Climate models exaggerate greenhouse gas impact on recent interhemispheric temperature patterns and tropical climate

Domain: chemistry
Published: 2026-02-27
Editorial outcome: major_revision

Abstract
The interhemispheric thermal contrast, defined as the mean sea surface temperature difference between the northern and southern hemispheres, crucially influences tropical climate. Climate models show a positive interhemispheric thermal contrast trend since 1950, with more warming in the northern hemisphere compared to the southern hemisphere, contradicting the observed negative trend. Here we show this discrepancy stems from models overestimating greenhouse gas responses via wind-evaporation-sea surface temperature feedback, while anthropogenic and natural aerosols combine to produce the negative trend in observations. Consequently, models with high equilibrium climate sensitivity exhibit larger discrepancies with observations. Despite model failure to reproduce the trend, the modeled multidecadal interhemispheric thermal contrast variability aligns with observations, enabling a constrained estimate of effective radiative forcing due to aerosol-cloud interactions of −0.6±0.3 𝑊/𝑚2, with a "likely" range 57% narrower than the latest IPCC report. Our study further suggests that future northward shifts of the tropical rain belt are likely to be less pronounced than predicted by climate models with high equilibrium climate sensitivity.

Introduction
The interhemispheric thermal contrast (IHTC) — the Northern Hemisphere (NH) mean sea surface temperature (SST) minus the Southern Hemisphere (SH) mean SST — is one of the dominant modes of global SST variability1,2. The IHTC imposes energetic constraints on the Hadley circulation in the tropics2–4 and storm tracks in the extratropics5, which in turn impact billions of people through their influence on various aspects of the global hydrological cycle. Understanding the factors that impact the IHTC and its sensitivity to perturbations in natural and anthropogenic sources has the potential to improve projections of future changes.

Accurately simulating the IHTC remains a significant challenge for climate models. While current state-of-the-art climate models simulate global mean SST reasonably well6, the same models struggle to replicate the observation when calculating the IHTC, the hemispheric contrast, over the past century7,8. Notably, our recent study9 reveals that models in Coupled Model Intercomparison Project Phase 6 (CMIP6) exhibit a systematically positive trend in IHTC that contradicts observations, though the underlying mechanism remains unknown.

The model-data difference in IHTC could stem from differences in the model response to external forcing and internal variability, particularly internal atmospheric and oceanic variability not captured in uninitialized CMIP6 model simulations. For example, coordinated paleoclimate proxies and numerical experiments suggest that the IHTC changes in past climates were mainly caused by the variability of the Atlantic meridional overturning circulation (AMOC)10,11. During 1960-1970s, a large influx of freshwater from the Arctic Ocean led to a salinity anomaly in the subpolar North Atlantic, known as the “Great Salinity Anomaly”, which weakened the deep water formation and potentially the AMOC12, coinciding with an abrupt decrease in the IHTC13,14.

In addition to internal variability, the IHTC change could be driven by various external forcings. In response to greenhouse gases (GHG), climate models suggest that the NH warms faster than the SH due to the land-ocean fraction difference15,16, the asymmetry of sea ice variability between the Arctic and the Antarctic17–19, and delayed warming in the Southern Ocean poleward of 50oS20,21. Additionally, anthropogenic aerosols (AER), predominantly emitted in the NH, are expected to have a greater cooling effect there compared to the SH, which causes an energy imbalance between hemispheres and shifts the tropical rain belt southward7,22–27. However, the cooling effect induced by AER can be offset by warming due to GHG, resulting in a nuanced net effect1. Though insightful, these findings are mainly based on climate models, which have various known biases in physical processes and radiative feedbacks28–32. As such, we hypothesize that discrepancies between climate models and real-world observations in IHTC and associated tropical climate can thus arise from differences in their sensitivities to external forcings, particularly since World War II when anthropogenic forcings have been strong.

Recent studies have improved our understanding of the climatological IHTC bias in CMIP6 models32. In this paper, we investigate factors influencing the transient IHTC since 1950 and address discrepancies between model simulations and observed data. We begin by analyzing statistics, decomposing the IHTC into a linear long-term trend and multidecadal variability to identify drivers of the recent IHTC variability and to uncover clues in the systematic differences between models and data. We conclude by examining the physical processes responsible for the IHTC pattern and the model-data discrepancies. We will show that current climate models reasonably simulate the multidecadal IHTC variability as a response to AER and natural forcings (NAT, such as solar activities and volcanic eruptions), but the modeled long-term trend is proportional to each model’s sensitivity to GHG due to wind-evaporation-SST (WES) feedback33,34 that results in systematic model-data differences in IHTC and its tropical impacts. The consistency between modeled and observed multidecadal IHTC provides observationally-constrained estimates of the real-world effective radiative forcing due to aerosol-cloud interactions (ERFaci, −0.6±0.3 𝑊/𝑚2). However, the discrepancy in long-term trend worsens in models with high equilibrium climate sensitivity (ECS), implying that the real-world ECS may be low35,36.

Results
Systematic bias in SST and tropical climate in CMIP6 models
Building on our previous work9, we begin by revisiting the comparison of simulated post-1950 IHTC with observations in a larger CMIP6 ensemble, which confirms a systematic bias in the IHTC and tropical climate in current state-of-the-art climate models. Fig. 1a depicts the SST trend in the ensemble mean of 542 CMIP6 historical simulations from over 50 models. The ensemble mean is an excellent approximation to the response to external forcings (e.g., GHG, AER, and NAT), as independent representations of internal climate variability in different members are largely cancelled out in the mean through averaging. The ensemble mean shows an enhanced warming in the North Atlantic and North Pacific. As a result, the SST trend between the NH and SH exhibits a positive difference. However, Fig 1b shows that observations are the opposite. The real world shows a relative cooling trend in parts of the North Pacific and Atlantic and a warming trend in most of the SH since 1950. The model-data difference is even more striking in Fig. 1c, which highlights that the modeled SST in the NH warmed faster than observed, whereas it warmed slower than observed in the SH. We examine the time series of the of the IHTC in Fig. 1f. The IHTC is defined as the mean SST difference between NH[0-60oN] and SH[40oS-0], which maximizes quality data coverage while capturing the primary zones of hemispheric asymmetry. We exclude the Southern Ocean (south of 40°S) to avoid regions with sparse pre-satellite observations that may confound the temperature signal. The observations indicate an overall decreasing trend in IHTC with strong multidecadal variability, while the modeled IHTC largely shows a positive trend on top of the multidecadal variability. Fig. 1g summarizes the trend in IHTC for simulations and observations, showing that simulations consistently exhibit a higher trend. In fact, the observations fall in ~1st percentile of the model distribution. We also verified that the IHTC based on the SST difference between [0-60oN] and [60oS-0] show quantitatively consistent results (Supplementary Fig. 1).

Interestingly, the model-observation surface temperature discrepancy only shows up in the interhemispheric SST, as the simulated interhemispheric land surface temperature contrast aligns well with observations and exhibits a response larger in magnitude than the SST contrast (Supplementary Fig. 2). However, slight changes in the interhemispheric SST difference can have dramatic climate impacts in the tropics. In both model and observations, a positive IHTC excites an anomalous Hadley Circulation (HC) in the tropics, which boosts (suppresses) upward motion in the NH (SH) and therefore causes a northward shift of the Intertropical Convergence Zone (ITCZ)4 (Supplementary Fig. 3). Figs. 1d and e underscore the differences in tropical climate between the model and observations, attributed to differences in the IHTC. In the model, the cross-equatorial anomalous HC (see Methods: Definition) is strongly anticorrelated with the IHTC (Fig. 1d), which transports energy to the SH (Supplementary Fig. 3b). Consequently, the intertropical precipitation contrast, as a measure of the ITCZ change (ref22,25, see Methods: Definition), is positively correlated with the IHTC, indicating a northward shift of the ITCZ. The observed HC and ITCZ also covary with the IHTC, which shows an overall opposite trend to the model simulation. Note that the observed IHTC is less correlated with the ITCZ than the Hadley Circulation, particularly after the 2000s. This is probably due to the calculation of the ITCZ relying on the land station precipitation, which is typically noisier but provides observational data prior to the satellite era37.

Largely forced observed IHTC
Given the observed IHTC is around the 1st percentile of the model distribution (Fig. 1g), the model-data difference is highly unlikely to be attributable to internal variability22, which is further confirmed by considering distributions of the 65-year trends from CMIP6 preindustrial control simulations (Supplementary Fig. 4). Therefore, the observed IHTC trend is most likely driven by external forcings, and we further hypothesize that the multidecadal variability of IHTC is also due to the external forcings. To show this, we regress the IHTC onto IHTCs calculated from the single forcing runs:

𝐼𝐻𝑇𝐶 = 𝛽 𝐼𝐻𝑇𝐶 +𝛽 𝐼𝐻𝑇𝐶 +𝛽 𝐼𝐻𝑇𝐶 +𝜖 (1)
𝐺𝐻𝐺 𝐺𝐻𝐺 𝐴𝐸𝑅 𝐴𝐸𝑅 𝑁𝐴𝑇 𝑁𝐴𝑇

in which the IHTC on the left-hand side of the equation is either from observations or CMIP6 all-forcing historical simulations. Eq. 1 assumes the timing of IHTC variability is well simulated in single-forcing runs and nonlinear interactions between forcings are small. As such, linearly scaling and summing single-forcing IHTCs could reproduce the observed IHTC, provided that the observation is primarily driven by external forcings. The potentially muted amplitude of the forced responses in simulations due to low signal-to-noise ratio in large ensembles9 would be compensated by the scaling factor, 𝛽𝑠, when Eq.1 is applied to the observed IHTC.

We first verify this approach by regressing the forced IHTC in CMIP6 (blue curve in Fig. 1f). Fig. 2 legend indicates that the regression closely replicates the forced IHTC in the simulation, with an R2 value approaching 1. The ability of the linear equation (1) to so fully capture all forcings IHTC response indicates that any nonlinear interactions among the individual forcings are negligible. The regressions for observations also show large R2 values, above 0.8 for Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) and Centennial in situ Observation-Based Estimates 2 (COBE2), and 0.9 for the Extended Reconstructed Sea Surface Temperature v5 (ERSSTv5) (See Methods: Observations). This regression result indicates a substantial impact (at least 80%) of the external forcing on the observed IHTC evolution7.

Given the observed IHTC is mainly driven by external forcings, we further hypothesize that the model-data difference arises from the difference in their SST sensitivity to different external forcings. The scaling factors, 𝛽𝑠, in Fig. 2a, illustrate these sensitivities. For the CMIP6 models, the contribution by GHG is nearly twice as large as AER, while the opposite is the case for observations. That is, the modeled IHTC is overly sensitive to the GHG and too muted in response to AER. This raises the next question: Is the bias primarily caused by sensitivity to GHG, AER, or both? The regression based on Eq. 1 cannot provide the answer due to the high collinearity between the modeled IHTCs in GHG and AER runs (with a correlation of -0.75, Supplementary Fig. 5a), which complicates the interpretation of the relative roles of predictors in the regression.

Exaggerated role of GHGs in modeled IHTC
To eliminate the collinearity between the 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 , we perform Principal Component Analysis (PCA) on them, which converts them into two orthogonal modes: 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 (See Methods: PCA). The first PC, 𝐼𝐻𝑇𝐶 , represents a nearly linear trend mode due to the long-term changes in GHG (positive) and AER (negative, Supplementary Fig. 5c), which resembles the leading mode of radiative forcing identified by spatial-temporal analysis in recent studies38–40. The second PC, 𝐼𝐻𝑇𝐶 , represents multidecadal variability dominated by AER (Supplementary Fig. 5d). Now, we regress the modeled and observed IHTC onto the PCs and 𝐼𝐻𝑇𝐶 again:

𝐼𝐻𝑇𝐶 = 𝛽 𝐼𝐻𝑇𝐶 +𝛽 𝐼𝐻𝑇𝐶 +𝛽 𝐼𝐻𝑇𝐶 +𝜖 (Eq. 2)
𝑃𝐶1 𝑃𝐶1 𝑃𝐶2 𝑃𝐶2 𝑁𝐴𝑇 𝑁𝐴𝑇

Fig. 2b presents scaling factors for Eq. 2, where the R2 values remain unchanged. The 𝛽 and 𝛽 for model and observation are consistent within the observational uncertainty, suggesting the AER-induced multidecadal and the NAT-induced IHTC are consistent between model and observation7,22–26,41. However, the modeled 𝛽 has the opposite sign as the observed, suggesting the major model-data difference originates from this mode. The individual timeseries of the three terms in Eq. 2 for model and observation are shown in Fig. 2c-d. The major model-data difference lies in the 𝛽 𝐼𝐻𝑇𝐶 . The positive 𝛽 implies that the long-term trend in IHTC is dominated by GHG in the model, while the negative 𝛽 in the observation suggests the long-term trend in observed IHTC is dominated by AER. The combined 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 account for more than 65% of the total variance in observations, suggesting that the real world is remarkably influenced by the AER and NAT. Notably, the abrupt cooling in the observed IHTC in 1960-1970s is substantially impacted by the Mount Agung volcanic eruptions in NAT22 (Fig. 2d, gray curve). After 1980, the observed IHTC shows a positive trend mostly driven by the multidecadal variability of the AER (Fig. 2d, blue curve), consistent with a dipole SST mode identified in a recent fingerprint analysis23.

Fig. 3 extends the above analysis to each single-model ensemble in CMIP6 to investigate model-to-model spread. We calculate the ensemble average of each model’s IHTC and then perform a regression using Eq. 2. Since PC1 represents a combined AER and GHG effect in the long-term IHTC trend, we scatterplot 𝛽 of each model against its ECS and ERFaci as proxies for the response/sensitivity to GHG and AER, respectively, to investigate the controlling factor for the model spread. The 𝛽 and ECS show a clear linear relationship, indicating that models with high ECS tend to produce a high IHTC trend in the historical period (Fig. 3a). The ERFaci is less correlated with the 𝛽 and combining ECS and ERFaci doesn’t improve their correlation with the 𝛽 either (Supplementary Fig. 6a and c). This implies that, in contrast to the observed IHTC, the systematic positive trend in IHTC of CMIP6 models largely results from their response to GHG. It should be noted that ECS and ERFaci are correlated to some extent in CMIP6 models35,43 (Supplementary Fig. 6a and c).

In contrast, the multidecadal variability in IHTC is regulated by AER, consistent with the observations23,38,44. As shown in Fig. 3b, the 𝛽 and ERFaci are well correlated, and the observation is within the model spread. This implies models with strong ERFaci tend to produce a strong multidecadal variability in IHTC. Though ECS and 𝛽 show a moderate correlation (Supplementary Fig. 6b), combining ECS and ERFaci does not show any improvement in correlation compared to Fig. 3b. In short, the modeled multidecadal variability in IHTC is predominantly influenced by AER, aligning with observations. Conversely, the modeled long-term trend in our analysis period is primarily driven by GHG, contradicting the observed IHTC that is driven by AER and NAT.

IHTC shaped by WES feedback
The strong correlation between ECS and 𝛽 suggests that the discrepancies between models and observations are linked to modeled SST responses to GHG. Energy budget analysis (see Methods: Energy budget analysis for SST trend) indicates that the trend of interhemispheric SST difference in the GHG run is primarily driven by turbulent heat flux, resulting in a positive SST difference between the NH and the SH. Radiative heat fluxes exhibit largely uniform SST response in the two hemispheres, while ocean dynamics produce a negative SST difference between the NH and SH (Supplementary Fig. 7). In mid- and high latitudes of the NH, the amplified air-sea temperature difference enhances turbulent heat uptake and thus warms the ocean surface (Supplementary Fig. 7e and f). In the tropics and subtropics, the SST pattern is regulated by the surface wind speed due to the wind-evaporation-SST (WES) feedback (Supplementary Fig. 7e, also see Fig. 2 in ref34).

The all-forcing CMIP6 surface wind and SST response is dominated by the GHG, rather than the AER (Fig. 4a-c). The WES feedback is more evident in Fig. 4a, which plots the forced trend of surface wind speed with overlaid contours representing SST trend in CMIP6 runs. Areas with reduced wind strength exhibit a relatively warmer SST pattern (solid contours), whereas areas with intensified wind display a relatively colder SST pattern (dashed contours). Mechanistically, weaker winds reduce evaporation, resulting in less turbulent heat flux being removed from the ocean surface, causing a warming anomaly; and vice versa. The WES feedback is even more apparent in the zonal mean profile, where wind speed and SST trends are normalized and show a mostly anticorrelated relationship in tropics and subtropics (Fig. 4a and b, right panel). Previous studies explicitly confirmed the role of the WES-feedback using a partial coupling experiment33, in which the SST change induced by the WES feedback resembles the SST pattern in our CMIP6 GHG runs (Fig 4e in ref33 vs. Fig 4b contours in present manuscript).

In addition to the ensemble mean of CMIP6, we further analyze the model spread of the IHTC in relation to the interhemispheric surface wind speed contrast (IHWC, see methods: Definition) and the air-sea temperature difference in mid-to-high latitudes [40-60oN] of the NH for 51 models. Supplementary Fig. 8a displays that the trends of IHTC and IHWC are well correlated. Most CMIP6 models exhibit a decreasing trend in IHWC and, consequently, an increasing trend in IHTC, which contradicts the observed negative IHTC trend (Fig. 1g and Fig. 3a). However, the relationship between the trend of IHTC and air-sea temperature difference is weaker (Supplementary Fig. 8b). In summary, while both surface wind speed and air-sea temperature difference contribute to the rising trend in the ensemble mean IHTC of CMIP6, surface wind speed has a greater impact on the spread of CMIP6 model results.

The SST trends in AER runs and observations are also substantially impacted by the WES feedback. However, the wind-SST relationship is not readily apparent in the AER and observation due to substantial multidecadal variability in surface wind speed, which may yield different outcomes in the linear trend (Fig. 4c and d). Supplementary Fig. 9 shows the trends in surface wind speed and SST in periods pre- and post-1980 in response to AER, which are anticorrelated between them across the global oceans. Note that the SST and surface wind speed trends are positively correlated in the subpolar North Atlantic resulting from an enhanced AMOC that delays the formation of the warming hole in the model compared to observations45. Supplementary Fig. 10 illustrates similar wind-SST relationship for the observation in both periods, though the observed wind and SST are less correlated in the pre-1980 period. The weakened correlation between wind and SST may result from less reliable sea level pressure observations in the early period, impacting the assimilation of surface wind speed46. However, the pre-1980 observed SST pattern closely resembles the AER-induced SST pattern (Supplementary Fig. 10b and 9b). This confirms the observed IHTC is dominated by AER and NAT (Fig 2d), possibly through the WES feedback (Supplementary Fig. 9a and b).

Implications for ECS and ERFaci
Given the model’s ERFaci and IHTC multidecadal variability are well correlated, we apply emergent constraints based on their linear relationship to estimate the real world ERFaci. The estimated ERFaci is −0.60±0.29 𝑊/𝑚2 (1𝜎, based on ERSSTv5), −0.67±0.30 𝑊/𝑚2 (HadISST), and −0.49±0.30 𝑊/𝑚2 (COBE2) (Fig. 3b and c). These estimates are less negative than the latest IPCC report6 of −1.0±0.7 𝑊/𝑚2, but are consistent with a recent estimation after assessing the actual impact of aerosols on cloud droplet number concentrations47. This difference in the mean value is likely caused by the overall less negative model’s ERFaci in the present study. We obtain these CMIP6 ERFaci estimates from Wang et al.35 and project them onto Smith et al.’s estimates48 due to their high covariance, since ERFaci estimated by Wang et al. is substantially lower (less negative) than those by Smith et al. To verify robustness, we also calculate emergent constraints using ERFaci from Smith et al. This constraint does produce more negative estimates for the ERFaci (Supplementary Fig. 11), though the correlation between ERFaci and 𝛽 is slightly reduced, from -0.76 to -0.63 (p<0.03), probably due to fewer samples. On the other hand, our estimates consistently reduce uncertainty in the ERFaci. Relative to the ‘likely’ range (equivalent to 66 percent confidence limit) of −1.7 to −0.3 𝑊/𝑚2 in IPCC report6, our constraint on ERFaci reduces the uncertainty by about 57%.

We also show that models with a high ECS also have an exaggerated positive IHTC. Though there is a high correlation between ECS and 𝛽 in Fig. 3a, using emergent constraints to estimate the real-word ECS should result in a substantially lower value. This is because the 𝐼𝐻𝑇𝐶 is also influenced by the cooling effect in AER, which suppresses the long-term warming due to GHG. More importantly, the observed IHTC is predominantly affected by AER and NAT, exhibiting a negative trend. That is, the observations and models are not in the same regime, hindering establishment of emergent constraints. Nevertheless, the models with low ECS tend to be more in line with the observations35,36.

Recent studies indicate that the global mean surface temperature observed since 1970 offers limited insight into climate sensitivity and suggest that previous observational constraints36 may skew estimates of the real-world ECS towards lower values49. Our present study suggests that these estimates remain valid when taking into account the SST pattern difference between the NH and SH since 1950. This follows because the modeled NH and SH SST warming rate is set by opposite surface wind speed trends in the two hemispheres (Fig. 4a and Supplementary Fig. 8a), in particular in the tropics and subtropics that cover 50% of the global surface. As such, the global warming rate, or equivalently, ECS, is affected by the surface wind speed. As expected, the trend of IHWC is correlated with the ECS (Supplementary Fig. 8c), indicating that models with high ECS possess a negative IHWC trend (and a positive IHTC trend, Supplementary Fig. 8a). In contrast, a few models with a positive IHWC trend are more in line with observations (with a negative IHTC trend), indicating a low ECS (less than 3.4K) (Supplementary Fig. 8c).

Implications for future tropical climate
Our study has so far suggested that the modeled response to AER aligns with the observed climate23–25, whereas the modeled long-term response of IHTC and tropical climate is dominated by GHG and is not aligned with the observed climate. Models with lower ECS are closer to observations though they still do not simulate the correct sign trend (except two models: #42 INM-CM4-8 and #33 GFDL-ESM4). In this section, we demonstrate the impact of models’ sensitivity to GHG (equivalently, ECS) on future projections of tropical rainfall. A model with a higher ECS generally is associated with in an increased IHTC trend (Fig. 3a). The increased IHTC trend in turn enhances the northward shift of the ITCZ2,22 (Fig. 5a).

Fig. 5b and c examine the spatial rainfall responses from 2020 to 2070 compared to that of 1950-2014 in high and low ECS models, respectively. We select the CanESM5 (#19) and IPSL-CM6A-LR (#45) as high ECS models, and MIROC-ES2L (#50), MIROC6 (#51), and GISS-E2-1-G (#34) as low ECS models. All these models have an ensemble size of at least 30 members. Note that these models have an ERFaci close to the real-world estimation (Fig. 3b). Both sets of models predict a northward shift of the ITCZ under Shared Socioeconomic Pathways 585 (SSP585) scenario. However, this shift is less pronounced in low ECS models, particularly in the Sahel-Amazon region. Similar results are also seen in the SSP245 scenario (Supplementary Fig. 12). A relatively smaller northward shift in the ITCZ, which is less disruptive of large-scale environment in the tropical Atlantic, could be associated with fewer Atlantic hurricanes50,51, though many other factors can also influence hurricane frequency. In closing, we demonstrate that the observed and modeled hemispheric responses to external forcings are quite different due to differences in their sensitivity. Future shifts in tropical climate are reliant on accurately quantifying both hemispheric differences in radiative forcing52, as well as the hemispheric responses to these forcings.

Methods
Definition of various metrics: The interhemispheric thermal contrast (IHTC) is defined as the SST difference between the NH[0-60oN] and the SH[40oS-0], a domain choice that maximizes data coverage quality while capturing the primary zones of hemispheric asymmetry. We exclude the Southern Ocean in the SH due to limited pre-satellite era observations. But including Southern Ocean [60oS-0] does not change current results (Supplementary Fig. 1). SSTs are area weighted to calculate the IHTC. Cross-equatorial Hadley Circulation (HC) is defined as the averaged column mass streamfunction in [15oS-15oN]. Changing the domain does not affect the HC index as the streamfunction is largely uniform in the deep tropics (Supplementary Fig. 3). The Intertropical Convergence Zone (ITCZ) is the difference in precipitation between the Northern Hemisphere (0-30°N) and Southern Hemisphere (30°S-0)25. Note that observed rainfall is mainly over land, so the observed ITCZ represents difference in land precipitation. The modeled ITCZ is also calculated over land to ensure a direct comparison with the observed data. The interhemispheric surface wind speed contrast (IHWC) is defined as the IHTC, but uses surface wind speed in place of SST.

Observations: The SST trend and IHTC is calculated from Extended Reconstructed Sea Surface Temperature version 5 dataset (ERSSTv5)53 from the National Oceanic and Atmospheric Administration (NOAA), Centennial in situ Observation-Based Estimates (COBE)54 SST2 data and the Hadley Centre Sea Ice and SST dataset version 1.1 (HadISST)55. The cross-equatorial Hadley circulation and surface wind speed are calculated from the NOAA 20th century reanalysis version 246, which only assimilates sea level pressure and SST. We specifically selected the 20th century reanalysis because other reanalyses that assimilate air observations show biased Hadley Circulation responses56. The ITCZ is calculated from the Global Precipitation Climatology Centre (GPCC)37, which covers only land but includes data for our entire study period whereas precipitation data over the ocean is inadequate in the pre-satellite period.

Model data: Model SSTs, precipitation and wind were taken from the CMIP657 archive: https://esgf-node.llnl.gov/projects/cmip6/. The forced response as the ensemble mean was then calculated by averaging 542 ensemble members from the 57 models (Supplementary Data 1). We include as many CMIP6 model simulations as possible without cherry-picking. To quantify the internal variability, the first member (r1i1p1f1) of the pre-industrial control runs was also downloaded from 34 models. For pre-industrial control simulations, we first detrended the entire time series for each model to remove long-term drift. Next, we randomly selected a continuous 65-year time series and calculated its trend. This process was repeated 100 times for each model (with replacement), resulting in a total of 3400 realizations. We also obtained these variables from DAMIP58 (https://damip.lbl.gov) to quantify the role of GHG (hist_GHG), AER (hist_aer) and NAT (hist_nat). All model data are linearly interpolated to a common grid (2ox1o, lat x lon). Model’s ECS and ERFaci are taken from ref35,48.

PCA: We conducted PCA onto the 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 to remove their collinearity and identify the main patterns of variability in GHG and AER runs. The relationship between the 𝐼𝐻𝑇𝐶 , 𝐼𝐻𝑇𝐶 , 𝐼𝐻𝑇𝐶 , and 𝐼𝐻𝑇𝐶 could be represented in matrix form:

𝐼𝐻𝑇𝐶 𝐼𝐻𝑇𝐶
[ 𝐺𝐻𝐺] = 𝐿[ 𝑃𝐶1]
𝐼𝐻𝑇𝐶 𝐼𝐻𝑇𝐶
𝐴𝐸𝑅 𝑃𝐶2

where 𝐿 is the loading matrix of the analysis that has been normalized to unit variance so 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 have unit 𝐾. Rewriting the equation above:
𝑃𝐶1 𝑃𝐶2

𝐼𝐻𝑇𝐶 𝐼𝐻𝑇𝐶
[ 𝑃𝐶1] = 𝐿−1[ 𝐺𝐻𝐺]
𝐼𝐻𝑇𝐶 𝐼𝐻𝑇𝐶
𝑃𝐶2 𝐴𝐸𝑅

0.708 −0.706
where 𝐿−1 = [ ]. At face value, 𝐼𝐻𝑇𝐶 is the sum of 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 .
0.706 0.708 𝑃𝐶2 𝐺𝐻𝐺 𝐴𝐸𝑅

The long-term trends of 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 cancel out because they have opposite signs, leaving the multidecadal variability dominated by AER. 𝐼𝐻𝑇𝐶 is the difference between the 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 , primarily influenced by their long-term trends. The successful separation of the collinearity between 𝐼𝐻𝑇𝐶 and 𝐼𝐻𝑇𝐶 in PCA results is due to the dominance of aerosols in the multidecadal IHTC in our study period. The PCA results are robust with +/-10 years of start year (e.g., 1940-2014), while the approach becomes less applicable if the period starts as early as 1900 prior to the rapid rise of the external forcing or after 1980 since the Clean Air Act. Since 1980, the lack of multi-decadal variability in aerosols has led to both aerosols and greenhouse gases contributing to an increasing trend in IHTC. This makes it challenging for PCA to differentiate between their individual effects.

Energy budget analysis for SST trend: We follow the methodology developed in ref 59,60 to calculate the mixed layer energy budget and SST trend in model simulations. We start from the energy budget for the mixed layer:

𝜕𝑇
𝜌𝐶 𝐻 = 𝑄 +𝑄 +𝑄 +𝑄 +𝑂𝐻𝑇
𝑝 𝜕𝑡 𝑆𝑊 𝐿𝑊 𝐿𝐻 𝑆𝐻

in which the tendency term on the left-hand side is the heat storage of ocean mixed layer. 𝜌,𝐶 ,𝐻, and 𝑇 are density of ocean, specific heat of ocean, mixed-layer depth of ocean, and mixed-layer temperature of ocean, respectively. The tendency term is fed by the energy uptake via net surface shortwave radiation 𝑄 , net surface longwave radiation 𝑄 , latent heat flux 𝑄 , sensible heat flux 𝑄 , and the convergence of ocean energy transports 𝑂𝐻𝑇, which includes oceanic processes across all scales and is not trivial to calculate using CMIP6 outputs. However, in the historical period, the heat storage tendency term is an order smaller than other terms on the right-hand side34, such that neglecting the tendency term and calculating the linear trend of the energy equation above, we are able to estimate the Δ𝑂𝐻𝑇 as a residual:

0 = Δ𝑄 +Δ𝑄 +Δ𝑄 +Δ𝑄 +Δ𝑂𝐻𝑇
𝑆𝑊 𝐿𝑊 𝐿𝐻 𝑆𝐻

where the Δ denotes time tendency. The temperature dependence of latent heat could be linearized:

Δ𝑄𝑇 = 𝛼𝑄̅ Δ𝑇
𝐿𝐻 𝐿𝐻

where 𝛼 = 𝐿 ; 𝑅 = 461 𝐽𝐾−1𝑘𝑔−1 is the gas constant for water vapor; 𝐿 = 2.5×106 𝐽/𝑘𝑔 is latent heat of evaporation. Other dependence of latent heat could be calculated as residual,
𝑅𝑣𝑇2 𝑣

Δ𝑄𝑜𝑡ℎ𝑒𝑟𝑠 = Δ𝑄 − Δ𝑄𝑇
𝐿𝐻 𝐿𝐻 𝐿𝐻

which is able to be further decomposed as in ref 61 to attribute to changes in surface wind speed, relative humidity, and air-sea temperature difference.

Combine them together, we have a diagnostic equation for mixed layer temperature tendency, equivalent to SST tendency:

Δ𝑄 +Δ𝑄 +Δ𝑄𝑜𝑡ℎ𝑒𝑟𝑠 +Δ𝑄 +Δ𝑂𝐻𝑇
𝑆𝑊 𝐿𝑊 𝐿𝐻 𝑆𝐻
Δ𝑇 = 
𝛼𝑄̅
𝐿𝐻

Supplementary Fig. 8 shows the NH and SH Δ𝑇 difference is dominated by the Δ𝑄𝑜𝑡ℎ𝑒𝑟𝑠 and Δ𝑄 term, which are driven by changes in air-sea temperature difference in high latitudes and surface wind speed in tropics and subtropics.

Emergent constraints on ERFaci: Least-squares linear regressions are performed on the ERFaci and 𝛽 . The probability density functions (PDFs) of the real-world ERFaci are then estimated based on the previously established framework62.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study focuses on the systematic biases of CMIP6 climate models in simulating the interhemispheric thermal contrast (IHTC). The article is scientifically interesting because it provides new explanations for the contrasting trends observed between model simulations and IHTC observations, disentangles the imprints of greenhouse gases and aerosol particles, and improves the estimation of key climate parameters. These results are highly impactful because they clarify the differences between observations and models and reduce the uncertainty in the estimated effective radiative forcing due to aerosol cloud interactions. In addition, The last section also demonstrate the impact of model’s sensitivity to GHG on future projections of tropical rainfall. The article is based on a large number of datasets, including reanalysis and a large ensemble of General Circulation Model (GCMs) outputs. The methodology employed is novel, particularly in its use of PCA to remove collinearity between aerosols and greenhouse gases.The article is well constructed and well presented. However, I have some comments that should be considered.\nGeneral comments:\n1.The authors define IHTC as the sea surface temperature difference between the Northern Hemisphere (0-60°N) and the Southern Hemisphere (40°S-0), explicitly excluding the 40°S-60°S region due to the limited observational data before the satellite era. However, the paper also notes that the delayed warming of the Southern Ocean south of 50°S affects the IHTC. It is therefore worth examining whether this definition could influence the study’s results.\n2.The authors employ the PCA to remove collinearity between GHG and AER. However, PCA results are sensitive to the temporal length and variability of the input data. It is unclear whether shortening or extending the analysis period could lead to substantial changes in the explained variance of and , which may in turn affect the robustness and reliability of the findings. The authors should clarify or assess the potential impact of this issue.\n3.Current models overestimate the recent interhemispheric temperature difference, leading to discrepancies between simulations and observations, while also highlighting the role of anthropogenic aerosols and showing that the models can capture the effects of this forcing. Would using low ECS models significantly reduce the discrepancies between simulated and observed results?\n4.In estimating , although an emergent constraint approach based on the linear relationship between model and was employed, the stability of this linear relationship has not been verified. it remains unclear whether the linear correlation between model and would significantly decrease if the analysis period were shortened from 1950–2014 to 1980–2014, when satellite observations are more complete.\n5.In comparing the high- and low-ECS models (e.g., CanESM5, IPSL-CM6A-LR, and MIROC-ES2L), this study notes that their effective radiative forcing due to aerosol–cloud interactions () is close to observational estimates. However, the analysis focuses only on the similarity of results (though some discrepancies remain in Fig. 3a) and does not clarify whether these models share consistent parameterization schemes for aerosol indirect effects. Consequently, it is difficult to rule out the possibility that some models may overestimate the impact of aerosols on cloud albedo, thereby biasing the simulated ITCZ shift. Moreover, the study does not verify whether low-ECS models employing different aerosol parameterizations would still exhibit a weaker northward ITCZ displacement than high-ECS models. Meanwhile, Since the study is based solely on the SSP585 high-emission scenario and does not consider the SSP245 intermediate-emission scenario, is the conclusion that “low ECS models exhibit a weaker northward shift of the ITCZ in the future” still valid?\nSpecific comments:\n1.Line 26, is→are\n2.Line 28, model→models\n3.Line 28, onto→on\n4.Line 85, an→a\n5.Line 130, equation→the equation\n6.Line 139, observation→observations\n7.Line 170, account→accounts\n8.Line 171, observation→observations\n9.Line 204, In tropics and subtropics→In the tropics and subtropics\n10.Line 301, The full term should be provided when it is first mentioned in the text (SSP585).\n11.Line 369, loading→loading matrix", "reviewer_2": "Review for “Climate models exaggerate the impact of greenhouse gases on recent interhemispheric temperature contrast and tropical climate” by He et al.\nThe study utilized the SST difference between north and south hemisphere as a proxy to examine the tropical climate variability. The authors compared the ensemble CMIP6 values to those from the observations to investigate the underlaying mechanisms generating the differences. The topic of the study is of interest to the community; however, the manuscript is cumbersome to read, with no definitions for most of the terms and large amount of grammar errors. Please see some of my line-by-line comments below for examples. In particular, the IHTC is used as the main proxy/mode for the whole study, but not enough detail is discussed in the manuscript for this choice and the calculation. In addition, no justification, reference, or evaluation for the choice of observations or simulations from CMIP6 are given. As the quality of the manuscript does not reach the standard for Nature Communications, I’d suggest an extensive restructuring of the manuscript and a resubmission.\nLine 18-20: Does the IHTC influences the tropical climate, or does the tropical climate also modulate the IHTC?\nLine 20: Please remove ‘Current’, as CMIP7 is expected to be released later this year.\nLine 21-22: Please rephrase this sentence, as it is hard to understand. For example, what exactly are the “trends”? What do the authors mean by “higher”?\nLine 24: Does ‘overly dominant role’ mean an overestimation in the simulated greenhouse gas contribution here?\nLine 25-26: Similar to line 21-22, it is unclear what the ‘trend’ and 'negative' are discussed here.\nLine 31: Please be more specific about the ‘shifts’ for tropical rain belt.\n---\nLine 37: Are there any evidence that the tropical storms are not constrained by the IHTC?\nLine 39: Please define “perturbations”.\nLine 43: Please rewrite “the its variability”.\nLine 42-43: This statement is hard to follow. Why would calculating the IHTC and reversing the sign impact the simulations themselves and make the mechanisms uncertain?\nLine 44: Rewrite “A recent our study”.\nLine 50: Define the “Great Salinity Anomaly”.\nLine 60: In which direct does the rain belt shift?\nLine 63-66: Is this statement a speculation or are there any references to support it?\n---\nLine 142: Please explain how “observed IHTC is mainly forced”."}, "author_response": "We appreciate positive and constructive comments provided by reviewer 1.\nGeneral comments:\n1.The authors define IHTC as the sea surface temperature diJerence between the Northern Hemisphere (0-60°N) and the Southern Hemisphere (40°S-0), explicitly excluding the 40°S-60°S region due to the limited observational data before the satellite era. However, the paper also notes that the delayed warming of the Southern Ocean south of 50°S aJects the IHTC. It is therefore worth examining whether this definition could influence the study’s results.\nGood question. We included another figure as Supplementary Fig.1 (Fig. R1), which shows the IHTC calculated between 60oS and 60oN. The results are quantitively similar to the results with the IHTC defined by 40oS-60oN. The observed IHTC trend now falls at the 4.4th percentile of those in model simulations, and the pattern of Southern Hemisphere cooling and Northern Hemisphere warming in the model-data diJerence remains consistent.\nRelevant discussions are added in the main context (near line 101-102)\nFig. R1. Systematic biases in CMIP6 simulated SST trend from 1950 to 2014 in 60oS – 60oN. a, SST trend of the ensemble mean of CMIP6 simulations; b, the same as a, but for observation (ERSSTv5); c, diJerence between the a and b; d, boxplot depicting the distribution of IHTC trends in CMIP6 all-forcing, where the edges of the box indicate the first and third quartiles and the whiskers extend to the most extreme data point within 1.5 times the interquartile range. 'N' denotes the ensemble size for each simulation. The observational trend is represented by the red line (ERSSTv5), which is at the ~4.4th percentile of the CMIP6 simulations. The IHTC is defined as the SST diJerence between NH[0-60oN] and SH[60oS-0].\n2.The authors employ the PCA to remove collinearity between GHG and AER. However, PCA results are sensitive to the temporal length and variability of the input data. It is unclear whether shortening or extending the analysis period could lead to substantial changes in the explained variance of and , which may in turn aJect the robustness and reliability of the findings. The authors should clarify or assess the potential impact of this issue.\nGreat point! The success of PCA to disentangle the eJect of greenhouse gases (GHG) and anthropogenetic aerosols (AER) requires that the AER dominates the multidecadal variability. The aerosol emissions increased from 1950-1980 before the Clean Air Act, and decreased afterwards, resulting in multidecadal variability in the IHTC. Here we performed PCA in 1940-2014, the results of which are very similar to those in 1950-2014 (Fig. R2). However, if we extend the analyzed period back to, for example, 1900, the PCA results change (Fig. R3) and the interpretation becomes more complicated.\nLikewise, if we restrict the PCA to 1980-2014, because there are no multidecadal variations in AER, both AER and GHG cause an increasing trend in IHTC, and the PCA cannot distinguish between eJects of GHG and AER. This is also related to your comment #4.\nWe intentionally focus our analysis on the post-1950 period when external radiative forcings significantly increased (He et al., 2023; (IPCC), 2023). Before this time, when the forcing was weaker and less accurately quantified, the likelihood of a forced IHTC is lower in real world. As a result, while even we could explain the PCs, the observed IHTC cannot be explained by PCs in the regression. Relevant discussions have been added into the Methods section (near line 392-397).\nFig. R2 PCA on IHTCs in AER and GHG runs in 1940-2014. a, forced IHTC due to AER and GHG. b, PCs of IHTC in a. c, PC1 and linear trend of the IHTC in AER and GHG. d, PC2 and detrended (or multidecadal) IHTC in AER and GHG. The loading has been normalized to unit variance, so the PC shown here has absolute units.\nFig. R3 Same as Fig. R2, but for period of 1900-2014.\n3.Current models overestimate the recent interhemispheric temperature diJerence, leading to discrepancies between simulations and observations, while also highlighting the role of anthropogenic aerosols and showing that the models can capture the eJects of this forcing. Would using low ECS models significantly reduce the discrepancies between simulated and observed results?\nLow-ECS models generally align more closely with observations in terms of IHTC than high-ECS models, as depicted in Fig 3a. However, most low-ECS models still exhibit a positive trend from 1950 to 2014. Only two models show a negative trend and indeed they have low ECS values (#42 INM-CM4-8 with ECS of 1.8 and #33 GFDL-ESM4 with ECS of 2.6).\n4.In estimating , although an emergent constraint approach based on the linear relationship between model and was employed, the stability of this linear relationship has not been verified. it remains unclear whether the linear correlation between model and would significantly decrease if the analysis period were shortened from 1950–2014 to 1980–2014, when satellite observations are more complete.\nThis is a good question and also related to the comment #2. Actually, it is ineJective to conduct the emergent constraint analysis for the period of 1980-2014 due to the positive trend in IHTCs induced by both AER and GHG after 1980. This trend shared by both forcings hinders PCA from separating the collinearity between GHG and AER, making the scaling factors (a.k.a. regression coeJicients) unreliable even though regression can still be performed.\nThe separation of greenhouse gases and aerosols in IHTC after 1980 may be feasible by analyzing the spatial pattern of surface temperature. Deser et al. (2020) analyzed the trend of sea surface temperatures in single-forcing runs and compared them spatially with ensemble mean to evaluate the relative importance of greenhouse gas and aerosol forcings in diJerent periods. While this topic is beyond the scope of our current study, it presents an intriguing topic for future research.\n5.In comparing the high- and low-ECS models (e.g., CanESM5, IPSL-CM6A-LR, and MIROC-ES2L), this study notes that their eJective radiative forcing due to aerosol–cloud interactions () is close to observational estimates. However, the analysis focuses only on the similarity of results (though some discrepancies remain in Fig. 3a) and does not clarify whether these models share consistent parameterization schemes for aerosol indirect eJects. Consequently, it is diJicult to rule out the possibility that some models may overestimate the impact of aerosols on cloud albedo, thereby biasing the simulated ITCZ shift. Moreover, the study does not verify whether low-ECS models employing diJerent aerosol parameterizations would still exhibit a weaker northward ITCZ displacement than high-ECS models. Meanwhile, Since the study is based solely on the SSP585 high-emission scenario and does not consider the SSP245 intermediate-emission scenario, is the conclusion that “low ECS models exhibit a weaker northward shift of the ITCZ in the future” still valid?\nIn this revision, we compare the same models in both high- and low-ECS groups under the SSP245 scenario. The conclusion remains consistent, although the response of rainfall anomalies is weaker than in the SSP585 scenario, as expected (Fig. R4). Fig. R4 has been added as Supplementary Fig 13. Relevant discussions have been added in our revision (near line 308).\nWe agree that model diJerences in aerosol parameterization scheme could have an impact on cloud albedo that could alter low clouds, the IHTC, and ITCZ shifts. This is an interesting question, but it is beyond the scope of the present study. We expect to follow up on this topic in a subsequent study. If we investigate diJerences between individual models, we will not be able to attribute diJerences solely to the aerosol parameterization because we cannot rule out that something else about the model is responsible for the diJerences. This demands a more elaborate study than will fit within the present paper.\nFig. R4 a, Precipitation response in high ECS models (CanESM5 and IPSL-CM6A-LR) for the period 2020–2070 in the SSP2-45 scenario, relative to their climatology of 1950–2014. b, as in a, but for low ECS models (MIROC6, MIROC-ES2L, and GISS-E2-1-G).\nSpecific comments:\n1.Line 26, is→are\nIt should be “is”\n2.Line 28, model→models\nFixed\n3.Line 28, onto→on\nFixed\n4.Line 85, an→a\nFixed\n5.Line 130, equation→the equation\nFixed\n6.Line 139, observation→observations\nFixed.\n7.Line 170, account→accounts\nIt should be “account”\n8.Line 171, observation→observations\nFixed.\n9.Line 204, In tropics and subtropics→In the tropics and subtropics\nFixed.\n10.Line 301, The full term should be provided when it is first mentioned in the text (SSP585).\nFixed.\n11.Line 369, loading→loading matrix\nFixed.\nReviewer #2 (Remarks to the Author):\nReview for “Climate models exaggerate the impact of greenhouse gases on recent interhemispheric temperature contrast and tropical climate” by He et al.\nThe study utilized the SST diJerence between north and south hemisphere as a proxy to examine the tropical climate variability. The authors compared the ensemble CMIP6 values to those from the observations to investigate the underlaying mechanisms generating the diJerences. The topic of the study is of interest to the community; however, the manuscript is cumbersome to read, with no definitions for most of the terms and large amount of grammar errors. Please see some of my line-by-line comments below for examples. In particular, the IHTC is used as the main proxy/mode for the whole study, but not enough detail is discussed in the manuscript for this choice and the calculation. In addition, no justification, reference, or evaluation for the choice of observations or simulations from CMIP6 are given. As the quality of the manuscript does not reach the standard for Nature Communications, I’d suggest an extensive restructuring of the manuscript and a resubmission.\nWe appreciate this reviewer’s critical and helpful comments. We have made thorough edits to correct grammar errors and elaborated more on the definition of interhemispheric thermal contrast (IHTC) in the main text (near line 93-96). The IHTC is defined as the SST diJerence between the NH[0-60oN] and the SH[40oS-0], a domain choice that maximizes data coverage quality while capturing the primary zones of hemispheric asymmetry. We exclude the Southern Ocean in the SH due to limited pre-satellite era observations. In response to your suggestion and Reviewer 1’s request, we expanded our investigation of IHTC to include the Southern Ocean (IHTC = SST[0-60oN] – SST[60oS-0]). Fig. R1 shows consistent results with our definition above (Note that Fig. R1 has been added as Supplementary Fig. 1). Relevant discussions have been included near line 101-102.\nOther definitions such as cross-equatorial Hadley circulation (HC) and Intertropical Convergence Zone (ITCZ) remain in the Methods section for clarity. We also keep description of observations and model simulations in the Methods section to allow a more concise manuscript. Below are the full description and rationale for these definitions, observations, and model simulations in our Methods section.\nDefinitions of various metrics: The interhemispheric thermal contrast (IHTC) is defined as the SST diJerence between the NH[0-60oN] and the SH[40oS-0], a domain choice that maximizes data coverage quality while capturing the primary zones of hemispheric asymmetry. We exclude the Southern Ocean in the SH due to limited pre-satellite era observations. But including Southern Ocean [60oS-0] doesn’t change current results (Supplementary Fig. 1). Cross-equatorial Hadley Circulation (HC) is defined as the averaged column mass streamfunction in [15oS-15oN]. Changing the domain doesn’t aJect the HC index as the streamfunction is largely uniform in the deep tropics (Supplementary Fig. 3). The Intertropical Convergence Zone (ITCZ) is the diJerence in precipitation between the Northern Hemisphere (0-30°N) and Southern Hemisphere (30°S-0) (Hwang et al., 2013). Note that observed rainfall is mainly over land, so the observed ITCZ represents diJerence in land precipitation. The modeled ITCZ is also calculated over land to ensure a direct comparison with the observed data. The interhemispheric surface wind speed contrast (IHWC) is defined as the IHTC, but for the surface wind speed.\nObservations: The SST trend and IHTC is calculated from Extended Reconstructed Sea Surface Temperature version 5 dataset (ERSSTv5) (Huang et al., 2017) from the National Oceanic and Atmospheric Administration (NOAA), Centennial in situ Observation-Based Estimates (COBE) (Hirahara et al., 2014) SST2 data and the Hadley Centre Sea Ice and SST dataset version 1.1 (HadISST) (Rayner et al., 2003). The cross-equatorial Hadley circulation and surface wind speed are calculated from the NOAA 20th century reanalysis version 2 (Compo et al., 2011), which only assimilates sea level pressure and SST. We specifically selected the 20th century reanalysis because other reanalyses that assimilate air observations show biased Hadley Circulation responses (Chemke & Polvani, 2019). The ITCZ is calculated from the Global Precipitation Climatology Centre (GPCC) (Becker et al., 2013), which covers only land but includes data for our entire study period whereas precipitation data over the ocean is inadequate in the pre-satellite period.\nModel data: Model SSTs, precipitation and wind were taken from the CMIP6 (Eyring et al., 2016) archive: https://esgf-node.llnl.gov/projects/cmip6/. The forced response as the ensemble mean was then calculated by averaging 542 ensemble members from the 57 models (Supplementary Table 1). We include as many CMIP6 model simulations as possible without cherry-picking. To quantify the internal variability, the first member (r1i1p1f1) of the pre-industrial control runs was also downloaded from 34 models. We also obtained these variables from DAMIP (Gillett et al., 2016) (https://damip.lbl.gov) to quantify the role of GHG (hist_GHG), AER (hist_aer) and NAT (hist_nat). Model’s ECS and ERFaci are taken from Smith et al. (2020) and Wang et al. (2021).\nLine 18-20: Does the IHTC influences the tropical climate, or does the tropical climate also modulate the IHTC?\nGood point. While we acknowledge that tropical climate variations can feedback onto IHTC through tropical-extratropical interactions, our analysis demonstrates that IHTC variability since 1950 is predominantly driven by external forcings. Specifically, we show that >80% of observed IHTC variance is explained by external forcings (R² > 0.8, Figure 2), with aerosols—concentrated primarily in the extratropical NH—playing a dominant role. This externally-forced IHTC then drives the tropical climate response (e.g., shifts in the ITCZ) through well-established energetic constraints on cross-equatorial heat transport. Our study cannot rule out the possibility that to some extent the external forcing drives the tropics, which then aJect the IHTC, but regardless, external forcing is still the driver.\nLine 20: Please remove ‘Current’, as CMIP7 is expected to be released later this year.\nFixed.\nLine 21-22: Please rephrase this sentence, as it is hard to understand. For example, what exactly are the “trends”? What do the authors mean by “higher”?\nFixed. We’ve rewritten the sentence.\nLine 24: Does ‘overly dominant role’ mean an overestimation in the simulated greenhouse gas contribution here?\nYes. We’ve rewritten the sentence.\nLine 25-26: Similar to line 21-22, it is unclear what the ‘trend’ and 'negative' are discussed here.\nWe’ve rewritten the sentence.\nLine 31: Please be more specific about the ‘shifts’ for tropical rain belt.\nFixed. Northward shift\n---\nLine 37: Are there any evidence that the tropical storms are not constrained by the IHTC?\nIHTC certainly aJects tropical storms. Here, we try to articulate that the IHTC aJects both tropical circulation (Hadley Cell) and extratropical circulation (storm tracks), in turn influencing various aspects of the global hydrological cycle.\nLine 39: Please define “perturbations”.\nFixed.\nLine 43: Please rewrite “the its variability”.\nFixed.\nLine 42-43: This statement is hard to follow. Why would calculating the IHTC and reversing the sign impact the simulations themselves and make the mechanisms uncertain?\nWe rewrote the relevant parts in line 37-42.\nLine 44: Rewrite “A recent our study”.\nFixed.\nLine 50: Define the “Great Salinity Anomaly”.\nFixed.\nLine 60: In which direct does the rain belt shift?\nFixed. Southward.\nLine 63-66: Is this statement a speculation or are there any references to support it?\nLine 63-66 is “Discrepancies between climate models and real-world observations in IHTC and associated tropical climate can thus arise due to diJerences in their sensitivities to external forcings, particularly since World War II when anthropogenic forcings have been strong.\nThis statement is a hypothesis, and the remaining part of the paper is proving this point. The observed IHTC is driven by anthropogenetic aerosols (AER), while the modeled IHTC is dominated by greenhouse gases (GHG) due to the high sensitivity of CMIP6 models to GHG. This statement only holds when external forcings are strong enough (post-World War II era), such that diJerences in sensitivity may translate to diJerent responses in observed and simulated IHTC.\n---\nLine 142: Please explain how “observed IHTC is mainly forced”.\nThe paragraph (line 141-147 in our revised manuscript) before line 142 (line 148 in current revision) shows that at least 80% of observed IHTC can be explained by external forcings. This is supported by Fig. 2 in our manuscript.\nWe rewrote the sentence “Given the observed IHTC is mainly driven by external forcing”\nReviewer #2 (Remarks to code availability):\nNo code is available yet, as the authors stated that the code will be made open source upon acceptance.\nThe code was included as a supplementary zip file in our initial submission and has now been uploaded to a permanent repository in our revision. We apologize for any misunderstanding caused by our statement."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The paper compared the ensemble CMIP6 values to those from the observations to investigate the underlaying mechanisms generating the differences. The research approach is clear, and the content is comprehensive. At present, the authors have satisfactorily addressed all of my comments. I have just a few notes they should take into account before further consideration. I also strongly agree with the second reviewer's comments.The definitions of several metrics are not sufficiently clear, and some data processing procedures lack detailed descriptions, which hinders a more comprehensive understanding of the study. I recommend that these elements be further clarified and elaborated upon in the revised manuscript.\n1.line 43：“The model-data difference in IHTC could stem from several factors.”->The model-data difference in IHTC could stem from differences in the model’s response to external forcing and internal variability. This seems to directly introduce the subject. Please consider this.\n2.line 86: The term \"external forcing\" is vaguely defined. Specify the main contributors (e.g., greenhouse gases, ozone depletion), or refer to CMIP6 protocol documentation for the historical forcings used. For completeness, the manuscript should also clarify why the multi-model ensemble mean can represent external forcing, as this point is not explicitly addressed.\n3.line 143:The external forcing accounts for at least 80%. Is this value obtained directly from the ratio of the multi-model ensemble mean to the observations, or is it derived from the regression coefficients?\n4.line 117-120: Please cite relevant references to provide supporting evidence for this assumption.\n5.Line 212,226:Did the authors perform significance tests when calculating the trends? In particular, Fig. 4 and Supplementary Fig. 9 do not provide any information on statistical significance, and adding such information would make the analysis more appropriate. In addition, please also include information on statistical significance when computing the correlation coefficients.The manuscript lacks essential information regarding the statistical significance of the results.\n6.Line 275: The βPC1 values derived from the reanalysis data exhibit substantial uncertainties. Does such a constraint still hold meaningful value? In addition, I do not quite understand the statement “This ECS could serve as the upper bound for the real-world ECS”. Is this because the model tends to overestimate IHTC?\n7.line 373:Could the manuscript provide more details on the data processing, such as whether the model data were interpolated? Did the calculation of the time series include latitudinal weighting? How is the picontrol data segmented? Do these data segments overlap? Even if some processes are already presented elsewhere in the manuscript, for completeness, I recommend that they be consolidated and presented in the Data section.\n8.line 397: Here, it would be helpful to explain why the applicability is reduced.As you explained, due to the absence of multi-decadal variability in aerosols during this period, both aerosols and greenhouse gases drive an increasing trend in IHTC, making it impossible for PCA to distinguish their individual effects.", "reviewer_2": "Review for He et al.: Climate models exaggerate the impact of greenhouse gases on recent interhemispheric temperature patterns and tropical climate\nI appreciate the authors’ detailed replies to my previous comments. The writing has been largely improved in the revised manuscript. I have some follow-up questions and comments, especially on how the GHG and AER contributing terms are separated and how PCs are linked to the IHTC-related variability. Please see below for both major and minor comments.\nMajor comments:\nEQ1/Fig2: (Line 129-132) are there studies or analysis to support the ignoring of the interaction between the two forcings? How are the interaction terms excluded?\nEQ2/supplementary Fig 5: According to the analysis and discussion, the conclusions seem to be somewhat period dependent and constrained to the impacts from 1950-1980. While I understand that the authors want to focus on the multidecadal timescales (using 1950-2014 instead of 1950-1980 only) to exclude the collinearity between GHG and AER by applying PCA, I am having a hard time to justify the links between the individual GHG/AER “long-term trend” and the representation of factors driving the PCs for the focused period (1950-2014). How the GHG contribution is separated from AER with the focused period PCA should be better described, especially when the AER trend is no longer negative after 1980 in runs (supplementary Figure 5) and the impacts of WES feedback on simulations vs observation can also be period dependent (supplementary Figure 10 and 11; Line 244-248).\nMinor comments:\nLine 17-19: Thank you for the reply to my previous comment, it makes sense. However, as the first sentence in the abstract, the readers might not understand it as the conclusion of this study. Please consider rephrase the sentence.\nLine 51-55: Given that the external forcing (especially GHG) is the main driver in simulations, are there studies quantifying their contributions from “land-ocean fraction difference” vs “asymmetric of Arctic and Antarctic sea ice”? Especially the Antarctic/Arctic regions are excluded from the IHTC definition in this study.\nLine 133-134: “the observation is primarily forced.” Same as my comment from the previous review (for the now modified line 144), this sentence/wording is confusing.\nLine 172-173: Does this statement still hold after 1980?\nLine 187-189: Please consider rewriting this part, as the implication may not be clear to the readers when PC1 represents a combined AER and GHG effect (line 181) and their interaction is ignored.\nLine 244-248: Is this statement only referring to the pre-1980 results? In addition, without the GHG-related SST pattern during the same period, it is hard to confirm that the IHTC is dominated by AER and NAT just based on the similarity between observed SST and AER-induced SST patterns."}, "author_response": "We appreciate the reviewer's positive and constructive feedback, which improved the clarity of our manuscript. We expanded on the definition and data processing procedures in our revision.\n1.line 43：“The model-data difference in IHTC could stem from several factors.”->The model-data difference in IHTC could stem from differences in the model’s response to external forcing and internal variability. This seems to directly introduce the subject. Please consider this.\nAdopted.\n2.line 86: The term \"external forcing\" is vaguely defined. Specify the main contributors (e.g., greenhouse gases, ozone depletion), or refer to CMIP6 protocol documentation for the historical forcings used. For completeness, the manuscript should also clarify why the multi-model ensemble mean can represent external forcing, as this point is not explicitly addressed.\nWe added more descriptions near line 85: “The ensemble mean is an excellent approximation to the response to external forcings (e.g., GHG, AER, and NAT), as independent representations of internal climate variability in different members are largely cancelled out in the mean through averaging.”\n3.line 143:The external forcing accounts for at least 80%. Is this value obtained directly from the ratio of the multi-model ensemble mean to the observations, or is it derived from the regression coefficients?\nThis is derived from the regression. We have clarified in the text.\n4.line 117-120: Please cite relevant references to provide supporting evidence for this assumption.\nAdded.\n5.Line 212,226:Did the authors perform significance tests when calculating the trends? In particular, Fig. 4 and Supplementary Fig. 9 do not provide any information on statistical significance, and adding such information would make the analysis more appropriate. In addition, please also include information on statistical significance when computing the correlation coefficients. The manuscript lacks essential information regarding the statistical significance of the results.\nGood point. We’ve added statistical test for Figures 1, 3, 4, and Supplementary Figures 1, 6, 8, 9, and 10.\n6.Line 275: The βPC1 values derived from the reanalysis data exhibit substantial uncertainties. Does such a constraint still hold meaningful value? In addition, I do not quite understand the statement “This ECS could serve as the upper bound for the real-world ECS”. Is this because the model tends to overestimate IHTC?\nGood question. Uncertainty in observations is typically high. For example, the uncertainty of 𝛽 is also large (Fig. 2b). However, after applying an emergent constraint, our estimated ERFaci reduces its uncertainty by over 50% compared to that in the IPCC report (Fig. 3c and d). Even though there is uncertainty in 𝛽 , it holds important implications. If the real world were consistent with the CMIP6-EM in every aspect, the derived CMIP6-EM ECS based on emergent constraint could be used for the real world. However, the CMIP6-EM overestimates the IHTC trend but shows consistent multidecadal variability (Fig. 2b). As such we suggest that the derived CMIP6-EM ECS could be the upper bound for the real world. We’ve removed this part in our revision.\n7.line 373:Could the manuscript provide more details on the data processing, such as whether the model data were interpolated? Did the calculation of the time series include latitudinal weighting? How is the picontrol data segmented? Do these data segments overlap? Even if some processes are already presented elsewhere in the manuscript, for completeness, I recommend that they be consolidated and presented in the Data section.\nWe have provided additional details on data processing in the Definition of various metrics and Model data sections in the method.\nIn short, model data is linearly interpolated to a common grid (1ox2o, lat x lon). Time series are area weighted. For pre-industrial control simulations, the first member (r1i1p1f1) was downloaded from 34 models. We first detrended the entire time series for each model to remove long-term drift. Next, we randomly selected a continuous 65-year time series and calculated its trend. This process was repeated 100 times for each model (with replacement), resulting in a total of 3400 realizations.\n8.line 397: Here, it would be helpful to explain why the applicability is reduced. As you explained, due to the absence of multi-decadal variability in aerosols during this period, both aerosols and greenhouse gases drive an increasing trend in IHTC, making it impossible for PCA to distinguish their individual effects.\nFixed.\nReviewer #2 (Remarks to the Author):\nReview for He et al.: Climate models exaggerate the impact of greenhouse gases on recent interhemispheric temperature patterns and tropical climate\nI appreciate the authors’ detailed replies to my previous comments. The writing has been largely improved in the revised manuscript. I have some follow-up questions and comments, especially on how the GHG and AER contributing terms are separated and how PCs are linked to the IHTC-related variability. Please see below for both major and minor comments.\nWe are pleased that our revision has addressed our questions, and we appreciate your critical and constructive comments that improved our manuscript. Below, you will find our responses to your new questions.\nMajor comments:\nEQ1/Fig2: (Line 129-132) are there studies or analysis to support the ignoring of the interaction between the two forcings? How are the interaction terms excluded?\nFor the model the R2 for linear regression Eq 1 is 0.97, so any nonlinear effects must be small, no more than 3% of the variance. Though Eq 1 explains less variance for the observed (>0.8), the remainder is plausibly attributable to model error. Previous studies using single forcing experiments also showed the nonlinear effects are small (Deser et al., 2020; Liu et al., 2014; Simpson et al., 2023).\nEQ2/supplementary Fig 5: According to the analysis and discussion, the conclusions seem to be somewhat period dependent and constrained to the impacts from 1950-1980. While I understand that the authors want to focus on the multidecadal timescales (using 1950-2014 instead of 1950-1980 only) to exclude the collinearity between GHG and AER by applying PCA, I am having a hard time to justify the links between the individual GHG/AER “long-term trend” and the representation of factors driving the PCs for the focused period (1950-2014). How the GHG contribution is separated from AER with the focused period PCA should be better described, especially when the AER trend is no longer negative after 1980 in runs (supplementary Figure 5) and the impacts of WES feedback on simulations vs observation can also be period dependent (supplementary Figure 10 and 11; Line 244-248).\nWe agree that the relationship between PCA results and the responses in aerosol and greenhouse gas runs requires careful interpretation. Supplementary Figs. 5 and Fig 2c-d (Fig 2c-d is Supplementary Fig 6 in our previous manuscript) are provided to help clarify this relationship. Using the observation as an example. The cooling trend in observed IHTC before 1980 is influenced by both PC1 and PC2. PC1 exhibits a decreasing trend attributed to the long-term aerosol trend, while PC2 shows a decreasing trend pre-1980 due to the cooling phase in the multidecadal variability (Fig 2d). In contrast, the increase in observed IHTC after 1980 is caused by PC2 during a positive phase of the multidecadal variability (Fig 2d). Related discussions on this question are elaborated in response to question Line 172-173: Does this statement still hold after 1980?\nWe have added one more sentence near line 181-183 in the main text to explain the trend of the post-1980 IHTC in the observation.\nWe agree that the WES feedback is more robust in the model simulations. In observations, it is noisier, as wind speed has large uncertainty. Please refer to the more in-depth discussion in question Line 244-248: Is this statement only referring to the pre-1980 results? In addition, without the GHG-related SST pattern during the same period, it is hard to confirm that the IHTC is dominated by AER and NAT just based on the similarity between observed SST and AER-induced SST patterns.\nMinor comments:\nLine 17-19: Thank you for the reply to my previous comment, it makes sense. However, as the first sentence in the abstract, the readers might not understand it as the conclusion of this study. Please consider rephrase the sentence.\nWe appreciate your suggestions. This sentence is a general statement emphasizing the impact of IHTC, which has been examined in multiple studies. Our main finding is that the model bias in IHTC originates from model’s high sensitivity to greenhouses gases, which also affect biases in the tropical climate. We respectfully decided to the sentence as is.\nLine 51-55: Given that the external forcing (especially GHG) is the main driver in simulations, are there studies quantifying their contributions from “land-ocean fraction difference” vs “asymmetric of Arctic and Antarctic sea ice”? Especially the Antarctic/Arctic regions are excluded from the IHTC definition in this study.\nGood question. To our knowledge, these questions remain to be investigated. Personal communication with Dr. Sarah Kang (MPI) indicates that their study does show “land-ocean fraction difference” enhances the difference in the SST warming in the Northern hemisphere. I believe their paper is also in review.\nLine 133-134: “the observation is primarily forced.” Same as my comment from the previous review (for the now modified line 144), this sentence/wording is confusing.\nWe have rephased the sentence to “Given the observed IHTC is mainly driven by external forcing”. It will be appreciated if you could advise how to further revise this for clarity.\nLine 172-173: Does this statement still hold after 1980?\nGood question. We are talking about the long-term trend associated with PC1 in the whole period (1950-2014), as the PCA results remain valid in the whole period.\nWe note that after 1980, the IHTC shows an increasing trend in both observation and models (Supplementary Fig. 6 in previous manuscript, now Fig 2), which probably makes you raise this question here. This increasing trend in the observation is mostly driven by the PC2 associated with multidecadal variability of the aerosol forcing (Fig 2d), while PC1 still has a negative trend in the observation. To highlight this part, we have moved the Supplementary Fig. 6 to Fig 2c-d. Bonfils et al. (2020) found similar results regarding the long-term trend and multidecadal variability of surface temperature. In their fingerprint analysis, the first mode is observed long-term SST (or surface temperature) trend, which mainly results from greenhouse gases. This trend, as shown in Fig 1c of Bonfils et al. (2020), does not exhibit a distinct contrast between hemispheres. In contrast, the observed IHTC is mainly caused by the aerosols with strong multidecadal variability (Fig. 2c of Bonfils et al. 2020).\nLine 187-189: Please consider rewriting this part, as the implication may not be clear to the readers when PC1 represents a combined AER and GHG effect (line 181) and their interaction is ignored.\nWe have rephased the sentence: “This implies that, in contrast to the observed IHTC, the systematic positive trend in IHTC of CMIP6 models largely results from their response to GHG. It should be noted that ECS and ERFaci are correlated to some extent in CMIP6 models (Supplementary Fig. 6a and c).”\nLine 244-248: Is this statement only referring to the pre-1980 results? In addition, without the GHG-related SST pattern during the same period, it is hard to confirm that the IHTC is dominated by AER and NAT just based on the similarity between observed SST and AER-induced SST patterns.\nYes. We can only conclude for the pre-1980 period here. But for the post-1980 period, we also observe the anticorrelated relationship between the surface wind and SST trends in the observations (Supplementary Fig. 10 c-d).\nBelow, we also show the GHG-induced SST and surface wind speed trends before and after 1980 (Fig. R1). The pre- and post-1980 SST trend patterns remain similar to the SST and wind speed trends in the whole period (Fig. 4b in main manuscript). In the pre-1980 period, the GHG-induced SST pattern shows a positive gradient between the two hemispheres, opposite to those in the AER and observations (Supplementary Fig.9 and 10).\nFig. R1 Linear trend of surface wind speed and SST in GHG simulations. a, GHG -induced surface wind speed trend in 1950-1980. b, as in a but for SST. c, d as in a, b but for 1980-2014. Note that in b and d, the global mean SST has been removed to emphasize the NH-SH gradient."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I am pleased to confirm that all of my suggestions have been incorporated. I hereby accept the article for publication.", "reviewer_2": "Review for He et al.: I would like to thank the authors for their replies to my previous comments. Most of my comments have been satisfactorily addressed. Please see below for my follow-up comments/questions for the rest of them.\n1. Following my previous major comment on Figure 2 and Figure S5, as well as the minor comments on previous line 172-173 and 244-248: Based on the authors’ replies (both to my comments and reviewer 1’s first-round comments), it is evident that the contributions from different factors (e.g., GHG, AER) disentangled by the PCA results are period dependent, and the results could change if different periods were analyzed. This remains my main concern for the manuscript, especially when the mechanisms explained for the “long term trend” may also depend on the period of choice. In addition to the mentioning of 1980-2014 as the focus period (and brief description in the Methods section), please consider emphasizing more on this caveat in the main discussion.\n2. Figure 2c, d and Figure S5: Please consider using the same colors (red and blue) for PC1 and PC2 in the figures for easier comparisons. (Now they are flipping between the two figures.)\n3. Following my previous minor comment for (previously) Line 133-134: I saw that the author rephrased the sentence I commented on during the first revision (now line 148). However, the exact wording “the observation is primarily forced” is now used in another paragraph/sentence (new line 136), which I still find confusing.\n4. Line 386: Is there any reason why the author chose to utilize the linear interpolation instead of an area-conservative method?"}, "author_response": "We have added a discussion section at the end of our manuscript to emphasize the PCA limitations. Please find the relevant texts below:\nDiscussion\nOur analysis reveals a fundamental discrepancy between CMIP6 climate models and observations in simulating the interhemispheric thermal contrast since 1950. While models systematically show a positive IHTC trend driven primarily by greenhouse gas forcing, observations exhibit a negative trend dominated by anthropogenic aerosol and natural forcings. This model-data diHerence stems from an exaggerated GHG response mediated by wind-evaporation-SST feedback, which is particularly pronounced in high-ECS models. These conclusions depend on separating the competing eHects of GHG and AER through our decomposition of IHTC into long-term trend and multidecadal variability components, which exploits the distinct temporal evolution of forcing agents during 1950-2014. This period captures the era when anthropogenic forcings became substantial, while AER exhibited strong multidecadal variability, which increased until ~1980 and declined thereafter following clean air legislation. This temporal signature enables PCA to eHectively separate the AER-dominated multidecadal variations (IHTC_PC2) from the long-term trend (IHTC_PC1), which is dominated by GHG in CMIP6 models.\nOur sensitivity tests show robust results with ±10 years adjustments to the start year in the PCA decomposition, but the approach may not be suitable for other periods, in particular after 1980. After 1980, as AER emissions declined, both reduced AER cooling and continued GHG warming contribute to positive IHTC trends, compromising PCA’s ability to isolate their individual eHects. Nevertheless, the physical mechanism we identify, WES feedback amplifying the interhemispheric SST response to GHG, represents a robust process that operates across diHerent time periods, even if the relative magnitude of GHG versus AER contributions varies.\n2. Figure 2c, d and Figure S5: Please consider using the same colors (red and blue) for PC1 and PC2 in the figures for easier comparisons. (Now they are flipping between the two figures.)\nBug fixed. Thank you for catching it.\n3. Following my previous minor comment for (previously) Line 133-134: I saw that the author rephrased the sentence I commented on during the first revision (now line 148). However, the exact wording “the observation is primarily forced” is now used in another paragraph/sentence (new line 136), which I still find confusing.\nWe have rephased it in our revision (line 136).\n4. Line 386: Is there any reason why the author chose to utilize the linear interpolation instead of an area-conservative method?\nWe use linear interpolation because it is computationally efficient. For our analysis, which focuses on spatial patterns and trends rather than integral quantities such as heat content, linear and area-conservative interpolations are similar."}, {"round": 4, "reviewer_comments": {"reviewer_2": "The authors have satisfactorily addressed my review comments. I do not have further questions and the manuscript can be accepted in its current form."}, "author_response": ""}]

Decision letter