All models participating in the Interactive Stratospheric Aerosol Model Intercomparison Project (ISA-MIP) are using interactive aerosol microphysical modules and some also interactive chemistry (see Table ). In the framework of the Historical Eruptions SO₂ Emission Assessment (HErSEA) experiments, modelling groups performed transient Atmospheric Model Intercomparison Project (AMIP)-type runs of the Mt. Pinatubo eruption in which sea surface temperatures (SSTs) and sea ice extent are prescribed as monthly climatologies between 1991 and 1995 from the Met Office Hadley Center Observational data set . Within HErSEA, five different emission scenarios were designed taking different amounts and altitudes of the volcanic SO₂ injection into account. Three of these scenarios are described by injections at a medium altitude (between 21–23 km) but different amounts of SO₂: low amount of 5 TgS (Low-22km), a medium 7 TgS (Med-22km) and high 10 TgS (High-22km). The medium-amount injection of 5 TgS has two additional scenarios with different injection altitudes: a shallow one at lower altitudes (18–20 km, Med-19km) and one over a deep altitude range (18–25 km, Med-18–25km). For brevity we refer to these experiments and the performing models hereinafter as ISA-MIP. We note in passing that EMAC model outputs are only presented in the analysis when discussing model similarities and differences in SO₄ concentrations and transport, as EMAC did not fully adhere to the ISA-MIP experimental protocol .

The ISA-MIP simulation period spans from January 1991 to December 1995 (for UM-UKCA only until December 1993) and the eruption of Mt. Pinatubo is timed on 15 June 1991. SO₂ injection is specified via a uniform vertical profile in a single grid cell at the respective altitudes close to the Mt. Pinatubo location (15° N, 120° E). The precision is defined by the specific vertical and horizontal model resolutions. The injection strategy differs only for EMAC (for which reason we flag it as EMAC^* in the figures and tables), where volcanic SO₂ is injected at a single point in time as 3D mixing ratio perturbations derived from satellite data using an inventory for the period 1990 to 2019 (10.26050/WDCC/SSIRC_3, ). The eruptions of Cerro Hudson (10 August 1991), Spurr (27 June 1992), and Lascar (18 April 1993) are included in EMAC and WACCM6-CARMA but they are not included in the remaining ISA-MIP simulations.

Following the experimental protocol, all models matched the observed post-Pinatubo QBO transition, either by nudging or from re-initialising from a prior control run. This ensures a consistent QBO state across different models, minimizing the effect of model-specific QBO dynamics on model spread on aerosols. Since the main focus of the HErSEA experiment was to improve our understanding of the long-term evolution of the Pinatubo volcanic cloud , the modelling teams agreed that radiative effects of ash, water vapour and SO₂, as mainly relevant in the initial weeks post eruption , could be excluded. For completeness, it shall be noted that these effects can be important. For example, fine ash, due to the additional radiative heating below the sulfate cloud, can affect the initial transport direction of the aerosol cloud and inclusion of this feature can help represent modeled transport better .

For each different injection setting a three-member ensemble was submitted, except for ULAQ-CCM and EMAC, which submitted only one realization. In the respective model description sections the generation of the ensemble members is described. Unless otherwise specified, the ensemble mean of models is shown in the results.

As noted above, the REMAP method which we use to derive mass-related stratospheric aerosol properties from observations is a successor to the algorithms used in CMIP6 and CCMI-2022 forcing preparations. After retrieving stratospheric aerosol size distributions the preparation of the forcing data sets for these MIPs included calculating not only the physical aerosol properties (effective radius, number density, and surface area density) but also the optical properties: aerosol extinction coefficient, single-scattering albedo and asymmetry factor – tailored to each model's spectral resolution. For CMIP6 these data were created with a similar best-fit algorithm – using, however, an earlier version of GloSSAC (v1.1) and selecting three out of four SAGE II wavelength channels. The data set was therefore termed SAGE-3λ and is described in detail in the Supplement to . The forcing for CCMI-2022 was then based on a further extended and updated version of GloSSAC (v2.0). A key difference in the REMAP code applied to the different products was a parameterization used for regions, where data was scarce.

We start by illustrating in Fig. a the time evolution of the mean temperature anomaly in the tropical lower stratosphere normalized to June 1991 for the five HErSEA-experiments from the ISA-MIP project along with the multi-reanalysis mean (comprising ERA5, MERRA2 and JRA55). The stratospheric heating due to volcanic aerosols, as widely discussed in the literature e.g.,, can be clearly seen in the reanalysis mean. After a short ramp-up period the heating peaks in September 1991 and stays relatively constant at approximately 2 K until January 1993. Thereafter, the tropical heating signal quickly diminishes and vanishes during boreal summer (JJA) 1993.

While the overall evolution of the temperature anomaly identified in the reanalyses is broadly reproduced by the multi-model mean across all experiments, the timing and persistence of the temperature anomaly peak differ from the pattern observed. Among the individual models the temperature anomaly signal fades faster than observed (already between June and October 1992) in ECHAM6-SALSA, ULAQ-CCM and MIROC-CHASER in all experiments. Regarding the magnitude of the temperature anomaly, we find a good agreement between reanalysis and the multi-model mean for all the experiments except the High-22km. In this experiment, the injection of 10 Tg of sulfur in the form of SO₂ results in an overestimation of the temperature signal in most of the models and thus in the multi-model mean. For the other experiments we find, despite good agreement between the reanalyses and the multi-model mean, large differences between individual models. The envelope in temperature anomalies ranges between ECHAM6-SALSA, which shows the smallest temperature anomaly and the least difference across experiments and SOCOL-AerV2, which shows the strongest temperature signal and pronounced sensitivity to different injection magnitudes and altitudes.

Given the similarities at the 50 hPa level in Low-22km, Med-22km, Med-19km and Med-18-25km we expand in Fig. b the analysis to the vertical temperature anomaly in the tropical region for the time period with the strongest signal across models, which corresponds also to the initial peak in the reanalysis mean (September to December 1991). During this period, the reanalysis shows a peak in temperature anomaly of around 2 K between 30 and 40 hPa. While the multi-model mean captures the altitude of the peak and overall vertical distribution of the temperature anomalies well in most experiments, the magnitude is overestimated in all but Low-22km. This overestimation in the multi-model mean is due to the majority of models showing larger anomalies than observed, with several models exceeding the 3σ confidence interval of the reanalysis. With regard to the altitude of the peak temperature anomaly, experiment Med-19km marks an exception. In this experiment the anomaly peaks already around 50 hPa which can be explained by the low injection height. In summary, Fig.  shows that the multi-model mean, for most experiments, agrees well with the reanalysis mean in both time evolution and vertical distribution. Additionally, we find that differences between the models are larger than differences of individual models across experiments.

Therefore, to focus our study, we selected one of the five experiments as the core experiment for further analysis hereinafter, and retained the additional experiments for the discussion of important differences if they emerge. To select this experiment we used the Root Mean Square Error (RMSE) between the multi-model mean and reanalysis for the time evolution analysing the pressure levels with the strongest signal (see Table ). As High-22km is overestimating the observed temperature response and the signal fades too fast in Med-18-25km, both experiments yield high RMSEs. While an overall best-agreeing experiment is not clearly emerging, the lowest mean RMSE is found for Low-22km and Med-22km. Given that Med-22km agrees better with reanalysis for most of the models than Low-22km (see Table ), we selected Med-22km as our core experiment.

Having set the scene by illustrating the large differences in temperature signal of the Mt. Pinatubo eruption across models, we turn to the model representations of the associated forcing. As discussed above, the stratospheric heating results mainly from the absorption of terrestrial LW and solar near-IR radiation. If the absorbing particle is much smaller than the wavelength, the absorption of terrestrial LW radiation and its stratospheric heating is proportional to the mass concentration of the sulfate aerosols . In the case of volcanic aerosols, the size distribution is comparable to near-IR wavelengths; thus, differences between modelled heating can originate from both mass concentration and size distribution and need to be considered in the subsequent analysis, even though the latter has less impact on the total absorption . If the aerosol radius is larger than ∼ 0.5 µm the absorption efficiency starts to increase strongly with increasing aerosol size .

analysed the evolution of stratospheric aerosol optical depth, stratospheric sulfate burden, and aerosol properties (effective radius and SAD) in the ISA-MIP models. The main reason for disagreement among the models analysed in that study was differences in stratospheric transport. ECHAM6-SALSA, ECHAM5-HAM, and SOCOL-AERv2 showed too fast transport from the tropics to high northern latitudes, while for UM-UKCA, transport was confined to the NH. Transport in ULAQ-CCM was found to be too confined to the tropics, likely affected by a different vertical advection scheme in comparison to the other models based on the same dynamical core, ECHAM5 or ECHAM6. Additional factors influencing the tropical confinement were differences in vertical and horizontal resolutions and the definition of the tropical pipe. Overall, most of the models showed a preference for transport to the NH. Exceptions were EMAC, which has been nudged to reanalysis to represent observed tropospheric meteorological conditions, and UM-UKCA when emissions have been spread between 15° N and the Equator instead of point injection. These models showed a better agreement with observations regarding transport to the SH. For the other models, state as reasons for the lack of aerosol (transport) in the SH, the omission of (i) ash injection, which would be crucial in the early days/months to better reproduce the initial evolution of the aerosol cloud, as well as, (ii) aerosol emissions emerging from the Cerro Hudson eruption in August 1991 in the southern extratropics. Below we build on the findings of and extend their analysis with a focus on the time evolution and vertical propagation of SO₄ concentrations and resulting temperature anomalies.

In Fig.  we show the time evolution of the zonal mean of SO₄ concentrations exceeding 1 µg m⁻³ across the upper atmosphere. For this comparison, the REMAP-GloSSAC-2023 data serves as an observational reference. REMAP-GloSSAC-2023 shows increasing SO₄ concentrations post-eruption in both hemispheres, which peak in the tropics until autumn 1991, and fade over the following year. In the models, zonal mean SO₄ concentrations peak earlier (in late summer/early autumn 1991) than observed. Furthermore, the initial distribution differs widely among models. While for ECHAM5-HAM and ULAQ-CCM the SO₄ concentrations are – similarly as for REMAP-GloSSAC-2023 – confined within a small and narrow fraction of the upper atmosphere, the SO₄ plume in SOCOL-AERv2 and WACCM6-CARMA spreads across large parts of the lower and middle stratosphere. These initial differences across models can be attributed to the combined effect of SO₂ conversion rates, transport and model vertical velocity . While some models (EMAC, ECHAM6-SALSA and SOCOL-AERv2) already start transporting SO₄ through the shallow branch of the Brewer-Dobson Circulation (BDC) into higher latitudes shortly after the eruption, others, such as ECHAM5-HAM, ULAQ-CCM, and UM-UKCA, have SO₄ more confined in the tropical pipe during the first months. By November 1991, all models show transport into higher latitudes; however, there are stark differences in transport pathways. Some models (e.g. EMAC, ECHAM6-SALSA, SOCOL-AERv2) show preferred transport through the shallow branch while others (e.g. UM-UKCA, WACCM6-CARMA, MIROC-CHASER) mainly transport through the deep branch until winter 1991/92. A special case is MIROC-CHASER for which SO₄ concentrations are quickly transported into the northern subtropics (20–30° N) and then further towards the pole, with limited sedimentation and no apparent subtropical transport barrier.

Despite these model differences several similarities emerge. As discussed above, a preferred meridional transport to the NH can be identified in all models but EMAC, and UM-UKCA if emissions are spread between 15° N and the Equator (see Fig. ), in agreement with . For all ISA-MIP model realizations a net descent of SO₄ concentrations begins in November 1991, likely reflecting the increased effective radius, and downward propagation of the SO₄ plume emerges between late winter and early spring 1992. From May 1992 onward, the peak in SO₄ concentration can be found over the northern polar region in all models, and only low SO₄ values remain in the lower latitudes. While this is in broad agreement with REMAP-GloSSAC-2023 observational composite retrievals, the latter shows stronger transport to the southern hemisphere than the models. Despite the northern hemispheric transport preference of the models, both, low resolution models such as SOCOL-AERv2 and intermediate resolution models such as ECHAM6-SALSA and EMAC, perform well in comparison to REMAP-GloSSAC-2023 observations regarding the magnitude and transport patterns of SO₄ concentrations. However, for ECHAM6-SALSA, the aerosol distribution between the hemispheres varies considerably across individual ensemble members, a feature highlighted in previous work  pointing to strong sensitivities to the dynamic state at the injection grid point at the time of SO₂ release.

Most importantly, Fig.  makes large differences in aerosol transport and concentrations across models apparent; thus, we investigate next how these relate to temperature signals and differences therein.

The largest post-Pinatubo SO₄ concentrations occurred in the tropics e.g., and we first assess the progression of each model's volcanic sulfate in the 20° S–20° N region. To allow for a direct comparison of SO₄ forcing and temperature anomaly we provide model-specific SO₄ concentration contour lines in all panels of Fig. . First, we note that for both, the multi-reanalysis mean and REMAP-GloSSAC-2023 observations, a strong relationship between the progression of peak temperature anomaly and SO₄ concentration appears in the spatial and temporal analysis. Second, in observations and in all models, the strongest temperature response occurs shortly after the eruption simultaneously with the highest concentrations in SO₄. Third, the temperature signal decays over time as the SO₄ plume propagates. Fourth, the strong correlation between temperature anomaly and SO₄ concentration identified in observations is also present in all models; however, the magnitude, timing, temporal and vertical extent of the signal differ substantially between them.

For one thing, MIROC-CHASER and ECHAM6-SALSA stand apart from the other models and the observations: MIROC-CHASER as it does not show a descending temperature signal, and ECHAM6-SALSA as it does not show any significant temperature anomalies in Med-22km. The absence of a significant anomaly in ECHAM6-SALSA might be explained by a strongly varying aerosol distribution across the individual ensemble members (see discussion above). We note in passing that in experiments resulting in a stronger temperature signal, some significant anomalies emerge (see Fig. ). Also, ULAQ-CCM differs markedly from the remaining models given the much faster descent and fade out of the temperature anomaly while its SO₄ anomaly remains. From the remaining four models, the UM-UKCA ensemble mean appears to resemble the magnitude and pattern of temperature anomaly identified in the reanalysis. ECHAM5-HAM, SOCOL-AERv2 and WACCM6-CARMA agree with the observations regarding pronounced temperature anomalies but show in parts marked differences in magnitude, propagation and vertical extent. We attribute the deficiencies in reproducing observed patterns not solely to model issues in transport. This is exemplified as follows: while ECHAM6-SALSA and SOCOL-AERv2 agree well with reanalysis regarding the transport of the SO₄ concentration plume (see Fig. ), they over- (SOCOL-AERv2) or underestimate (ECHAM6-SALSA) the corresponding temperature anomalies.

To investigate inter-model differences in the simulated Pinatubo aerosol vertical profile and associated temperature effects, we focus on the time period of the strongest temperature signal-to-noise ratio across models (September to December 1991) in Fig. . Starting with the observations, reanalyses highlight that the peak SO₄ concentrations and temperature anomalies reside in the tropics (20° S–20° N) and across the lower and middle stratosphere (70–20 hPa). Further, the propagation of the volcanic signal over time can be clearly seen, i.e. hemispheric transport and descent (compare with Fig. ).

When probing the models, the observed relationship of the temperature anomalies and SO₄ concentrations is present in all. Somewhat an exception is ULAQ-CCM, for which the location of the largest temperature anomalies can be found below the maximum of the SO₄ concentrations. One may attribute this to a larger effective radius (exceeding 0.5 µm in radius in the tropics) in ULAQ-CCM compared to the other models in the lower stratosphere. However, given that WACCM6-CARMA also shows an tropical effective radius exceeding 0.5 µm while still smaller than ULAQ-CCM (see Fig. ), such interpretation may not hold also pointing to limitations of effective radius in explaining the location of temperature anomalies. Also, MIROC-CHASER differs from the remaining models as its maximum SO₄ concentrations and thus peak temperature anomalies emerge due to too strong transport (see Fig. ) outside of the tropics. For the remaining models, the spatial structure of the SO₄ concentrations agrees quite well with the reanalysis data. However, temperature responses across these models are very different in magnitude. Given the similarities in the SO₄ concentrations, we do not attribute these differences to transport but rather to model specifics in radiative transfer and on the simulated particle size distributions and thus consequently atmospheric heating rates.

In addition, the vertical structure and altitude of aerosol-driven temperature anomalies differ within the model ensemble. While the majority of the models show the most pronounced tropical warming signal centred around approximately 40 hPa (while expanding between 70 and 20 hPa), the peak anomaly for ULAQ-CCM is located substantially lower. The peak temperature response in WACCM6-CARMA and MIROC-CHASER emerges primarily at higher altitudes (see Fig. ). In summary, the magnitude of the temperature anomaly corresponds to the spatial structure of SO₄ concentration for individual models, but comparison across models shows that the magnitude of the obtained warming differs widely. We note that the magnitude of warming also varies across experiments, with the largest (smallest) signal in High-22km (Low-22km), see Fig. . Therefore, we investigate next the model-specific warming per µg m⁻³ of SO₄, taking all the experiments into account.

In this section we analyse the model sensitivity to SO₄ forcing. This metric enables us to assess potential structural differences among the models in the magnitude of stratospheric heating in response to differences in simulated sulfate aerosol. The normalisation to simulated sulfate enables the assessment solely of differences in the sensitivity of models, avoiding the problem of there also being differing heating effects from spatio-temporal differences in simulated SO₄ mass. Specifically, to calculate the post-Pinatubo sensitivity, we regress the temperature anomaly for each grid point over time against SO₄ concentration and average the regression coefficients with p-values smaller than 0.05 across the tropical stratosphere (see Fig. ). Having previously addressed ensemble means, we apply this method to all ensemble members individually. Further, we use all available experiments with varying injection height and amount in this analysis to increase data availability. This allows us to build the relationship between SO₄ concentrations and resulting temperature anomalies considering the full range of responses for each model. As an observational benchmark we use REMAP-GloSSAC-2023 SO₄ concentrations to regress the temperature signal in the reanalysis data. To be consistent with all previous analyses, we use the pressure range in which the strongest signal in observations and most models is observed (70 to 20 hPa, see Fig. ). Focusing on the median sensitivity across models, Fig.  reveals large differences, from hardly any sensitivity to a response of up to 2 K per µg m⁻³. It further appears that the spread in individual models broadens with increasing sensitivity to SO₄, i.e., models with low sensitivity provide a small temperature response quasi-independent of SO₄ concentration, while models with high sensitivity cover a broad range of temperature response dependent on SO₄ availability.

For example, ECHAM5-HAM (median: 1.72) and SOCOL-AerV2 (1.02) show a particularly high sensitivity, also larger than estimated from the reanalyses (0.63). This high sensitivity, however, has a different root in each model: for ECHAM5-HAM it emerges from an underestimation of the SO₄ concentrations, while in SOCOL-AERv2 a high sensitivity emerges from an overestimation of the temperature response. In contrast, ECHAM6-SALSA (0.11), ULAQ-CCM (0.22) and UM-UKCA (0.28) show lower sensitivity to SO₄, but also for different reasons. As discussed above, in ULAQ-CCM the altitudes of the peak temperature signal and peak SO₄ concentrations do not align as well as for the other models. This mismatch results in regressing a mixed signal that falls to lower sensitivity. For ECHAM6-SALSA and UM-UKCA the lower sensitivity can be explained by the weak temperature response despite the well-reproduced SO₄ concentrations. The sensitivities of MIROC-CHASER (0.88), and WACCM6-CARMA (0.70) complete the analysis and are those that lie closest to the reanalysis estimate. We note that these sensitivities need to be interpreted with caution as they do not characterize the pure temperature response to the SO₄ concentration, i.e. the model-specific estimate also includes the contributions from aerosol size distribution and the effective heating emerging from the radiative transfer scheme, and QBO effects.

These results show that even when following a strict simulation protocol, as put forward by ISA-MIP HErSEA, model outcomes for aerosol concentration and subsequent temperature change in the middle and lower stratosphere differ widely. Some of these model differences may be attributed to the use of specific aerosol schemes and/or interactive chemistry in some of the models (see Table ). Thus, we expect that the inter-model spread can be reduced if even stricter protocols are applied. We test this hypothesis through recent MIPs under the auspices of the World Climate Research Programme (WCRP) that use prescribed SADs: CCMI-2022 REF-D1 and CMIP6-AMIP. While for the ISA-MIP models a Control run without the Mt. Pinatubo eruption is available and used for computing forced anomalies, no such Control is available for CCMI-2022 and CMIP6-AMIP. Thus, for these two MIPs, and also for the reanalyses in this comparison, we compute anomalies with respect to the mean of the period 1980–2000 (21 years centred around the Mt. Pinatubo eruption). We note in passing, that such anomaly calculation yields only a slightly broader range of anomalies for the reanalysis than the MLR calculation used above (see Fig. ), which is, however, still substantially narrower than for the ISA-MIP models, see Fig. . We focus on the time period, latitude band and pressure range in which the strongest signal in observations is found (September to December 1991, 20° S–20° N, 70 to 20 hPa).

As in our MLR analysis, we find that the temperature anomalies derived for ERA5, MERRA2, and JRA55 agree well with each other and also show a similar spread for the selected period and vertical range (see Fig. ). Our analysis also shows that the median/mean of the multi-model temperature anomaly agrees well with reanalyses for all MIPs considered, while the distribution of the temperature anomaly is much wider for MIPs than for reanalyses, indicating that the agreement in the median/mean occurs through error compensation when averaging across models.

For CCMI-2022 we find a slightly lower magnitude of temperature anomaly compared to ISA-MIP, but a median still in close agreement with reanalyses. More interestingly, however, the intra-ensemble spread (evaluated from minimum to maximum values) in CCMI-2022 is even increased (longer whiskers, wider box) compared to ISA-MIP. We interpret this outcome as follows: model complexity (i.e. inclusion/absence of interactive aerosol microphysical schemes) appears to be of secondary importance compared to other factors such as the radiative transfer scheme or model selection. Expansion of this analysis to CMIP6-AMIP further supports this interpretation as for these models the intra-model spread is even larger (longer whiskers, narrower box) while the median is marginally larger than for ISA-MIP models or reanalyses. The hypothesis that there is strong model-dependency of the temperature anomalies obtained is further supported when for the same comparison only models with more than one ensemble member are taken into account (see light orange, light green and light purple boxplots in Fig. , respectively). On the one hand, an increase or decrease in the multi-model median is found for individual MIPs when subset, on the other, also the intra-model spread is altered. For convenient reference we indicate individual models with dots per MIP (and subset), which further corroborates the sensitivity to model selection as visual inspection clearly shows that selecting or excluding a model (or subset of models) would strongly affect the overall result.