spheric values are very low throughout and only increase in the troposphere. The largest stratospheric extinction coefficients are seen in ECHAM6-SALSA, which is consistent with the higher burdens in this model, followed by SOCOL-AERV2 and ULAQ-CCM. CAM5-CARMA and both WACCM6 models have mid-range values, consistent with GloSSACV2.2, while ECHAM5-HAM has the lowest extinctions, also consistent with its overall aerosol burdens. In Quaglia et al. (2023), the extinction coefficients also vary a lot among models for volcanically perturbed conditions.

## 4 Conclusions

In this study, we present an analysis of the atmospheric sulfur budget using nine state-of-the-art global circulation models with interactive aerosol modules and sulfur chemistry. In particular, we showcase the burdens of the main sulfur species represented in these models (OCS, sulfate aerosols, and SO₂), as well as their latitudinal and vertical distribution and seasonal variability. Emission and deposition fluxes are also discussed. Sulfate aerosol, OCS, and SO₂ behave very differently in the atmosphere, providing insight into the modeled processes. OCS is almost chemically inert in the troposphere and is primarily influenced by transport mechanisms but undergoes photolysis in the stratosphere. Conversely, SO₂, which has a lifetime of a few days to a few weeks, is more responsive to chemical processes in the troposphere.

Previous studies have revealed the main sulfur species abundant in the atmosphere to be OCS, SO₂, and sulfate aerosol, which we here find to make up about 95% of the total tropospheric and 98% of the stratospheric sulfur mass, averaging over all models which include these three species. However, variability across models in the stratospheric burden of each of these main species is large, with burdens of 319 ± 50 Gg (S) for OCS, 12 ± 7 Gg (S) for SO₂, and 156 ± 51 Gg (S) for sulfate aerosol. Anthropogenic emissions of SO₂ dominate the sulfate aerosol burden in the NH troposphere and increase the aerosol mass in the lowest stratosphere by 10%–80%, which is very model-dependent. The SH, both in the troposphere and the stratosphere, is less affected by anthropogenic activity (10%–30%). The total deposition varies across models by about a factor of 2 between 99–692 and 51–211 Gg (S) yr⁻¹ (or 86–693 ± 18–115 Gg (S) yr⁻¹). Models also disagree on the form in which sulfur is deposited, as well as the split between wet and dry deposition. More sulfur being deposited as aerosol precursor gases could lead to a lower aerosol burden, as discussed by Textor et al. (2006). We do, however, not explicitly observe such behavior. Furthermore, the relative importance of wet and dry deposition is expected to depend on the solubility of the compound, as well as the treatment of clouds and precipitation in the respective models (Textor et al., 2006). Evaluating model performances with respect to

clouds and precipitation is beyond the scope of this study, and we refer to each model's documentation for details, as well as to dedicated model intercomparison activities on this topic (e.g., Webb et al., 2017).

In terms of the spatial distribution, the models agree very well on the distribution and seasonality in the SH for all species. However, in the NH, where anthropogenic emissions contribute significantly to the aerosol burden, especially at low to mid-latitudes, more uncertainties persist. This is in part due to dynamical uncertainties in the northern polar vortex (Karpechko et al., 2022) affecting the transport into high latitudes. The highest values in the northern extratropics are seen in ULAQ-CCM, which are associated with a slower and warmer vortex compared to the other models. Additionally, resolution-dependent isentropic transport through the sub-tropical tropopause (Holton et al., 1995; Gettelman et al., 2011) could play a major role in increasing the extratropical burdens of OCS and sulfate in some models, which may be even more pronounced during the Asian monsoon, during which aerosol transport to the stratosphere is facilitated (Yu et al., 2017). A low horizontal resolution also increases diffusion across transport barriers, such as the polar vortex or the tropopause, where it crosses the isentropes in the sub-tropics (Dietmüller, 2018). The speed of the BDC also could be a major factor of uncertainty (Abalos et al., 2021) affecting both the transport through the shallow branch, as well as upwelling, and thus the confinement of aerosol in the tropics. Idealized tracer experiments using SO₂ emissions might help to isolate the dynamical biases.

The analysis on the effective radius, SAD, and extinction in the tropics and at Laramie reveals notable differences among models. While the effective radius shows some agreement among models and is within the uncertainty in the OPC measurements in Laramie in all models, SAD exhibits larger discrepancies, reflecting the variations in aerosol burdens. Extinction levels also vary significantly, with ECHAM6-SALSA showing the highest values. Elaborating further on the reasons for the size distribution uncertainties would require a closer look at the individual microphysical processes, as was also highlighted by Quaglia et al. (2023), but such data were not available in most of the models in our study. Recently, concerns have arisen regarding nucleation schemes, such as Vehkamäki et al. (2002), which may overestimate the nucleation of new particles (Laakso et al., 2022; Yu et al., 2023). However, these studies focus on stratospheric aerosol injection scenarios, where sulfur is much more abundant than in the background conditions presented in this study. Using observational data, Wrana et al. (2023) showed that small volcanic eruptions affect the background size distribution of aerosols in unexpected ways, sometimes decreasing instead of increasing the effective radius. The volcanic events highlighted there can be further used as model test cases, contributing knowledge to the model performance in terms of microphysics and its dependence on the background conditions.
spheric values are very low throughout and only increase in the troposphere. The largest stratospheric extinction coefficients are seen in ECHAM6-SALSA, which is consistent with the higher burdens in this model, followed by SOCOL-AERV2 and ULAQ-CCM. CAM5-CARMA and both WACCM6 models have mid-range values, consistent with GloSSACV2.2, while ECHAM5-HAM has the lowest extinctions, also consistent with its overall aerosol burdens. In Quaglia et al. (2023), the extinction coefficients also vary a lot among models for volcanically perturbed conditions.

## 4 Conclusions

In this study, we present an analysis of the atmospheric sulfur budget using nine state-of-the-art global circulation models with interactive aerosol modules and sulfur chemistry. In particular, we showcase the burdens of the main sulfur species represented in these models (OCS, sulfate aerosols, and SO₂), as well as their latitudinal and vertical distribution and seasonal variability. Emission and deposition fluxes are also discussed. Sulfate aerosol, OCS, and SO₂ behave very differently in the atmosphere, providing insight into the modeled processes. OCS is almost chemically inert in the troposphere and is primarily influenced by transport mechanisms but undergoes photolysis in the stratosphere. Conversely, SO₂, which has a lifetime of a few days to a few weeks, is more responsive to chemical processes in the troposphere.

Previous studies have revealed the main sulfur species abundant in the atmosphere to be OCS, SO₂, and sulfate aerosol, which we here find to make up about 95% of the total tropospheric and 98% of the stratospheric sulfur mass, averaging over all models which include these three species. However, variability across models in the stratospheric burden of each of these main species is large, with burdens of 319 ± 50 Gg (S) for OCS, 12 ± 7 Gg (S) for SO₂, and 156 ± 51 Gg (S) for sulfate aerosol. Anthropogenic emissions of SO₂ dominate the sulfate aerosol burden in the NH troposphere and increase the aerosol mass in the lowermost stratosphere by 10%–80%, which is very model-dependent. The SH, both in the troposphere and the stratosphere, is less affected by anthropogenic activity (10%–30%). The total deposition varies across models by about a factor of 2 between 99 692 and 51 211 Gg (S) yr⁻¹ (or 86 693 ± 18 115 Gg (S) yr⁻¹). Models also disagree on the form in which sulfur is deposited, as well as the split between wet and dry deposition. More sulfur being deposited as aerosol precursor gases could lead to a lower aerosol burden, as discussed by Textor et al. (2006). We do, however, not explicitly observe such behavior. Furthermore, the relative importance of wet and dry deposition is expected to depend on the solubility of the compound, as well as the treatment of clouds and precipitation in the respective models (Textor et al., 2006). Evaluating model performances with respect to

clouds and precipitation is beyond the scope of this study, and we refer to each model's documentation for details, as well as to dedicated model intercomparison activities on this topic (e.g., Webb et al., 2017).

In terms of the spatial distribution, the models agree very well on the distribution and seasonality in the SH for all species. However, in the NH, where anthropogenic emissions contribute significantly to the aerosol burden, especially at low to mid-latitudes, more uncertainties persist. This is in part due to dynamical uncertainties in the northern polar vortex (Karpechko et al., 2022) affecting the transport into high latitudes. The highest values in the northern extratropics are seen in ULAQ-CCM, which are associated with a slower and warmer vortex compared to the other models. Additionally, resolution-dependent isentropic transport through the subtropical tropopause (Holton et al., 1995; Gettelman et al., 2011) could play a major role in increasing the extratropical burdens of OCS and sulfate in some models, which may be even more pronounced during the Asian monsoon, during which aerosol transport to the stratosphere is facilitated (Yu et al., 2017). A low horizontal resolution also increases diffusion across transport barriers, such as the polar vortex or the tropopause, where it crosses the isentropes in the subtropics (Dietmüller, 2018). The speed of the BDC also could be a major factor of uncertainty (Abalos et al., 2021) affecting both the transport through the shallow branch, as well as upwelling, and thus the confinement of aerosol in the tropics. Idealized tracer experiments using SO₂ emissions might help to isolate the dynamical biases.

The analysis on the effective radius, SAD, and extinction in the tropics and at Laramie reveals notable differences among models. While the effective radius shows some agreement among models and is within the uncertainty in the OPC measurements in Laramie in all models, SAD exhibits larger discrepancies, reflecting the variations in aerosol burdens. Extinction levels also vary significantly, with ECHAM6-SALSA showing the highest values. Elaborating further on the reasons for the size distribution uncertainties would require a closer look at the individual microphysical processes, as was also highlighted by Quaglia et al. (2023), but such data were not available in most of the models in our study. Recently, concerns have arisen regarding nucleation schemes, such as Vehkamäki et al. (2002), which may overestimate the nucleation of new particles (Laakso et al., 2022; Yu et al., 2023). However, these studies focus on stratospheric aerosol injection scenarios, where sulfur is much more abundant than in the background conditions presented in this study. Using observational data, Wrana et al. (2023) showed that small volcanic eruptions affect the background size distribution of aerosols in unexpected ways, sometimes decreasing instead of increasing the effective radius. The volcanic events highlighted there can be further used as model test cases, contributing knowledge to the model performance in terms of microphysics and its dependence on the background conditions.
With this study, we have provided a first multi-model analysis of the background burdens of sulfur in atmospheric models. We mainly assessed the burdens and latitudinal and vertical distributions of sulfur species, allowing us to identify potential reasons for model diversity. As burdens are merely the result of fluxes, the next step would be to compare chemical and microphysical fluxes, as well as emission, cross-tropopause, and deposition fluxes. For SO₂ in particular, cross-tropopause fluxes in the mid-latitudes have the potential to provide more insight into the underlying processes causing differences in stratospheric burdens.

Overall, this study sheds new light on the atmospheric sulfur budget and, for the first time, presents it in a multi-model context. Our results highlight the importance of an interplay between the chemical, microphysical, and dynamical processes in atmospheric models. The interdependence of these processes complicates the attribution of biases when looking only at their final products, namely the distribution and variability in sulfur species in the atmosphere. The same holds true for the recent similar studies focused on volcanic events (e.g., Quaglia et al., 2023; Clyne et al., 2021; Marshall et al., 2018) and stratospheric aerosol injections (e.g., Weisenstein et al., 2022). Some conclusions could be drawn by relating different variables. However, more detailed investigations of the reasons for inter-model disagreement would require process-oriented experiments such as the sensitivity experiments proposed by ISA–MIP for the Pinatubo eruption in the Pinatubo Emulation in Multiple models (PoEMS) (e.g., Timmreck et al., 2018). However, these experiments still include the full range of complexity and may therefore be difficult to interpret. Much more illuminating would be experiments in which the degrees of freedom are reduced so that specific questions can be addressed. Comparison of standalone parts of the respective model codes, i.e., box model versions of the microphysical and chemical schemes, short and long wavelength radiative transfer modules, and treatment of the Mie calculation, is one possible solution. The other would be to perform dedicated tracer studies or simple sulfur cycle experiments (with a prescribed aerosol size distribution). Revisiting the ISA–MIP experiments in this sense and developing a set of dedicated benchmark simulations related to available observations would therefore be a valuable next step to validate and improve global stratospheric aerosol models but also to reduce uncertainties in solar radiation modification scenarios.
With this study, we have provided a first multi-model analysis of the background burdens of sulfur in atmospheric models. We mainly assessed the burdens and latitudinal and vertical distributions of sulfur species, allowing us to identify potential reasons for model diversity. As burdens are merely the result of fluxes, the next step would be to compare chemical and microphysical fluxes, as well as emission, cross-tropopause, and deposition fluxes. For SO₂ in particular, cross-tropopause fluxes in the mid-latitudes have the potential to provide more insight into the underlying processes causing differences in stratospheric burdens.

Overall, this study sheds new light on the atmospheric sulfur budget and, for the first time, presents it in a multi-model context. Our results highlight the importance of an interplay between the chemical, microphysical, and dynamical processes in atmospheric models. The interdependence of these processes complicates the attribution of biases when looking only at their final products, namely the distribution and variability in sulfur species in the atmosphere. The same holds true for the recent similar studies focused on volcanic events (e.g., Quaglia et al., 2023; Clyne et al., 2021; Marshall et al., 2018) and stratospheric aerosol injections (e.g., Weisenstein et al., 2022). Some conclusions could be drawn by relating different variables. However, more detailed investigations of the reasons for inter-model disagreement would require process-oriented experiments such as the sensitivity experiments proposed by ISA–MIP for the Pinatubo eruption in the Pinatubo Emulation in Multiple models (PoEMS) (e.g., Timmreck et al., 2018). However, these experiments still include the full range of complexity and may therefore be difficult to interpret. Much more illuminating would be experiments in which the degrees of freedom are reduced so that specific questions can be addressed. Comparison of standalone parts of the respective model codes, i.e., box model versions of the microphysical and chemical schemes, short and long wavelength radiative transfer modules, and treatment of the Mie calculation, is one possible solution. The other would be to perform dedicated tracer studies or simple sulfur cycle experiments (with a prescribed aerosol size distribution). Revisiting the ISA–MIP experiments in this sense and developing a set of dedicated benchmark simulations related to available observations would therefore be a valuable next step to validate and improve global stratospheric aerosol models but also to reduce uncertainties in solar radiation modification scenarios.
Appendix A

<figure><img src="image_13.png" /><figcaption>**Figure A1.** The SO₂ emissions in the NAT (a) and REF (b) experiments. NAT is composed of volcanic outgassing (c) and biomass burning (e), while the REF experiment additionally includes anthropogenic emissions (d).</figcaption></figure>
Appendix A

<figure><img src="image_14.png" /><figcaption>**Figure A1.** The SO₂ emissions in the NAT (a) and REF (b) experiments. NAT is composed of volcanic outgassing (c) and biomass burning (e), while the REF experiment additionally includes anthropogenic emissions (d).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure A2.** Total deposition fluxes of sulfate aerosol (as a sum of dry and wet deposition) as absolute values are given in panels (a)–(f) and as a percent difference between the REF and NAT experiments in panels (g)–(l). The percent difference is calculated as REF–NAT and divided by REF. The data are time-averaged over the whole time period.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure A2.** Total deposition fluxes of sulfate aerosol (as a sum of dry and wet deposition) as absolute values are given in panels (a)–(f) and as a percent difference between the REF and NAT experiments in panels (g)–(l). The percent difference is calculated as REF–NAT and divided by REF. The data are time-averaged over the whole time period.</figcaption></figure>
<figure><img src="image_15.png" /></figure>

**Figure A3.** The difference in the time slice simulations averaged over 20 years for each season for temperature and zonal winds. Anomalies are calculated with respect to 1999–2004 ERA-I data, which was regridded to the respective model grid. Temperature is shown in color, while winds are in gray contours. Solid lines indicate stronger-than-observed westerly zonal winds, while dashed lines are weaker than observed. The numbers along with the contours are the anomalies (in m s⁻¹). Each column represents one season, while each row represents one model. The simulated tropopause is shown as a black line, also averaged over each season, respectively.
<figure><img src="image_16.png" /></figure>

**Figure A3.** The difference in the time slice simulations averaged over 20 years for each season for temperature and zonal winds. Anomalies are calculated with respect to 1999–2004 ERA-I data, which was regridded to the respective model grid. Temperature is shown in color, while winds are in gray contours. Solid lines indicate stronger-than-observed westerly zonal winds, while dashed lines are weaker than observed. The numbers along with the contours are the anomalies (in m s⁻¹). Each column represents one season, while each row represents one model. The simulated tropopause is shown as a black line, also averaged over each season, respectively.
<figure><img src="image_16.png" /></figure>

**Figure A4.** The percent difference between the REF experiment and the NAT experiment of the SO₂ volume mixing ratio in panels (a)–(f) and the sulfate mass mixing ratio in panels (g)–(l). The percent difference is calculated as REF–NAT divided by REF. All data are zonally averaged and over the whole time period of each simulation.

<figure><img src="image_17.png" /></figure>

**Figure A5.** The tropopauses of each model, as well as the ERA-I-derived tropopause, which was used to calculate stratospheric burdens for SAGE-3λ.
<figure><img src="image_17.png" /></figure>

**Figure A4.** The percent difference between the REF experiment and the NAT experiment of the SO₂ volume mixing ratio in panels (a)–(f) and the sulfate mass mixing ratio in panels (g)–(l). The percent difference is calculated as REF–NAT divided by REF. All data are zonally averaged and over the whole time period of each simulation.

<figure><img src="image_18.png" /></figure>

**Figure A5.** The tropopauses of each model, as well as the ERA-I-derived tropopause, which was used to calculate stratospheric burdens for SAGE-3λ.
**Data availability.** All model data used in this study can be accessed through https://doi.org/10.5281/zenodo.10411013 (Brodowsky et al., 2023). The MIPAS combined SO₂ dataset is publicly available (https://doi.org/10.35097/1788, Höpfner, 2023), as is MIPAS OCS (https://doi.org/10.35097/1821, Höpfner and Glatthor, 2023). The GloSSACv2.2 data are available at https://doi.org/10.5067/GLOSSAC-L3-V2.2 (NASA/LARC/SD/ASDC, 2022). The SAGE-3λ data are also based on this dataset. The ERA-Interim reanalysis is available from the Copernicus Climate Change Service (2023) (https://doi.org/10.24381/cds.f2f5241d). OPC balloon measurements can be accessed through https://doi.org/10.15786/c.6379371. SAGE II v7 data are available from https://doi.org/10.5067/ERBS/SAGEII/SOLAR_BINARY_L2-V7.0 (NASA/LARC/SD/ASDC, 2012). The full raw dataset for all models is also available on the DKRZ Levante HPC system and can be made available upon request.

**Author contributions.** The analysis and the main text were done by CVB, and contributions were also made by TSu, MH, AL, GWM, UN, CT, IQ, ST, DV, PY, YZ, and TP. TSu, TP, GC, and VA supervised CVB. CT, SSD, and GWM conceptualized the study. The simulations were run by CVB, AL, GWM, UN, GP, IQ, TSe, DV, PY, and YZ. All authors contributed to the discussion of the results and the corrections to the paper.

**Competing interests.** At least one of the (co-)authors is a member of the editorial board of *Atmospheric Chemistry and Physics*. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

**Acknowledgements.** We thank Beiping Luo for providing the SAGE-3λ aerosol data used in this work. Furthermore, we thank the editor and the two anonymous referees, who have provided valuable feedback on the article. This work is a contribution to the “Interactive Model Intercomparison Project (ISA–MIP)” from the WCRP/SPARC activity “Stratospheric Sulfur and its Role in Climate (SSiRC)”. ECHAM5–HAM computations and analysis were performed on the computer of the Deutsches Klimarechenzentrum (DKRZ), using resources granted by its Scientific Steering Committee (WLA, under project ID bm0885). NCAR’s Community Earth System Model project has been supported primarily by the National Science Foundation. Computing and data storage resources, including the Cheyenne supercomputer (https://doi.org/10.5065/D6RX99HX, National Center for Atmospheric Research, Computational and Information Systems Lab, 2024), were provided by the Computational and Information Systems Laboratory (CISL) at NCAR. SOCOL–AERv2 simulations

have been performed at the ETH cluster EULER and Swiss National Supercomputing Centre (CSCS) under project s1191. Valentina Aquila has been supported by the NASA Interdisciplinary Research in Earth Science Program (program manager Ben Phillips) and the NASA Aura Science Team (program manager Richard Eckman). The UM–UKCA simulations were carried out on the UK ARCHER national supercomputing service, with data analysis and storage within the UK collaborative JASMIN data facility. We acknowledge Mohit Dalvi, Nicolas Bellouin, James Brooke, Lauren Marshall, and Kamalika Sengupta for their involvement with the UM–UKCA aerosol code. Slimane Bekki acknowledges the support of CNES (Centre National d'Études Spatiales) to the BeSAFE balloon mission. Earth Simulator was used for the MIROC-CHASER simulations via the support of the Japan Agency for Marine-Earth Science and Technology.

**Financial support.** Claudia Timmreck and Ulrike Niemeier received support from the Deutsche Forschungsgemeinschaft (DFG) Research Unit VolImpact (FOR2820, grant no. 398006378) within the projects VolARC and VolClim. Yunqian Zhu received funding from NOAA's Earth Radiation Budget (ERB) Initiative (CPO, grant no. 03-01-07-001) and NOAA (grant nos. NA170AR4320101 and NA220AR4320151). Timofei Sukhodolov, Eugene Rozanov, and Christina V. Brodowsky received funding from the Swiss National Science Foundation for this study (grant no. 200020-182239, project POLE (Past, present, and future of the ozone layer)). Timofei Sukhodolov also received support from the Karbacher Fonds, Graubünden, Switzerland. Gabriel Chiodo received funding from the Swiss National Science Foundation via Ambizione (grant no. PZ00P2_180043). Sandro Vattioni has been funded via ETH (grant no. ETH-17 19-2). Graham W. Mann and Sandip S. Dhomse have been funded by NERC highlight topic consortium project SMURPHS (grant no. NE/N006038/1) and the standard grant project MeteorStrat (grant no. NE/R011222/1). Graham W. Mann received funding from the UK National Centre for Atmospheric Science (NCAS) through the NERC multi-center Long-Term Science program on the North Atlantic climate system (ACSIS, NERC grant no. NE/N018001/1) and the Copernicus Atmospheric Monitoring Service (CAMS), one of six services that together form Copernicus, the EU's Earth observation program.

**Review statement.** This paper was edited by Marc von Hobe and reviewed by two anonymous referees.

## References

Abalos, M., Calvo, N., Benito-Barca, S., Garny, H., Hardiman, S. C., Lin, P., Andrews, M. B., Butchart, N., Garcia, R., Orbe, C., Saint-Martin, D., Watanabe, S., and Yoshida, K.: The Brewer-Dobson circulation in CMIP6, Atmos. Chem. Phys., 21, 13571–13591, https://doi.org/10.5194/acp-21-13571-2021, 2021.

Abraham, N. L.: Documentation for the vn8.4 GA4.0 CheST+GLOMAP-mode release job RJ4.0, UK Chemistry and Aerosol project, https://www.ukca.ac.uk/wiki/index.php/Release_Job_RJ4.0 (last access: 4 April 2023), 2014.
**Data availability.** All model data used in this study can be accessed through https://doi.org/10.5281/zenodo.10411013 (Brodowsky et al., 2023). The MIPAS combined SO₂ dataset is publicly available (https://doi.org/10.35097/1788, Höpfner, 2023), as is MIPAS OCS (https://doi.org/10.35097/1821, Höpfner and Glatthor, 2023). The GloSSACv2.2 data are available at https://doi.org/10.5067/GLOSSAC-L3-V2.2 (NASA/LARC/SD/ASDC, 2022). The SAGE-3λ data are also based on this dataset. The ERA-Interim reanalysis is available from the Copernicus Climate Change Service (2023) (https://doi.org/10.24381/cds.f2f5241d). OPC balloon measurements can be accessed through https://doi.org/10.15786/c.6379371. SAGE II v7 data are available from https://doi.org/10.5067/ERBS/SAGEII/SOLAR_BINARY_L2-V7.0 (NASA/LARC/SD/ASDC, 2012). The full raw dataset for all models is also available on the DKRZ Levante HPC system and can be made available upon request.

**Author contributions.** The analysis and the main text were done by CVB, and contributions were also made by TSu, MH, AL, GWM, UN, CT, IQ, ST, DV, PY, YZ, and TP. TSu, TP, GC, and VA supervised CVB. CT, SSD, and GWM conceptualized the study. The simulations were run by CVB, AL, GWM, UN, GP, IQ, TSe, DV, PY, and YZ. All authors contributed to the discussion of the results and the corrections to the paper.

**Competing interests.** At least one of the (co-)authors is a member of the editorial board of *Atmospheric Chemistry and Physics*. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

**Acknowledgements.** We thank Beiping Luo for providing the SAGE-3λ aerosol data used in this work. Furthermore, we thank the editor and the two anonymous referees, who have provided valuable feedback on the article. This work is a contribution to the “Interactive Model Intercomparison Project (ISA–MIP)” from the WCRP/SPARC activity “Stratospheric Sulfur and its Role in Climate (SSiRC)”. ECHAM5–HAM computations and analysis were performed on the computer of the Deutsches Klimarechenzentrum (DKRZ), using resources granted by its Scientific Steering Committee (WLA, under project ID bm0885). NCAR’s Community Earth System Model project has been supported primarily by the National Science Foundation. Computing and data storage resources, including the Cheyenne supercomputer (https://doi.org/10.5065/D6RX99HX, National Center for Atmospheric Research, Computational and Information Systems Lab, 2024), were provided by the Computational and Information Systems Laboratory (CISL) at NCAR. SOCOL–AERv2 simulations

have been performed at the ETH cluster EULER and Swiss National Supercomputing Centre (CSCS) under project s1191. Valentina Aquila has been supported by the NASA Interdisciplinary Research in Earth Science Program (program manager Ben Phillips) and the NASA Aura Science Team (program manager Richard Eckman). The UM–UKCA simulations were carried out on the UK ARCHER national supercomputing service, with data analysis and storage within the UK collaborative JASMIN data facility. We acknowledge Mohit Dalvi, Nicolas Bellouin, James Brooke, Lauren Marshall, and Kamalika Sengupta for their involvement with the UM–UKCA aerosol code. Slimane Bekki acknowledges the support of CNES (Centre National d'Études Spatiales) to the BeSAFE balloon mission. Earth Simulator was used for the MIROC-CHASER simulations via the support of the Japan Agency for Marine-Earth Science and Technology.

**Financial support.** Claudia Timmreck and Ulrike Niemeier received support from the Deutsche Forschungsgemeinschaft (DFG) Research Unit VolImpact (FOR2820, grant no. 398006378) within the projects VolARC and VolClim. Yunqian Zhu received funding from NOAA's Earth Radiation Budget (ERB) Initiative (CPO, grant no. 03-01-07-001) and NOAA (grant nos. NA170AR4320101 and NA220AR4320151). Timofei Sukhodolov, Eugene Rozanov, and Christina V. Brodowsky received funding from the Swiss National Science Foundation for this study (grant no. 200020-182239, project POLE (Past, present, and future of the ozone layer)). Timofei Sukhodolov also received support from the Karbacher Fonds, Graubünden, Switzerland. Gabriel Chiodo received funding from the Swiss National Science Foundation via Ambizione (grant no. PZ00P2_180043). Sandro Vattioni has been funded via ETH (grant no. ETH-17 19-2). Graham W. Mann and Sandip S. Dhomse have been funded by NERC highlight topic consortium project SMURPHS (grant no. NE/N006038/1) and the standard grant project MeteorStrat (grant no. NE/R011222/1). Graham W. Mann received funding from the UK National Centre for Atmospheric Science (NCAS) through the NERC multi-center Long-Term Science program on the North Atlantic climate system (ACSIS, NERC grant no. NE/N018001/1) and the Copernicus Atmospheric Monitoring Service (CAMS), one of six services that together form Copernicus, the EU's Earth observation program.

**Review statement.** This paper was edited by Marc von Hobe and reviewed by two anonymous referees.

## References

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