North Atlantic Warming Hole Modulates Interhemispheric Asymmetry of Future Temperature and Precipitation

The observed cooling in the subpolar North Atlantic, known as the warming hole, is receiving much attention because of its relationship with the climate sensitivity in the Earth System Models (ESMs). However, the impact of its future projection on the global climate remains unclear due to large uncertainties. Here, we show that the future warming hole changes will affect the interhemispheric asymmetry of temperature and precipitation by modulating the Northern Hemisphere (NH) warming. Models with a weaker warming hole in the future project stronger NH warming by injecting more non‐radiative fluxes to the atmosphere. This leads to an asymmetric warming contrast between the two hemispheres, resulting in a meridional shift of the Inter‐Tropical Convergence Zone and more precipitation increases in the NH. Our study implies that the future warming hole controls the interhemispheric heat exchanges and associated changes in the global temperature and precipitation, suggesting that its improved simulation is essential.


Introduction
Sea surface temperatures (SSTs) in the North Atlantic play an important role in modulating climate in the Northern Hemisphere (NH), including hurricane frequency, storm tracks, and climate oscillations (Josey et al., 2018;Park et al., 2023;Smith et al., 2010;Woollings et al., 2012).Despite significant global warming, the subpolar North Atlantic has cooled in recent decades, known as the North Atlantic warming hole (hereafter, the warming hole) (Chemke et al., 2020;Rahmstorf et al., 2015).The slowdown of the Atlantic Meridional Overturning Circulation (AMOC) has contributed substantially to the observed warming hole with reduced poleward ocean heat transport and increased freshwater flux in the North Atlantic (Caesar et al., 2018;Liu et al., 2017;Rugenstein et al., 2013;Sévellec et al., 2017).However, other climate processes such as shortwave cloud feedback, upper-layer Ekman heat transports, and storminess could also contribute to the observed warming hole (He et al., 2022;Hu & Fedorov, 2020;Keil et al., 2020).A slowdown of the AMOC, combined with the warming hole, could dampen the observed global warming rate in recent decades (Bonnet et al., 2021).Indeed, the timing and magnitude of the recent observed warming hole along with a weakened AMOC is associated with a combination of external forces and internal variability that has not been adequately simulated in current Earth System Models (ESMs) (Jackson et al., 2016;Latif et al., 2022;Sgubin et al., 2017).For example, natural and anthropogenic aerosols may also have played a role in the temporal discrepancy between the evolution of the warming hole and the AMOC (Booth et al., 2012;Fiedler & Putrasahan, 2021;Robson et al., 2022).
While it is accepted that the future warming hole intensity is associated with increases in greenhouse-gas concentrations (Qasmi, 2023), current ESMs project the warming hole with large inter-model spread (Menary & Wood, 2018).The inter-model spread among ESMs in simulating the future warming hole reflects uncertainty in ocean heat uptake and changes in ocean circulation (Cheng et al., 2013;Frölicher et al., 2015;Reintges et al., 2017).The warming hole is an important pathway of the AMOC to influence atmospheric circulation, including shifting of the mid-latitude jet stream location and precipitation distribution through a combination of direct linear responses and transient eddy responses (Gervais et al., 2019;Liu et al., 2020).Therefore, understanding the effects of the warming hole is important for projecting future global warming and AMOC changes with reduced uncertainty.In this study, we defined the warming hole using 45 ESMs from the latest Coupled Model Intercomparison Phase 6 (CMIP6) and found that the future warming hole change modulates the NH warming rate more than that of the Southern Hemisphere (SH), resulting in the strengthening of the interhemispheric asymmetry of future temperature as well as precipitation.

Earth System Models and Observational Data Set
We used 45 coupled general circulation models (CGCMs) in CMIP6 and 33 CGCMs in CMIP5.The model names and modeling groups are given in Table S1 in Supporting Information S1.Surface air temperature, air temperature, precipitation, SST, meridional velocity, and surface and top of the atmosphere (TOA) heat fluxes were used, and the criterion for including a given model was the inclusion of full values for historical and SSP5-8.5 experiments at the time of data download (August 2023).All model simulations cover the period from 1850 to 2099 (1861-2099 for GFDL-CM3 and 1860-2099 for HadGEM2-AO, HadGEM2-ES, and HadGEM2-CC) and follow historical changes in greenhouse gases, aerosols, and natural forces for 1850-2005 (CMIP5) and 1850-2014 (CMIP6).For CMIP5, the simulations follow RCP8.5 for 2006-2100, and for CMIP6, they follow SSP5-8.5 for 2015-2100.We used the 1850-1900 mean in historical simulations for the pre-industrial climate and the 2070-2099 mean under SSP5-8.5 as the future climate.The differences represent future changes under anthropogenic warming.We used only one ensemble out of 45 CMIP6 ESMs to give equal weight to each ESM.The pre-industrial period of the historical simulation is used to compare future changes under different climate change scenarios, in line with the Paris Agreement warming targets of 1.5°C and 2°C.The results are consistent with the use of the piControl experiment rather than historical period (Figure S1 in Supporting Information S1).To determine whether the greenhouse gas forcing is the dominant forcing on future temperature and precipitation changes associated with the warming hole, 1% CO 2 increase, an experiment that includes only the greenhouse gas forcing, is used to compare the results of SSP5-8.5.In SSP5-8.5, the average atmospheric CO 2 concentration from 2070 to 2099 is 926.87 ppm.The 1% CO 2 experiment, which increases 1% per year from 284.3 ppm in piControl, has a 30-year average atmospheric CO 2 concentration of 927.83 ppm from the model year of 104-133, a similar environment but with the effect of aerosols removed.The change in 1pctCO 2 was calculated by subtracting the 200-year average of piControl (model year of 50 to 249-year average).Only 38-ESMs with available 1% CO 2 experiment used.For observations, we used SSTs from the Hadley Center Sea Ice and Sea Surface Temperature data set v1.1.A common 1°× 1°horizontal grid interpolation was applied to all the model outputs and observations.

Single Model Initial-Condition Large Ensemble
The Max Planck Institute for Meteorology Grand Ensemble (MPI-GE) simulations are based on the fully coupled climate model.There are 100 members spanning the interval from 1850 to 2100 (Maher et al., 2019).All ensemble members have the same radiative forcing: historical forcing before 2005 and RCP8.5 forcing from 2006 to 2100.Other ESMs in CMIP6 that provide large ensembles (at least 30 members), including CanESM5 with 50 ensembles, MIROC6 with 100 ensembles, and MPI-ESM1-2-LR with 30 ensembles, are examined.

Location of the ITCZ
The location of the ITCZ is estimated as the latitude closest to the equator where the stream function (vertically averaged with mass weighting between 700 and 300 hPa) is zero (Byrne et al., 2018): This method represents the latitude of the boundary between the northern and southern Hadley cells.

Atmospheric Cross-Equatorial Heat Transport
To identify the relationship between warming hole and the asymmetric warming that determines the location of the ITCZ, we calculated the net atmospheric heat flux by subtracting the net flux at the surface from the net heat flux at the TOA.The atmospheric cross-equatorial energy transport (AHT EQ ) can be calculated as: where F ATM (NH) and F ATM (SH) are integrated heat fluxes entering the atmosphere in the NH and SH, respectively, and are calculated as where ϕ, λ, and a denote latitude, longitude, and the Earth's radius, respectively.F TOA and F SFC are heat fluxes at the TOA and at the ocean/land surface, respectively, and can be calculated as where SW net is net shortwave radiation, LW net is net longwave radiation.The turbulent term is the sum of latent heat and sensible heat, and the radiation term is the sum of SW net and LW net .Positive values indicate downward.

Warming Hole Changes and the Future Warming Rate
Historical simulations and Shared Socioeconomic Pathway (SSP) 5-8.5 experiments from 45 ESMs in CMIP6 (see Table S1 in Supporting Information S1) were used to represent future (2070-2099) climate changes relative to the pre-industrial period (1850-1900) (Eyring et al., 2016;O'Neill et al., 2016).Figure 1a shows the future multi-model ensemble mean (MMEM) SST changes relative to the global mean SST changes using the 45 ESMs.
Projected future SST changes relative to the global mean SST changes under the SSP5-8.5 show either warming or cooling trends, while the subpolar North Atlantic (green box in Figure 1a, 45°N-65°N, 50°W-15°W) has the strongest cooling in the NH, but with large inter-model uncertainty, defined as one standard deviation of SST changes among ESMs (Figure 1b).
Indeed, future changes of the warming hole, defined as the area-weighted mean SST in the subpolar North Atlantic, range from 1.9°C to 9.3°C (Figure S2a in Supporting Information S1).Four ESMs (GISS-E2-1-G, GISS-E2-2-G, FGOALS-g3, NorESM2-MM) project a future cooling in the subpolar North Atlantic (i.e., strong warming hole), while the others project a warming of the warming hole (i.e., weak warming hole), with large inter-model spread (Figures S2a and S2b in Supporting Information S1).This results in low agreement on the sign of the warming hole trend in the ESMs (model agreement <90%, stipples in Figure 1a).Although the CMIP6 MMEM simulates the observed warming hole well during the historical period, the inter-model spread of the warming hole becomes large in the future (Figure S2c in Supporting Information S1).These biases would be partly attributed to the observed chemical processes, including the influence of halogenated greenhouse gases, which are not perfectly cooperated in ESMs (Lu, 2022(Lu, , 2023)).
Regression of future surface temperature changes on future warming hole changes shows that ESMs with stronger warming of the warming hole tend to simulate strong warming in the high latitudes of the NH, centered on the North Atlantic, and this correlation weakens as one moves toward the high latitudes of the SH (stipples in Figure 1c).Consequently, the future warming hole change has a strong positive correlation with the future NH warming rate (correlation coefficient, 0.85; p-value <0.001) (Figure 1d).There is in fact a significant interhemispheric asymmetry of the future surface temperature changes on future warming hole changes (see Figure S3 Earth's Future in Supporting Information S1).This indicates that the future warming rate of the warming hole projected by the ESMs, which occupies a relatively small area though, will be associated with the overall future global warming rate through greater warming in the NH.Although the warming hole is small enough to be used as a proxy for the AMOC (Rahmstorf et al., 2015), it is closely tied to ocean circulation, which affects global climate and plays an important role in the atmosphere-ocean interaction loop.Therefore, the high inter-model correlation of the warming hole with temperature may be a consequence of this ocean circulation.We also find a significant positive correlation coefficient between future changes in the warming hole and the NH warming rate using the four large ensemble simulations (MPI-GE, CanESM5, MPI-ESM1-2-LR, and MIROC6).This implies that the future change in the warming hole modulates the NH warming rate, and that the internal climate variability does not mask out this relationship (Figure S4 in Supporting Information S1).We also performed a sensitivity test for the warming hole domain by analyzing the Empirical Orthogonal Function (EOF) of the North Atlantic (40°N-80°N, 70°W-0°).The EOF results showed that the most variable region was further west compared to the original warming hole, but the effect of the domain difference was not significant (Figure S5 in Supporting Information S1).The standard deviation of future warming hole changes ranged from a minimum of 0.12°C (MPI-GE) to a maximum of 0.24°C (CanESM2), which is less than 10% smaller than the inter-model standard deviation of 2.56°C using 45 CMIP6 ESMs.This indicates that the contribution of model differences is large compared to the impact of internal variability on future changes in the warming hole (Park & Yeh, 2024).

Strong Link Between Warming Hole and NH Warming
To explain how changes in the warming hole affect future NH warming, we regressed the net atmospheric heat flux onto the NH surface warming rate in the CMIP6 ESMs (Figure 2a).The net atmospheric heat flux is the energy flux entering the atmosphere and is calculated by subtracting the net surface heat flux from the net heat flux at the TOA.Although the spatial distribution of atmospheric heat fluxes associated with NH warming rates is heterogeneous, there is a significant positive correlation around the subpolar North Atlantic (green box in Figure 2a).This means that despite its very small area, the large atmospheric heat flux caused by a stronger warming of the warming hole will lead to a stronger NH warming in the future.We argue that atmospheric heat flux changes in the warming hole will play a key role in modulating the NH warming rate in the future.
To investigate this further, we compared the contribution of net atmospheric heat fluxes in the subpolar North Atlantic using two groups representing the warmest (warm10) and coldest (cold10) future warming hole projections (Figure 2b; Table S1 in Supporting Information S1).We find that changes in the warming hole are associated with a larger change in heat flux at the Earth's surface than at the TOA.The most significant change in the net surface heat flux between the two groups is mainly due to turbulent surface heat fluxes (sensible heat plus latent heat), rather than radiation fluxes (sum of net shortwave and longwave radiation).Given that the atmospheric heat flux in the subpolar North Atlantic modulates the future NH warming rate, significant atmospheric circulation changes are projected to occur in response to future changes in the warming hole.ESMs with stronger warming of the warming hole tend to project larger geopotential height (GPH) increases in the global tropospheric layers than ESMs with less warming of the warming hole (Figure 2c), implying that changes in the warming hole are closely associated with NH warming rate.An increase in the tropospheric GPH is mostly caused by the wavelike propagation of thermal forcing from the warming hole to the globe.Indeed, there is a statistically significant positive correlation between changes in the future warming hole and the NH GPH at 500 hPa (Figure 2d).This indicates that stronger warming of the warming hole implies less heat uptake by the ocean and more heat available for tropospheric warming and vice versa.
We further found that ESMs with stronger warming of the warming hole tend to project stronger Arctic and upper tropospheric warming in the tropics than ESMs with less warming of the warming hole (Figure 3a).Stronger warming of the warming hole (i,e, weak slowdown of the AMOC) acts to effectively increase the amount of warm water in transit to the high latitudes, leading to stronger Arctic warming (Yeager et al., 2015;Zhang, 2015).This pattern leads to asymmetric future warming rates between the two hemispheres.Indeed, ESMs with stronger warming of the warming hole tend to project a larger asymmetry in the warming difference between the two hemispheres than ESMs with less warming of the warming hole (Figure 3b), because the thermal forcings caused by the change in the warming hole enhances the warming of the NH atmosphere (Figures 2 and 3a), leading to a larger asymmetry in the warming rate between the two hemispheres.
Asymmetric warming between the two hemispheres is closely related to changes in the interhemispheric energy imbalance, which modulates shifts in the ascending branch of the Hadley cell (Kug et al., 2022;Schneider et al., 2014).In ESMs with greater warming of the warming hole, the NH will gain more net heat flux than the SH, compared to ESMs with less warming of the warming hole.The resulting interhemispheric energy imbalance drives anomalous southward cross-equatorial atmospheric energy transport, resulting in a northward shift of the ascending branch in the Hadley cell (Figure 3c).It also collocates with the location of the ITCZ (Byrne et al., 2018;Donohoe et al., 2013;Kang et al., 2008;Marshall et al., 2014), defined as the latitude closest to the equator where the stream-function (vertically averaged with mass weighting between 700 and 300 hPa) is zero, so that a greater northward shift of the ascending branch in the Hadley cell due to stronger warming of the warming hole is associated with a more northerly shift of the ITCZ (Figure 3d), although such a shift is not zonally homogeneous (Mamalakis et al., 2021) due to the diversity of the equatorial SST warming rate (Heede & Fedorov, 2021;Karamperidou et al., 2017;Park et al., 2022;Watanabe et al., 2021) (Figure 1).
Earth's Future  In summary, the strong warming of the warming hole accompanies with the atmospheric heat transport across the equator along with the stronger warming in the NH and a northward shift of the Hadley and ITCZ.Indeed, the correlation coefficient between future changes in the warming hole and the location of the ITCZ is 0.66, which is statistically significant at the 99% confidence level.

Effects of Warming Hole Changes on Global Precipitation
The shift in the ascending branch of the Hadley circulation and the ITCZ caused by changes in the warming hole also alter future global precipitation patterns (Figure 4a).ESMs with stronger warming of the warming hole (warm10 minus cold10) are associated with more precipitation in the NH, particularly over the subpolar North Atlantic and high latitudes (Figure 4a), resulting in the strengthening of hemispherical asymmetry of precipitation in the future.Moreover, in the Indian and Atlantic Oceans, precipitation increases are evident in the NH near the equator, while its future changes near the equatorial SH show relatively drier conditions, including southern America, if the future warming hole warming is strong.This is consistent with a strong relationship between the warming hole changes and the ITCZ location shift (Figure 3d).This is confirmed by zonal mean precipitation changes between warm10 and cold10.The zonal mean precipitation increase is significantly larger in the warm10 than in the cold10 in the NH, in particular, there is zero overlap between warm10 and cold10 precipitation in the middle-to-high latitudes in the NH (Figure 4b). Figure 4c displays the relationship of future changes in the warming hole and future precipitation in the NH.Indeed, the more warming of the warming hole is, the larger precipitation amount is in the NH (correlation coefficient is 0.84 with the 99% confidence level).Concurrently, the hemispherical asymmetry of precipitation is also enhanced along with more warming of the future warming hole (Figure 4d).Note that the correlation coefficient between the hemispherical asymmetry of precipitation, defined as the precipitation difference between the two hemispheres (NH minus SH), and the warming hole change is 0.68 with the 99% confidence level.In conclusion, the ITCZ is expected to move further north due to increased warming in the NH caused by stronger warming of the warming hole, which also leads to an increase in the hemispherical asymmetry of future precipitation.Meanwhile, the future SH precipitation changes are insignificantly correlated with the warming hole change (Figure S6 in Supporting Information S1), which is consistent with the result in Figure 4a in which the future precipitation change is either reduced or increased in the SH between warm10 and cold10.The Interhemispheric asymmetry in temperature and precipitation changes could be caused by an external forcing asymmetry, such as anthropogenic aerosols (Schneider et al., 2014).To determine whether the interhemispheric asymmetry in temperature and precipitation changes associated with the warming hole change is due to greenhouse gases, we analyzed the CMIP6 1% CO 2 experiment, which includes only the influence of greenhouse gases and excludes the influence of aerosols (Figure 5).ESMs with stronger warming in the warming hole region tend to project stronger warming in the NH, which amplifies the asymmetric warming calculated as NH minus SH (Figures 5a and 5b).In addition, these models increase precipitation more in the NH, which increases the asymmetry of precipitation changes between the Northern and Southern Hemispheres (Figure 5).This indicates that the changes in precipitation and temperature associated with the warming hole in the SSP5-8.5 at the end of the 21st century are dominated by the influence of greenhouse gases.

Conclusions
We have shown that ESMs with stronger future warming of the warming hole tend to project more warming in the NH by adding more non-radiative fluxes into the atmosphere.The zonal propagation of local thermal forces due to changes in the warming hole leads to more warming in the NH, resulting in asymmetric warming between the hemispheres, with the NH warming more than the SH due to an imbalance in the atmospheric heat flux.Consequently, a stronger warming of the warming hole in the future is associated with a greater global warming  S1 in Supporting Information S1).The relationship between the future change in the warming hole and the ITCZ shift is smaller in CMIP5 than in CMIP6, which could be associated with the improved simulation performance of the North Atlantic subpolar SST in CMIP6 (Borchert et al., 2021).
Changes in the warming hole are associated with AMOC strength (Bellomo et al., 2021;Keil et al., 2020;Liu et al., 2020;Orihuela-Pinto et al., 2022).The AMOC is expected to weaken in the future, and there is a positive correlation between the degree of AMOC weakening and changes in the warming hole, such that less AMOC weakening correlates with more intense subpolar North Atlantic warming (Figure S8a in Supporting Information S1).Therefore, ESMs with weaker AMOC declines tend to project strong warming of the warming hole due to less turbulent flux in the ocean surface (Figure 2b; Figure S8b in Supporting Information S1).However, the correlation between the change in AMOC strength and NH surface temperature (correlation coefficient, 0.31) is much lower than that between the warming hole and NH surface temperature (Figure S8c in Supporting Information S1).The warming hole plays an important role in feedback loops in ocean circulation, such as the decline of the AMOC, and in feedback in the atmosphere-ocean interaction through the turbulent air-sea heat flux feedback (Hausmann et al., 2017).It is necessary to better understand the atmosphere-ocean interactions and ocean dynamics that contribute to the warming hole and the asymmetric temperature and precipitation response.In particular, ocean circulations including the Southern Ocean upwelling and Arctic sea ice melting could contribute to hemispheric asymmetry in future temperature changes (Marshall et al., 2014).Future studies will therefore need to understand the mechanisms of ocean dynamics, such as Arctic sea ice melt and associated ocean circulation in regions adjacent to the warming hole, and the Southern Ocean upwelling, which are essential for predicting future interhemispheric asymmetries.This suggests that continued observations of the warming hole and an increased quantitative understanding of future projections will reduce the uncertainty in future climate projections.
Our results indicate that the warming hole intensity determines the projected interhemispheric surface warming, which is essential for understanding the formation of climate change patterns at basin scales.Therefore, future changes in the warming hole are crucial for generating reliable future climate projections and understanding climate sensitivity in the climate models (Figure S9 in Supporting Information S1) (Meehl et al., 2020).An improved ability to understand the formation mechanism of the warming hole and continuous observations will help to improve the credibility of the simulated projections needed for climate mitigation and adaptation policies.The warming hole is also expected to affect the SH by modulating the rate of warming in the NH, which is associated with the inter-hemispheric different and shift of the ITCZ.Also, it is closely linked to ocean dynamics, such as the decline of the AMOC, and boundary layer coupling (atmospheric feedback and upper-layer Ekman heat transport) with global implications.

Figure 1 .
Figure 1.Future changes in sea surface temperature (SST) and the importance of the warming hole.(a) Multi-model ensemble mean (MMEM) and b, inter-model standard deviation of annual SST changes (shading, °C) in the future (2070-2099) based on 45 Coupled Model Intercomparison Phase 6 Earth System Models (ESMs) under the SSP5-8.5 scenario.Shadings in (a) show the future MMEM SST changes relative to the global mean SST changes (3.28°C) and stipples indicate the area where the ESMs have less than 90% agreement in sign (41 ESMs out of 45 in total).Green boxes indicate the subpolar North Atlantic (45°N-65°N, 50°W-15°W).(c) Regression pattern of future surface temperature changes for the future warming hole (in units of °C°C 1 ).Stipples indicate where the regression is not statistically significant at the 99% confidence level.(d) Statistically significant ( p-value <0.001) relationship between future changes in the warming hole and future Northern Hemisphere surface warming.Shading indicates corresponding global mean surface temperature (GMST) changes and the correlation coefficient between the GMST change and the warming hole change is 0.75 ( p-value <0.001).The purple dashed ellipse in (d) indicates the 5%-95% range, derived from the multivariate normal distribution.The correlation coefficient (corre.coeff.),slope, and p-value obtained by a two-tailed Student's t-test are also provided with a regression line (solid black).

Figure 2 .
Figure 2. Future heat flux and thermal condition changes associated with the future warming hole under SSP5-8.5 scenarios.(a) Regression pattern of future changes in the atmospheric heat flux on changes in the future Northern Hemisphere (NH) surface warming (in units of W m 2 °C 1 ).Green box indicates the subpolar North Atlantic (45°N-65°N, 50°W-15°W).(b) Contribution of heat flux terms to the atmospheric heat flux change in the subpolar North Atlantic.The bars indicate the net atmosphere, net top of the atmosphere, net surface with radiation (longwave plus shortwave), and turbulence (sensible heat plus latent heat) in two groups based on the 10 Earth System Models with the coldest (blue) and warmest warming hole (red).Error bars indicate the range of the 95% confidence interval, and a positive sign indicates downward.(c) Regression pattern of future changes in the meridional mean of geopotential height (GPH) over the subpolar North Atlantic (45°N-65°N) on changes in the future warming hole (in units of m °C 1 ).Green shading indicates the subpolar North Atlantic.The stipples in (a, c) indicate where the correlation is statistically significant at the 99% confidence level.(d) Statistically significant ( pvalue <0.001) relationship between future changes in warming hole and future GPH in the NH at 500 hPa.Shading indicates corresponding changes in the NH surface temperature.The purple dashed ellipse indicates the 5%-95% range, derived from the multivariate normal distribution.The correlation coefficient (Corre.coeff.),slope, and p-value obtained by a two-tailed Student's t-test are also provided with a regression line (solid black).

Figure 3 .
Figure 3. Future changes in the atmospheric circulations associated with future changes in the warming hole under SSP5-8.5 scenarios.(a) Regression pattern of projected changes in air temperature on changes in the future warming hole (in units of °C°C 1 ).(b) Statistically significant ( p-value <0.001) relationship between future changes in warming hole and future surface warming asymmetry between the Northern Hemisphere and Southern Hemisphere.(c) Regression pattern of projected changes in zonal mean atmospheric mass stream-function changes (units of 10 9 kg s 1 °C 1 ) on changes in the future warming hole.d, Statistically significant ( p-value <0.001) relationship between future changes in the warming hole and future shifts of the ITCZ location.In (a and c) stipples indicate where the correlation is statistically significant at the 99% confidence level.Contours indicate the multi-model ensemble mean of pre-industrial (1850-1900) temperature (°C) and mass stream-function (10 10 kg s 1 ).In b and d, shading indicates corresponding changes in atmospheric heat transport between the two hemispheres (positive is southward transport).The purple dashed ellipse indicates the 5%-95% range, derived from the multivariate normal distribution.The correlation coefficient (Corre.coeff.),slope, and p-value obtained by a two-tailed Student's t-test are also provided with a regression line (solid black).

Figure 4 .
Figure 4. Effect of future changes in the warming hole on precipitation.(a) Difference in projected precipitation changes from warm group (warm10) minus cold group (cold10, units of mm d 1 ).Stipples indicate where the difference is statistically significant at the 99% confidence level by two-tailed Student's t-test.(b) Future zonal mean precipitation changes in, the warm10 (red) and the cold10 (blue) based on the future warming hole.Thin lines indicate each value of Earth System Models in two groups.Thick black lines in the bottom indicate the latitude where difference between the two groups is statistically significant at the 99% confidence level by Student's t-test.(c, d) Statistically significant ( p-value <0.001) relationship between future changes in the warming hole and future precipitation in (c) the Northern Hemisphere (NH) and (d) interhemispheric asymmetry.Interhemispheric asymmetry is defined as the difference between the Southern Hemisphere and NH.The purple dashed ellipse indicates the 5%-95% range, derived from the multivariate normal distribution.The correlation coefficient (Corre.coeff.),slope, and p-value obtained by a twotailed Student's t-test are also provided with a regression line (solid black).

Figure 5 .
Figure 5. Future changes in temperature and precipitation associated with future changes in the warming hole under the 1% CO 2 experiment.(a) Statistically significant ( p-value <0.001) relationship between future changes in the warming hole and future Northern Hemisphere (NH) surface warming.Shading indicates the corresponding global mean surface temperature (GMST) changes and the correlation coefficient between the GMST change and the warming hole change is 0.72 ( p-value <0.001).(b) Statistically significant relationship between future changes in the warming hole and surface warming asymmetry between the NH and the Southern Hemisphere (SH).Shading indicates the corresponding ITCZ location changes.(c) Statistically significant relationship between future changes in the warming hole and future NH precipitation changes.Shading indicates the corresponding interhemispheric asymmetry of precipitation changes between the NH and the SH.The purple dashed ellipse indicates the 5%-95% range, derived from the multivariate normal distribution.The correlation coefficient (corre.coeff.),slope, and p-value obtained by a two-tailed Student's t-test are also provided with a regression line (solid black).