We use the Hadley Centre Global Environment Model version 3 (HadGEM3) variant of the Met Office Unified Model (MetUM) version 8.4, which has been used for both numerical weather prediction and climate simulation. It is configured with the Global Atmosphere (GA4.0) and comprises a non-hydrostatic fully compressible dynamical core that uses a semi-implicit semi-Lagrangian advection scheme in terrain-following hybrid height coordinates (Walters et al., 2014). We run the atmosphere-only configuration (HadGEM3-A) at N96 horizontal resolution (1.875∘ × 1.25∘, ∼135 km in mid-latitudes) with 85 levels (L85) from the surface to an altitude of ∼85 km. Interactions of the flow-blocking drag associated with the orographic gravity wave drag (OGWD) are parameterized, as detailed in Webster et al. (2003). Similarly, a spectral sub-grid parameterization is used for the representation of the gravity wave drag induced in the upper stratosphere and mesosphere, forced by non-orographic gravity wave drag (NOGWD) such as convective processes and fronts, which enables HadGEM3 to simulate a realistic quasi-biennial oscillation (QBO) as detailed in Scaife et al. (2002).

Seven 50-year-long time-slice simulations were performed with HadGEM3-A with fixed boundary conditions including prescribed SSTs and sea ice. The experiment names and IDs are shown in Table 1. The reference simulation (run A) uses boundary conditions, including greenhouse gas (GHG) concentrations and natural and anthropogenic primary aerosol or reactive gas emissions, set to pre-industrial (year 1850) values following the Coupled Model Intercomparison Project 5 protocol (CMIP5; Lamarque et al., 2010; Taylor et al., 2012). The reference SSTs and sea ice concentrations (SICs) are annually repeating fields taken as the monthly-mean multi-model mean (MMM) from the CMIP5 piControl simulations (Taylor et al., 2012). The MMM reference SST and SIC fields are constructed from the average of the last 150 years of the piControl experiments from the 26 CMIP5 models listed in the Supplement (Table S1).

Six perturbation experiments are performed to isolate different components of the long-term response in the CMIP5 abrupt 4×CO2 experiment, which instantaneously quadruples CO2 from its pre-industrial concentration. We first calculate the CMIP5 monthly-mean MMM SST in the abrupt 4×CO2 experiment using the final 50 years (years 101–150) of each model run (Table S1). The annual-mean SST anomalies compared to the reference pre-industrial state are shown in Fig. 1a. Note that in all the perturbation experiments, SIC is held fixed at the reference values. This is artificial, but it enables the effects of SSTs on the BDC and associated mechanisms to be isolated from the possible effects of changing sea ice on the stratosphere (e.g. Kim et al., 2014; McKenna et al., 2018). We performed a separate experiment in which SIC was also changed to the CMIP5 MMM 4×CO2 response along with global SSTs and atmospheric CO2, but this showed no significant effect of changing SIC on the BDC (not shown) and therefore will not be discussed further.

The first perturbation experiment (run B) accounts for the full (atmosphere + SST) abrupt 4×CO2 response and is designed to simulate the long-term centennial response to CO2 forcing. The second perturbation experiment (C) only accounts for the CO2 rapid adjustment by quadrupling atmospheric CO2 concentrations while holding SSTs and SIC at their pre-industrial values. The third experiment (D) imposes a monthly-varying globally uniform SST anomaly derived from the global-mean multi-model mean 4×CO2 SST anomaly relative to the control. In the annual and multi-model mean this is equal to 3.4 K (Fig. 1b). Note the CMIP5 MMM global SST anomaly is smaller than the global-mean surface air temperature (GSAT) change in the abrupt 4×CO2 experiment because land areas warm more than the ocean (e.g. Joshi and Gregory, 2008). In the fourth perturbation experiment (E), we subtract the monthly-varying uniform warming value from the 4×CO2 anomalies to impose the local deviations in SST from the global uniform value (i.e. the SST pattern). The SST pattern is shown in Fig. 1c; it is comprised of relatively stronger warming across the tropics in the Pacific, Atlantic, and Indian Ocean basins and in the North Pacific and relatively weaker warming across the Southern Ocean, in the North Pacific warming hole region, and in the vicinity of the South Pacific stratocumulus decks.

By construction, the sum of the SST anomalies in runs D and E equals the full SST anomalies of run B. Note that the change in annual-mean GSAT simulated in runs B and D (4.3 and 4.0 K, respectively) is larger than the imposed global-mean SST anomaly, partly because of the enhanced warming response over land. While SSTs are held fixed in run C, there are changes to land temperatures that cause a small GSAT response (0.43 K). Finally, although the global-mean SST change in run E is zero by construction, there are changes to land temperatures that lead to a small GSAT response (0.45 K).

There is substantial inter-model spread in the modelled global-mean SST change in the abrupt 4×CO2 experiments (Flato et al., 2013). To investigate the effect of this spread on the BDC, and to place the rapid adjustment and SST pattern effects into the context of model uncertainty in the global surface warming due to CO2, we perform two further uniform SST warming sensitivity runs. These are chosen to be the lowest (annual-mean ∼2.1 K; run F) and highest (annual-mean ∼4.9 K; run G) global-mean SST changes from the 26 CMIP5 models used in this study. These values come from the INMCM4 (Volodin, 2013) and IPSL-CM5A-LR (Dufresne et al., 2013) models, respectively. The annual-mean GSAT change in runs F and G is 3.0 and 6.1 K, respectively.

Since HadGEM3-A does not include interactive chemistry, we prescribe zonal-mean pre-industrial ozone concentrations in all the experiments following the Coupled Model Intercomparison Project 6 (CMIP6; Eyring et al., 2016) protocol, based on the CMIP6 experiments run with HadGEM3-GC3.1 (Kuhlbrodt et al., 2018; Williams et al., 2018). It should be noted that keeping ozone concentrations fixed in all our experiments will implicitly neglect the effects of any ozone feedbacks from both the chemical effects of increased CO2 and the transport effects from an altered BDC; this includes effects on the thermal structure of the upper troposphere, especially around the tropical upper troposphere and lower stratosphere (Nowack et al., 2015; Chiodo and Polvani, 2017) and on upper-stratospheric temperatures (Maycock, 2016).

To diagnose the BDC and its changes, we make use of the transformed Eulerian mean (TEM) circulation diagnostics (Andrews et al., 1987; Andrews and McIntyre, 1976, 1978) as calculated internally by the model. The TEM residual circulation velocities (v‾*, w‾*) are defined as in Andrews et al. (1987): 1v‾*=v‾-1ρ0∂∂zρ0v′θ′‾∂θ‾/∂z,w‾*=w‾+1acos⁡φ∂∂φv′θ′‾cos⁡φ∂θ‾/∂z, where overbars denote a zonal-mean quantity and primes the departure from the zonal mean. v and w are the meridional and vertical components of wind velocity, respectively, ρ0 is the log-pressure density, z=-Hln⁡(p/ps) is the log-pressure vertical coordinate (height), H is the scale height, p is the pressure at a specified level with ps the pressure at the surface, v′θ′‾ is the eddy heat flux, θ is the potential temperature, α is the Earth radius, and ϕ is the latitude. Using v‾* from Eq. (1) we further calculate the residual mass streamfunction Ψ‾*(ϕ, z) as 2Ψ‾*(ϕ,z)=2παcos⁡ϕg∫bottomtopv‾*dp, where g is the acceleration due to gravity. Equation (2) is integrated from the top of atmosphere to the surface using the boundary condition that Ψ‾*=0 at the top of the atmosphere (p=0). Subsequently, we calculate the net downward mass flux in each hemisphere, by finding Ψ‾max* and Ψ‾min* in the NH and SH, respectively, at each pressure level. The net tropical upward mass flux, which is equal to the sum of the downward mass fluxes in each hemisphere, can then be expressed as (Rosenlof, 1995) 3tropicalupwardmassflux=2πaΨ‾max*-Ψ‾min*. We apply the “downward control” principle (DCP; Haynes et al., 1991) to further separate the contributions to the tropical upward mass flux from resolved waves due to the divergence of Eliassen–Palm flux (EPF) and contributions from OGWD and NOGWD. Resolved waves and parameterized gravity wave drag (OGWD/NOGWD) constitute the eddy-induced total zonal forces F‾. Under steady-state conditions, the Ψ‾*(ϕ, z) at a specified log(pressure) height, z, is related to the vertically integrated F‾ above that level along a surface of constant zonal-mean absolute angular momentum m‾=acos⁡ϕ(υ‾+aΩcos⁡ϕ), where υ‾ is the zonal-mean zonal wind and Ω is Earth's rotation rate (Haynes et al., 1991). Outside of the tropics, m‾ is approximately constant at a fixed latitude, ϕ, resulting in the following equation (Haynes et al., 1991): 4Ψ‾*(ϕ,z)=∫z∞ρ0a2F‾cos⁡2ϕm‾ϕϕ=ϕ(z′)dz, where m‾ϕ≈-2Ωa2sin⁡ϕcos⁡ϕ is the quasi-geostrophic limit. The boundary conditions are Ψ‾*→0 and ρ0w‾*→ as z→∞.

Figure 2 shows latitude–pressure cross sections of the annual-mean and zonal-mean temperature anomalies from the reference pre-industrial simulation for perturbation runs B–E. The full response (Fig. 2a) exhibits the canonical pattern of temperature change due to increased CO2, with tropospheric warming that maximizes in the tropical upper troposphere (by ∼8 K) and stratospheric cooling that increases with height (Collins et al., 2013). Note that Arctic amplification in the lower troposphere is small here compared to coupled atmosphere–ocean models (Collins et al., 2013), presumably because we do not impose sea ice changes in the runs.

The rapid adjustment due to changes in atmospheric CO2 (Fig. 2b) accounts for most of the stratospheric cooling seen in the full response, with cooling of ∼15 K in the upper stratosphere. However, the stratospheric cooling in run C (Fig. 2b) is more uniform in latitude than in the full experiment and more closely resembles the purely radiative response to CO2 (Fels et al., 1980). In the troposphere, the rapid adjustment induces a weak (<1 K) warming that is fairly homogeneous and comes partly from the small changes in GSAT, since land temperatures are not held fixed. Most of the tropospheric zonal-mean warming is reproduced by imposing the uniform SST warming (Fig. 2c), including the tropical upper-tropospheric amplification of up to 9 K and the extension of warming into the subtropical lower stratosphere in both hemispheres. In the stratosphere, the uniform SST warming induces an anomalous meridional temperature gradient, with cooling of 2–3 K in the tropical middle and upper stratosphere and warming in the extratropics and polar regions. This pattern accounts for most of the latitudinal variation in stratospheric cooling seen in the full response (Fig. 2a).

The SST pattern experiment (Fig. 2d) exhibits a similar morphology in the temperature response to the uniform SST warming run, albeit much weaker in amplitude. In the troposphere, the SST pattern induces a weak warming that is comparable in magnitude to the rapid adjustment (Fig. 2b), but with a weak upper-tropospheric amplification that enhances the effect of the uniform warming (Fig. 2c). This upper-tropospheric amplification suggests enhanced tropical deep convection, which may be consistent with the imposed anomalous tropical SST warming (Fig. 1c).

The thick yellow lines in Fig. 2 denote the tropopause pressure for each perturbation experiment. These can be compared to the climatological tropopause in the reference simulation (thick black lines). The lifting of the tropopause by ∼1 km within the deep tropics in the full experiment comes mainly from the uniform SST warming (∼80 %) with the remaining 20 % coming from the SST pattern. However, the maximum tropopause lifting (>1.2 km) occurs in the extratropics of both hemispheres, especially over the Arctic polar cap (not shown).

The annual-mean zonal-mean zonal wind anomalies in the four perturbation experiments are shown in Fig. 3. The full 4×CO2 response (Fig. 3a) shows the familiar pattern of a strengthening and upward shift of the subtropical jets, a strengthening and poleward shift of the mid-latitude westerlies in the SH, and increased westerlies in the SH stratosphere (Collins et al., 2013). The strengthened subtropical jets arise mainly from the uniform SST warming (Fig. 3c) with a small contribution from the SST pattern (Fig. 3d). In contrast, the rapid adjustment (Fig. 3b) does not induce a strengthening of the subtropical jets, but it does explain a significant part of the increased westerlies in the SH extratropics, particularly in the upper stratosphere. The SST pattern effect also contributes to the increased SH stratospheric westerlies, but the uniform SST warming shows the largest increase. In the NH, the full experiment shows stronger westerlies in the lower stratosphere and weakened westerlies near the subtropical stratopause. The anomalous lower-stratospheric westerlies are contributed by the uniform warming in the subtropics and mid-latitudes and the rapid adjustment in the extratropics and polar region. The uniform warming also causes weakened westerlies in the subtropical upper stratosphere, with a smaller effect from the rapid adjustment.

The full 4×CO2 response shows significant zonal wind anomalies in the tropical stratosphere between 50 and 1 hPa, which is also seen in the uniform SST warming experiment. This is likely related to changes to the QBO properties under climate change, which have been noted in other idealized GCM experiments (e.g. Kawatani et al., 2011), though a detailed investigation of the QBO is beyond the scope of this study.

The zero wind lines (u‾=0), which demarcate the “critical lines” for linear stationary Rossby waves (Dickinson, 1968), are shown by the thick lines in Fig. 3. In the stratosphere, there is a clear equatorward contraction of the zero wind lines in both hemispheres in the full 4×xCO2 experiment. Previous studies have connected this to increased penetration of Rossby wave activity into the subtropical lower stratosphere (Shepherd and McLandress, 2011). The contraction of the zero wind lines is primarily due to the uniform SST warming, with a modest contraction also seen in the rapid adjustment and SST pattern experiments.

Figure 4 shows latitude–pressure cross sections of the annual-mean residual vertical velocity (w‾*) anomalies with respect to the reference simulation for experiments B–E. The uniform SST warming accounts for most of the increased tropical lower-stratospheric upwelling (∼70 % between 30∘ S and 30∘N over the layer 100–50 hPa) seen in the full 4×xCO2 response. However, there are also significant, but small, increases in tropical lower-stratospheric upwelling induced by the rapid adjustment (∼17 %) and the SST pattern perturbations (∼13 %) (Fig. 4b and d). While comparatively small compared to the effect of the uniform SST warming, the increases in w‾* in the tropical lower stratosphere from the SST pattern are broadly comparable in magnitude to the effects of ENSO on tropical upwelling found in other modelling studies (Calvo et al., 2010; Simpson et al., 2011).

The turnaround latitudes are overlaid as thick lines in Fig. 4. A quadrupling of CO2 leads to a narrowing of the upwelling region in the lower and middle stratosphere that maximizes around ∼30 hPa (Hardiman et al., 2014). This arises predominantly from the uniform SST warming (Fig. 4c), with additional weaker contributions from the rapid adjustment and SST patterns (Fig. 4b and d). In contrast, in the upper stratosphere (10 hPa) the upwelling region widens in the NH in particular (see Hardiman et al., 2014). The widening of the upwelling region in the NH upper stratosphere arises almost entirely from the rapid adjustment, while the smaller tropical widening in the SH upper stratosphere is contributed by all three components.

We move now to evaluating the changes in downwelling in the extratropics. The full 4×CO2 experiment shows enhanced downwelling over the Arctic throughout the stratosphere. Both the rapid adjustment and uniform SST warming induce comparable increases in downwelling in the Arctic, while the SST patterns do not produce significant w‾* changes in this region. In the SH, the full perturbation generates stronger downwelling in the upper stratosphere and weaker downwelling in the middle and lower stratosphere below 10 hPa. All three components produce increased downwelling in the Antarctic upper stratosphere, with the largest change from the uniform SST warming and the rapid adjustment. In the lower stratosphere, the uniform SST and SST patterns both generate reduced downwelling as seen in the full 4×CO2 experiment.

The relationship of the changes in residual circulation to the overall mass transport in the stratosphere can be seen in Figs. 5 and 6, which show the residual mass streamfunction anomalies (Ψ*) in the solstice seasons December–February (DJF) and June–August (JJA) in the four experiments. For comparison, the Supplement (Fig. S1) shows the annual-mean Ψ* responses. As the winter hemisphere cell is the dominant one, the climatological circulation in DJF and JJA is significantly stronger in the NH and SH, respectively. The largest response in both hemispheres occurs in DJF (Fig. 5), while the NH exhibits a stronger response compared to the SH. In DJF, the response to the SST patterns in the NH is confined to the subtropical lower stratosphere (Fig. 5d), while the rapid adjustment (Fig. 5b) and uniform SST warming (Fig. 5c) induce increased poleward transport across most of the stratosphere, with the latter showing around 3 times larger anomalies near the maximum in the subtropical lower stratosphere. The peak NH anomaly due to the rapid adjustment is around double that for the SST patterns in DJF. Specifically, in the lower stratosphere (100–50 hPa) between 0 and 60∘ N, the uniform SST warming accounts for ∼65 % of the full response, the rapid adjustment contributes ∼26 %, and the SST patterns contribute the remainder. Conversely, in the middle and upper stratosphere between 30 and 1 hPa, over the same latitude bands, the rapid adjustment effect becomes more important, surpassing the contribution of the uniform SST warming accounting for 48 % and 46 % of the full response, respectively. In JJA (Fig. 6), the increase in the SH mass transport is largely is largely present in the subtropics while the opposing changes in the mid-latitude lower stratosphere seen as a reduction in the streamfunction arise from both the uniform SST warming (Fig. 6c) and the SST patterns (Fig. 6d). In the SH subtropical (0–30∘ S) lower stratosphere (100–50 hPa), the uniform SST warming accounts for ∼70 % of the full response with the rapid adjustment contributing roughly 20 % and the remaining 10 % due to the SST pattern. The strengthened SH poleward transport due to the uniform SST warming is confined to the SH subtropical lower stratosphere, while the rapid adjustment (Fig. 6b) induces poleward flow that also extends into the NH and is associated with the deep branch of the BDC. However, it should be noted that the SH response is generally weaker than in the NH, especially in the middle and upper stratosphere over both solstice seasons. The deep branch of the circulation exhibits distinct hemispheric asymmetries, explaining the differences in the magnitude of downwelling over the SH and NH polar caps seen in Fig. 4. This asymmetry is associated with a significantly stronger poleward NH branch of the circulation compared to its SH counterpart with important contributions by an equally stronger NH mesospheric cell overall (not shown).

We lastly consider the extent to which the combined residual circulation anomalies from the rapid adjustment, global uniform SST, and SST pattern experiments match the full 4×CO2 response. This comparison is shown in Fig. S2. The main differences are that the combined responses overpredict the enhanced poleward flow in the NH extratropical lower stratosphere, while there are dipole anomalies straddling the Equator in the tropical mid-stratosphere associated with the differences seen in the QBO features across the experiments. Nevertheless, the differences between the linear sum of responses and the full experiment are generally small compared to the overall changes, which supports the use of the experiments to decompose the total response into separate parts.

To understand the changes in residual circulation shown in Figs. 4–6, we now focus on the wave forcing in each experiment. As the distribution of wave forcing shows a strong annual cycle, we separate the changes into the winter and summer seasons in each hemisphere (DJF and JJA) as in Figs. 5 and 6. Figure 7 shows the DJF average Eliassen–Palm flux divergence (EPFD) anomalies from the pre-industrial era for runs B–E along with the anomalous EPF vectors. We multiply the EPFD anomalies with cos⁡φ to represent the torque exerted on the zonal flow. The full experiment (Fig. 7a) shows increased EPF divergence in the NH extratropical upper stratosphere and in the mid-latitude middle stratosphere. In the SH, there is a broad region of enhanced EPF convergence peaking around 50–60∘ S over a layer spanning 3 to 70 hPa. There is a reduction in EPF convergence near the SH subtropical stratopause. Between ∼50∘ and 70 hPa, there is enhanced EPF convergence in the tropics and subtropics in both hemispheres. This modulation in the location of the maximum in the resolved wave forcing is associated with the equatorward movement of the critical layers (Fig. 3), allowing more Rossby wave activity to penetrate into the subtropical latitudes, accelerating the shallow branch of the BDC, consistent with the findings of Shepherd and McLandress (2011).

The rapid adjustment and uniform SST warming contribute similar increases in EPF convergence in the NH upper stratosphere in DJF (Fig. 7b and c). In the NH middle stratosphere, the uniform SST warming explains most of the increase in EPF convergence seen in the full experiment, but the rapid adjustment does contribute in the region 20–40∘ N. The uniform SST warming also contributes to most of the increase in EPF convergence in the lower to middle SH extratropical stratosphere in austral summer, but the rapid adjustment and SST pattern (Fig. 7d) do make smaller but significant contributions to the increased wave forcing in that region. The uniform SST warming produces most of the enhanced EPF convergence in the tropical and subtropical upper troposphere–lower stratosphere (UTLS).

Figure 8 shows the EPFD anomalies in JJA in each experiment. The picture in the summer NH in the full experiment is similar to that in the SH in DJF (Fig. 7a). Specifically, there is anomalous EPF divergence in the extratropical lower stratosphere and anomalous EPF convergence in the middle to upper stratosphere, representing an upward shift and extension of the region of climatological EPF convergence in this region (contours). Near the subtropical stratopause there is anomalous EPF divergence that comes mainly from the rapid adjustment (Fig. 8b). The anomalous EPF convergence in the middle stratosphere comes mainly from the uniform SST warming (Fig. 8c) with smaller but significant contributions from the rapid adjustment and SST patterns (Fig. 8d). The winter SH is rather different from the NH in DJF. The full experiment shows anomalous EPF divergence in the SH upper stratosphere, which represents a weakening of the climatological EPF convergence in this region (contours). This is attributed mainly to the uniform SST warming, but there are also significant EPF convergence anomalies near the SH subtropical stratopause from both the rapid adjustment and the SST patterns. The changes in EPFD in the SH middle and lower stratosphere in austral winter have a more complex structure. The full experiment shows a tripolar pattern between 30 and 70 hPa, with anomalous EPF convergence poleward of 60∘ S and between 20 and 40∘ S and anomalous divergence between 40 and 60∘ S. This pattern is mainly reproduced in the uniform SST warming experiment but with a smaller contribution to the two regions of anomalous EPF convergence from the rapid adjustment. Previous studies have demonstrated mechanisms for tropospheric warming to influence the stratospheric EPFD and residual circulation (e.g. Shepherd and McLandress, 2011), but the mechanism through which the rapid adjustment acts on EPFD in the upper stratosphere is less well understood. The radiative cooling in the stratosphere due to increased CO2 is relatively uniform in latitude (Fels et al., 1980), so we do not expect large direct changes in zonal wind through thermal wind balance. However, the temperature response to CO2 represents a weakening of the vertical temperature gradient, particularly in the upper stratosphere where the cooling is larger. The characteristics for wave propagation and refraction can be quantified using a measure of refractive index (e.g. Matsuno, 1970) that is dependent on the Brunt–Väisälä frequency (N2=g/θ(dθ/dz)). Hence, we hypothesize that the changes in background temperature structure due to the CO2 radiative effects alter the propagation of Rossby waves, particularly in the upper stratosphere, and this leads to the changes in EPFD shown in Figs. 7 and 8.

The anomalous residual circulation is driven by both resolved and parameterized wave forcing. The seasonal parameterized wave forcing (NOGWD and OGWD) anomalies are shown in Figs. S3 and S4 for DJF and Figs. S5 and S6 for JJA. The peak changes in parameterized wave forcing are smaller than the anomalous resolved wave forcing by around a factor of 2. The anomalous NOGWD is mainly in the upper stratosphere and comes from the uniform SST warming. There is anomalous OGWD (Figs. S4 and S6) in the winter hemispheres near the edge of the polar vortex, which has comparable contributions from the rapid adjustment and the uniform SST warming.

We now quantify the contributions of the different wave types to the anomalous mass circulation in the lower and upper stratosphere. Figures 9 and 10 show latitudinal profiles of the annual-mean mass streamfunction anomalies in each experiment at 70 and 10 hPa, respectively, along with the DCP inferred contributions from the resolved and parameterized components of the wave forcing. The DCP calculation for the total wave forcing underestimates the directly calculated maximum streamfunction anomaly in the model by around 20 %.

In the lower stratosphere at 70 hPa, the estimated streamfunction anomalies from the total wave forcing in the full 4×CO2 experiment come mainly (>80 %) from the resolved wave forcing (Fig. 9a), with a smaller and more homogeneous contribution from the parameterized wave drag. The resolved wave forcing explains almost all of the DCP estimated response in the rapid adjustment experiment (Fig. 9b) and most of it in the uniform SST warming (Fig. 9c) case. The component that contributes the smallest increase in streamfunction at 70 hPa, the SST pattern experiment (Fig. 8d), shows roughly equal contributions from parameterized and resolved wave forcing. The overall dominance of the resolved wave forcing for the strengthened BDC in the lower stratosphere is consistent with the larger changes in resolved wave drag in this region (Figs. 7 and 8) compared to the parameterized wave forcing changes in this region (Figs. S3–S6).

In the upper stratosphere (10 hPa), the full 4×CO2 experiment shows contributions to the enhanced streamfunction from both resolved and parameterized wave forcing (Fig. 10a). In the NH, the EPFD contribution explains around two-thirds of the total DCP estimated streamfunction anomalies and GWD around one-third. The positive NH streamfunction anomaly from EPFD poleward of 30∘ N comes from both the rapid adjustment (Fig. 10b) and the uniform SST warming (Fig. 10c). In contrast, the positive streamfunction anomaly in the upper stratosphere from parameterized wave drag comes mainly from the uniform SST warming (Fig. 10c).

In the SH, the results for the full experiment are somewhat more complex, with the major contribution to the enhanced poleward mass transport coming from GWD, which is partly offset by an opposite contribution from the EPFD. This positive SH streamfunction anomaly associated with EPFD comes mainly from the uniform SST warming (Fig. 10c), which also generates enhanced SH poleward transport via enhanced GWD. This increased poleward flow in the SH upper stratosphere is further increased by the rapid adjustment (Fig. 10b) with contributions from both resolved and parameterized wave drag. In both hemispheres, the SST pattern has little effect on the wave forcing in the upper stratosphere (Fig. 10d).

Figure 11 summarizes the results by showing the annual-mean tropical upward mass flux anomalies in the different experiments at 70 hPa (Fig. 11a) and 10 hPa (Fig. 11b). Also shown are the mass flux anomalies from the high- and low-uniform-warming experiments (runs F and G), which span the spread in 4×CO2 global-mean SST response across the CMIP5 models. In the lower branch of the BDC, the annual-mean tropical upward mass flux increases by 45 % in the full experiment compared to piControl (3.1×109 kg s-1). The uniform SST warming accounts for ∼70 % of this increase, with the rapid adjustment (∼20 %) and SST patterns (∼10 %) contributing the remainder in comparable amounts. The central estimates of the mass flux anomalies at 70 hPa in the three uniform SST warming (2.1, 3.4, 4.9 K) experiments are 1.4, 2.3, and 3.4×109 kg s-1, which gives an approximate linear scaling of 0.7×109 kg s-1 K-1 (∼10 % K-1). In the lower stratosphere, the uncertainty from the CMIP5 model spread in global-mean SST response to 4×CO2 is larger than the contribution from the rapid adjustment and the SST pattern effect.

In the upper stratosphere at 10 hPa, the total mass flux increases by around 35 % in the full experiment (0.6×109 kg s-1). This increase comes almost equally from the rapid adjustment (∼40 %) and the uniform SST warming (∼45 %), with the remaining ∼15 % contribution coming from the SST pattern effect, though the latter is not statistically distinguishable from internal variability. The central estimates of mass flux anomalies at 10 hPa in the three uniform SST warming experiments are 0.17, 0.29, and 0.50×109 kg s-1, which gives an approximate linear scaling with global-mean SST of 0.11×109 kg s-1 K-1 (∼7 % K-1). In the upper stratosphere, the magnitude of the anomalous mass flux due to the rapid adjustment is therefore comparable to the uncertainty from the model spread in global-mean SST response to 4×CO2.