2.1 Model

We perform simulations with the climate model MPI-ESM 1.2 in the low-resolution setup (Mauritsen et al., 2019). The atmospheric component, ECHAM6 (Stevens et al., 2013), is resolved with 1.875°×1.875° at 47 levels. It is coupled to the ocean component, MPIOM (Jungclaus et al., 2013), which runs on a bipolar grid with a resolution of 1.5° near the Equator. MPI-ESM also includes modules for land processes and ocean biogeochemistry (Reick et al., 2021; Ilyina et al., 2013). Since no interactive atmospheric chemistry processes are included, aerosol and trace gases are prescribed with monthly climatological fields that represent unforced pre-industrial conditions.

Figure 2Forcing input for the simulations. (a) Aerosol radiative properties that serve as input for the Aero simulation: extinction as a function of latitude and pressure and aerosol optical depth (AOD, vertically integrated extinction) as function of latitude, computed with EVA (Toohey et al., 2016). (b) Annual-mean field of CO₂ concentrations (in units of the pre-industrial CO₂ concentration) that serves as input for the pCO₂ simulation. In the actual simulation, monthly varying fields are used (Figs. A1 and A2 in the Appendix). The fields were computed with the algorithm described in Appendix A.

2.2 Simulations

We perform simulations with three forcings: an abrupt halving of the CO₂ concentration (0.5 × CO₂), an abrupt increase in the stratospheric aerosol concentration (Aero), and a patterned CO₂ simulation with spatially and seasonally varying CO₂ concentrations (pCO₂).

The Aero simulations are designed to represent the time-mean forcing induced by a strongly idealized tropical volcanic eruption or by deliberate stratospheric aerosol injection. We derive monthly and zonal mean fields of aerosol optical properties from the EVA forcing generator (Toohey et al., 2016) for one January and one July eruption, both with an injection mass of 20 Tg sulfur. The July eruption is then shifted by 6 months, and the average of both phase-matched eruptions is computed in order to remove seasonal transport asymmetries while preserving a realistic poleward mass transport. We prescribe the average of the first 3 post-eruption years as a time-invariant forcing to MPI-ESM. Constructing the aerosol forcing to be step-like in time allows for a consistent comparison to the 0.5 × CO₂ forcing. The aerosol is only coupled to the radiation, and it is not transported by the model, does not evolve in time, and does not interact directly with clouds or ozone. While these restrictions certainly limit realism, they allow us to isolate the effects of stratospheric aerosol in an idealized, interpretable framework. The most important radiative properties of the aerosol input are shown in Fig. 2a.

In pCO₂, CO₂ concentrations in each grid box and month are chosen such that they give rise to an effective TOA-forcing field which is approximately equal to the TOA radiative forcing of Aero in space and time. The rationale for this experiment's design is as follows: if the WP-enhanced TOA-forcing pattern of stratospheric aerosol is responsible for the WP-enhanced temperature pattern then the same effect should appear in a CO₂-forced simulation with a WP-enhanced forcing pattern. The iterative process that was used to determine the CO₂ concentrations is described in Appendix A. The annual-mean input field of spatially varying CO₂ concentrations is shown in Fig. 2b. The CO₂ concentrations are lowest over the WP and are slightly higher than the pre-industrial value over the poles. The resulting field of effective forcing shares these broad features and is shown in Fig. 3a.

To test the hypothesis that the effective-forcing pattern from stratospheric aerosol causes the enhanced WP temperature change, we perform the three sets of simulations summarized in Table 1.

2.2.3 Coupled simulations with q-flux forcing

Forcing the climate system not radiatively but with a “ghost forcing” (Hansen et al., 1997) at the surface allows for an examination of the way the surface forcing pattern affects the temperature pattern without any perturbations to the atmosphere's radiative properties. We derive the surface effective forcing from the fixed-SST simulations as the difference between all surface fluxes (radiative and turbulent) of the perturbed simulations and piClim-control. We then prescribe these flux anomalies as an additional heat source or sink (q flux) to the ocean and compute an ensemble of 40 simulations for each forcing agent, where each simulation lasts for 10 years. Note that the atmosphere is still fully coupled to the dynamical ocean.

Table 1Overview of the MPI-ESM simulations.

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2.3 CMIP6 output

We complement the dedicated MPI-ESM simulations with the output of the piControl and historical simulations from phase 6 of the Coupled Model Intercomparison Project (CMIP6; Eyring et al., 2016) to test the results using other models. We include all 23 models that provide the necessary output to compute adiabatic cooling in the stratosphere according to Eq. (2) (see Sect. 2.4.4). For models with multiple realizations, the ensemble-mean is calculated after applying Eq. (2) so that each model is weighted equally. A list of all models and the number of ensemble members can be found in Table D1 in the Appendix.

2.4 Defining forcing, feedback, WP enhancement, and adiabatic cooling

2.4.4 Adiabatic cooling in the stratosphere

Upwelling in the tropical stratosphere causes adiabatic cooling at rate K (in Ks⁻¹), which is proportional to the residual mean vertical velocity ${\stackrel{\mathrm{‾}}{w}}^{*}$ and the deviation of the temperature profile $\frac{\partial T}{\partial z}$ from a dry adiabat $-\frac{g}{c_p}$ (Birner and Charlesworth, 2017):

$$\begin{array}{}\text{(1)}& K=-{\stackrel{\mathrm{‾}}{w}}^{*}\left({\displaystyle \frac{\partial T}{\partial z}}+{\displaystyle \frac{g}{c_p}}\right),\end{array}$$

with the specific heat capacity of dry air c_p and gravitational acceleration g. The residual mean vertical velocity ${\stackrel{\mathrm{‾}}{w}}^{*}$ is obtained from a transformed Eulerian mean analysis (e.g., Butchart, 2014). ${\stackrel{\mathrm{‾}}{w}}^{*}$ combines the mass flux contributions from the mean velocity w and the eddies (Butchart, 2014) and therefore better represents the mass flux than w alone. Using the hydrostatic approximation $\mathit{\rho }\mathrm{d}z=-\mathrm{d}p/g$, we calculate the integrated adiabatic cooling of the stratosphere as the power flux density Q_adi (in Wm⁻²) according to

$$\begin{array}{}\text{(2)}& Q_{\text{adi}}=c_p\underset{\text{strat.}}{\int }K\left(z\right)\mathit{\rho }\left(z\right)\mathrm{d}z=-{\displaystyle \frac{c_p}{g}}\underset{\mathrm{100}\text{hPa}}{\overset{\mathrm{1}\text{hPa}}{\int }}K\left(p\right)\mathrm{d}p.\end{array}$$

By vertically integrating over the stratosphere, we effectively treat it as one layer that causes adiabatic cooling. Changing the lower limit to 70 hPa changes the numbers by up to 25 % but not in a way that would affect the conclusions.

The changes in K can be decomposed linearly into contributions from changes in ${\stackrel{\mathrm{‾}}{w}}^{*}$ and $\frac{\partial T}{\partial z}$:

$$\begin{array}{}\text{(3)}& {\displaystyle }{\mathrm{\Delta }}_{{\stackrel{\mathrm{‾}}{w}}^{*}}K={\displaystyle \frac{\partial K}{\partial {\stackrel{\mathrm{‾}}{w}}^{*}}}{|}_{\mathrm{0}}\mathrm{\Delta }{\stackrel{\mathrm{‾}}{w}}^{*}=-({\displaystyle \frac{\partial T}{\partial z}}{|}_{\mathrm{0}}+{\displaystyle \frac{g}{c_p}})\mathrm{\Delta }{\stackrel{\mathrm{‾}}{w}}^{*},\text{(4)}& {\displaystyle }{\mathrm{\Delta }}_{\frac{\partial T}{\partial z}}K={\displaystyle \frac{\partial K}{\partial \frac{\partial T}{\partial z}}}{|}_{\mathrm{0}}\mathrm{\Delta }{\displaystyle \frac{\partial T}{\partial z}}=-{\stackrel{\mathrm{‾}}{w}}^{*}{|}_{\mathrm{0}}\mathrm{\Delta }{\displaystyle \frac{\partial T}{\partial z}}.\end{array}$$

The notation |₀ indicates values in the unperturbed state, i.e., from the piClim-control or piControl simulation. Plugging these cooling rates into Eq. (2) yields the adiabatic-cooling changes ΔQ_adi due to changes in ${\stackrel{\mathrm{‾}}{w}}^{*}$ and $\frac{\partial T}{\partial z}$.

Figure 3(a) Annual-mean TOA effective forcing obtained from the difference between the forced simulations with fixed SST and the control simulation with fixed SST. (b) Ensemble-mean 2 m temperature change patterns (ratio of local to global mean temperature change) of the radiatively forced coupled simulations. Values greater than 1 (green) indicate cooling stronger than the global average, while values lower than 1 (pink) indicate cooling that is weaker than average. Values lower than zero indicate warming. The WP and tropics are shown with solid and dashed lines, and the field average over each region is shown in the respective box. The global mean is shown at the top of each panel. Standard errors are negligible compared to the shown precision in (a). In (b), standard errors of the means over the WP and the tropics are ≈0.04–0.05 KK⁻¹.

3.1 Effects of the TOA-forcing pattern on the temperature change pattern

First, we explore the hypothesis that the WP-enhanced forcing pattern from volcanic aerosol causes the WP-enhanced temperature response. The TOA effective-forcing fields of the radiatively forced simulations are shown in Fig. 3a. All fields average globally to approximately −3.5 Wm⁻² but exhibit different patterns. Compared to the relatively uniform 0.5 × CO₂ TOA effective-forcing pattern, Aero exhibits a pronounced forcing pattern. The TOA forcing of Aero is 1.5 Wm⁻² more negative in the WP than in the global mean, mainly due to three effects (Fig. C1 in the Appendix): first, a stronger instantaneous forcing in the tropics than in the extratropics due to higher aerosol concentration and insolation (−1 Wm⁻²); second, a weaker LW effect over the WP than over the entirety of the tropics (−0.2 Wm⁻²) due to the LW effect being weaker over high clouds than over low clouds or the surface; third, more negative SW cloud adjustments over the WP than over the entirety of the tropics (−0.3 Wm⁻²). The last point may be model-dependent and differs from Marshall et al. (2020), who find strong positive SW cloud adjustments in UK-ESM.

By design, the pCO₂ TOA-forcing field shares the Aero forcing field's main features, although it is slightly less enhanced over the WP, which we will address later. The TOA effective-forcing fields of Aero and pCO₂ agree well – not only in terms of the annual mean but also in each month (Figs. A1 and A2 in the Appendix).

The temperature change patterns of all coupled 10-year simulations are broadly similar (Fig. 3b). Temperature change is amplified in the Arctic; moderate in low latitudes, including the WP; and suppressed over the Southern Ocean. The most relevant region for the feedback is the WP, where small differences have substantial impacts on the global feedback, with changes of roughly −0.2 ${\mathrm{Wm}}^{-\mathrm{2}}{\mathrm{K}}^{-\mathrm{1}}$ per 0.1 WPI_T points in MPI-ESM (Fig. 1). The definition ${\text{WPI}}_T=\text{d}{T}_{\text{WP}}/\text{d}{T}_{\text{global}}$ is equivalent to the WP average of the temperature pattern shown in the black box in Fig. 3b. Despite the fact that the temperature pattern differences among the simulations over the WP are relatively small compared to those in other regions, these small changes dominate the global mean radiative feedback parameter (Dong et al., 2019; Günther et al., 2022).

Although Aero and pCO₂ are almost equally strongly forced in the WP, the WPI of the temperature pattern of pCO₂ (0.92) is smaller than that of Aero (1.03). We perform Student's t tests on the distributions of WPI_T from the 40 ensemble members of each forcing agent under the null hypothesis that they are drawn from distributions with the same average. While the WPI_T values of 0.5 × CO₂ and pCO₂ are not significantly different (p=0.2), the WPI_T values of Aero and pCO₂ are distinct ($p={\mathrm{10}}^{-\mathrm{6}}$). Although the TOA-forcing patterns of pCO₂ and Aero are similar, their temperature change patterns are not when measured by WPI_T (Fig. 1). This contradicts the hypothesis that the WP-enhanced TOA-forcing pattern of Aero causes the WP-enhanced temperature change pattern. If that were the case, the WP should cool equally strongly in Aero and pCO₂.

This result is limited by the fact that the forcing pattern of pCO₂ is not quite as WP-enhanced as in Aero: the WPI_F (WP forcing divided by global mean forcing) is only 1.36 in pCO₂ but is 1.44 in Aero. However, even when applying a correction factor of $\mathrm{1.44}/\mathrm{1.36}$ to the WPI_T values of pCO₂, the WPI_T values remain significantly different from Aero, albeit with a higher p value (p=0.02).

In summary, the pCO₂ simulation with a TOA-forcing pattern almost as WP-heavy as Aero does not produce a temperature change pattern as WP-heavy as Aero. Instead, its temperature change pattern is rather similar to the 0.5 × CO₂ simulation (see also Fig. 1). Hence, we arrive at the conclusion that another process which is specific to aerosol forcing must cause the temperature pattern differences.

Figure 4Effective forcing of the radiatively forced simulations at the TOA (a, b, c) and at the surface (d, e, f) and their difference (g, h, i). The difference between TOA and surface effective forcing is the effective forcing on the atmosphere, and this can be interpreted as a redistribution of negative forcing from blue to red regions when going from the TOA to the surface. The WP and tropics are shown with solid and dashed lines, and the field average over each region is shown in the respective box. The global mean is shown at the top of each panel. The standard errors are generally negligible compared to the shown precision, except for the WP mean of the surface and TOA–surface (≈0.2 Wm⁻²) and the tropical mean of the surface and TOA–surface (≈0.1 Wm⁻²).

3.2 Surface forcing pattern

The rationale of the TOA-forcing hypothesis was that stronger forcing in the WP could lead to stronger temperature change in the WP. However, the ocean does not directly respond to the forcing at the TOA but rather responds directly to the forcing at the surface, which might therefore be more relevant. In the following section, we examine the surface effective forcing and how it differs from the TOA effective forcing.

There are multiple constraints to surface forcing: the land and atmosphere have small heat capacities and therefore cannot act as energy reservoirs on timescales of the 100-year fixed-SST simulation. If there were substantial fluxes into the atmosphere or the land, they would heat up or cool down until the fluxes become zero. The timescale of these adjustments is fast due to the small heat capacities of the land and atmosphere. Only the ocean (due to its fixed SST) and the TOA can support non-zero fluxes in the steady state of the fixed-SST simulations. These considerations imply that the surface effective forcing over land must be zero. The fact that the global-mean flux into the atmosphere is zero implies that the global-mean effective forcings at the TOA and the surface must be equal (see also Eq. 5).

Figure 4 shows the annual-mean effective radiative forcing at the TOA and the surface, as well as their difference, diagnosed from the fixed-SST simulations. The surface forcing exhibits a richer spatial structure than the TOA forcing. Furthermore, the WP intensification of the forcing in Aero is much more pronounced at the surface than at the TOA: at the WP surface, it is more than twice as strong as in the global mean. In comparison, the surface forcing in pCO₂ is only slightly more WP-enhanced than in 0.5 × CO₂.

The difference between the TOA and surface forcing is the effective forcing that acts on the atmosphere, which is zero in the global mean but has a pattern. It must be locally balanced by changes in the horizontal heat flux divergence Q since the atmosphere has no relevant sinks or sources of energy on long timescales.

F_TOA and F_surface denote the effective forcing at the TOA or at the surface, respectively. F_atm denotes the effective forcing on the atmosphere. All effective-forcing fields are a function of longitude and latitude. Both sides of Eq. (5) can be globally averaged to zero.

The forcing on the atmosphere equals the change in the horizontal atmospheric heat flux divergence at fixed SST. Considering the perspective from the TOA looking down to the surface, the atmosphere shifts the negative forcing from grid points with negative values towards grid points with positive values. The negative forcing is redistributed from columns over land to columns over ocean in all simulations (Fig. 4, bottom row). This effect arises somewhat artificially from the fact that effective forcing is diagnosed at fixed SST concentrations and sea ice concentrations but not fixed land temperatures. In Aero, there is an additional convergence of negative forcing at the WP surface (2.4± 0.2 Wm⁻² compared to 1.0± 0.2 Wm⁻² in pCO₂ and 1.3± 0.2 Wm⁻² in 0.5 × CO₂).

We argue that the surface forcing is the critical factor that distinguishes aerosol from CO₂ forcing. The differences between the TOA and surface forcing are imposed by heat transport changes that arise from anomalous circulations. They come about as adjustments which are specific to the forcing agent. We hypothesize that the WP surface in Aero is so strongly forced because the anomalous atmospheric circulation leads to an anomalous energy transport out of the WP or, equivalently, moves positive forcing away from the WP surface. In the following sections, we aim to (1) explain how the differences in atmospheric-forcing divergence arise from the circulation changes and (2) determine if these differences cause the distinctions among the temperature change patterns.

3.3 Explaining the atmospheric-forcing divergence

What explains the different structures of the forcing on the atmosphere (bottom row of Fig. 4)? Most of the spatial structure arises from variations in the latent heat flux at the surface (not shown). Therefore, it is mostly the latent heat flux that reacts to energetic constraints from the atmosphere, consistently with previous studies (Fajber and Kushner, 2021; Fajber et al., 2023). However, this does not explain why the atmosphere redistributes energy and which circulations accomplish this energy transport.

Equation (6) states that the forcing on the atmosphere is balanced by heat transport. We focus on the anomalous energy export out of the WP and on the question of why this anomaly is stronger for Aero. To this end, we partition the energy export into a meridional component, i.e., the energy transport from the tropics to the extratropics, and a tropical–zonal component, i.e., the transport from the WP to tropical non-WP regions. In the TOA–surface row of Fig. 4, the meridional energy transport is equal to the average over the tropics (1.0± 0.1 Wm⁻² in Aero compared to 0.1± 0.1 Wm⁻² in 0.5 × CO₂), and the zonal energy transport is measured by the difference between the WP mean and the tropical mean (1.4± 0.2 Wm⁻² in Aero compared to 1.2± 0.3 Wm⁻² in 0.5 × CO₂).

Obvious explanations for these transports could be changes in gross moist stability, the Hadley or Walker circulations, or eddy energy fluxes. Indeed, the tropical tropospheric zonal overturning circulation has been shown to weaken as a consequence of stratospheric heating (Ferraro et al., 2014; Simpson et al., 2019). However, a weaker zonal overturning circulation cannot be the reason for increased energy flux out of the WP unless it is overcompensated for by increases in gross moist stability. We argue that the circulation changes associated with the atmospheric energy budget do not project onto the Hadley and Walker circulations. Instead, the meridional transport is accomplished via the BDC, and the tropical–zonal transport arises from an anomalous ocean–land circulation. This only applies to the direct circulation adjustments, and we do not make any statement about temperature-dependent changes to the Hadley or the Walker circulations from stratospheric aerosol forcing. The meridional and tropical–zonal components will be treated separately in the following.

Table 2Anomalous adiabatic cooling in the stratosphere calculated according to Eq. (2) and averaged over the tropics (30° N to 30° S). Negative values represent cooling. Standard errors are only shown where they are at least on the order of the precision shown, i.e., O(0.1 Wm⁻²). The lower rows show the contributions from changes in the upwelling speed and the lapse rate, respectively.

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3.3.3 Sum of meridional and zonal terms

In total, the atmosphere exports 1.3 Wm⁻² out of the WP in the 0.5 × CO₂ simulation but 2.4 Wm⁻² in Aero, which leads to enhanced negative forcing at the WP surface in Aero (Fig. 4). In Aero, the atmosphere absorbs 0.9 Wm⁻² of positive forcing in the tropics and exports it to the extratropics via the BDC (Table 2). The energy transport via the BDC explains most of the meridional energy transport and the difference between the surface forcing in the Aero and 0.5 × CO₂ experiments. The cooling of the land surface causes an additional zonal transport of energy from the WP ocean to tropical land regions via the free troposphere in all simulations. While the anomalous meridional transport via the BDC does not show substantial year-to-year variation, the zonal energy transport varies substantially interannually. Even using 100 years of fixed-SST simulations, its standard error (standard deviation in time divided by square root of sample size) is on the order of 10 % to 15 %, which is 1 order of magnitude higher than the standard error of the meridional transport. This implies the existence of substantial interannual variability, which originates from the atmosphere alone. Furthermore, the tropical–zonal energy transports of Aero and 0.5 × CO₂ differ only within 1 standard error and arise at least partly from the specifics of fixed-SST simulations, where temperatures are only prescribed at the ocean surface but not at the land surface. We therefore emphasize the BDC changes as the more important result and recommend caution in the interpretation of the zonal energy transport. In the following, we examine the forcing patterns and the meridional energy transport mechanism in CMIP6 models.

Figure 5Tropical mean changes in stratospheric adiabatic cooling in the CMIP6 historical simulations in the pre-eruption (1882 and 1990) and post-eruption years (1884 and 1992) of Krakatau and Pinatubo, respectively, compared to the piControl simulations. The value from each model is shown by a circle. The green circles are from the five models with at least 10 realizations. Together, these models account for 80 % of all realizations. All values are calculated using Eq. (2). The error bars show the multi-model mean and standard error. Negative values indicate increased adiabatic cooling.

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3.4 Testing the energy export mechanism with CMIP6 models

Salvi et al. (2023) provide an analysis of CMIP6 forcing patterns at the TOA and the surface (see their Fig. 10). For aerosol forcing from the Krakatau and Pinatubo eruptions, they find enhanced forcing in the tropics at the TOA and at the surface. However, while the WP enhancement of aerosol forcing at the surface is clearly visible, it is not substantially stronger than in the case of greenhouse gas forcing. This calls into question the existence of the BDC mechanism in CMIP6 models.

We explicitly test if the energy export due to the BDC increases after volcanic eruptions. A total of 23 models provide the necessary output to compute the adiabatic cooling in the historical coupled simulations. We compute the changes in the adiabatic cooling in the tropics according to Eq. (2) for the first post-eruption year of the Krakatau and Pinatubo eruptions (1884 and 1992, respectively). Since we restrict the computations to the tropics, where the eddy contribution is small, we simplify the analysis by using w instead of ${\stackrel{\mathrm{‾}}{w}}^{*}$ for the CMIP6 analysis. In MPI-ESM, this leads to an underestimate of the additional adiabatic cooling from aerosol forcing of approximately 10 %.

Most CMIP6 models show a moderate increase in adiabatic cooling, with multi-model averages of 0.12 and 0.13 Wm⁻² for the Krakatau and Pinatubo eruptions, respectively (Fig. 5). The multi-model mean ± standard error does not overlap with zero, indicating the presence of a significant effect. The 20 % to 80 % intervals are [−0.22, −0.01] for Krakatau, [−0.25, 0.01] for Pinatubo, and [−0.11, 0.05] for the pre-eruption years. The adiabatic cooling in the pre-eruption years (1882 and 1990) is indistinguishable from the control simulation, which implies that the additional adiabatic cooling in the post-eruption years is indeed caused by the eruption and not some other historical forcing agent.

The effect is smaller than what we find in the fixed-SST simulations of MPI-ESM: assuming a peak global mean effective forcing from Krakatau and Pinatubo of approximately 1.8 Wm⁻² (Salvi et al., 2023), the BDC cools the tropics by about 7 % of the global mean forcing in CMIP6 compared to about 25 % in our simulations. This difference is diminished when only taking into account the models with at least 10 realizations, where the influence of internal variability is reduced. In these models, the transport from the BDC is −0.16 [−0.24, −0.07] Wm⁻² for Krakatau and −0.25 [−0.33, −0.16] Wm⁻² for Pinatubo, corresponding to roughly 9 % and 14 % of the global mean forcing, respectively. Apart from model differences, the remaining disparity between our results and the CMIP6 results could arise for three systematic reasons: first, using w instead of ${\stackrel{\mathrm{‾}}{w}}^{*}$ leads to a small underestimation. Second, the aerosol is short-lived, and not all of the post-eruption years are equally strongly affected by the presence of the aerosol. Third, the CMIP6 estimate is likely to be biased low because the historical coupled simulations cool in the post-eruption year, and there is a positive correlation between temperatures and the strength of the BDC (Garfinkel et al., 2017). The last point does not compromise our finding that the BDC reshapes the surface forcing pattern since the forcing is defined at zero surface temperature change.

In agreement with our CMIP6 analysis, model studies consistently show an acceleration of the BDC after volcanic eruptions (Garfinkel et al., 2017; Garcia et al., 2011; Pitari and Rizi, 1993; Pitari and Mancini, 2002; Aquila et al., 2013; Toohey et al., 2014; Muthers et al., 2016). In contrast, studies using reanalysis or observations provide mixed results. Some studies find enhanced wave activity in at least one hemisphere (Graf et al., 2007; Schnadt Poberaj et al., 2011), while others do not find stratospheric circulation changes after volcanic eruptions (Diallo et al., 2012; Seviour et al., 2012; SPARC, 2022). Since reanalysis products do not assimilate aerosol data and are hence ignorant to the ensuing heating rate anomalies in the stratosphere, they might not be a suitable tool to study the links between stratospheric heating and the BDC (Abalos et al., 2015). The absence of the upwelling effect in observational records might also be related to the choice of the metric: Toohey et al. (2014) argue that the upwelling change might be most pronounced in the middle and upper stratosphere, while observational studies focus on upwelling in the lower stratosphere.

Figure 6Ensemble-mean 2 m temperature change patterns (ratio of local to global mean temperature change) of the radiatively forced simulations (a–c) and the q-flux-forced simulations (d–f), as well as their difference (g–i). In panels (a) to (f), values greater than 1 (green) indicate cooling that is stronger than the global average, while values lower than 1 (pink) indicate cooling that is weaker than average. Values lower than zero indicate warming. In  (a)– (f), the standard errors of the means over the WP and the tropics are ≈0.04–0.05 KK⁻¹. For the differences (g–i), the standard errors are ≈0.07 KK⁻¹.

3.5 Does the surface forcing pattern cause the surface temperature pattern?

If the previously demonstrated differences in the surface forcing cause the temperature pattern differences then these differences should appear in surface-forced simulations without any changes in aerosol or CO₂ concentrations. While this seems intuitive, it is not straightforward that stronger surface forcing in the WP causes stronger temperature changes in the WP. Results from q-flux Green's functions have shown that the temperature response to a localized surface flux is typically non-local (Lin et al., 2021; Liu et al., 2018a, b, 2022). We use the q-flux simulations to establish the link between local forcing and local temperature change in the WP. They are forced by a surface heat sink or source, each of them with a global mean of −3.5 Wm⁻², but with the patterns being diagnosed from the fixed-SST simulations (Fig. 4d–f).

Results from the q-flux simulations in terms of the temperature pattern and feedback are shown in Fig. 1. The simulations with more strongly concentrated surface forcing in the WP also cause stronger temperature changes in the WP (Aero > pCO₂ $>\mathrm{0.5}\times$ CO₂). These results support our hypothesis that stronger surface forcing in the WP leads to stronger surface temperature change in the WP. However, the temperature patterns differ between the q-flux-forced simulations and the corresponding radiatively forced simulations (Fig. 6), particularly with respect to temperature changes in the WP and the tropics. All q-flux-forced simulations cool more strongly in the WP and in the tropics than their radiatively forced counterparts. Generally, the pattern differences between radiatively and q-flux-forced simulations of the same forcing agent are on the same order of magnitude as the differences among the forcing agents. Possible reasons for these deviations are (i) the lack of changes in the atmospheric CO₂ concentrations and/or aerosol load, which affects the vertical structure of the atmosphere and the general circulation; (ii) the lack of forcing over land; (iii) the fact that we only include heat fluxes and no momentum or freshwater fluxes to force the ocean surface. Aquaplanet simulations show little difference between radiatively forced and q-flux-forced simulations (Haugstad et al., 2017), rendering hypothesis (i) – the absence of CO₂ and/or aerosol in the atmosphere – as a cause for the differences unlikely. On the other hand, both CO₂-forced simulations show a more positive PDO (Pacific Decadal Oscillation)-like temperature change pattern in the radiatively forced simulations compared to the q-flux-forced simulations, which could be an indication that this part of the temperature pattern is due to the direct effect of CO₂. In CESM2 simulations with historical forcing, the absence of wind stress forcing causes statistically significant changes in the SST pattern (McMonigal et al., 2023) towards a more WP-enhanced temperature pattern, consistent with the bias in our simulations and with hypothesis (iii), the momentum-forcing hypothesis.

The exact causes are beyond the scope of this study and warrant further research. Despite the shortcomings, we interpret the results from the q-flux-forced simulations to support our hypothesis that strong surface forcing in the WP leads to strong surface cooling in the WP.