1 Introduction

Increasing evidence from paleoproxy data and paleoclimate simulations suggests a close linkage between high latitude climate change and tropical climatic variations. In particular, the effect of thermal perturbations confined to extratropical North Atlantic appear to spread over many parts of the world. For instance, the influence of the Atlantic meridional overturning circulation (AMOC) shutdown during Heinrich events and the Younger Dryas exhibits the near-global footprint (Hemming 2004). The North Atlantic effects are found in the eastern tropical Pacific where a temperature drop is synchronous with the high latitude North Atlantic cooling (Kienast et al. 2006). High sea surface salinities in the eastern equatorial Pacific are also shown to coincide with Heinrich events and with Greenland stadials (Leduc et al. 2007). In the western tropical Pacific warm pool, the salinity variability is shown to vary in accord with Dansgaard/Oeschger cycles over Greenland (Stott et al. 2002). In the Indian Ocean, the precipitation variability bears a close correlation to the oxygen-isotope record from Greenland ice cores (Burns et al. 2003).

Modeling studies support the notion that changes of the AMOC are capable of inducing substantial far-reaching climatic anomalies around the globe. The pioneering coupled GCM study by Manabe and Stouffer (1988) showed that the climatic impact of a shutdown of the AMOC can be global, as is also suggested by recent state-of-the-art coupled ocean-atmosphere GCMs (e.g. Zhang and Delworth 2005; Stouffer et al. 2006). Furthermore, whether the sea ice is imposed in the North Atlantic or North Pacific the Intertropical Convergence Zone (ITCZ) is shifted in all the three ocean basins (Chiang and Bitz 2005; Chiang and Friedman 2012). Thus, it is of particular interest to study how the climate perturbations that originated in the high latitude North Atlantic region perturb tropical basins beyond the Atlantic.

An energy flux perspective for interpreting the changes in tropical precipitation as a response to extratropical forcing is supported by recent studies (Kang et al. 2008, 2009), in a context of zonally symmetric climate. A key component of the theory is the cross-equatorial atmospheric energy transport, as its direction is opposite to low-level moisture transport that determines the direction of tropical precipitation shift: as the Hadley circulation is required to transport energy toward the colder hemisphere, the ITCZ has to be shifted toward the warmer hemisphere, regardless of the location of anomalous heating. Moreover, the magnitude of tropical precipitation shift is shown to be proportional to the magnitude of cross-equatorial atmospheric energy transport changes. Hence, the energy flux perspective provides an important constraint on the bulk response of tropical precipitation (see also Chiang and Friedman 2012; Marshall et al. 2013).

Although the response is constrained by these energetic considerations, the actual mechanism by which the tropics respond to the extratropical forcing generally involves changes in tropical sea surface temperature (SST). Chiang and Bitz (2005) proposed that the wind–evaporation–SST (WES) feedback in the subtropics is responsible for the southward ITCZ shift to the northern North Atlantic cooling. As the cooling reaches the subtropics by advection, the anomalous meridional pressure gradient drives an anomalous northerly wind. Then, the intensified northeasterly trade winds increase the latent heat release to cool the northern tropics, thereby shifting the ITCZ southward. However, by suppressing the WES feedback in a model, a few studies (e.g. Mahajan et al. 2010; Kang and Held 2012) demonstrated that the WES feedback is not essential for the propagation of extratropical cooling to the tropics. Instead, Mahajan et al. (2010) proposed that the near-surface specific humidity changes can sustain the tropical SST changes in the absence of the WES feedback: climatological trade winds transport dry cold air from the extratropics into the northern tropics; the near-surface specific humidity in the northern tropics decreases; the loss of surface longwave radiation increases and the surface cools.

The preceding mechanisms do not provide a straightforward understanding of how the zonally asymmetric extratropical forcing produces the widespread tropical response that is evident in paleoclimate records and modeling studies. Previous studies with the focus on the tropical Pacific response to the weakened AMOC propose that the changes in the tropical Atlantic are critical to perturb the tropical Pacific. This tropical pathway can be enabled by processes such as Rossby waves (Dong and Sutton 2002), advection across Central America (Zhang and Delworth 2005; Xie et al. 2008), and air-sea interaction over the tropical Atlantic (Wu et al. 2008), which would propagate the tropical Atlantic response into the eastern tropical Pacific. Alternatively, the North Pacific cooling, which is identified as a robust response to a shutdown of the AMOC (Timmermann et al. 2007; Wu et al. 2008), can be a conduit of the AMOC influence on the tropical Pacific, as was hinted by Dong and Sutton (2002). Ceppi et al. (2013) also notes that the localized extratropical forcing can become significantly spread out in longitude by the prevailing westerlies before affecting the tropics. This extratropical pathway has been suggested to play a role in perturbing the western and central equatorial Pacific through the WES feedback (Wu et al. 2008).

In this study, we further present evidence that emphasizes the importance of the extratropical pathway. We adopt a similar strategy to Kang et al. (2008) where an atmospheric model coupled to an aquaplanet slab mixed layer ocean is perturbed by prescribing heat fluxes beneath the mixed layer. The effect of the weakened AMOC is represented by prescribing idealized anomalous southward oceanic heat transport in a region of finite zonal extent. Otherwise, the lower boundary is a zonally symmetric aquaplanet to ensure that the zonal asymmetry of the system is only created by zonal asymmetry of prescribed oceanic heat transport. The results may change when considering an asymmetric mean state, but we believe that this perturbation to a zonally symmetric state is an important point of comparison for the more realistic case.

2 Experiment design

2.1 Model setup

We employ the Geophysical Fluid Dynamics Laboratory (GFDL) AM2, an atmospheric general circulation model (Anderson et al. 2004). The model has 24 vertical levels, with horizontal resolution of 2° latitude × 2.5° longitude. As in Kang et al. (2008), aqua-planet simulations are considered in which the atmosphere is coupled to a 2.4 m-deep motionless slab ocean. The small heat capacity is chosen to reduce the time required to reach equilibrium. Some of the modest effects of increasing the heat capacity are discussed in Kang et al. (2008) for the case of zonally symmetric heating. The model is run under equinox condition for 9 years and the first 2 years are discarded as spin up.

The experiments are designed to perturb the distribution of tropical precipitation by forcing high latitudes over a finite longitudinal extent. To mimic the response to the weakened AMOC, we prescribe the thermal forcing, H, beneath the mixed layer that provides cooling poleward of 40°N with equal and opposite heating poleward of 40°S (Fig. 1a). In addition, to examine the tropical Atlantic pathway for AMOC to induce widespread tropical response, the experiment with cooling and heating confined to 20°S and 20°N is performed (Fig. 1b). The experiments with high latitude heating are referred to as HIGH, and those with tropical heating as TROP. Moreover, as an intermediate step between HIGH and TROP, we take into account the tropical response to circumglobal heating, i.e. \(H=-A\,\hbox{sin}(2\theta)\), which is referred to as SINE (Fig. 1c).

Fig. 1
figure 1

Global distribution of prescribed heating (H in Wm−2) for a HIGH with f a  = 1/6 and A = 60, b TROP with f a  = 1/6 and A = 60, and c SINE with f a  = 1/4 and A = 60. d The associated implied oceanic transport (F O in PW) in HIGH (blue), TROP (red), and SINE (green). A quarter of F O is plotted for SINE

The heating H is imposed over a fraction of the globe (e.g. 1/6, 1/3, or 1/2), and the maximum amplitude of the forcing A (in Wm−2) is adjusted accordingly to ensure that the zonal average of the prescribed forcing has A = 10 in HIGH and TROP, and A = 15 in SINE. The fraction of the forced area is denoted as f a . Since the global mean of H is ensured to be zero, its zonal average can be described in terms of an implied meridional oceanic heat transport F O with

$$ \overline H = -\frac{1}{2\pi a^2\,\hbox{cos}\theta}\frac{\partial F_O}{\partial\theta} $$
(1)

where overbars denote the zonal average. For reference, the distribution of prescribed heating H with the zonal extent of 60° (f a  = 1/6) and A = 60, and the associated zonal mean oceanic heat transport F O are plotted in Fig. 1. In all of the experiments F O is negative, equivalent to a north-to-south oceanic transport. Note that F O in HIGH is meridionally of global scale, while that in TROP is meridionally confined to the tropics.

Moreover, we perform identical experiments with the model where wind speed in the evaporation calculation is prescribed as in the control climatology with no time dependence so as to suppress WES feedback, as in Kang and Held (2012), to study the effect of WES feedback on the zonal structure of tropical responses. The results with inhibited WES feedback will be described briefly in the conclusions.

2.2 A measure of zonal asymmetry

Kang et al. (2008, 2009) show that the magnitude of the tropical precipitation response is dependent on the degree of compensation between the atmospheric energy transport and the imposed oceanic transport. For the steady state energy budget for the atmosphere over a mixed layer, we have

$$ \overline{R_{TOA}}-\frac{1}{2\pi a^2\,\hbox{cos}\theta}\frac{\partial F_O}{\partial\theta} =\frac{1}{2\pi a^2\,\hbox{cos}\theta}\frac{\partial \overline F}{\partial\theta} $$
(2)

where R TOA is the time mean incoming net radiation at top-of-atmosphere (TOA), F O is the imposed cross-equatorial oceanic transport in Eq. (1), and F is the meridional moist static energy transport. The changes in zonal mean atmospheric energy transport can be scaled by F O as

$$ C\equiv\left\vert \left( \overline{F}-\overline{F_{ctl}}\right)/F_O \right\vert $$
(3)

where the subscript ctl denotes the control integration, symmetric about the equator, which is integrated without any surface flux adjustments (A = 0). Eq. (3) is defined to be the degree of compensation (C) that measures the fraction of the imposed oceanic fluxes that is balanced by the meridional atmospheric energy transport rather than the radiative fluxes. In the zonally asymmetric case, the zonal mean degree of compensation C can be decomposed into that within the forced region and that outside of the forced region. Since only the divergent part of the atmospheric energy transport matters for the energy budget in Eq. (2), the degree of compensation within the forced region, i.e. C F , is defined to be

$$ C_F=\frac{\int_{\lambda_1}^{\lambda_2} \left( F^{\psi}-F^{\psi}_{ctl} \right) d\lambda }{\int_{0}^{2\pi} \left( F-F_{ctl} \right) d\lambda} $$
(4)

where λ is longitude in radians, and the oceanic flux is imposed between λ1 and λ2. \(F^{\psi}\) is the divergent part of F with \(\nabla\times F^{\psi}=0\), so that

$$ \int\limits_{0}^{2 \pi} \left( F^{\psi}- F^{\psi}_{ctl} \right) d\lambda = \int\limits_{0}^{2 \pi} \left( F- F_{ctl} \right) d\lambda. $$

C F measures how much of the changes in meridional atmospheric energy transport is carried out within the forced area. If the response of atmospheric energy transport is perfectly zonally symmetric, as an example, then C F  = f a . An extreme case in which C F  = 1 implies that the energy transport response is completely localized over the forced region. Therefore, comparing C F with the fraction of the forced area f a is a measure of the extent to which the response to localized forcing is zonally symmetric.

3 Response to zonally asymmetric extratropical forcing

Figure 2 shows the global SST anomalies for HIGH with the zonal extent of 60° and A = 60. The extratropical SST anomalies are naturally large over forced regions. The maximum anomaly reaches 12 K over warmed area and −16 K over cooled area. The cause of this asymmetry is interesting but not central to the main concern of this paper. The SST responses zoomed in to the tropics are shown in Fig. 3, with corresponding tropical precipitation anomalies. The tropical responses of SST and precipitation are highly zonally symmetric, especially compared to those in TROP (refer to Fig. 8), consistent with the near-global response to weakened AMOC suggested by paleoclimate records and modeling studies. The high degree of zonal symmetry of tropical responses can be quantified by C F being less than 1 and close to f a (Fig. 4). The tropical responses may become even more zonally symmetric when transient variability is removed by averaging over longer time period.

Fig. 2
figure 2

Time-mean change in SST (K) for HIGH with f a  = 1/6 and A = 60

Fig. 3
figure 3

Time-mean change in a SST (K) and b precipitation (mm day−1) between 20°S and 20°N for HIGH with f a  = 1/6 and A = 60

Fig. 4
figure 4

The fraction of the prescribed forcing that is balanced by the atmospheric energy flux, C, in solid. The fraction of C balanced by the divergent part of atmospheric energy flux within the forced region, C F , in dashed. Averages over 10°S–10°N (in %) are plotted as a function of the zonal extent of the forced region f a for HIGH

One possibility is that heat diffusion in the extratropics is sufficient to homogenize the response in longitude. To test this idea a two-dimensional energy balance model (EBM) is constructed, as described in the “Appendix”. Fitting the EBM’s difffusivity D to fit the meridional temperature distribution in the aquaplanet version of AM2, and then using this diffusivity isotropically, the resulting changes in SST are far from zonally symmetric (Fig. 5). The resulting tropical response in the EBM is still much more localized than in AM2 even when D is increased by one order of magnitude. The diffusive EBM, hence, fails to predict the zonal symmetry of the tropical response, implying that a diffusive picture with isotropic diffusivity cannot explain the zonal homogenization.

Fig. 5
figure 5

The surface temperature averaged between the equator and 10°N for HIGH with f a  = 1/6 and A = 60 for AM2 (solid) and that obtained from EBM (dashed)

An important factor missing in the EBM is the advection by mean winds. It is possible that the localized extratropical forcing is homogenized by these winds before passing on to the tropics. The examination of transient evolution indeed suggests that the midlatitude winds are important. We use ensemble simulation with 4 members where the extratropical forcing H is abruptly introduced using the identical model. Each ensemble member is started from a different day after the spin-up period of the control run, and run out for 1 year (the climate mostly reaches the equilibrium state in about 2 years). The length of time needed to establish the zonally symmetric tropical response is somewhat surprising, given the very shallow (2 m) mixed layer utilized here, suggesting that there is more to be understood about this evolution.

Figure 6a shows the monthly evolution of midlatitude temperature response at 500 hPa (T500) in longitude averaged over 35–50°N. For simplicity, most of the following discussion will be confined to the Northern Hemisphere. The cold T500 anomaly preferentially propagates eastward following the direction of mean advection by westerlies. Within the forced region, the magnitude of cold surface anomaly reaches about 3 K at month 7. By month 10, the midlatitude cold anomaly extends around the globe, indicating that the localized extratropical response is homogenized within the extratropics within a year. In the tropics, as shown in Fig. 6b, the surface cooling response that starts to form at month 2 propagates eastward until month 10, despite mean easterly trade winds, which is the sign of midlatitude influence on the tropics. The specific mechanisms by which the tropical SSTs are modified depend on whether WES feedback is on or off, but the broad features of the SST and precipitation evolution are similar. The tropical SST response leads the tropical precipitation response by about 2 months (Fig. 6b). Once the midlatitude SST response extends over all longitudes at month 10 (Fig. 6a), the tropical responses become zonally homogenized (Fig. 6b). The examination of the transient period suggests that the localized high latitude forcing is homogenized by prevailing westerlies, especially in the mid-to-upper troposphere, before passing on to the tropics, which then induces zonally symmetric tropical response. As a result, the tropical precipitation response to localized extratropical forcing is zonally symmetric: the tropical responses are the same no matter where in high latitudes the anomalous heating is imposed.

Fig. 6
figure 6

Hovmoller diagram of a temperature response at 500 hPa (in K) averaged over 35–50°N and b precipitation response (in mm day−1) in shading and surface temperature response (in K, contour interval is 0.4 K) in contours with negative values in dash, averaged over 1–5°N for HIGH with f a  = 1/6 and A = 60. 1-2-1 smoothing is applied to the monthly-mean data in time

Figure 7 shows the zonally averaged response of SST and precipitation in HIGH with varying zonal extent of the forced region (f a ). The zonal mean responses are nearly independent of f a as long as the zonally averaged forcing is kept the same. In particular, the maximum precipitation anomaly differs by less than 5 %. It implies that the zonal mean responses of integrations with finite zonal extent (f a  < 1) can be determined by the response to the zonally symmetric component of the forcing (f a  = 1), justifying the use of zonally symmetric forcing in Kang et al. (2008, 2009) to understand the mechanism by which the ITCZ displacements can be forced from a localized region in high latitudes. The insensitivity of zonal mean tropical precipitation response to f a is consistent with the zonal mean compensation C in the tropics being more or less independent of f a , only differing by 5 % at most (black in Fig. 4). Thus, C is the key for determining the magnitude of the zonally averaged precipitation response. The implication is that the stationary eddies do not affect the zonal mean response of tropical precipitation to extratropical forcing. It is possible, however, that the zonal mean response is independent of the width of the forced region only because we are starting with a zonally symmetric climate. With zonal asymmetry in the climatological wind that originates from land-sea contrast, orography, and ocean circulation, the extratropical response may preferentially propagate equatorward along certain longitudinal bands, and zonal mean responses may be less strongly constrained and produce some zonal asymmetry in the tropical response.

Fig. 7
figure 7

Time mean, zonal mean anomalies of a SST in K and b precipitation in mm day−1 for varying zonal extent of the forced region for HIGH. Black, red, green, and blue are for f a  = 1, 1/2, 1/3, and 1/6 with A = 10, 20, 30, and 60, respectively

4 Response to zonally asymmetric tropical forcing

In this section, we examine the tropical precipitation response to localized tropical heating to examine the tropical Atlantic pathway for AMOC to affect the tropical Pacific. Figure 8 shows the tropical distribution of SST changes overlapped with low-level wind vectors (upper panel) and precipitation changes with the ITCZ location (lower panel), in TROP with f a  = 1/6 and A = 60. The ITCZ is defined as the latitude of the tropical maximum in precipitation, obtained by differentiating the precipitation with respect to latitude and linearly interpolating to obtain the zero crossing. The tropical responses in TROP are highly localized within the forced region with slight westward extension, in contrast to zonally symmetric tropical responses in HIGH (compare Fig. 8 with Fig. 3). The easterly trade winds in the tropics force the SST contours to be slanted westward, making a southward shift of the ITCZ more skewed to the west. The stronger westward extension north of the equator indicates that the advection by mean easterlies is responsible for the westward extension since the easterly trades are stronger in the cooled Northern Hemisphere. The tropical anomalies extend to the west of the forced region by about 40° longitude, which is smaller than that described in Xie (1996) who suggested that WES feedback extends the response by 80° longitude. Since the meridional gradients of upper tropospheric temperature has to stay nearly flat within the tropics (Sobel et al. 2001), the hemispherically anti-symmetric SST anomalies can produce only a modest tropospheric temperature response. The tropospheric anomalies, hence, cannot easily force a propagating signal in the SST anomalies away from the forced region, and act as a mixing mechanism that dissipates the anti-symmetric surface response across the equator. The degree of zonal asymmetry can be confirmed by the near 100 % C F in Fig. 9 (dashed). A weak zonally symmetric component in addition to the enhanced response over and west of the forced region suggests that the tropical Atlantic pathway can be important for affecting the eastern tropical Pacific, but not sufficient to explain global response to a weakened AMOC.

Fig. 8
figure 8

Shading indicates time-mean change in a SST (K) and b precipitation (mm day−1) between 20°S and 20°N for TROP with f a  = 1/6 and A = 60. Vectors in a show 876 hPa horizontal wind vectors and a blue solid in b indicates the ITCZ latitude when f a  = 1/6, compared with the zonally symmetric case (f a  = 1) in dashed blue

Fig. 9
figure 9

Same as Fig. 4, but for TROP

Another distinctive feature in Fig. 8 is that the cooling response in the northern tropics is much larger than the warming response in the southern tropics. The SST drop in the north reaches up to 4 K, whereas there is only 1 K SST rise in the south. This can be understood from changes in cloud radiative forcing (CRF), which are mostly due to changes in lower tropospheric cloud (>400 hPa; for brevity, we will call it low cloud) amount associated with the ITCZ shift (Fig. 10). The southward ITCZ shift accompanies low cloud amount increase (decrease) in the southern (northern) tropics. Because of strengthened northeasterlies in the northern tropics (Fig. 8a), the responses of low cloud amount and CRF extend more to the west in the north than in the south (Fig. 10). The CRF response is to partly offset the prescribed forcing, as low cloud amount reduction in the cooled north results in decrease in shortwave reflection and vice versa. The changes in CRF induce cooling of 50 Wm−2 in the south and warming of 30 Wm−2 in the north, so that the offsetting effect of the prescribed forcing is larger in the south, resulting in weaker responses of tropical SST and precipitation in the south. However, we note that these cloud responses may be highly model dependent. For instance, Cvijanovic and Chiang (2013) find that the Community Atmospheric Model version 3 produces larger changes in high cloud than low cloud associated with the ITCZ shift, so that the changes in CRF represent a positive feedback to the imposed forcing, which is opposite to our results.

Fig. 10
figure 10

Shading indicates the time-mean changes in cloud radiative forcing (Wm−2, positive values downward) and contour indicates those in low cloud amount (in %) with positive values in solid and negative in dotted (contour interval is 5 %), between 20°S and 20°N for TROP with f a  = 1/6 and A = 60

Figure 11 compares the zonally averaged response of SST and precipitation for cases with varying f a in TROP. The response of zonally averaged SST is not well constrained, especially over mid- to high-latitudes. The tropical precipitation response seems to be more constrained, but the maximum anomaly differs by 20 %, as the zonal mean compensation C is not as independent of f a as in HIGH (compare solid lines in Figs. 4, 9).

Fig. 11
figure 11

Same as Fig. 7, but for TROP

5 Response to zonally asymmetric circumglobal forcing

The changes in global distribution of SST and tropical precipitation when f a  = 1/8 and A = 120 in SINE are shown in Fig. 12. In the lower panel, the ITCZ location (blue solid) is compared with that in the case with zonally symmetric heating (blue dashed). The global temperature response clearly shows the effect of mean advection: westward extension poleward of 70°N, eastward extension in the midlatitudes, and southwestward extension in the tropics. The tropical responses exhibit the characteristics of both TROP and HIGH, which is localized response with westward tilt superimposed on the zonally symmetric response. The westward extension is clearly illustrated by the ITCZ location. As shown in Sect. 4, the prescribed heating over low latitudes is responsible for the localized tropical SST response with a distinct structure coincident with the spatial footprint of the northeasterly trades in the cooled northern tropics. The zonally homogenized tropical response outside of the forced region is the result of the forcing imposed in the extratropics, as discussed in Sect. 3.

Fig. 12
figure 12

Shading indicates time-mean change in a SST (K) and b precipitation (mm day−1) between 20°S and 20°N for SINE with f a  = 1/8 and A = 120. A blue solid in b indicates the ITCZ latitude when f a  = 1/8, compared with the zonally symmetric case (f a  = 1) in dashed blue

More quantitatively, the degree of zonal asymmetry is shown in Fig. 13 that compares the zonal mean compensation C and its fraction within the forced region C F for HIGH, TROP, and SINE. In SINE, C is independent of f a , implying that the zonally averaged response stays the same, which seems to be the effect of extratropical portion of the prescribed forcing. C F is in between that in TROP and HIGH, indicating that the tropical response in SINE is not only zonally symmetric in response to extratropical forcing but also zonally asymmetric in response to tropical forcing.

Fig. 13
figure 13

a The zonal mean degree of compensation C (%) and b its fraction within the forced region C F (%) as a function of zonal extent of forced area f a . Solid, dashed, and dash-dot lines are for HIGH, TROP, and SINE, respectively. Crosses in a, b denote C and C F , respectively, in AM2 with prescribed clouds

Kang et al. (2008) show that the magnitude of tropical precipitation response to zonally symmetric extratropical thermal forcing is highly sensitive to radiative feedbacks from cloud responses. Hence, to study the robustness of the zonal structure of tropical response to zonally asymmetric forcing, cloud radiative feedback is suppressed in SINE. Details on prescribed cloud simulations can be found at Kang et al. (2008). Figure 14 shows the tropical CRF, precipitation and ITCZ responses in SINE with f a  = 1/8 and A = 120 for full AM2 and AM2 with prescribed clouds. In full AM2 (Fig. 14a), tropical changes in CRF, with positive and negative values straddling around 5°S, are directly associated with the ITCZ shift. Increase in tropical precipitation is associated with cooling, and vice versa, because the CRF change in AM2 is dominated by its shortwave component associated with low cloud amount. In addition to these tropical changes, there is substantial cooling of nearly 80 Wm−2 resulting from changes in cloud amount in the cooled northern subtropics, extending slightly westward of the forced region. This could be due to increased static stability in response to lower tropospheric cooling. This localized cooling in the northern subtropics not only amplifies the prescribed cooling but also drives southward winds, so that it can contribute to shifting the tropical precipitation more southward than other longitudes, resulting in a westward extension of the ITCZ response. With prescribed clouds (Fig. 14b), the local subtropical cooling does not exist and the ITCZ location exhibits no sign of westward extension. This confirms that changes in cloud forcing contribute to the westward extension of tropical responses to zonally asymmetric forcing.

Fig. 14
figure 14

The changes in cloud radiative forcing (shading, in Wm−2, positive downward), overlapped with changes in precipitation (contours, in mm day−1) for a full AM2 and b AM2 with prescribed clouds for SINE with f a  = 1/8 and A = 120. Contour interval is 5 mm day−1 with positive in green and negative in brown. Thick blue contours indicate the ITCZ location

Lastly, we note that identical experiments are performed with the model where wind speed is prescribed to the control climatology with no time dependence for the evaporation calculation to suppress the WES feedback, as in Kang and Held (2012), to study the effect of WES feedback on the zonal structure of tropical responses. The zonal structure of SST and precipitation is largely independent of WES feedback in both HIGH and TROP (compare Fig. 15a with Fig. 3b, and Fig. 15b with Fig. 8b). The wind pattern supports WES feedback (Fig. 8a) but when WES feedback is suppressed, the coupled system finds alternative ways to propagate extratropical forcing and affect tropical SST and convection (Mahajan et al. 2010). Coupled ocean-atmospheric processes for the extratropical to tropical influence and zonal extension need to be further investigated in future studies.

Fig. 15
figure 15

The changes in tropical precipitation (mm day−1) for a HIGH and b TROP with f a  = 1/6 and A = 60 in the model with inhibited WES feedback

6 Conclusion

In this paper, we study the tropical responses to zonally asymmetric heating/cooling that is confined in the extratropics (HIGH) or in the tropics (TROP). In terms of an implied meridional oceanic heat transport, the forcing in HIGH is meridionally of global scale, while that in TROP is meridionally confined to the tropics. We also study the tropical responses to zonally asymmetric circumglobal forcing (SINE), which can roughly be understood as the sum of the separate responses to HIGH and TROP.

In HIGH, the tropical responses of SST and precipitation are highly zonally symmetric. The zonal symmetry is not predicted from a two-dimensional diffusive energy balance model, indicating that the diffusive process by extratropical eddies is not sufficient for the zonal homogenization. The examination of the evolution of midlatitude SST and tropical precipitation in the transient period suggests that the localized high latitude forcing is homogenized by the prevailing midlatitude westerlies before passing on to the tropics, which then induces zonally symmetric tropical response. In contrast to zonally symmetric tropical responses in HIGH, the tropical responses in TROP are strongly localized with westward extension. In SINE, the tropical responses are the sum of those from HIGH and TROP, characterized by localized response with westward extension superimposed on zonally symmetric response. The westward extension of enhanced response that emerges in TROP and SINE is shown to be the result of advection by mean easterly trades and cloud responses.

In HIGH and SINE, when the zonal extent of the forced region is varied while keeping the zonally averaged forcing the same by adjusting the amplitude of the forcing, there is little change in the zonally averaged response of SST and precipitation. The insensitivity of the zonally averaged response is associated with the degree of compensation C, which measures the fraction of the prescribed forcing that is balanced by the atmospheric energy transport, being independent of the zonal extent of the forced region. In contrast, the zonal mean response in TROP is not as well constrained, which is also consistent with varying C. Thus, the compensation C is indeed the key diagnostic for the magnitude of the zonally averaged response.

However, we note that the zonal symmetry of the control climate may be partly responsible for the two main findings: a high degree of zonal symmetry of tropical response to localized extratropical forcing and the insensitivity of the zonal mean response to the degree of zonal asymmetry of the imposed extratropical forcing. The zonally asymmetric control climate may introduce some zonal asymmetry in the tropical responses since zonally asymmetric background wind may preferentially propagate the extratropical forcing along certain longitudinal bands. Nonetheless, a large zonal asymmetry in tropical responses in TROP suggests that the North Pacific pathway is more important than the tropical Atlantic pathway for the AMOC to produce global impact.

Lastly, the identical experiments are performed with the model in which wind speed is prescribed for surface latent heat fluxes. It turns out that inhibiting the wind–evaporation–SST (WES) feedback has little effect on the zonal structure of tropical responses regardless of the forcing location.