The Community Earth System Model version 2 with the Whole Atmosphere Community Climate Model version 6 (CESM2-WACCM6, , hereafter CESM2) is used with comprehensive stratospheric and upper-atmospheric chemistry as well as interactive aerosol microphysics using the Modal Aerosol Module (MAM4) . Its horizontal resolution is 1.25∘ longitude by 0.9∘ latitude, with 70 vertical levels and a model top at about 140 km. An evaluation of the model response to past volcanic eruptions was performed in and using the previous version of the model, CESM1(WACCM). Unlike the CESM2 version described in , which includes both comprehensive tropospheric and stratospheric chemistry, the version used here includes comprehensive stratospheric chemistry but only a simplified chemistry of importance in the troposphere; this is thus similar to the chemistry scheme in the CESM1(WACCM) version used for previous geoengineering studies.

NASA's ModelE is developed by the Goddard Institute for Space Studies (GISS). The current version, ModelE2.1, has a horizontal resolution of 2.5∘ longitude by 2∘ latitude and 40 vertical layers extending up through the mesosphere (model top of ∼80 km). The version used in this study, GISS-E2.1-G, has a fully interactive ocean with 32 vertical layers based on the Russell ocean . While GISS ModelE also has the ability to use the HYCOM ocean , that option is not employed here. GISS has two methods of representing aerosol microphysics that we employed here. The bulk aerosol treatment (referred to as One-Moment Aerosol, OMA, in , called “GISS-OMA” in this study) involves specification of an aerosol dry radius, and the aerosols grow hygroscopically as a function of the relative humidity . The more complex aerosol treatment (referred to as Multiconfiguration Aerosol TRacker of mIXing state, MATRIX, in , called “GISS-MATRIX” in this study) involves computation using quadrature of moments and can represent aerosol microphysical growth via condensation and coagulation. While not strictly a modal treatment, as it computes aerosol size using a quadrature of moments approach (usually termed a two-moment approach), it is most comparable to the modal treatments used in the other two models. For anthropogenic, tropospheric aerosols, a comparison between the two aerosol treatments in GISS is presented in . Both aerosol methods have representations of heterogeneous halogen chemistry on the aerosol surfaces and are coupled to the same chemistry scheme, which in the stratosphere includes chlorine and bromine chemistry as well as a treatment of polar stratospheric clouds .

The UKESM1 Earth system model was developed jointly by the UK's Met Office and Natural Environment Research Council and consists of the physical atmosphere–land–ocean–sea ice model HadGEM3-GC3.1 coupled to components which deal with terrestrial and ocean biogeochemistry . Its comprehensive stratospheric–tropospheric chemistry (StratTrop) scheme is described in and includes detailed tropospheric chemistry and a somewhat simplified stratospheric chemistry with “lumped” treatment of long-lived halogenated ozone-depleting substances. The model is further coupled to a modal aerosol microphysics scheme described in and (GLOMAP-mode). The horizontal resolution is 1.875∘ longitude × 1.75∘ latitude, with 85 vertical levels up to ∼84 km on terrain-following hybrid height coordinates. An evaluation of simulations of past volcanic eruptions has been recently performed in for on older version of this model using a similar version of the aerosol scheme, as well as in .

None of the models used in this study employ sectional aerosol microphysics, whereby the size domain is divided into intervals, or bins, and the evolution of the number concentrations in each size bin is calculated separately for each species. Instead, these models employ a more simplified approach, either modal (or comparable to modal in the case of GISS-MATRIX), whereby the aerosol population is described by a number of lognormal distributions, or bulk, whereby the size distribution is prescribed; we will describe both briefly below.

CESM2 and UKESM1 use a very similar modal approach, whereby the aerosol population is described by at least three main modes (at least for sulfate) called nucleation (only for UKESM1), Aitken, accumulation and coarse, whose distribution is assumed to be lognormal with a fixed geometric standard deviation σg and a geometric mean diameter that can vary in a certain predefined size range: particle number and mass are transferred to the larger mode when the diameter exceeds the upper limit for that mode. In each mode, all aerosol species are considered internally mixed: that is, they are described by a single size distribution; this has been shown to lead to changes in upper-tropospheric aerosol concentrations when large quantities of stratospheric sulfate settle down, unrealistically reducing the size distribution and thus the settling velocities of species that should not interact with the sulfate .

The GISS in its bulk version incorporates a much simpler aerosol parameterization, whereby the size distribution is specified for each aerosol species. There is no calculated number concentration and water uptake effects are solely dependent on relative humidity for gravitational settling purposes. GISS-MATRIX sits in between the complexity of the other two models and GISS-OMA: the sulfate population is described by two lognormal distributions (Aitken and accumulation) of fixed σg, but separated from other aerosol species, defined as particles with a diameter smaller or larger than 0.1 µm, respectively. Instead of tracking the size distribution itself, however, only key moments of the aerosol population such as number and mass are tracked based on the quadrature method of moments framework described in , leading to a set of equations to be solved for each population as described in detail in . To prevent the mean diameter of the Aitken mode from approaching that of the accumulation mode too often, a transfer function that completely moves all particles from the Aitken to the accumulation mode when the two sizes approach each other in value is used (see Sect. 2.8 in ). For a straightforward comparison, all information for the aerosol populations in each model is described in Table . For GISS-OMA, the only prescribed value is the bulk diameter (which for simplicity we included in the accumulation row in the table) with no assumptions regarding the geometric standard deviation; the actual value of 0.3 µm used in the current version of GISS used here is different from the one given in (0.4 µm).

We note that in the GISS with bulk treatment, there is one specified aerosol dry radius for all sulfate aerosols, both tropospheric and stratospheric. We used the default aerosol size, which is calibrated to represent tropospheric sulfate and the background sulfate layer in the stratosphere but is far too small for the aerosols that would result from a high stratospheric loading of sulfate. Past experiments using an earlier version of this model increased the aerosol size, resulting in a better match to stratospheric sulfate aerosols compared to observations but was far larger than should have occurred for tropospheric aerosols. This had non-negligible effects on radiative forcing, tropospheric chemistry and aerosol deposition e.g.,, limiting the ability to compare the SAI run with a corresponding baseline run. The approach chosen in the present study avoids these issues, but in doing so limits the applicability of the GISS-OMA simulations to SAI. Nevertheless, these simulations serve as a useful point of comparison and reveal understanding.

As shown in Table , the modal aerosol schemes present differences in the definition of the size ranges per each mode, and we will show that this significantly changes which modes the aerosols find themselves in. While the width of the smallest mode is similar between all three models, it is significantly different for the coarse mode, being 1.2 for CESM2 and 2 for UKESM. Considering that σg is a parameter that remains constant in the whole atmosphere, this difference may have arisen if the two models considered different types of aerosol size distributions to which they desired their mode to be more similar. For instance, if one considers the stratospheric size distribution of aerosols post-Pinatubo, σg has values lower than 1.5 , whereas for background conditions or small eruptions, the value is closer to 1.8 . As detailed in , CESM modified its coarse mode in MAM4 to better reproduce the Pinatubo plume.

For these experiments, we selected the baseline Shared Socioeconomic Pathway (SSP) 2-4.5 . Each experiment is run for 10 years starting on 1 January 2035. The choice of a particular background scenario is of secondary importance here, as all comparisons of the SAI responses will be performed relative to the control SSP2-4.5 simulation, thereby evaluating climate changes due solely to the increased sulfate aerosol concentrations. However, in planning for more comprehensive experiments in the future (as those detailed in , and ), we will use a similar background greenhouse gas scenario.

In the experiments discussed in , the altitudes of SO2 injections were defined in terms of a fixed height above the annual mean tropopause. This led to two different injections altitudes, one for 15∘ N and 15∘ S injections at 25.0 km and one for injections at 30∘ N and 30∘ S at 22.4 km. Here we define a single injection altitude for all latitudes at 22 km. We chose this injection altitude for two separate reasons. First, it is closer to the upper limit of altitudes achievable by traditional aircraft while still being sufficiently far above the tropopause for aerosols not to be removed too quickly (as opposed to 25 km, which is likely too high for practical considerations). Second, we aimed to inject SO2 in all models at the same latitude but also in just one grid box; however, there is a challenge in prescribing a fixed injection altitude in kilometers but having a hybrid height vertical coordinate (UKESM1) or a hybrid sigma–pressure coordinate (CESM2, GISS). After performing some tests, the specific choice of 22 km ensured that all three models could always be reasonably expected to inject in the same grid box, as that altitude is not close to the vertical edges of a grid box in any of the models. In CESM2, this meant injecting at the grid box bounded by the 47 and 39 hPa pressure interfaces (with a midpoint of 43 hPa), which has an average geometric height of 21.6 km at all considered latitudes of injection and is 1.2 km thick. In UKESM1, this meant injecting at the level with a midpoint height of 21.8 km, which is roughly 1 km thick. In GISS, this meant injecting at the grid box bounded by the 43 and 31 hPa interfaces, with an approximate midpoint of 37 hPa (23.1 km assuming a 7 km scale height) and approximately 2.3 km thick.

SO2 is injected continuously throughout the year in the same quantity in each experiment: each simulation includes the injection in only one location, either 30∘ N, 15∘ N, 0∘ N, 15∘ S or 30∘ S, and at one longitude (180∘ E for GISS and CESM2, 0∘ E for UKESM1) at the altitude described above. Simulations are performed for 10 years each. The selected SO2 injection rate in each model is 12 Tg SO2 per year to allow for an easier comparison with past simulations with CESM1-WACCM in .

Figure  shows the evolution of the global mean changes in stratospheric aerosol optical depth (AOD, calculated for all models at 550 nm) and surface temperatures. Relatively good agreement is found between CESM2, GISS-MATRIX and UKESM1 in terms of the global mean AOD responses, whereas the global mean temperature response is similar for CESM and UKESM1, as well as for the two GISS versions separately. GISS-OMA presents AOD values larger than the other two models and GISS-MATRIX, with differences ranging from values that are 2 times larger (for equatorial and 15∘ N injections) to 33 % larger (for 30∘ N injections). Larger values of sulfate burden can result in a number of nonlinear effects , for instance on atmospheric dynamics and thus the latitudinal aerosol distribution or on surface climate . The uncertainties in the SAI process that leads from SO2 injection to surface impacts can be separated into three different parts: (i) at each latitude how much SO2 is needed to achieve a certain optical depth (i.e., the efficiency of SO2 to H2SO4 conversion and of the removal processes), (ii) the resulting distribution of AOD under specific injection location(s) (largely driven by large-scale dynamics and mixing), and (iii) the impacts of a specific aerosol distribution on climate. Simulations with fixed SO2 injections at fixed locations, as used in this paper, allow us to explore better points (i) and (ii). In contrast, simulations like those described in , wherein the amount of SO2 injected is adjusted each year in order to achieve some specified surface temperature goals, allow better understanding of the response to some specific pattern of AOD forcing (as the injection rate can be adjusted to achieve a desired AOD). In the following analyses we separate and discuss both the overall simulated zonal mean response and that normalized by the global magnitude of the response to highlight these different contributors to the overall uncertainty.

Figure  shows the latitudinal distributions of the simulated stratospheric AOD. The inter-model spread is different depending on the injection location in terms of both overall magnitude and the spatial distribution. Equatorial injections show by far the greatest differences, with UKESM1 simulating twice as much AOD in the tropics compared to CESM2 and the two GISS versions differing by up to a factor of 5 between them. Similar differences between UKESM1 and CESM2 have also been documented for the GeoMIP G6 experiment in . Some of these differences are driven by differences in the global mean values of AOD: as mentioned above, AOD in GISS-OMA is over 2 times larger than in GISS-MATRIX for the equatorial injection case. In the right panels of Fig.  the zonal mean AOD values are scaled by the respective global mean values; this highlights the differences in the latitudinal distribution of the responses. This way, the difference in the normalized magnitudes of the equatorial peak (defined here as the average between 5∘ N and 5∘ S) between CESM2 and UKESM1 is reduced from 1.8 to 1.4; similarly, the two GISS versions show much more similar results, especially in the tropical region. In general, injections in the Southern Hemisphere (SH) show larger inter-model differences compared to the Northern Hemisphere (NH) injections, especially at high latitudes. In the 30∘ S case, global mean values are more than twice as large in GISS-OMA (0.25) compared to UKESM1 (0.12), and the SH high-latitudinal AOD differs by a factor of 3. In the NH, the largest difference is 60 % between UKESM1 (0.12) and GISS-OMA (0.20) in the 30∘ N case, and high-latitudinal AOD differs by a factor of 2. When normalized, the differences are largely reduced, but a clear differentiation remains for UKESM1, which shows a larger tropical confinement of aerosols than the other models. There are also some notable differences in the interannual variability between models: while both GISS versions and CESM2 have standard deviations that range between 1 % and 5 % of the mean values (depending on the precise latitude), UKESM1 shows a much larger variability (up to 33 % in the 30∘ N injection case at 60–90∘ N). In future longer simulations this observation would need to be considered when also considering the interannual variability of the surface changes.

The differences in AOD can be better understood by looking at the changes in aerosol mass mixing ratios (Fig. ) and the overall sulfate column burden (Fig. ). Compared to the other models, UKESM1 shows a much stronger confinement of the aerosol mass in the tropical pipe (for equatorial injections, the peak is 1.5 µgSO4kg-1 of air, whereas it is 1.1 µgSO4kg-1 of air for CESM2 and GISS-OMA and 0.5 for GISS-MATRIX) and far less transport in the opposite hemisphere for both 15∘ injections. On the other hand, CESM2 shows a much stronger poleward transport of sulfate aerosols, as indicated by aerosol values twice as large for 30∘ injections compared to other models considering values above 60∘ in latitude. All of these characteristics can largely be explained by the characteristics of the climatological transport in each of these models, as discussed in depth in Part 2.

GISS-OMA also shows a larger poleward transport in all cases, but the underlying cause for this might be different between GISS and CESM2. As analyzed in depth in Part 2, the baseline stratospheric dynamics are very similar between the two GISS realizations, and hence the differences in the overall aerosol distribution cannot be found there. Analyses of the stratospheric aerosol surface area density (SAD, shown in Part 2 due to its importance for stratospheric ozone chemistry) indicates a far larger number of particles in GISS compared to the other models. The SAD in GISS-OMA is 3 times as large poleward of 60∘ compared to CESM2, even for mass values that only differ by 30 % (for instance, in the 30∘ N injection case). GISS-OMA simulates much smaller particles (the prescribed bulk dry radius is 0.15 µm) that imply higher residence times, as gravitational settling is much lower , so the particles are more easily transported towards the pole even in the presence of a similar dynamical regime compared with the other GISS realization. The presence of aerosols at higher altitudes even close to the poles (where the large-scale circulation should be transporting aerosols downward) further supports this observation. Smaller aerosols are also more efficient scatterers, explaining why the optical depth differences are larger than the mass differences.

Finally, panels (f)–(h) in Fig.  give an overview for all cases of the ratio between the overall mass of the produced aerosols (shown alone in Fig. f) and the injected amount of SO2. This ratio, shown in Fig. g, represents the lifetime of the added sulfate: as we are in a steady state, wherein no new mass is added to the global burden, this lifetime can be calculated as the burden divided by its constant source (the injection) . All models show larger amounts of mass for injections closer to the Equator due to the tropical confinement increasing the aerosol lifetime. This effect is less noticeable for GISS-OMA, which shows far less confinement. However, models show a distinct difference in the ratio between the overall mass of SO4 and resulting AOD (Fig. h): this indicates substantial inter-model differences in the average size of the aerosol, with obvious consequences for the efficiency of the cooling that we will analyze next.

A comparison of the effective radius (Reff) is shown in Fig. . The values for Reff are indirectly derived for all models as Reff is not a direct output for either UKESM1 or GISS. Therefore, we use the common available output of mass mixing ratio (χ) and number concentration (N) for each mode in each model to derive the mean radius ri. We calculate the mean volume vi using 1vi=χiρsulfate⋅Ni, where ρsulfate is the density of sulfate as considered in each model in kilograms per cubic meter (kg m-3) (usually 1770 kg m-3 as in ). The mean radius is then derived considering that the aerosol population is assumed to be a lognormal distribution with a geometric standard deviation σg and is thus connected to the mean volume by 2vi=43⋅π⋅ri3⋅exp⁡92⋅ln⁡2(σg). Finally, Reff is calculated considering the definition 3Reff=∑iri3Ni∑iri2Ni, where i is the number of modes considered and is therefore 3 for CESM2 (all modes relevant to sulfate in MAM4, ), 4 for UKESM1 and 2 for GISS-MATRIX. The single wet radii for each mode are shown in Fig. S1 in the Supplement. The validity of our derivation is ensured by the comparison of the derived values of Reff in CESM2 and the ones obtained as a direct output from the CESM2 simulations (not shown); while the off-line derivation leads to slightly smaller Reff values than calculated online in the model, the overall results are similar enough for a confident comparison. A number of important features become apparent: the population-weighted radius in GISS-MATRIX is almost always larger than the GISS-OMA one, confirming our observation of the differences in high-latitudinal concentration. CESM2 also presents a radius always larger than the GISS-MATRIX and UKESM1 one, which explains most of the discrepancies between AOD and column mass between the CESM2 and GISS models: even if CESM2 shows larger mass concentrations, smaller particles such as those in GISS are more efficient scatterers; thus, GISS AOD is more comparable to CESM2. If dynamics were similar between the two models, one would also expect less mass in CESM2 compared to GISS due to reduced lifetime caused by the increased gravitational settling, but in this case, the dynamical differences dominate in determining the final mass concentrations; these differences are discussed in more depth in Part 2 and indicate a substantially stronger climatological shallow branch of the Brewer–Dobson circulation in CESM2 compared to other models (see Fig. 2 in Part 2). UKESM1 has intermediate radii between CESM2 and GISS-MATRIX.

Looking at the mean radii for each mode (Fig. S1), differences in the microphysical approaches become more evident between the models, also based on the values given in Table . Given that UKESM1 defines the coarse mode as particles larger than 0.5 µm, all of the stratospheric aerosols are found in the accumulation mode (as they are in GISS), whereas CESM2, which defines the coarse-mode threshold at around 0.4 µm, simulates most of the sulfate aerosols in that mode and very few in the accumulation mode. This particular observation should not significantly influence the aerosols' behavior in the stratosphere, since the coagulation and condensation processes happen in all modes. It could, however, have some impacts on the tropospheric interactions of sulfate with cloud nuclei; for instance, some models (such as CESM2) treat coarse-mode and accumulation-mode aerosols differently when calculating the presence of heterogeneous and homogeneous ice nuclei (see, for example, , for a discussion of undesired side effects this might have on ice nucleation rates in the upper troposphere in CESM1(WACCM)).

The resulting zonal mean cooling achieved by the AOD increase in each simulation is shown in Fig. , including both the absolute temperature changes and values normalized by the global means. Differences between models are still evident, but a direct correlation with the AOD changes in Fig.  is not present; for instance, the general temperature responses between the two GISS realizations are much more similar than their simulated AOD, as was already visible in Fig. . This is because temperature responses compound many sources of uncertainty, including those related not only to the magnitude and spatial pattern of the simulated stratospheric AOD (thus related to the model microphysics and transport), but also to the resulting radiative, dynamical and chemical processes operating in the troposphere and lower stratosphere (including the associated changes in ozone and water vapor, which are discussed in Part 2) that modulate how much cooling AOD produces and how the regional patterns of cooling differ. We find very large differences between the models in the magnitude of the global mean cooling per unit AOD (Fig. ). CESM2 and UKESM1 show, on average, 4.7 and 5.4 K cooling per unit of AOD, respectively. This is roughly in line with the multi-model average of the GeoMIP G6sulfur experiment (six models, resulting in 4.6 K per unit AOD for injections between 10∘ N and 10∘ S in GeoMIP – – compared to the 3.9 and 4.8 K cooling per unit AOD in CESM2 and UKESM1, respectively, for the equatorial injections here).

In contrast, the GISS models show significantly larger cooling per unit AOD, with 8.6 K on average in GISS-OMA and 16.7 K on average in GISS-MATRIX; the latter is more than 3 times as high as in CESM2. As noted for Fig. , this large normalized difference is mainly due to differences in the global cooling produced between the two GISS realizations (the sensitivity to the aerosol amount); even if there is a much smaller amount of AOD simulated in GISS-MATRIX, it results in a similar level of surface cooling as is simulated in GISS-OMA under much larger AOD values. The cause for the discrepancies between the two GISS realizations is most likely found in similar tuning procedures for the model (described for GISS-E2.1 in ); while these mainly target the global radiative balance, they often also try to constrain the aerosol forcing (this is described, for instance, in , where both GISS and CESM1 tuning procedures are explained in some detail). The two GISS versions used here show large differences in the baseline aerosol optical depth from sulfate: in the midlatitudinal NH, where anthropogenic sulfate aerosol production is maximized, GISS-MATRIX shows an average AOD of 0.03, just like CESM2, while GISS-OMA shows an average AOD of 0.11 (see Fig. S2). Further investigations will be warranted in the baseline GISS simulations to understand if this difference is relevant for the observed differences in the sensitivity to stratospheric aerosols between the two versions.

Another possible contributor to the differences in the magnitude of global cooling simulated in GISS could be the substantial tropospheric ozone reduction simulated in the two model versions (see Sect. 3.3.4 of Part 2). As a greenhouse gas, reduction in tropospheric ozone would thus act to magnify the cooling from the direct aerosol forcing, and this effect is generally not present in CESM2 or UKESM1.

The normalized values in the right panels of Fig.  show some level of consistency in the temperature response amongst the models. In particular, the models agree that equatorial injections tend to cool the NH more than the SH and that the cooling produced by the NH injections is strongest in the NH (this is particularly marked in CESM2 for the 15∘ N injection), whereas the cooling produced by the SH injections is more evenly distributed between the two hemispheres. In contrast, the models tend to disagree with respect to responses in the NH high latitudes much more than for the SH high latitudes; this can be explained by the role of dynamical atmospheric variability and sea ice variability, which in the NH both may contribute to increasing model spread .

Finally, in Fig.  we show the zonal mean changes in precipitation. In this case, we show both the magnitude of the change in millimeters per day (mm d-1) and the corresponding percent changes with respect to the baseline precipitation pattern in each model. The precipitation response also depends on the climatological precipitation, which differs more between the models than the climatological temperature does (not shown). We find general qualitative agreement between the models in the tropics. All models show shifts in tropical precipitation depending on the hemisphere of injection, with decreased precipitation in that hemisphere and increased precipitation in the opposite one. The equatorial injections in turn result in an overall reduction of tropical precipitation. Changes at middle and high latitudes, which are much smaller in absolute terms than those in the tropics, can be as high in terms of percentage changes as those in the tropics, but the models disagree on the sign and magnitude of the responses there far more than they do in the tropics. We also show percent in order to highlight the significance of the absolute changes based on the overall received precipitation. This, for instance, helps to show that, compared to the baseline values, the very small changes observed at high latitudes may also be significant.

In general, precipitation changes depend on even more factors than temperature changes . Differences in the inter-hemispheric cooling patterns produce shifts in the precipitation by moving the Intertropical Convergence Zone (ITCZ, see below and, e.g., ); this is compounded by differences in the cloud responses and by the large-scale dynamical changes resulting from the aerosol-induced stratospheric heating (see Sect. 3.2 to 3.5 in Part 2; also ). Furthermore, precipitation responses tend to be regionally dependent: for instance, previous G6 GeoMIP simulations showed consensus in the winter precipitation response over Europe (with increased precipitation in northern Europe and decreased over southern Europe associated with the SAI-induced positive phase of the North Atlantic Oscillation); however, the same models showed little consensus over the North American continent .

Figure  shows changes in the position of ITCZ, which we define here as the latitude near the Equator where the meridional mass streamfunction at 500 hPa changes sign. The models qualitatively agree with respect to the simulated ITCZ shifts, despite the significant differences in the climatological ITCZ locations (shown on the left side of Fig. ). The larger simulated ITCZ shifts for the NH injections compared to the SH injections are also consistent with the different cooling patterns, with stronger and more NH-confined cooling for the 30 and 15∘ N injections. A similar behavior of the ITCZ was also previously found for volcanic eruptions occurring in the equatorial or extra-equatorial regions as well as for previous single-point SAI simulations .