depth is shallower, altering the time scale of the tropical responses.

3. The influence of dynamical ocean: We have not considered the role of the dynamical ocean, which is reported to damp the tropical atmospheric circulation responses in many recent studies (Deser et al. 2015; Kay et al. 2016; Tomas et al. 2016; Hawcroft et al. 2017; Kang et al. 2018). While we do not expect changes in ocean dynamics playing critical roles for stage-1 responses, the time scale of the cross-equatorial Hadley cell response may be affected by the damping mechanism of Ekman transport (Schneider et al. 2014; Green and Marshall 2017; Kang et al. 2018). Through investigating responses in long simulations (more than 50 years) in fully coupled models, Wang et al. (2018), Lin (2020), and Kang et al. (2020) further suggest that a hemispherically symmetric Hadley cell response emerges as some oceanic processes affect SST along the cold tongue, potentially overwhelming the stage-2 cross-equatorial cell responses on decadal time scales.

a. The baroclinic mechanism: A reduction of wave source

Based on Eq. (2.3), the horizontal heat flux $\overline{{\upsilon }^{\prime }{\theta }^{\prime }}$, the stability ${\overline{\theta }}_z$, and the vertical eddy momentum flux $\overline{{\upsilon }^{\prime }{w}^{\prime }}$ can all influence the vertical component of the E-P flux. The imposed heating reduces the temperature gradient (blue contours in Fig. A1e) and thus leads to the weakening of poleward eddy heat flux (red contours in Fig. A1e). Also, the imposed heating propagates horizontally and vertically, increasing temperature at around 750 hPa more than those near the surface. The lower tropospheric stability between 30° and 60°S increases (blue contours in Fig. A1f). Both reducing horizontal heat flux and increasing stability contribute positivity to the reduction of the vertical component of the E-P flux. The contribution from vertical eddy momentum flux is an order of magnitude smaller (not shown). We hypothesize that the reduction of baroclinicity on the equatorward side of the forcing reduces the wave source near the surface and thus decreases the momentum flux aloft. The reduction of wave sources and the associated momentum flux changes are consistent with those in global warming simulations, although the initial triggers differ (Frierson 2008; Lorenz and DeWeaver 2007).

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Responses of the E-P flux and its divergence. Climatological E-P flux (arrows), divergence of E-P flux (shading; m s⁻²), vertical gradient of potential temperature (blue contours; K m⁻¹, with CI = 0.001, zero contour bolded and negative dashed) along with (a) eddy heat flux (red contours in left panel, K m s⁻¹, with CI = 2) and (b) meridional gradient of potential temperature (red contours; K m⁻¹, with CI = 40). Anomalous E-P flux, divergence of E-P flux, vertical gradient of potential temperature (blue contours; K m⁻¹, with CI = 0.0001) along with (c) eddy heat flux (red contours in left panel; K m s⁻¹, with CI = 1), and (d) meridional gradient of potential temperature (red contours; K m⁻¹, with CI = 1). (e)–(h) As in (c) and (d), but for stage 1 in (e) and (f) and stage 2 in (g) and (h).

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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b. The barotropic mechanism: Eddy–mean flow interactions

Another possible explanation for the weakening of eddy momentum flux divergence at the edge of the Hadley cell is the barotropic eddy–mean flow interaction mechanism (Chen et al. 2008; Lu et al. 2008). As shown in Fig. A2, we do not find it to be the key mechanism leading to the reduction of eddy momentum flux divergence $\overline{S}$ in the subtropics. As reviewed by Shaw (2019), the mechanism is as follows: The imposed warming modifies the meridional temperature gradient in the baroclinic zone. Through thermal wind adjustments, zonal mean zonal wind alters. The eddy phase speed is expected to change, which shifts the critical latitudes (where background zonal mean zonal wind equals eddy phase speed) and affects eddy momentum flux divergence $\overline{S}$. While imposing heating does lead to decreasing temperature gradient and reducing zonal mean zonal wind in midlatitudes in our simulation, the eddy phase speed does not change significantly. The limited influence of the background wind on the eddy phase speed is likely due to the baroclinic zone being more equatorward (around 40°S) than the regions with strong background wind speed change (50°–60°S). The zonal mean zonal wind changes in the subtropics are also small in stage 1. The largest contribution of anomalous eddy momentum flux appears to arise from eddies with the phase speeds that are similar to that contribute to most of the eddy momentum flux in the control case, implying changes in eddy momentum flux may originate from changes in eddy sources described in the baroclinic mechanism.

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Responses of zonal wind and eddy momentum flux. Zonally average zonal wind at 300 hPa divided by cosθ (heavy lines; m s⁻¹; solid line is climatology and dashed line is ensemble mean of the MLD200 heating case), climatological (shading; m² s⁻²) and anomalous (contours, with CI = 0.05 m² s⁻²; zero contour omitted and negative dashed) eddy momentum flux in stage 1 at 300 hPa. The hatching denotes the significance at 95% confidence level.

Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0151.1

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