Magnitude uncertainty dominates intermodel spread in zonal-mean precipitation response to anthropogenic aerosol increase

Abstract

Anthropogenic aerosols are an important driver of historical climate change but the climate response is not fully understood and the climate model simulations suffer large uncertainties. On the basis of a multimodel ensemble of historical aerosol forcing simulation for a period of global aerosol increase during 1965 to 1989, here, we show that the precipitation response shares a common southward displacement of tropical rain bands but the magnitude differs markedly among models, accounting for 76% of the intermodel uncertainty in zonal-mean precipitation change. Our analysis of atmospheric energetics further reveals key mechanisms for magnitude uncertainty: aerosol radiative forcing drives, cloud radiative feedback amplifies, and ocean circulation damps the intermodel uncertainty in cross-equatorial atmospheric energy transport change and the meridional shift of tropical rain bands. This has important implications for understanding and reducing intermodel uncertainty in anthropogenic climate change.

Aerosol radiative forcing drives and radiative feedback amplifies the large magnitude uncertainty in precipitation change.

INTRODUCTION

Anthropogenic aerosols induced an effective global radiative forcing of −1.1 (−1.7 to −0.4) W/m² over 1750 to 2019 with large uncertainty (1). This net cooling effect is due to the direct effects [e.g., sulfate aerosols scattering and black carbon absorbing shortwave radiation (2, 3)] and indirect effects as cloud condensation nuclei and by interacting with clouds to influence cloud albedo, lifetime, and precipitation efficiency (4–6). The spatial distribution of anthropogenic aerosol emissions has evolved considerably over time. From the industrialization up to the 1980s, aerosol emissions increased over Asia, North America, and Europe (fig. S1), resulting in a cooling of −0.58° ± 0.21°C that partially offsets global warming of +0.71° ± 0.15°C caused by greenhouse gas (GHG) emissions (7–10).

On the basis of state-of-the-art Coupled Model Intercomparison Project Phase 6 (CMIP6) single-forcing simulations, large-scale climate responses to anthropogenic aerosol increase have been investigated in comparison with GHG forcing (7, 10). Anthropogenic aerosols are geographically inhomogeneous due to their short atmospheric residence time. Uncertainty in climate responses remains large among different climate models (11–17), in part, because aerosols are the largest source of intermodel spread in anthropogenic effective radiative forcing (18, 19) due to the differences among models in representing aerosol-radiation and aerosol-cloud interactions (14, 20–23).

The present study investigates intermodel uncertainty in precipitation response in the CMIP6 multimodel historical single-forcing (GHG or aerosol) ensemble during the period of 1965 to 1989 when both anthropogenic GHGs and aerosols increased. We show that zonal-mean precipitation response to anthropogenic aerosol forcing shares a common latitudinal pattern but the magnitude varies among models. By developing a two-dimensional atmospheric energy transport (AET) analysis, we identified the driver and feedbacks for the intermodel uncertainty, which has implications for understanding and reducing intermodel uncertainty in anthropogenic climate change.

RESULTS

Spatial patterns of precipitation change

We focus on the sample between the 1965–1989 and 1850–1899 means. Here, the period of 1850 to 1899 is regarded as a reference when anthropogenic aerosol emissions were still low. During 1965 to 1989, industrial aerosol emissions increased markedly in Europe and North America, as well as in Asia (fig. S1). Our results are insensitive to the choice of aerosol increase period. In response to the anthropogenic aerosol forcing, the multimodel ensemble (MME) mean precipitation shows robust decrease on and north of the equator but increase to the south, especially along the South Pacific convergence zone (Fig. 1A). It also features a decrease of 6 mm/month over East Asia and 4.5 mm/month over the midlatitude Northwest Pacific. Despite distinct forcing structure, the spatial correlation of precipitation changes in the global domain under GHG and anthropogenic aerosol forcing is −0.53 (Fig. 1, A and B), suggesting that climate responses induced by GHGs and aerosols share key ocean-atmosphere feedbacks, such as the Bjerknes feedback and wind–evaporation–sea surface temperature (SST) feedback (24).

Fig. 1. Precipitation change under anthropogenic aerosol and GHG forcing.

Spatial patterns of MME-mean precipitation change (1965–1989 mean minus 1850–1899 mean; unit: millimeters per month) under (A) anthropogenic aerosol and (B) GHG forcing. All changes are computed for the annual mean. The gray contours in (A) and (B) show the isopleth (210 mm month⁻¹) of the precipitation climatology from the preindustrial control simulation. Stippling indicates that at least 70% of the models agree on the sign of the MME mean. The black and red lines represent the MME mean and leading empirical orthogonal function (EOF) of latitude-weighted zonal-mean precipitation change under (A) anthropogenic aerosol and (B) GHG forcing. (C) Histogram of spatial correlation of precipitation change in the global domain between all possible pairs of models (0.1 intervals) in historical anthropogenic aerosol (hist-aer; red) and historical-GHG (hist-GHG; light blue) runs.

Spatial correlations of precipitation change between models are systematically higher in anthropogenic aerosol than GHG single-forcing run both in the global domain (Fig. 1C) and the tropical domain (fig. S2), indicating that the spatial patterns of anthropogenic aerosol–induced precipitation response are more consistent, but the magnitude of the response varies among different models. Hence, anthropogenic aerosol–induced precipitation change in individual models strongly resembles the CMIP6 MME mean (table S1).

The intermodel spread of precipitation change can be decomposed into intermodel empirical orthogonal functions [EOFs (25–27)]

$$P(x,y,\mathrm{m})={\displaystyle \sum _{n=1}^N}\mathrm{P}{\mathrm{C}}_n\left(\mathrm{m}\right)·P_n(x,y)$$ (1)

where x and y represent longitude and latitude, respectively, m denotes individual models, and $P_n$ and ${\text{PC}}_n$ are the nth EOF and principal component (PC), respectively. The leading EOF of zonal-mean precipitation change under anthropogenic aerosol forcing features an interhemispheric antisymmetric structure (red line in Fig. 1A), which aligns closely with the MME mean [black line in Fig. 1A; correlation coefficient (r) = 0.95]. Under GHG forcing, the leading EOF of zonal-mean precipitation change also displays an interhemispheric asymmetry in the tropics (red line in Fig. 1B), which is entirely different from the MME mean that peaks at the equator (black line in Fig. 1B; r = 0.04). The results are similar for the two-dimensional horizontal distribution. The leading intermodel EOF of precipitation change under anthropogenic aerosol forcing (fig. S3A) has a spatial correlation of 0.67 with the MME mean (Fig. 1A), while the spatial correlation between the intermodel EOF (fig. S3B) and the MME mean (Fig. 1B) is much smaller under GHG forcing (r = 0.10). These results consistently indicate that the precipitation responses to anthropogenic aerosol forcing share a common spatial pattern among models.

Magnitude uncertainty in precipitation change

Anthropogenic aerosols, mainly sulfate aerosols, are mostly confined in the Northern Hemisphere (NH), causing tropical SST to cool more in the NH and displacing the intertropical convergence zone (ITCZ) southward (28, 29). All climate models exhibit interhemispheric contrast in precipitation response (fig. S4), but the response magnitude differs markedly from each other (pink shading in Fig. 2A). To quantify the magnitude uncertainty, we decompose the intermodel spread in zonal-mean precipitation response into a component of the MME mean structure (denoted with an overbar; $\overline{P}$)

$$P(y,\mathrm{m})=a_{\mathrm{m}}\overline{P}\left(y\right)+\mathrm{\epsilon }(y,\mathrm{m})$$ (2)

where y represents latitude and m denotes individual models. We compute $a_{\mathrm{m}}$ as the regression of each model against the MME mean $\overline{P}$ . The intermodel spread in $a_{\mathrm{m}}\overline{P}$ represents the magnitude uncertainty in precipitation change, and $\mathrm{\epsilon }$ is the residual term.

Fig. 2. Reducing the magnitude uncertainty narrows intermodel spread in zonal-mean precipitation response to anthropogenic aerosol increase.

(A) MME mean (black line) and standard deviation (SD; pink shading) of the zonal-mean tropical precipitation change (unit: millimeters per month) under anthropogenic aerosol forcing. The SD of the residual term ( $\mathrm{\epsilon }$ ; pale turquoise shading) is markedly reduced after removing the magnitude uncertainty. Scatter plots of the intermodel PC1 for zonal-mean precipitation change versus (B) global mean surface temperature change (unit: °C) and (C) the intermodel PC1 for two-dimensional AET potential change. Each point represents a specific CMIP6 model (model names listed in the right-hand legend). The r and its P value are indicated. EQ, equator; GMST, global mean surface temperature; Pr, precipitation.

The decomposition in Eq. 2 is successful for representing the uncertainty in zonal-mean precipitation change in the historical aerosol run. The intermodel spread in precipitation response to anthropogenic aerosol forcing is larger by a factor of two compared to that under GHG forcing (Table 1). The magnitude uncertainty (variance of $a_{\mathrm{m}}\overline{P}$ ) explains 76% of the total intermodel variance of precipitation change ( $P$; Table 1) under anthropogenic aerosol forcing. By removing the contribution of $a_{\mathrm{m}}\overline{P}$ , we calculate the SD of the residual term ( $\mathrm{\epsilon }$ ), which greatly narrows the intermodel spread in simulated precipitation change, especially in the tropics (pale turquoise shading in Fig. 2A). This indicates that the aerosol-induced Precipitation change shares a similar latitudinal pattern, and the intermodel difference in the magnitude of this pattern dominates the overall uncertainty. For comparison, the magnitude uncertainty (variance of $a_{\mathrm{m}}\overline{P}$ ) only explains 13% of the total variance of precipitation change ( $P$; Table 1) in the historical-GHG (hist-GHG) ensemble.

Table 1. Meridionally integrated variance of zonal-mean precipitation change in the historical aerosol and GHG runs.

Unit: millimeters per month.

Variance	$\mathit{P}$	${\mathit{a}}_{\mathbf{m}}\overline{\mathit{P}}$
hist-aer	94	71
hist-GHG	45	6

Under anthropogenic aerosol forcing, the intermodel PC1 for zonal-mean precipitation change is nearly perfectly correlated with the regression coefficient $a_{\mathrm{m}}$ at r = 0.99, indicating that either can be used to quantify magnitude uncertainty in precipitation response. We note that the intermodel PC1 for zonal-mean precipitation change is highly correlated with intermodel spread in global mean surface temperature change (Fig. 2B; r = −0.80), the latter being a widely used magnitude measure of climate response.

AET potential

To examine the physical mechanisms responsible for the similar spatial pattern but different magnitude of precipitation response to anthropogenic aerosol forcing, we use the atmospheric energetic framework (30), which is widely used to study the precipitation response to external forcings. This framework establishes the link between AET and precipitation as follows: averaging statistically, the tropical atmosphere generally features higher atmospheric energy in the upper troposphere than the lower troposphere but more moisture in the lower troposphere. Hence, an upward motion with mass divergence above and mass convergence below causes a net AET divergence and a net moisture convergence, resulting in precipitation. It also provides a way to quantify the impact of the top of the atmosphere (TOA) and surface energy flux on the AET, aiding to identify the key processes that influence zonal-mean precipitation change (31, 32). Here, we mainly focus on the column-integrated AET potential ${\mathrm{\chi }}_h$ (see the “AET analysis” section in Materials and Methods for definition) that is closely related to precipitation in the tropics but spatially smoother. The atmospheric column energy conservation is expressed as (33)

$${\nabla }^2{\mathrm{\chi }}_h=\nabla ·{\mathbf{v}}_h=Q_{\text{TOA}}+Q_{\text{sfc}}$$ (3)

where ${\mathbf{v}}_h=(u_h,v_h)=\nabla {\mathrm{\chi }}_h$ is the column-integrated transport of moist static energy h and the right-hand side is the net vertical energy flux into the atmospheric column at the TOA and surface. Thus, the AET potential is the inverse Laplacian of the vertical energy flux and hence a smoother spatial function than the flux. The sea surface heat flux $Q_{\text{sfc}}$ is approximately equal to the vertically integrated ocean heat transport divergence.

In the deep tropics (10°N/S), the baroclinic overturning circulation (Hadley and Walker cells) dominates the energy transport

$$\nabla {\mathrm{\chi }}_h={\mathbf{v}}_h\approx \widehat{h}{\mathbf{v}}_{\mathrm{m}}$$ (4)

where ${\mathbf{v}}_{\mathrm{m}}$ is the upper-troposphere mass transport and $\widehat{h}$ is the gross moist stability approximated as the upper minus lower troposphere moist energy difference. Equation 4 allows us to infer the tropical overturning circulation and ITCZ (30, 33, 34) from the AET potential field as shown in the schematic (Fig. 3). Outside the deep tropics, stationary and transient eddies dominate the zonal-mean meridional energy transport (35). The extratropical AET potential is still useful for the discussion of atmospheric circulation and regional precipitation patterns (36–41). When the ocean takes up heat (cooling the atmospheric column) in a narrow band in the NH extratropics and gives out heat (warming the atmospheric column) in the Southern Hemisphere (SH) extratropics (Fig. 3), it induces a broad AET potential field between the extratropical bands of ocean heating and cooling. The interhemispheric gradient implies a northward AET across the equator and a southward displacement of the ITCZ.

Fig. 3. Schematic of the cross-equatorial AET.

When the ocean takes up heat (cooling the atmospheric column) in the NH extratropics and gives out heat (warming the atmospheric column) in the SH extratropics, it induces a broad AET potential field between the extratropical bands of ocean heating and cooling and calls for a northward AET from the negative to positive center of AET potential. This corresponds to a meridional overturning Hadley circulation with the ITCZ displaced toward the warmer SH.

We perform an intermodel EOF for the AET potential change ${\mathrm{\chi }}_h$(x, y, m) under anthropogenic aerosol forcing (fig. S5), which maps out how the atmosphere responds to interhemispheric energy perturbations. The PC1 for two-dimensional ${\mathrm{\chi }}_h$(x, y, m) is highly correlated with the PC1 for zonal-mean precipitation $P$(y, m) at r = 0.89 (Fig. 2C). In other words, the two-dimensional leading EOF for AET potential captures the meridional one-dimensional EOF mode for zonal-mean precipitation. This indicates how prominent the meridional AET is in climate response to anthropogenic aerosols. Here, we regress the AET potential change onto the PC1 of intermodel spread in zonal-mean precipitation change (the x axis in Fig. 2C). This approach allows us to interpret the large magnitude uncertainty and pattern similarity of precipitation response to anthropogenic aerosol forcing from the AET perspective. Specifically, we can identify sources of intermodel uncertainty in AET potential by decomposing it into TOA and surface flux contributions.

Anthropogenic aerosol–induced AET potential change

Anthropogenic aerosols are heterogeneous in space. The MME-mean AET potential change is from the SH to NH, converging into local maxima over North America, Europe, and East Asia (Fig. 4A), broadly consistent with local aerosol maxima (fig. S1). Following Eq. 3, we further decompose the AET potential into components due to energy fluxes at the TOA and surface, the latter due largely to ocean heat transport divergence (42, 43). The TOA component of ${\mathrm{\chi }}_h$ is dominated by an interhemispheric asymmetry with a strong energy transport into the NH extratropics (Fig. 4C) to compensate for energy loss due to the aerosol cooling. The surface component of ${\mathrm{\chi }}_h$ is large in the North Atlantic basin and damps the AET change due directly to TOA radiation change (Fig. 4B) (8). This aligns with recent studies showing that the aerosol-induced NH cooling accelerates the deep Atlantic meridional overturning circulation [MOC (44–48)] and a clockwise cross-equatorial shallow MOC in the Indo-Pacific oceans (43), resulting in a northward ocean heat transport.

Fig. 4. AET potential change under anthropogenic aerosol forcing.

Left: MME-mean changes (unit: terawatts) of (A) the AET potential, (B) surface energy flux potential, and (C) TOA energy flux potential in historical aerosol single-forcing run. Contours in (A) show the MME-mean precipitation change [red contours denote the isopleth (−4.5 mm month^–1), and blue contours denote the isopleth (4.5 mm month^–1)]. Middle: The regressions of (D) AET potential change against the intermodel PC1 for zonal-mean precipitation change (unit: terawatts), (E) the surface, and (F) TOA energy flux components. Stippling indicates where the regression passes a t test at the 95% significance level. Contours in (D) show the regressed precipitation change against the intermodel PC1 [red contours denote the isopleth (−2.1 mm month^–1), and blue contours denote the isopleth (2.1 mm month^–1)]. Right: Latitude-weighted zonal-mean–regressed changes (unit: terawatts) in (G) AET potential (red line), (H) surface (blue), and (I) TOA energy flux contributions (green), along with the respective MME mean (black line).

Both the MME-mean AET potential change and the regressed intermodel spread exhibit strong interhemispheric asymmetry (black and red lines in Fig. 4G). This pronounced asymmetry in the regressed AET potential change is largely due to the TOA energy flux (Fig. 4F and green lines in Fig. 4I), half of which can be attributed to anthropogenic aerosol effective radiative forcing (Fig. 5A). Further decomposition shows that the TOA energy flux is dominated by its shortwave component (red line in Fig. 5B), with the clear-sky (green line) and cloud (blue line) components accounting for 57 and 43% of the interhemispheric asymmetry, respectively. These results indicate that anthropogenic aerosol radiative forcing drives and cloud radiative feedback amplifies the intermodel uncertainty in cross-equatorial AET and precipitation change.

Fig. 5. Latitude-weighted zonal-mean–regressed TOA energy flux potential changes against the intermodel PC1 for zonal-mean precipitation change under anthropogenic aerosol forcing (unit: terawatts).

(A) Regressed potential changes of TOA net energy flux (black solid line) and anthropogenic aerosol effective radiative forcing (ERF; black dashed line). (B) Regressed TOA shortwave energy flux potential change (red line), clear-sky (green line), and cloud components (blue line). (A) is based on a subset of seven models for which the atmospheric model run with fixed SST is available. SW, shortwave.

We use regression analysis to identify the sources of intermodel uncertainty. Under anthropogenic aerosol forcing, the regressed two-dimensional precipitation change shows robust decreases on and north of the equator but increases to the south (contours in Fig. 4D). This is highly correlated with the spatial pattern of the MME-mean precipitation change (contours in Fig. 4A; r = 0.79 in the global and r = 0.83 in the tropical domain). The spatial similarity in aerosol-induced precipitation change can be primarily attributed to the strongly hemispherically asymmetric distribution of anthropogenic aerosol emissions. Supporting this, spatial patterns of the MME-mean (Fig. 4C) and regressed TOA energy flux changes (Fig. 4F) are highly correlated (r = 0.85), both exhibiting a robust interhemispheric asymmetry (black and green lines in Fig. 4I) and the convergence center in the mid-to-high latitudes of NH. In comparison, the regressed surface flux contribution is somewhat small (blue line in Fig. 4H), with a weak dipole between the northwestern and southeastern Pacific Ocean (Fig. 4E). The cross-equatorial northward oceanic energy transport (OET; approximately represented by the meridionally integrated downward surface net flux anomaly from 90°N) reduces the need for and thereby damps the cross-equatorial northward AET, both for the MME mean (Fig. 6A) and spread (Fig. 6B). This indicates that OET is a negative feedback on aerosol-induced AET change.

Fig. 6. Northward AET (black) and OET (blue) changes under anthropogenic aerosol forcing.

(A) MME-mean AET and OET changes (unit: petawatts) by meridional integration of atmospheric net energy gain and downward surface net flux anomaly, respectively. (B) Regressed AET and OET changes against the intermodel PC1 for zonal-mean precipitation change (unit: petawatts).

GHG-induced AET potential change

For comparison with anthropogenic aerosols, here, we investigate the AET potential change under GHG forcing. In the MME mean, the AET convergence centers, where ${\mathrm{\chi }}_h$ reaches maxima, are in the Southern Ocean and extratropical North Atlantic (Fig. 7A) to compensate for the large ocean heat uptake (Fig. 7B) due to the mean upwelling of the global deep overturning circulation and slowdown of the Atlantic MOC, respectively (49–51). In comparison, the TOA flux contribution to ${\mathrm{\chi }}_h$ is small (Fig. 7C), consistent with nearly uniform radiative forcing of GHGs.

Fig. 7. AET potential change under GHG forcing.

Left: MME-mean changes (unit: terawatts) of (A) the AET potential, (B) surface energy flux potential, and (C) TOA energy flux potential in historical GHG single-forcing run. Contours in (A) show the MME-mean precipitation change [red contours denote the isopleth (−4.2 mm month⁻¹), and blue contours denote the isopleth (4.2 mm month⁻¹)]. Middle: The regressions of (D) AET potential change against the intermodel PC1 for zonal-mean precipitation change (unit: terawatts), (E) the surface, and (F) TOA energy flux components. Stippling indicates where the regression passes a t test at the 95% significance level. Contours in (D) show the regressed precipitation change against the intermodel PC1 [red contours denote the isopleth (−1.8 mm month⁻¹), and blue contours denote the isopleth (1.8 mm month⁻¹)]. Right: Latitude-weighted zonal-mean–regressed changes (unit: terawatts) in (G) AET potential (red line), (H) surface (blue), and (I) TOA energy flux contributions (green), along with the respective MME mean (black line).

Spatial patterns of MME-mean and regressed AET potential changes are dissimilar (r = −0.10; Fig. 7, A and D), consistent with the lack of spatial similarity between MME-mean and regressed precipitation changes (r = 0.02; contours in Fig. 7, A and D). In the MME mean, the zonal-mean AET potential change is nearly symmetric about the equator in the tropics (black line in Fig. 7G), while the regressed intermodel spread is antisymmetric about the equator (red line in Fig. 7G), especially in the Atlantic Ocean (Fig. 7D; see also the leading intermodel EOF; fig. S6). The surface flux contribution to intermodel spread in ${\mathrm{\chi }}_h$ also displays a pronounced interhemispheric asymmetry (blue line in Fig. 7H), especially in the North Atlantic (Fig. 7E). This aligns with previous findings that under GHG-induced warming, the degree of Atlantic MOC slowdown varies considerably among climate models (52–54), driving interhemispheric asymmetry in tropical climate change (32). Unlike the intermodel spread for the anthropogenic aerosol forcing simulation (Fig. 4, right), the regressed TOA flux reinforces the interhemispheric AET potential anomaly (Fig. 7, right), likely due to positive low-cloud feedback (55, 56) in the subtropical southeast Pacific and Atlantic (Fig. 7, D and F).

DISCUSSION

We investigated climate response to anthropogenic aerosol increase based on CMIP6 historical single-forcing simulations, focusing on precipitation and AET that are mutually related in the deep tropics through the atmospheric overturning circulation (8, 30, 33). Our results show that under anthropogenic aerosol forcing, the precipitation response shares similar spatial patterns across models due to the heterogeneous geographical distribution of anthropogenic aerosol emissions, but the magnitude of the response varies among models. By decomposing AET potential into TOA and surface energy flux components, we identified key mechanisms for magnitude uncertainty. We show that aerosol radiative forcing drives, cloud radiative feedback amplifies (Fig. 5), and ocean circulation damps (Fig. 6) the intermodel uncertainty in cross-equatorial AET. In contrast, the Atlantic MOC slowdown drives and cloud radiative feedback amplifies the intermodel spread in GHG-induced AET change (32) because uncertainty in the radiative forcing is relatively small.

Our results have important implications for climate change dynamics. First, reducing magnitude uncertainty is the key for robust simulations of historical aerosol–induced climate change. To that end, further research is necessary into radiative and ocean circulation feedbacks in addition to the aerosol radiative forcing that has been extensively studied (18, 57, 58). Cloud feedback is perceived uncertain for global mean surface temperature but could be more robust than thought for interhemispheric asymmetry on which we focus here. Last, the zonal variations in climate response are equally important and deserve close attention.

MATERIALS AND METHODS

CMIP6 multimodel simulations

Detection and Attribution Model Intercomparison Project (DAMIP) (59) uses historical simulations (including single forcing from anthropogenic GHGs, anthropogenic aerosols, and natural forcing) to evaluate the relative contributions of anthropogenic and natural forcing to climate change. The monthly mean outputs from 13 CMIP6-DAMIP models in historical anthropogenic aerosol (hist-aer) and hist-GHG single-forcing simulations (table S2) are used to study climate response. Internal climate variability may limit the identification of climate change patterns induced by aerosols and GHGs in individual realizations during the historical period (7), the assessment of which requires the use of large ensemble simulations (7, 60, 61). To minimize the internal climate variability, we first obtained the multimember average for each model and then analyzed the MME mean and spread. All the model outputs were interpolated onto a common grid of 2.5° $\times$ 2.5°.

We also used the piClim-histaer simulation, which is an Atmospheric General Circulation Model experiment where SST is kept constant at the preindustrial monthly climatology and only the anthropogenic aerosol radiative forcing varies historically over time. We use this simulation to calculate the TOA net downward flux change (the difference between the 1965–1989 and 1850–1899 means) as the anthropogenic aerosol effective radiative forcing. The seven models available in the piClim-histaer simulation are listed in table S2.

Climate change is calculated by subtracting the 1850–1899 mean from the 1965–1989 mean. The period of 1850 to 1899 is taken as a reference when anthropogenic aerosol emissions were low. During 1965 to 1989, aerosol emissions in Europe and North America increased to near their peaks, while emissions in Asia continued to rise (fig. S1). We selected the same period for analysis of the GHG forcing run.

AET analysis

We apply an AET analysis to diagnose the dominant source of the uncertainty under anthropogenic aerosol forcing. Recent studies have applied this analysis to identify divergent AET (33, 34, 36, 62) and its relationship with the zonal and meridional shifts in tropical rain bands (63). The AET potential ${\mathrm{\chi }}_h$ is defined as follows [see (33)]

$${\nabla }^2{\mathrm{\chi }}_h=\nabla ·{\displaystyle \underset{0}{\overset{p_{\mathrm{s}}}{\int }}}\mathbf{v}h\frac{\mathit{dp}}{g}$$ (5)

where $\mathbf{v}$ is the horizontal wind, $h$ is moist static energy, $g$ is gravitational acceleration, and the vertical integration is from surface pressure $p_{\mathrm{s}}$ to TOA. Here, we neglected atmospheric energy storage. According to Eq. 3, we further decompose the AET potential ${\mathrm{\chi }}_h$ into the TOA downward ( ${\mathrm{\chi }}_{\text{TOA}}$ ) and surface upward ( ${\mathrm{\chi }}_{\text{sfc}}$ ) net energy flux potentials separately

$${\nabla }^2{\mathrm{\chi }}_{\text{TOA}}=Q_{\text{TOA}}$$ (6)

$${\nabla }^2{\mathrm{\chi }}_{\text{sfc}}=Q_{\text{sfc}}$$ (7)

where $Q_{\text{TOA}}$ is the TOA downward net energy flux and $Q_{\text{sfc}}$ is the surface upward net energy flux. This decomposition helps us to identify different dominant sources of the uncertainty in AET potential change.

Sea surface heat flux change often features narrow bands of alternating signs. The shape and position of these surface flux bands vary among models, resulting in low intermodel correlation. Even if the heat-exchange bands in Fig. 3 shift meridionally between models, the AET potential field remains largely unchanged, representing the same cross-equatorial northward energy transport. Thus, the AET potential changes in these two cases are highly correlated. This example illustrates that AET potential analysis is effective to study intermodel uncertainty in interhemispheric AET and zonal-mean precipitation response to anthropogenic aerosol forcing. The PC1 for two-dimensional AET potential change is highly correlated with the PC1 for zonal-mean precipitation change at r = 0.89 (Fig. 2C).

Intermodel EOF analysis

We perform an intermodel EOF analysis with the space-model field instead of the common space-time field. Intermodel EOF analysis was broadly used to identify the intermodel differences of climate response in previous studies (25–27). In this study, we apply the intermodel EOF analysis to the precipitation and AET potential changes and then select the leading EOF mode to study the intermodel spread. If the spatial pattern of the leading EOF mode resembles the MME-mean pattern, then we take this as evidence in support of the hypothesis of the similar response pattern. Using this method requires checking whether the PC1 shows multiple models exhibiting near-zero value to further identify the hypothesis.

Supplementary Materials

This PDF file includes:

Figs. S1 to S6

Tables S1 and S2