Large volcanic eruptions are capable of injecting very large quantities of sulfate aerosols into the stratosphere. In the years following such an eruption, temperature forcing by stratospheric volcanic aerosol concentrations plays an important role in the interannual variability of the climate, and leads to significant and persistent anomalous climate states. In the first part of this series of papers (; hereafter Part 1), we investigated the large-scale mechanisms that control post-eruption zonal wind anomalies using the Transformed Eulerian Mean (TEM) analysis framework. We saw that the wind response was intermittent, with a notable seasonal dependence, but that the timescale of both the temperature and wind anomalies is ultimately governed by the volcanic aerosol decay. From a climatological point of view, the response is approximately instantaneous with respect to the radiative forcing, and we generally expect that the stratospheric dynamics and aerosol concentrations will return to their climatological averages in tandem. In the simulations used in Part 1, this timescale is about two years.

We now turn our attention to the stratospheric composition. In Part 1, the meridional and vertical residual circulation (v‾*, w‾*) was discussed, primarily with respect to its seasonal forcing of the zonal wind. This forcing mechanism, as expressed in the TEM framework, is a combination of direct advection of momentum and a Coriolis torque induced by the meridional component of the circulation. The strength of these effects develops and deteriorates over the year, with minimum (maximum) forcing in the summer (winter) hemisphere. This may naively lead us to conclude that the most important modes of stratospheric variability are essentially seasonal-to-annual. However, advection of trace gases by the residual circulation, and thus the genesis and depletion of stratospheric chemical concentrations, operates on much longer timescales. In this paper, it is shown that the volcanic effects on zonal temperature and momentum are progenitors of robust, decadal-scale anomalies in the distributions of trace gases in the stratosphere. It will be demonstrated that these anomalies are due to a global acceleration of the meridional Brewer–Dobson Circulation (BDC), but also a damping of the seasonal BDC cycle.

The BDC was first inferred and described in the works of and in an effort to explain observed concentrations of ozone, water vapor, and other stratospheric tracer constituents. This circulation approximates the mean Lagrangian transport of mass in the meridional plane as a superposition of the Eulerian mean circulation and an eddy-driven component accounting for the Stokes drift induced by the wave field . Tracer isopleths (surfaces of constant mixing ratio) are raised and lowered in the tropics and polar regions, respectively, by the thermally-direct overturning cell that is the mean residual circulation. Throughout the stratosphere, breaking planetary waves cause vertical diabatic mixing across isentropes, and especially in the midlatitude surf-zone, isopleths are homogenized by two-way adiabatic mixing of mass along isentropes (e.g. ). In other words, the BDC is essentially an expression of the TEM balance from a tracer perspective.

Through both observations and model studies, it is now understood that the full traversal of the BDC, in a Lagrangian sense, takes up to 5–7 years . This traversal timescale can be measured by the so-called stratospheric age of air (AoA), which has a rich history in the literature since at least the 1990s (see and for comprehensive reviews). The “age” of an air parcel is defined as the elapsed time since its last contact with some reference location, which is usually taken to be the tropical tropopause. In a modeling context, AoA is often implemented as a scalar “clock tracer” with a globally uniform and constant source, and gridpoint-level mixing ratios which correspond to the mean stratospheric age-of-air.

Early implementations were published by , and . More recently, implemented AoA tracers in a variety of dynamical cores to test their sensitivity to numerical schemes and spatial discretizations. Meanwhile, several recent works have made strides in disentangling the advective and eddy-driven components of the BDC, and their contributions to the climatological AoA distribution. A key development was by , who introduced the residual circulation transit time (RCTT), which identifies the age distribution arising purely from advective transport. The RCTT is obtained by solving for “backward trajectories” connecting each point in the latitude-altitude plane to a crossing of the tropopause, by integrating over the time-varying meridional and vertical residual circulation (v‾*, w‾*) in reversed time. Later, pointed out that the difference (AoA - RCTT) could be used to approximately isolate aging by isentropic mixing, which throughout much of the upper atmosphere was shown to be at least as important as aging by residual circulation advection. While this type of differencing is a useful procedure, it is also a blunt one, as it cannot separate contributions of mixing by resolved wave breaking and diffusion. Nor can it identify any contributions by unresolved advective affects, such as recirculation of Lagrangian tracers, or nonlinear or transient wave contributions which affect the Lagrangian mean circulation, but are only partially represented in the residual circulation of the TEM.

On the other hand, we know from the analysis outlined in Part 1 that a more fine-grained decomposition of AoA tendencies should be theoretically feasible. and demonstrated a method to this end, by computing a set of RCTT trajectories, and then integrating the components of the eddy-tracer flux vector M in time over those trajectories.

AoA anomalies arising in response to both persistent and transient forcing sources are numerous in the literature. Long-term AoA trends in coupled historical simulations have been used to study the response of the BDC to anthropogenic climate change, where the typical finding is decreased age (an accelerated BDC) throughout the lower stratosphere . In the case of the stratospheric aerosol injection (SAI) geoengineering simulation studies of , the authors showed anomalies in the residual vertical velocity w‾* consistent with an accelerated BDC, but did not show the associated AoA effects. Several works have also concluded a likely accelerated BDC after large volcanic eruptions , while some have directly shown decreases in stratospheric AoA by several months for the 1991 Mt. Pinatubo event specifically.

The goal of the present article is to study the significant post-volcanic impacts on the AoA tendency balance, as we did for the zonal-mean zonal wind u‾ in Part 1. The key question is: what are the relative contributions of perturbed residual circulation advection and perturbed mixing in producing the net impact on stratospheric AoA post-eruption?

To this end, we draw some inspiration from adjacent works that pose the same problem to different tracer species. For example, showed the closed TEM tracer budget in the meridional plane for ozone (O₃) and carbon monoxide (CO) over a 6-year dataset. In a generalization of this work, they later investigated the closed TEM budget for an artificial tracer called e90 , which is defined such that its distribution is uniquely sensitive to perturbations to troposphere-stratosphere mass exchange. Therefore, e90 qualitatively resembles the behavior of real-world substances in this region, like ozone (O₃) and carbon monoxide (CO). The artificial e90 tracer is indeed a suitable proxy to investigate the impact of the Mt. Pinatubo volcanic eruption on the flow field as also outlined in . For conciseness, this aspect has not been included here, and we point the reader to the above reference.

In this work, we seek not to emulate the behavior of a real-world substance, but rather use the AoA tracer to understand the behavior of the stratospheric circulation itself. Section  describes the simulated datasets employed. Section  introduces the analysis framework, including the tracer definition, the tracer TEM balance, and the method of computing the RCTT. Section  presents the climatological behavior of AoA in our simulations, and Sect.  explores the identified impacts. Section considers the sensitivity of the identified impacts with eruption magnitude, and Sect.  closes the paper with a discussion of the results and concluding remarks.

The research is built upon the same simulations as in Part 1, described in detail in Sect. 2 therein. Briefly, we use the fully-coupled E3SMv2-SPA model to simulate the eruption of Mt. Pinatubo as an emission of sulfur dioxide (SO₂) over 6 h and 9 grid cells between 18 and 20 km near 15° N, and evolve the resulting sulfate aerosols via a prognostic treatment. The simulations utilize a ∼1° horizontal grid and 72 vertical levels that extend to approximately 60 km, and feature an internally-generated QBO with a period of approximately 24 months (see Sect. 4.2 of Part 1). We again use the paired limited-variability volcanic ensemble (LV) and its counterfactual ensemble (CF), introduced by , for the impact analysis. Both ensembles include 15 members covering an approximately 7.5-year time period from 1 June 1991 to 1 January 1999. The CF ensemble omits the Mt. Pinatubo volcanic eruption, and each LV–CF member pair shares identical initial conditions. Statistically significant departures of the LV ensemble mean from the CF ensemble mean are therefore interpreted as the isolated volcanic impact. We primarily use the same 10 Tg SO₂ eruption as Part 1, while Sect.  additionally includes a brief analysis of the tracer sensitivity with respect to eruption magnitude. This is accomplished through additional LV ensembles with 3, 5, 7, 13, and 15 Tg SO₂ eruptions. All data products from the LV and CF ensembles were provided as daily-averaged fields.

The AoA is computed as a tracer mixing ratio at each gridpoint during the model run. Here, we will use the zonal mean of the daily-averaged tracer field. For computing the residual circulation transit time, the history of the daily-averaged residual velocity components v‾* and w‾* is required for a period of ten years prior to the time of analysis. A 10-year prior history was chosen so that the RCTT distribution would be well-represented in the time-averaged ensemble mean. This period needs to be long enough to represent transit times in regions with the longest backward trajectories, which tend to be the polar lower stratosphere. The choice of ten years was inspired by testing the RCTT calculation on our data and using guidance from previous studies. For example, found that the longest transit times measured in their simulations were “4–5 years in the lowest stratosphere above the poles”. In addition, state that “10 years of data are sufficient to represent the mean state of the simulations”, while their climatological RCTT distributions also reach only 4–5 years in the polar lower stratosphere. We similarly found that our 5-year averaged ensemble mean RCTT distributions reached maxima of 5–6 years near the poles, but that individual backward trajectories in individual ensemble members may require up to ten years or more to cross the tropical tropopause. Choosing ten years does result in missing data for a few gridpoints in the polar lower stratosphere for some ensemble members (i.e. ten years was not long enough). Still, the missing data are minimal, and ten years was enough to converge on a well-represented, time-averaged, ensemble-mean RCTT distribution.

Because the LV ensembles were all initialized on 1 June 1991, we were required to concatenate the v‾* and w‾* time series from the LV runs, and the control simulation from which the perturbed LV ensemble initial conditions were seeded, in order to obtain a 10-year history. The concatenation of the control simulation and a single LV ensemble member is illustrated in Fig.  for a midlatitude gridpoint at 10 hPa. RCTT integration bounds for selected dates are plotted as a reference.

The control simulation was generated from E3SMv2-SPA with an equivalent configuration to the LV and CF runs, though in principle there are discontinuities at the concatenation point. In part, this is because the LV ensemble initialization involved random temperature perturbations on the order of 10-14 K to drive differences between the members. There is also a second instance of a temperature perturbation of the same magnitude on 1 January 1988 in the control simulation that was inherited from the parent dataset, and is unrelated to the present study. In addition, while the winds across the LV initialization point are approximately continuous, non-volcanic climate forcing sources are not. This is because the control and LV calendars are different, and needed to be manually aligned (again, this is due to an inherited experimental design that is unrelated to the present study; see for full details). Because the RCTT results from long-time integrations over monthly-averaged v‾* and w‾*, we expect the consequences of these features on the results to be negligible. To whatever extent that these discontinuities are present in the recovered transit times, they are present equally in the LV and CF ensembles, and thus will be removed when taking the (LV - CF) impact.

As in Part 1, we express the post-eruption anomalies in a variable x as impacts, defined as the ensemble mean of the difference between each pair of LV and CF simulations: 1Δx≡1N∑n=1Nx(n)-xCF,(n). where N is the ensemble size, n is each ensemble member enumerated, x is the data from the volcanic simulation, and xCF is the data from the counterfactual simulation. For assessing the statistical significance of the impact Δx, we use a two-sided Student's t-test with a p-value threshold of 0.05 (95 % confidence). See Sect. 3.1 of Part 1 for full details on the statistical calculations. Both a tracer form of the TEM equations and the RCTT will be used to diagnose the impacts on residual circulation advection and mixing separately. The tracer sources and sinks, as well as the TEM and RCTT formulations, are defined below.

Before investigating the volcanic impacts on the AoA tracer, the climatological behavior in the CF ensemble should be understood for reference. Figure  shows the 5-year average ensemble-mean AoA distribution from 1 January 1994 to 1 January 1999. AoA is younger than six months throughout the troposphere, and quickly increases vertically from the tropopause. Because tropospheric air reliably enters the stratosphere through the tropical pipe, the youngest air at a given pressure level is found in the tropics, and the oldest is found at the poles, with flattening age contours throughout the midlatitudes. The oldest air is less than 5.5 years old, which occurs as low as 30 hPa at the poles and near 1 hPa in the tropics.

This age distribution is well within the intra-model spread derived from reanalyses, both by in-situ and offline transport models . It is also comparable to but slightly older than results from other coupled models simulating a similar historical period. For example, the E3SMv2-SPA mean age distribution is older than published results for the Whole Atmosphere Community Climate Model (WACCM) by up to ∼6 months . This is primarily because those studies compute the AoA with respect to a reference point at the tropical tropopause, whereas our reference point is closer to the surface. We did not test this or perform a specific intercomparison, though we note that the 6-month contour in Fig.  correlates with the average position of the tropopause. The tropopause position is an E3SMv2-SPA output variable and is determined via the lapse rate tropopause definition of the World Meteorological Organization.

We now turn to the climatological tracer flux balance for the AoA. Figure  again shows the CF ensemble-mean AoA averaged over 1994–1999, as well as the RCTT over the same period, and the difference (AoA - RCTT). The residual circulation streamfunction is overplotted in each panel. In order to visualize the backward trajectory integration which computes the RCTT at each point in the meridional plane, Fig.  shows the 5-year mean trajectories, as well as the trajectories for the last month in the averaging period, December 1998, for a single CF ensemble member. The 1998 trajectories exhibit oscillations in the midlatitudes, which are imprints of the seasonal movement of the BDC. This seasonal signal is smoothed out in the time-averaged trajectories.

The RCTT in Fig.  shows the age due to advective residual circulation transport alone, which has a decreased vertical gradient in the tropics with respect to the AoA, and a much steeper meridional gradient in the midlatitudes. It appears that when wave-driven isentropic mixing is removed from the aging process, older and younger air are effectively segregated on either side of the surf zone. At 100 hPa, the mean age poleward and equatorward of 80° N is about 6 years and 3 years, respectively. Following , we then interpret the difference in panel (c) as “aging by mixing”, i.e. aging that is not captured by the residual circulation advective transport. There are positive signals of up to 2.5 years of aging between 20–60° throughout the stratosphere in each hemisphere and negative signals of -4 years in the lower stratosphere at high latitudes. This difference, in principle, also includes any other parameterized transport or diffusion. However, showed that these effects only comprise about 10 % of the net aging (or less) in their simulations. Thus, the primary mechanism is two-way exchange of old and young air across the meridional RCTT gradient by breaking resolved (Rossby) waves in the surf zone.

While the RCTT and its implied aging by mixing provide a view of the time-integrated tendencies along advective transport trajectories, further insight can be gained by instead considering local age tendencies. By “local”, we mean the instantaneous forcing imposed on the AoA in an Eulerian sense. For this, we recruit the TEM decomposition of the net age tendency, shown in Fig. . The panels show the (a) advection by the residual circulation (Eq.  plus Eq. ), (b) local tracer mixing tendency by resolved waves (Eq. ), (c) diffusion (Eq. ), (d) sum of the resolved mixing and diffusion, and (e) net tendency, respectively. The data are averaged over the same 5-year time period as Fig. . The annual-mean AoA is very stable, and so the net tendency has been multiplied by a factor of 100 for visibility.

Figure tells the same story as Fig. , i.e. advection by the residual circulation decreases age in the tropics, and increases age poleward, peaking near the polar tropopause. The mixing tendency has the opposite behavior. At 100 hPa, the positive and negative diffusion signals peak near ±1 or less d d⁻¹, while the net mixing peaks in excess of ±4 d d⁻¹. Diffusion thus contributes at most 25 % of the mixing signal in the lower stratosphere, usually less. Above 30 hPa and poleward of 60° N, there are stronger diffusion contributions, which serve to nearly cancel large resolved mixing tendencies.

Note that the meridional position of the sign reversal in each of these quantities is located near 40° N, which is equatorward of the same feature as identified by the RCTT. To be clear, this difference is due to the local nature of the measurement; rather than being integrated, Fig. a shows the age by residual circulation advection given the simultaneous, pre-mixed AoA distribution.

went on to show that one can obtain the cumulative effect of diffusion by integrating the resolved local mixing tendency (Fig. b) along RCTT backward-trajectories, and subtracting it from the RCTT–inferred mixing (Fig. c). We did not perform this calculation, but the relatively small local diffusion tendencies we see throughout the tropical column in Fig. c are consistent with the result of that aging by diffusion is a secondary contribution.

The net tendency is much larger in seasonal averages than it is in the annual mean of Fig. e. Seasonal AoA TEM balances for winter and summer are provided in Appendix , Figs.  and . The AoA tendency exhibits a seasonal signal, with enhanced aging occurring in the midlatitude winter hemisphere, and decreased negative aging shifted from the equator to 30° in the summer hemisphere. These effects are explained by the polar vortex-associated wave activity in the winter hemisphere (and lack of wave-driven mixing in the quiescent summer hemisphere), and the shift of the residual circulation streamfunction zero-line into the summer hemisphere. We note that these findings are consistent with , where a Lagrangian transport model driven by reanalysis winds was used to estimate the seasonality of the TEM AoA forcing.

With the mean and seasonal counterfactual behavior established for the AoA tracer, we now investigate the Mt. Pinatubo eruption impacts on the tracers and the force balance governing their evolution in the LV ensemble. First, it is useful to look at the volcanic effect on the residual circulation itself. It was noted in Part 1 that the most significant dynamical impacts on zonal momentum in the northern hemisphere occur during boreal summer 1991, late winter 1992, and summer 1992. Moreover, the primary impact driver was a strengthened residual circulation and the associated Coriolis effect during the boreal summer months, and modification of the EP flux divergence involving equatorward deflection of planetary waves near 30 hPa during the winter months. With this in mind, Fig.  shows the LV ensemble–mean Δw‾* and ΔΨ* averaged over August 1991, January 1992, and August 1992.

In each of the seasons shown, there is enhanced residual (diabatic) vertical motion in the tropics, and enhanced downwelling in the high latitude upper stratosphere, though the strength and significance of these features are notably diminished by August of 1992, one year post-eruption. By continuity, this implies an accelerated residual circulation, which is observed in panels (d) and (f). In particular, the impact pattern indicates an enhanced overturning circulation centered on the aerosol forcing, which is near the injection latitude at 15° N in summer of 1991, and migrates poleward thereafter . The result is that the volcanic effect lacks the seasonality of the background residual circulation, and does not always project onto the CF Ψ*. In August of 1991 and 1992, the robust ΔΨ* indicates acceleration of the shallow branch of the BDC in both hemispheres, while the deep branch in the summer hemisphere is weakened. During January of 1992, the southern shallow-branch cell is enhanced along its northern edge, the Ψ* zero line moves northward, and the positive overturning circulation in the SH is decelerated.

We found that the statistical significance of the residual velocity impacts extend to about 2 years post-eruption, after which the magnitude decreases and becomes statistically insignificant (not shown), which matches the timescale of the dynamical anomalies presented in Part 1. However, these relatively short–lived perturbations to the residual circulation are able to establish much more persistent changes to stratospheric composition, as indicated by the AoA.

Thus far, we have not explored the sensitivity of our results to the forcing strength and instead limited our focus to a single volcanic scenario. This section provides a brief inspection of the qualitative relationship between the AoA tracer distribution and the initial eruption magnitude expressed in Tg of the aerosol precursor SO₂. As we have seen, the volcanic effect on global tracer concentrations is an indirect one, depending on interactions with the simultaneous background conditions. As such, it is difficult to make any a priori estimate of the trend. An idealized model of aerosol forcing as an exponential attenuation of longwave radiation (as in ) suggests that the local heating rates should respond linearly at small mixing–ratio. However, we should not make the extrapolation that the local temperature response shares this scaling, let alone the nonlocal response after the downstream dynamical development.

Figure  shows the ΔAoA time series and eruption magnitude trend at 10 and 30 hPa averaged over 20–40° in each hemisphere. These positions were chosen to match the impact peaks in Fig. d, e. In the lower panels of Fig. a–d, the trend of the maximum |ΔAoA| is shown as a function of SO₂ mass, normalized such that the result for the 10 Tg eruption is set to unity. The maximum |ΔAoA| is identified uniquely for each SO₂ mass choice, and thus the occurrence of each in time are not always the same (marked with colored triangles in the figure). A linear fit to the normalized data is also shown for reference.

In the NH, the trend is approximately linear from 3 to 10 Tg, after which there is a hint of saturation in the ΔAoA from 10–15 Tg. The positive aging anomaly in the SH at 30 hPa qualitatively shows this effect as well, while at 10 hPa the trend is approximately linear from 3 to 15 Tg. Once the peak impacts are realized, panels (a), (b) and (d) suggest that larger anomalies also remain detectable for longer, as seen in the persistence of the significance of each impact curve with time. In panel (c), we see that the sudden drop in the SHLS aging occurs simultaneously for all eruption magnitudes, consistent with our earlier suggestion at the end of Sect.  that this behavior is controlled by the background BDC seasonal cycle.

The combination of Fig. c, d shows that both of the opposing southern and northern hemisphere responses scale together with eruption size, which implies that the seasonal damping effect on the BDC in general is linearly controlled over at least the tested forcing range. It is an open question whether or not the effect should saturate given even larger SO₂ loading. Either way, some nonlinear behavior should probably be expected, since the interaction between volcanic impacts and background dynamics could change approaching the condition |Δw‾*|≈|w‾*|.

Our conclusions are as follows

The main effect of the Mt. Pinatubo eruption on tracer transport is to strengthen the tropical pipe, which lowers age of air throughout the tropics and in the middle-to-upper stratosphere globally.

Our interpretation of the BDC seasonal damping is an extrapolation from the observations presented here; while the finding in the SHLS is robust across the ensemble and also across the tested eruption magnitude range, it is limited to a single year and eruption location. Verification of this conclusion generically would be better suited to an experiment involving persistent and hemispherically symmetric aerosol forcing, rather than a transient and localized volcanic event. Fortunately, the plethora of simulated stratospheric aerosol injection (SAI) geoengineering experiments conducted during the past decade offer some insight. published a model intercomparison study of meridionally-varying aerosol injections, and concluded that w‾* anomalies are generally positive in the NH subtropics, and negative in the SH subtropics for injections near 15°. Notably, the negative anomalies in the SH occur north of the turn-around latitude (their Fig. 6). This resulted in excess concentrations of ozone in the SHLS in three out of four models they analyzed, consistent with our finding of increased AoA in that region (their Fig. 7). For the case of an equatorial injection, they showed positive anomalous upwelling near the equator, and downwelling poleward in each hemisphere, all of which occurred mostly within a region of climatological w‾*>0. Associated with this vertical motion effect was an ozone increase symmetric about the equator near 70 hPa.

Later, performed a similar series of SAI simulations with varying injection latitudes, and analyzed the resulting AoA anomalies (their Fig. 5). Consistent with , they identified increases in aging of up to ∼3 months, near 70 hPa and within ±40° in latitude. They also reported AoA anomaly results from the ARISE-SAI-1.5 simulations . Those simulations included simultaneous injection locations at ±30 and ±15° in latitude, but with overall more SO₂ injected in the NH (see Fig. 2a). Consistent with both our work and , for this scenario they identified AoA anomalies of nearly 3 months in the SHLS.

Though our results are consistent with the highlighted findings of and , neither of those authors describe the aging effect in the lower stratosphere in terms of the BDC, saying instead that “The response results from local deceleration of upwelling in the tropical troposphere … brought about by the increase in static stability associated with heating in the lower stratosphere and cooling in the troposphere … This deceleration of tropospheric upwelling slows down the transport of ozone-poor tropospheric air into the lower stratosphere, thus increasing ozone in the region.” . This is perhaps at odds with our findings, since we observe robust SHLS aging despite the fact that the tropospheric vertical velocity impacts are not significant (Fig. a–c), though admittedly we did not pay special attention to the troposphere and did not plot Δw‾* below 400 hPa. If there is a contribution from negative stratospheric w‾* anomalies to the lower stratosphere increases in age and ozone in and , then it is also unclear if the seasonal effect that we have proposed here is contributing to the hemispherically symmetric response that they demonstrated for equatorial injections. In particular, they did not consider the meridionally-resolved time series of the response, which might have clarified the seasonal contributions to the long-time mean of their tracers. We hypothesize that their symmetric aging in the subtropical lower stratosphere is an average of SHLS aging in austral winter, and NHLS aging in boreal winter, which would be consistent with our conclusions.

In terms of volcanic eruption simulations, there are several works which support our findings. used a paired–ensemble strategy similar to ours, and showed that changes of up to 0.1 mm s⁻¹ in w‾* follow the eruption of Mt. Pinatubo averaged on ±20° at 30 hPa. In latitude, the positive w‾* anomaly peaked near 10° N, and became negative at 10° S and 30° N. This is most likely consistent with our finding that the residual streamfunction anomaly does project onto the background condition during the summer of the eruption (Fig. d). They further showed that tropical and northern subtropical AoA decreased by several months, as well as the meridional age gradient. They did not show changes in age below 30 hPa, and so they may or may not have simulated the SHLS aging. looked at the circulation response to the Mt. Pinatubo eruption with a 64–member ensemble, composed of four sets of 16 simulations, which averaged over different prescribed forcing datesets. They observed that the residual circulation averaged over boreal winter of 1991 was accelerated between 0 and 60° N below 1 hPa, and decelerated in the SH between 0 and 50° S (their Fig. 10f), the latter of which is consistent with our Fig. e.

A future study could be designed to test our seasonal BDC hypothesis more specifically, by simulating similar volcanic eruptions occurring at different latitudes and/or seasons, or by studying the meridionally– and vertically–resolved temporal evolution of residual circulation anomalies in SAI simulations. There could be any number of other variables to consider as well. An aspect that we did not discuss here is whether the phase of the quasi-biennial (QBO) complicates a potential interaction between volcanic forcing and BDC seasonality. A hint of this complication is found in , who showed that the global symmetry of the post-eruption vertical velocity response depended strongly on the simultaneous QBO phase for equatorial eruptions in their simulations (their Fig. 10). It would also be enlightening to understand how exactly wave activity balances (or fails to balance) the global residual circulation response, which we only described in a more local sense in Part 1. Finally, there may be interest in exploring the sensitivity in the age impacts analyzed here to the SO₂ injection altitude, which was recently shown by to strongly control to the aerosol lifetime (and thus forcing timescale) in the stratosphere.