Originally a branch of CESM1, E3SMv1 diverged with a focus on computational efficiency, scalability, vertical and horizontal resolution, and aerosol and cloud parameterizations, as well as more physically based biogeochemistry, river, and cryosphere models (Leung et al., 2020). Simulations in this study are run with E3SMv2, in which clouds are parameterized with an improved version of the Cloud Layers Unified by Binormals (CLUBB) scheme (Larson, 2017), cloud microphysics are simulated by a two-moment bulk microphysics parameterization (MG2; Gettelman and Morrison, 2015), and mixed-phase ice nucleation depends on aerosol type and concentration as well as temperature (Wang et al., 2014; Hoose et al., 2010). Aerosols are simulated with MAM4 (Liu et al., 2016). The explosive volcanic eruption treatment prescribes stratospheric volcanic light extinction from version 1 of the GloSSAC reanalysis dataset (Thomason et al., 2018), which is mainly derived from SAGE II (Stratospheric Aerosol and Gas Experiment II) satellite measurements (Sect. 3.1.1, 3.5.1) assuming a sulfate refractive index from Palmer and Williams (1975) and aerosol volume and surface area assumptions from Thomason et al. (2008). E3SM uses the Rapid Radiative Transfer Method for GCMs (RRTMG, where GCMs stands for general circulation models) (Iacono et al., 2008; Neale et al., 2012), a two-stream approximation for calculating multiple scattering in the atmosphere from gas- and condensed-phase (i.e., aerosol, liquid cloud droplets, cloud ice, and hydrometeors) optical properties. Atmospheric chemistry is represented with version 2 of the interactive stratospheric ozone (O3) model (O3v2; Tang et al., 2021). This model uses linearized stratospheric chemistry (Linoz v2; Hsu and Prather, 2009), which calculates net O3 production as a function of temperature, local O3 concentration, and overhead column O3.

The major CESM2 atmosphere model improvements from CESM1 are the inclusion of CLUBB, MG2 cloud microphysics, MAM4, and orographic wave drag parameterizations (Danabasoglu et al., 2020). These are the same in E3SMv2 (Golaz et al., 2022) with the exception of a stratospheric prognostic aerosol treatment in MAM4 in CESM2-WACCM6 (Mills et al., 2016, 2017) (see Sect. 2.1.2). WACCM6 includes updated atmospheric chemistry, aerosol microphysics, and gravity wave drag parameterizations from previous versions of WACCM. Atmospheric chemistry is treated comprehensively through the whole atmospheric column, representing key chemical species and reactions across the troposphere, stratosphere, mesosphere, and lower thermosphere (Gettelman et al., 2019). Within the stratosphere and mesosphere, WACCM6 explicitly calculates the net production and transport of 97 different chemical species described by nearly 300 reactions (Mills et al., 2017). This comprehensive chemical treatment is a key difference between CESM2-WACCM6 and E3SMv2 (including E3SMv2-PA and E3SMv2-SPA), as E3SMv2 prescribes from observationally derived climatologies of OH and other relevant chemical species in sulfur and ozone chemistry (Hsu and Prather, 2009).

E3SMv2 simulations are run from 1990–1993 (1989 discarded for aerosol spinup). The model uses the horizontal and vertical resolution described in Golaz et al. (2022), with the dynamics run on a ∼ 110 km horizontal grid, the physics run on a coarsened ∼ 165 km horizontal grid, and both dynamics and physics using the same 72-layer vertical grid with a model top at approximately 0.1 hPa. Simulations have prescribed sea ice and sea surface temperatures (Taylor et al., 2000) and nudged column-resolved U and V winds to 6-hourly Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), reanalysis data (Gelaro et al., 2017). CESM2-WACCM6 simulations are run over the same time period on a 0.95° × 1.25° grid over 88 pressure levels (model top at ∼ 4.5 × 10-6 hPa). In addition to nudging model U and V winds to 6-hourly MERRA-2 reanalysis data, the CESM2-WACCM6 simulations also nudge column-resolved model temperature to the reanalysis to constrain temperature-dependent stratospheric chemical reactions. Note that both E3SM and CESM2-WACCM6 have a variety of stratospheric dynamics biases (e.g., Gettelman et al., 2019) that are avoided here through atmospheric nudging. An upcoming publication on E3SM stratospheric processes details a variety of biases in E3SM that may impact free-running volcanic eruption modeling, including a weak-amplitude tropical quasi-biennial oscillation which oscillates too frequently and a weak Brewer–Dobson circulation (Christiane Jablonowski, personal communication, 2024).

For simulations that prognostically simulate volcanic aerosol formation (E3SMv2-PA, E3SMv2-SPA, CESM2-WACCM6), the SO2 emissions for explosive volcanic eruptions are from VolcanEESMv3.11, a modified version of Neely and Schmidt (2016). The VolcanEE3SMv3.11 dataset contains estimates of SO2 from volcanic eruptions on a 1.9 × 2.5° latitude-by-longitude grid, with 1 km altitude spacing from the surface to 30 km. In our period of interest (1991–1993), this includes the Pinatubo, Hudson, Spurr, and Lascar eruptions. SO2 emissions are provided in molecules cm-3 s-1, and all eruptions occur over a 6 h period. The modifications to Neely and Schmidt (2016) are described in Mills et al. (2016) and include a reduction in SO2 emissions for eruptions of over 15 Tg of SO2 by a factor of 0.55 to compensate for missing ice and ash removal processes. In the case of Pinatubo, while 18–19 Tg of SO2 erupted in the atmosphere, only ∼ 10 Tg remained in the stratosphere 7–9 d after the eruption (Guo et al., 2004b). This rapid reduction in SO2 corresponds to >99 % removal of volcanic ash mass (Guo et al., 2004a). Therefore, 10 Tg of SO2 is emitted in this dataset for further chemical and microphysical evolution (Mills et al., 2016). The emission takes place between 18–20 km, at a single latitude–longitude grid cell (i.e., no spreading). For all simulations, the VolcanEESMv3.11 file was merged with the monthly CMIP6 SO2 emissions for non-explosive volcanic sources and then remapped to 1 × 1°.

A prescribed volcanic forcing simulation (E3SMv2-presc) is run in addition to the prognostic volcanic aerosol simulations. This simulation uses the default prescribed forcing dataset in E3SMv2 (GloSSAC V1) and allows for an additional validation of prognostic aerosol model performance where observational data are lacking.

Table 1 provides a summary of some of the key model characteristics for the different sensitivity studies used in this work. These studies include E3SMv2 with prescribed volcanic forcing and no emission of volcanic SO2 (E3SMv-presc), E3SMv2 with the default MAM4 prognostic aerosol treatment (i.e., no stratospheric aerosol modifications) and emission of volcanic SO2 (E3SMv2-PA), E3SMv2 with the prognostic stratospheric aerosol modifications and emission of volcanic SO2 (E3SMv2-SPA), and CESM2-WACCM6 with emission of volcanic SO2 (hereon referred to as CESM2-WACCM).

Aerosol size distributions in the model provide information about how MAM4 represents volcanic aerosol evolution and can also help explain changes in radiation balance in the Earth system. Here we calculate the effective radius (Reff) and use this in single-particle Mie scattering to understand how changes in size affect diffuse–direct radiation at the surface and absorption of longwave radiation in the stratosphere. We also plot stratospheric size distributions for our model simulations to visualize the evolution of volcanic injection of SO2 into sulfate. See Appendix A and B for more details on these calculations.

Figure 1 shows the stratospheric mass burden of the sulfur component of sulfate aerosol in the different model sensitivity tests, the HIRS observational dataset (Baran and Foot, 1994), and the SAGE-3λ dataset (Revell et al., 2017). When compared to HIRS and SAGE-3λ, E3SMv2-SPA improves the modeled stratospheric aerosol burden over E3SMv2-PA, especially in the years following the Pinatubo eruption. The increased aerosol burden – and thus, aerosol lifetime – in the stratosphere is mainly due to our modifications to the coarse-mode σg in E3SMv2-SPA. While E3SMv2-PA reaches a similar peak in sulfate burden, the underestimated aerosol burden following Pinatubo in E3SMv2-PA is mainly caused by too wide an aerosol number distribution, causing fast sedimentation of the larger coarse-mode particles in the upper tail of the distribution. The E3SMv2-SPA tends to overestimate aerosol burden compared to HIRS and SAGE-3λ in the 6 months after Pinatubo but agrees well with the slow decay reported in observations during 1992. In the 4 months following Pinatubo, models agree best with HIRS over SAGE-3λ, likely due to saturation issues identified in SAGE II limb-occultation data (Russell et al., 1996; Sukhodolov et al., 2018; Quaglia et al., 2023). From 1992 onward, stratospheric mass burden in E3SMv2-SPA agrees the best with SAGE-3λ, which reports higher burdens in 1993 than HIRS. E3SMv2-SPA and WACCM are similar in atmosphere and aerosol treatments but have very different atmospheric chemistry, which seems to impact lifetime.

In CESM2-WACCM, the interactive hydroxyl radical (OH) treatment causes OH depletion in the vicinity of the plume as the oxidation of SO2 to form sulfate aerosol depletes available OH and therefore limits the reaction rate (Mills et al., 2017). This is in contrast to E3SMv2, which assumes an OH climatology unaffected by the oxidation of SO2. The result is faster depletion of SO2 and higher initial sulfate concentrations in the stratosphere in E3SMv2 (Fig. S5). The difference in OH treatment can be seen in Fig. 1, marked by the faster increase in the stratospheric sulfate burden in E3SMv2-PA and E3SMv2-SPA. Another significant difference between the two chemical treatments is the presence of carbonyl sulfide (OCS) in CESM2-WACCM, which is a largely inert tropospheric chemical species that is oxidized and photolyzed when it enters the stratosphere, forming sulfate. This is a major contributor to non-volcanic stratospheric sulfate and will lead to higher pre-Pinatubo sulfate concentrations in the stratosphere in CESM2-WACCM than in E3SMv2 (Mills et al., 2016). In Fig. 1, the effect of OCS is shown in larger pre-Pinatubo stratospheric burdens in CESM2-WACCM.

Figure 1 shows that E3SMv2-SPA performs reasonably well when forming sulfate from SO2 and simulating increased aerosol lifetimes. The following sections will address how well the model parameterizes the aerosol microphysical properties and their impacts on the global radiative balance.

In Fig. 2, the stratospheric contribution is isolated by subtracting the monthly mean AOD from pre-Pinatubo years, relying on the assumption that non-volcanic background aerosol in the atmosphere is similar in the near term. Model data are normalized to 1990 monthly means, while AVHRR is normalized to the monthly means for the period June 1989 to May 1991, with the exception of missing data from October–December 1990. Normalized model data are masked to reflect the same temporal and spatial sampling as AVHRR data from 1991–1993 over the oceans only and between 60° N–60° S. Here, AOD from the models is reported at 0.55 µm, while the AVHRR AOD is 0.6 µm.

The AVHRR AOD peaks 2 months after Pinatubo, linearly decreasing except for periods of flattening in the months March–July 1992 and January–July 1993. The flattening in 1992 is attributed to the continual growth of aerosols due to coagulation, which increases sulfate aerosol scattering efficiency (Russell et al., 1996; Stenchikov et al., 1998) even as aerosol burden continues to decay (Fig. 1). This is supported by a simulated increasing accumulation-mode – and, to a lesser extent, coarse-mode – Dg (Sect. 4.6; Fig. 7) and a slight increase in global average stratospheric aerosol Reff (Sect. 4.5; Fig. 6). The flattening in 1993 for both observations and models may be due in part to the influence of the smaller Chilean volcanic eruption Lascar (30 January 1993; 23.36° S), which has a discernable impact on modeled global accumulation-mode aerosol mean diameters >0.2 µm (Sect. 4.6; Fig. 7).

In the first year following Pinatubo, AVHRR and the volcanically parameterized models (i.e., E3SMv2-SPA, E3SMv2-presc, and CESM2-WACCM) follow a similar trend, decreasing and leveling off near the beginning of 1992. As in aerosol mass burden, the overly short stratospheric aerosol lifetime in E3SMv2 leads to a rapid decay in AOD. All models consistently underpredict AOD in the first year after the eruption but tend to overpredict AOD in the third year following the eruption. Underprediction may be due in part to a lack of volcanic ash and incorrect number/size representation in the models. Overprediction is likely a factor of aerosol removal assumptions. Of the models, CESM2-WACCM has the closest agreement with AVHRR in 1993, due to a faster decline in AOD than E3SMv2-SPA. This indicates that the comprehensive chemistry in CESM2-WACCM may better represent aerosol size distributions than E3SMv2-SPA (see Sect. 4.4).

A surprising finding is the close agreement between E3SMv2-SPA and E3SMv2-presc. These models utilize very different approaches: prognostic aerosol microphysics from emitted SO2 in MAM4 (E3SMv2-SPA) and prescribed stratospheric aerosol extinction from a range of observations in GloSSAC (E3SMv2-presc). As noted in Quaglia et al. (2023), the dependence of GloSSAC on SAGE II data – which are saturated at AOD ∼ 0.15 – means that E3SMv2-presc values may be underestimated in the months shortly after the eruption, suggesting that the close agreement between these datasets may be partly coincidental. Regardless, their similarities indicate that the changes to aerosol microphysics in MAM4 reasonably recreate the reanalysis data product, especially from 1992 onward when instrument saturation is less of a concern.

Figure 3 shows a zonal average of the stratospheric AOD values described in Fig. 2. As in the 60° S–60° N average, AVHRR exhibits much higher maximum AOD values in the stratosphere (0.428) than all other models (E3SMv2-PA: 0.175; E3SMv2-SPA: 0.204; E3SMv2-presc: 0.152; CESM2-WACCM: 0.25). The stratospheric parameterized models (E3SMv2-SPA (Fig. 3b), CESM2-WACCM (Fig. 3d)) have the closest agreement with AVHRR in the tropical plume shortly after the eruption. E3SMv2-PA, E3SMv2-SPA, and CESM2-WACCM fail to simulate the tropical confinement of aerosol present in AVHRR and E3SMv2-presc, simulating peak AOD that occurs further north and a weaker Southern Hemisphere AOD signal up to 1993 compared to observations and prescribed forcing datasets. Quaglia et al. (2023) identified this behavior in a range of models simulating the Pinatubo eruption, attributing this feature to model resolution, vertical wind structure, and the vertical distribution of the model volcanic cloud shortly after the eruption. Specifically, during the atmospheric conditions under which Pinatubo occurred, aerosols at levels <∼20 km are transported north while aerosols at levels >∼20 km are more effectively confined to the tropics (McCormick and Veiga, 1992). While E3SMv2-PA, E3SMv2-SPA, and CESM2-WACCM have the same injection parameters, E3SMv2-SPA has slightly more southern transport than CESM2-WACCM, which may be related to higher concentrations of sulfate above 20 km than CESM2-WACCM (Fig. S6). We speculate that this disagreement may arise from interactive chemistry in CESM2-WACCM and its effect on sulfate nucleation, growth, and SO2 lifetime given the similarities in aerosol transport (i.e., nudged atmospheric dynamics), vertical resolution aerosol microphysics, and injection between the two models. E3SMv2-presc (Fig. 3c) has a noticeable low bias in AOD over the Northern Hemisphere over 1992, and we believe this is related to our use of an older version of the GloSSAC dataset (Thomason et al., 2018) in which higher latitudes have a low bias in AOD attributed to linear interpolation of the SAGE II data (Kovilakam et al., 2020). This may contribute to the close agreement between E3SMv2-SPA and E3SMv2-presc pointed out earlier, likely indicating a higher E3SMv2-presc signal with an updated GloSSAC dataset. Lastly, when compared to other model simulations in Quaglia et al. (2023), the volcanic Pinatubo signals in E3SMv2-SPA and CESM2-WACCM without land and AVHRR-missing-data masks (Fig. S7) show qualitatively similar patterns and magnitudes to ECHAM6-SALSA and ECHAM6-HAM with a comparable injection treatment (18–20 km; 7 Tg SO2).

Figure 4 compares the global TOA radiative flux from model simulations to the all-sky ERBS observations over 1991–1993, subtracting out corresponding monthly means from the pre-Pinatubo year 1990 (note that this is a different non-volcanic period than used in previous publications (2001–2005 – Allan et al., 2014, and Liu et al., 2015; 1999 – Mills et al., 2017), which will result in differing magnitudes for ERBS over 1991–1993). Model TOA flux is shown for all-sky (solid lines), clear-sky (faint dashed lines), and aerosol-impact-only (faint dotted lines) conditions. The radiative flux is reported as absorbed shortwave radiation (ASR, positive downward flux; Fig. 4a), outgoing longwave radiation (OLR, positive upward flux; Fig. 4b), and net radiative flux (NET, positive downward flux; Fig. 4c). In Fig. 4a, ASR shows the clearest model separation 3–4 months after Pinatubo, corresponding to peak AOD (Fig. 2). There is close agreement between E3SMv2-SPA, E3SMv2-presc, and CESM2-WACCM during the year 1992, which corresponds to the largest sulfate particles during the Pinatubo plume evolution (see Sect. 4.5 and 4.6). The all-sky signal exhibits noise due to differences in atmospheric conditions (i.e., cloud cover, tropospheric aerosol) and surface albedo between the period of interest and our control year (1990). There is a clear seasonal increase in ASR in the 1991/92 and 1992/93 Northern Hemisphere winters relative to Northern Hemisphere summer. When clear-sky conditions (no influence from clouds) are compared to all-sky conditions in the models, the seasonality disappears, implying that the seasonality is cloud-related and cloud albedo was greater in the Northern Hemisphere winter of 1990 than the Northern Hemisphere winters of 1991/92 and 1992/93. Even with noise introduced by non-Pinatubo factors, there is a distinct all-sky ASR signal in E3SMv2-SPA, CESM2-WACCM, and E3SMv2-presc that is improved compared to ERBS.

The all-sky OLR (Fig. 4b), which is affected by both aerosol absorption of infrared emissions from the Earth's surface and the cooling of the troposphere and surface by the scattering of solar radiation, has a weaker response across these models than ASR. This is due in part to a less efficient absorption of outgoing longwave radiation than scattering of incoming solar radiation, leading to a lower sensitivity of OLR to aerosol growth and evolution (see Sect. 4.8). The largest spread in model simulations occurs during 1992 when aerosols are at their largest (i.e., highest absorption efficiency of longwave radiation; Sect. 4.8) and the highest reduction in surface temperatures was observed (Parker et al., 1996). All-sky E3SMv2-SPA has the greatest reduction in OLR from April 1992 to the end of 1993 and overestimates the longwave flux reduction compared to ERBS. This corresponds to E3SMv2-SPA overestimation of global AOD values compared to AVHRR over this period (Fig. 2). During this same period, CESM2-WACCM has slightly better agreement with ERBS, which may be related to the temperature nudging in this simulation which will modulate CESM2-WACCM surface temperature reduction and stratospheric temperature. When clear-sky OLR fluxes are compared, there is a weaker reduction in OLR for E3SMv2-PA, E3SMv2-SPA, and CESM2-WACCM and nearly no change in E3SMv2-presc during 1992. Due to the lack of stratospheric aerosol in E3SMv2-presc, this appears to be evidence of volcanic influence on high-altitude clouds which act to reduce OLR further, supporting conclusions from Liu and Penner (2002) and Wylie et al. (1994). Lastly, the aerosol-only model simulations remove the 1991/92 and 1992/93 wintertime peaks in the OLR signal, indicating similar or smaller OLR in 1990 compared to our period of interest due to cooler surface conditions.

The improvements in all-sky NET (Fig. 4c; solid lines) with volcanic parameterizations are less apparent across the models than in ASR (Fig. 4a) but do show improvement during the first 6 months after the eruption and during 1992. Differences in cloud cover and surface conditions between our period of interest and 1990 introduce substantial noise into this comparison, but the removal of clouds (clear-sky) and the isolation of aerosol TOA forcing (aerosol only) show a clear separation of volcanic parameterizing models and E3SMv2-PA.

The radiation interactions described in Sect. 4.3 will lead to changes in atmospheric temperature, namely a warming of the stratosphere due to aerosol absorption of outgoing longwave radiation and a cooling of the surface due to reflection and scattering of incoming solar radiation by the aerosol plume. Figure 5 shows the 1992 annual mean atmospheric temperature anomalies (subtracting the 1990 annual mean) in the models (Fig. 5a–d), MERRA-2 reanalysis data (Fig. 5e), and RICH-obs radiosonde product (Fig. 5f). The year 1992 was chosen given the highest model spread in TOA flux (Fig. 4), peak modeled reduction in ASR (Fig. 4a) and reduction in OLR (Fig. 4b), and peak surface cooling (Parker et al., 1996) over this period. Models and observations share similar anomaly spatial patterns, with the exception of RICH-obs in the 60–90° S upper troposphere and near the tropical tropopause. Differences in RICH-obs may be related to temperature interpolation errors introduced in these remote regions due to fewer radiosonde datasets (Haimberger et al., 2012; Free and Lanzante, 2009). There is greater stratospheric warming in E3SMv2-SPA (Fig. 5b), E3SMv2-presc (Fig. 5c), and CESM2-WACCM (Fig. 5d) compared to E3SMv2-PA (Fig. 5a). Furthermore, there is an improvement in midlatitude warming at higher altitudes (i.e., 50 hPa and above) over E3SMv2-PA when comparing Fig. 5a–d to observations (Fig. 5f), reflecting the higher plume heights in these models (Fig. S6). CESM2-WACCM and MERRA-2 have very similar temperature magnitudes and distributions, which is due to temperature nudging of CESM2-WACCM to the latter reanalysis dataset. There is not as obvious a surface cooling difference between E3SMv2-PA and other models and observations. All datasets show a large cooling signal in the northern troposphere that roughly corresponds with early-1992 max AOD between 30 and 50° N (Fig. 3), but this cooling signal could be influenced by internal variability in the normalization year of 1990 (Sect. 4.3).

Table 2 shows 50 and 850 hPa pressure level averages from Fig. 5. These comparisons represent stratospheric and near-surface changes in temperature, with the 850 hPa level chosen to accommodate the lowest pressure level in the RICH-obs data. These latitude-weighted averages range from 65° S–65° N to avoid missing data in the upper atmosphere and surface RICH-obs data (Fig. 5f). This comparison shows stratospheric warming that is overestimated in E3SMv2-SPA (1.57 K) and underestimated in CESM2-WACCM (0.9 K) compared to MERRA-2 reanalysis (0.89 K) and previously reported estimates of ∼ 1 K (Ramachandran et al., 2000). RICH-obs struggles to represent lower-stratospheric warming due to either the aforementioned sparsity of data or their low horizontal resolution (5°) compared to models (1°) and MERRA-2 (0.5°) or both. E3SMv2-presc shows a stratospheric warming more than 3 times that of MERRA-2, which is likely due to a known error converting CLAES infrared extinction to the SAGE II- and GloSSAC V1-reported 1020 nm extinction coefficient, resulting in an exaggeration of peak aerosol extinction (Kovilakam et al., 2020). The 850 hPa cooling in CESM2-WACCM (-0.33 K) agrees best with MERRA-2 (-0.36 K) and RICH-obs (-0.29±0.007 K) anomalies, due in part to nudging of CESM2-WACCM temperatures to MERRA-2. There is small improvement in E3SMv2-SPA (-0.23 K) and E3SMv2-presc (-0.26 K) compared to E3SMv2-PA (-0.22 K), but it is unclear how much internal variability is influencing these values.

This comparison gives an all-sky snapshot of surface and stratospheric 1992 temperature anomalies due to Pinatubo. The 50 hPa height shows a clearer improvement in the simulated temperature anomaly in E3SMv2-SPA and CESM2-WACCM than the 850 hPa height due to the influence of interannual differences in internal variability (Sect. 4.3) and internal modes of variability (e.g., ENSO; Santer et al., 2014) in the troposphere. The model trends in stratospheric and near-surface temperature changes are consistent with changes in OLR and ASR (Fig. 4), respectively. Temperature trends also tend to agree better with observations and reanalysis with stratospheric volcanic parameterizations (E3SMv2-SPA, CESM2-WACCM) and prescribed volcanic aerosol (E3SMv2-presc). The next sections explore the microphysical representation within the models and how this influences lifetime, AOD, TOA flux, and temperature.

Reff has frequently been used to characterize stratospheric aerosol properties, with stratospheric Reff of less than ∼ 2 µm leading to a net solar radiation scattering effect and surface cooling (Lacis et al., 1992; McGraw et al., 2024). Based on a range of in situ and remote sensing datasets, background stratospheric Reff is estimated at 0.17–0.19 µm and following Pinatubo reaches average values of around 0.5 µm with observed values as large as 0.8 or 1.0 µm (Russell et al., 1996, and references therein). In the month following Pinatubo, there is little change in Reff. This is due to a rapid increase in very small (i.e., Aitken-mode sulfate) and very large (i.e., ash) aerosol particles following the eruption. Enhanced coagulation and condensation, coupled with low sedimentation rates, lead to a steady increase in Reff over the next 3–6 months. Aerosol growth continues until approximately mid-1992, when Reff peaks, lagging peak values in other metrics such as mass burden and AOD. The smaller-magnitude eruptions of Hudson, Spurr, and Lascar also contribute to an increased Reff over this period, with more of an impact in near-source regions.

Figure 6a shows global Reff, in addition to Reff from three different regional zones specific to different observational datasets: comparisons at 40° N and 7° S latitude bands and less than 100 hPa with UARS (Fig. 6b); 41° N, 105° W between 130–10 hPa with WOPC (Fig. 6c); and 20° S–20° N between 50–20 hPa with SAGE II (Fig. 6d). Observations tend to measure a minimum size that falls in the middle of the Aitken mode in the model. To account for this characteristic of the data, the model Reff is an average of effective radii calculated with and without the Aitken mode, with the range between the two Reff calculations represented by shading about the line. Maximum differences tend to occur before Pinatubo, shortly after Pinatubo, and with other volcanic eruptions (e.g., Hudson (8 August 1991; 45.9° S)). There is much larger spread between these two approaches in CESM2-WACCM in the Northern Hemisphere winter–spring, which may be due to enhanced stratosphere–tropopause exchange leading to higher concentrations of lower-stratospheric Aitken-mode particles (Sect. 4.6 and Fig. 7). In Fig. 6a the models reproduce the expected background Reff of 0.17–0.19 µm, and the improvements to aerosol lifetime in E3SMv2-SPA and CESM2-WACCM can be seen in the slower decrease in Reff compared to E3SMv2-PA. There is also a nearly identical pattern in E3SMv2-SPA and CESM2-WACCM data but with slightly higher Reff in CESM2-WACCM.

All of these models underestimate Reff compared to observations (Fig. 6b–d). In Fig. 6b, the finer temporal responses to the Pinatubo eruption in the UARS data are less apparent in the model, namely the large peak in Reff at 7° S associated with short-lived volcanic ash in the stratosphere and the delayed peak at 40° N and 7° S due to particle aggregation (Stenchikov et al., 1998). The models neglect volcanic ash contributions, explaining the more gradual particle growth at 7° S. While the models do not show the same sensitivity to increases in Reff at these latitude bands – possibly due to the higher vertical and horizontal spatial scale in the number concentrations from SAGE II observations – E3SMv2-SPA does show a flattening of the 7° S Reff akin to the UARS estimate. This corresponds to the eruption of Hudson in Chile and the resulting high influx of smaller Aitken-mode particles into the southern stratosphere, which drives down Reff. The sensitivity to this eruption in E3SMv2-SPA may be due to higher Aitken-mode production in this model than in CESM2-WACCM (see Sect. 4.7).

The tropical regions tend to have a larger Reff than the midlatitudes in the simulations. This is true of UARS regions 6–12 months after the eruption and also the SAGE II (tropics; Fig. 6d) data. These larger Reff values persist in the tropics a year or more after the eruption. While all models exhibit similar modal aerosol diameters (Fig. S8), the higher Reff is correlated with higher number concentrations in all aerosol modes and a slower decrease in aerosol number (i.e., reduced sedimentation) (Fig. S9). The reduced removal is likely due to higher initial concentrations of SO2 in the volcanic plume over the tropics (Fig. S10) contributing to more rapid local aerosol growth and a net positive aerosol production. Furthermore, the presence of the upwelling branch of the Brewer–Dobson circulation in this latitude band may help suspend larger aerosol species, slowing aerosol sedimentation rates and increasing their lifetime. The eruption of the Lascar volcano in northern Chile in around February 1993 also contributes to a bump in SO2, as well as the Aitken- and accumulation-mode aerosol number at the 7° S band (Figs. S9, S10).

When comparing the models to WOPC (Fig. 6c) and SAGE II (Fig. 6d), E3SMv2-PA has the closest agreement to these datasets in its initial aerosol growth. This growth is more rapid than the other models and leads to a peak in Reff that, while being closer to observed values, drops off precipitously. The Reff values in E3SMv2-SPA and CESM2-WACCM have the best agreement with observational values and decay rate a year or more after Pinatubo. Differences across the models are due to the different microphysical assumptions, which can be explored by looking at aerosol size distributions.

While Reff is a good representation of aerosol size in the context of optical properties, it is not always a good indicator for behavior of aerosol microphysical processes. For example, an increase in the accumulation-mode particle number and a decrease in the coarse-mode particle number could manifest as an unchanging Reff. An examination of the aerosol size distribution can be more informative when understanding how aerosol chemistry and the MAM4 microphysics contribute to model performance.

Figure 7 shows the globally averaged stratospheric aerosol distributions from the three models used in this study and their evolution from 1991 to the end of 1993. The contour fill represents aerosol number (dN/dlogD; cm-3) with dashed and dotted lines indicating modal Dg (µm). In all three models, there is growth in the Aitken mode due to new sulfate particle formation following major and minor volcanic eruptions during this period: Pinatubo (June 1991; vertical dotted line), Hudson (August 1991), Spurr in the Aleutian Islands (27 June 1992; 61.3° N), and Lascar (February 1993). In E3SM (Fig. 7a–b), the prescribed concentrations of OH lead to a rapid oxidation of available SO2 and higher concentrations of Aitken-mode aerosol compared to CESM2-WACCM (Fig. 7c), in turn resulting in higher aerosol number concentrations in E3SM. It also appears that CESM2-WACCM has higher tropospheric aerosol transport into the stratosphere based on a higher concentration of Aitken-mode aerosol across the period of interest. CESM-WACCM has seasonal peak concentrations occurring asynchronously with volcanic eruptions and corresponding to Northern Hemisphere winter (e.g., 1991 and 1992). The increased Aitken-mode number concentration is also seen at 40° N (Fig. S9). These peaks are attributed to a lower tropopause in Northern Hemisphere winter (i.e., enhanced troposphere–stratosphere exchange) and may also be due to the inclusion of OCS in CESM-WACCM.

The larger volcanic eruptions, Pinatubo and Hudson, inject enough SO2 into the stratosphere for Aitken-mode aerosols to grow through condensation and coagulation into the accumulation mode, which then grow through coagulation into the coarse mode. The exception to this is in E3SMv2-PA, which lacks the ability to transfer sulfate mass into the coarse mode and so retains a roughly constant coarse-mode Dg derived from trace mass (10-22–10-21 kg cm-3; global average) and number (10-5–10-4 cm-3; global average) concentrations of dust, sea salt, and sulfate aerosol advected from the troposphere (note that mass and number are related to aerosol size through Eqs. S1 and S2 in the Supplement). Aerosol growth through the modes can be seen in the increased number and an increasing trend in aerosol size. Dips in modal Dg correspond to sudden increases in aerosol number (e.g., Aitken-mode nucleation from freshly injected SO2, transfer of a large aerosol number from Aitken to accumulation mode), while mass remains relatively unchanged. This leads to a division of mass across a larger number of aerosols and a subsequent decrease in Dg.

Overall, the aerosol modal diameters are similar across the three models, but slight differences exist. There are slightly larger accumulation-mode and coarse-mode Dg values in CESM2-WACCM (0.262 µm; 0.843 µm) compared to E3SMv2-SPA (0.259 µm; 0.749 µm). This could be because of the interactive chemistry in CESM2-WACCM, where lower nucleation rates lead to fewer Aitken-mode aerosols that initially grow faster through condensation as the longer-lived SO2 in the stratosphere condenses on preexisting particles. Contrast this with E3SM, where high nucleation rates lead to more numerous smaller aerosols that consume the available SO2 more quickly. The E3SMv2-PA model accumulation-mode Dg reaches a higher maximum Dg (0.285 µm) than E3SMv2-SPA or CESM2-WACCM (∼ 0.26 µm). This is due to the missing coarse-mode treatment in this model coupled with a larger Dg,high (Sect. 2.1.2). The result is an accumulation mode that grows to Dg,high following Pinatubo, whereby the number is increased to maintain this size instead of transferring the mass and number to a larger mode. This also explains the better initial agreement in Reff between E3SMv2-PA and observations in Fig. 6b–d.

Figure 8 compares modeled aerosol size distributions to in situ measurements from WOPC, tracking the evolution of a slice of the plume from pre-Pinatubo (19 April 1991) to the end of 1993 (16 November 1993). Daily samples taken with the WOPC over Laramie, Wyoming, at a single level (18 km; roughly corresponding to the peak plume Reff across the period (Fig. S11)) are used to validate daily data from E3SMv2-PA and E3SMv2-SPA. Modal Dg (vertical lines) and dN/dlogD are denoted by dotted and dashed lines, as in Fig. 7. The effective diameter (Deff) for models and WOPC is included to relate the changing distributions to aerosol–light interactions.

What follows is a breakdown of Fig. 8 into a rough timeline evolution in aerosol size distributions and Deff.

Pre-Pinatubo conditions (Fig. 8a) are very similar between E3SMv2-PA and E3SMv2-SPA, and the Deff values are nearly identical between model and observations. CESM2-WACCM has higher background number concentrations than E3SM.

A month after Pinatubo (Fig. 8b), all datasets exhibit rapid growth in the smaller-diameter aerosols, with some growth in the modeled accumulation mode but little sign of the coarse mode in E3SMv2-SPA. CESM2-WACCM has a massive increase in Aitken- and accumulation-mode number, possibly due to transport of SO2 and Aitken-mode aerosol into the region from the tropics. This Aitken-mode peak is also seen at 17 and 19 km levels (Figs. S12–S13), resulting in a decrease in Reff over this height range (Fig. S11), and may be related to lower-altitude sulfate aerosol in CESM2-WACCM (<20 km; Fig. S6) being more effectively transported into northern latitudes (McCormick and Veiga, 1992). The Deff values are still similar across the different datasets, with the exception of CESM2-WACCM, which is smaller due to the Aitken-mode influence.

At 6 months after the eruption (Fig. 8c), a clear coarse-mode signal emerges in WOPC, E3SMv2-SPA, and CESM2-WACCM along with a sharp increase in the modeled accumulation-mode number. Models and WOPC are all comparable in their bimodal Dg and accumulation-mode number, while the WOPC coarse mode has a lower number than E3SMv2-SPA and CESM2-WACCM. E3SMv2-PA has a larger Deff than other datasets (though it is still within the uncertainty in WOPC Deff). This peak in Deff – which is also noted in Reff in Fig. 6 – is attributed to a wider accumulation mode and larger modal Dg in E3SMv2-PA. CESM2-WACCM has a larger modal number than all other datasets.

At 11 months after the eruption (Fig. 8d), the WOPC data continue to grow in the accumulation and coarse mode. The accumulation-mode number decreases while the coarse mode is increasing in E3SMv2-SPA, suggesting conversion of accumulation mass into the longer-lived coarse mode. The WOPC coarse-mode Dg (1.92 ± 0.19 µm) is more than twice that of E3SMv2-SPA (0.828 µm), while the WOPC accumulation-mode best fit (Dg=0.909 ± 0.09 µm, sg=1.23) is close to the E3SMv2-SPA coarse mode (Dg=0.828 µm, sg=1.2) and is nearly identical to the CESM2-WACCM coarse mode (Dg=0.918 µm, sg=1.2). The overall larger aerosols in the WOPC distributions lead to the largest difference in Deff between the model and WOPC.

For 1 year and longer after the eruption, the accumulation mode in E3SMv2-PA follows a steady and rapid decay that can be tracked in size and number (Fig. 8d–i). Over this period, E3SMv2-SPA and CESM2-WACCM generate very similar size distributions, with a slightly lower coarse-mode number and slightly larger coarse Dg in CESM2-WACCM. Overall, WOPC and E3SMv2-SPA/CESM2-WACCM have similar distributions and similar Deff values, with E3SMv2-SPA showing a slightly smaller Deff, but it is still within the uncertainty of WOPC data. A peak in the Aitken-mode aerosol in the models in Fig. 8h may be due to the Lascar eruption in February 1993.

The previous timeline shows an improved aerosol evolution in E3SMv2-SPA compared to WOPC and exhibits the similarities between CESM2-WACCM and E3SMv2-SPA. It also indicates that E3SMv2-SPA does not simulate large enough aerosol compared to the observations. Similar behavior in Deff and relative size bias is noted at the 17, 19, and 20 km levels as well (Figs. S12–S13). Given that the model is nudged to meteorology and that the aerosols in the stratosphere tend to evolve relatively slowly over time, it is assumed that the resolution artifacts of comparing a 1° × 1° model grid cell to in situ measurements are minimal. We present a couple of possibilities for this size bias. One is that the aerosol density is too large due to the model assumption of ammonium bisulfate density of 1.7 kg m-3 instead of the sulfuric acid density of ∼ 1.6 kg m-3 (Seinfeld and Pandis, 2006). This may bias the aerosol to be small while also contributing to more rapid removal of coarse-mode aerosol. Another possibility is the lack of van der Waals forces in both E3SMv2 and CESM2-WACCM. This intermolecular attraction has been shown to aid in the coagulation of smaller particles, enhancing Reff (English et al., 2013). The impact of this size bias on aerosol climate impact is now explored through effective single-particle scattering.

The Reff can be used to characterize the evolving aerosol size distribution, which conveniently can be used in the offline calculation of single-particle optical properties using Mie theory (see Appendix B). We choose to use offline Mie code for both the model and observations to allow for a direct comparison between optical properties derived from modeled and observed Reff. Figure 9 shows the scattering efficiency (Qs) of sulfate particles of size Reff for the same time and height samples as Fig. 8. Additionally, this plot marks the approximate wavelength of peak solar blackbody irradiance (λsolar=0.5 µm) to identify when aerosol scattering of solar radiation has the largest impact on radiative balance. Qs is proportional to the effective size parameter (xeff=2πReff/λ) to the fourth power (xeff4) (i.e., λ-4) (Petty, 2006). This scattering feature can be seen in Fig. 9, where, as wavelengths increase, there is a rapid decrease in Qs.

The peak in Qs shifts from λ of ∼ 0.2 µm before and shortly after Pinatubo (Fig. 9a–b) to 0.5–0.7 µm 6 months after the eruption (Fig. 9c) with the onset of rapid particle growth. For the remainder of the time (Fig. 9d–i), E3SMv2-SPA and CESM2-WACCM Reff result in a Qs peak right around λsolar, indicating a very efficient scattering of sunlight by these simulated aerosols. The WOPC reports larger Reff than the models, which have a Qs that is 10 %–80 % higher than observations at λsolar during 1992 (Fig. 9d–f), becoming more similar during 1993 with the decay of stratospheric Reff (Fig. 9g–i). E3SMv2-PA has a similar Qs to E3SMv2-SPA/CESM2-WACCM until the end of 1992 (Fig. 9f), when there is a quick progressive drop in Reff due to rapid stratospheric aerosol deposition.

These results indicate an optimal sulfate scattering Reff of ∼ 0.3–0.4 µm, which is similar to estimates of the optimal sulfate aerosol size of 0.3 µm in geoengineering applications (Dykema et al., 2016). Given that WOPC predicts larger Reff and smaller Qs at λsolar 6–18 months after Pinatubo, our results suggest that E3SMv2-SPA/CESM2-WACCM overestimates aerosol scattering and the global cooling effect of the Pinatubo aerosol at this level. This is supported by Fig. 4a, where both E3SMv2-SPA and CESM2-WACCM scatter more strongly than ERBS and E3SMv2-presc from April–August 1992 (though differences in clouds may also be contributing to this result). Temperature comparisons at 850 hPa over 1992 do not reflect a cooler surface in E3SMv2-SPA and CESM2-WACCM compared to observations (Table 2), but this comparison is not ideal for making a connection between perturbations in scattering and surface temperature due to the unknown role of internal variability on temperature. Figure 9 relates size distribution differences in models and WOPC to climate impact at a single level. For a better validation of the stratospheric plume and to see if the model disagreement changes when looking across multiple levels, the next step is to calculate Qs from the stratospheric Reff.

Figure 10 shows monthly Qs generated from averaged stratospheric Reff at a midlatitude site (solid line) (Fig. 6c) and the tropics (dotted line) (Fig. 6d). As in Fig. 9, a similar pattern is shown where smaller modeled Reff values lead to higher modeled Qs values at λsolar compared to observed Qs. However, the differences between modeled and observed Qs at λsolar are not as stark for the monthly stratospheric average values, with maximum differences on the order of 5 %–14 % as opposed to the 10 %–80 % seen in the daily 18 km level data. The larger Reff in the tropics leads to a higher Qs at λsolar 1 month after Pinatubo (Fig. 10b) and lower Qs at λsolar 18 months after Pinatubo (Fig. 10f) compared to midlatitude measurements in the stratosphere. The E3SMv2-SPA and CESM-WACCM maximum Qs values from both regions hover around λsolar, with higher modeled Qs at λsolar in the tropics 2 years after the eruption (Fig. 10h) due to a consistently larger Reff in this region.

While the Pinatubo eruption resulted in a net climate cooling effect due to increased scattering, it also contributed to stratospheric warming through the absorption of outgoing longwave radiation within the aerosol layer (Kinne et al., 1992). Figure 13 shows the Qa calculated offline from model and in situ Reff, with a dark-red line indicating the wavelength of peak terrestrial blackbody irradiance (10 µm; λearth). While sulfate scatters strongly at visible wavelengths (λsolar in Figs. 10 and 9), it is not an effective absorber in the visible band (Qa=0 at λsolar), and the determining factor in stratospheric heating is the magnitude of Qa at λearth. The wavelength dependence of Qa is weaker than Qs (proportional to xeff (i.e., λ-1)) due to a weaker longwave absorption sensitivity to Reff (Lacis, 2015), and Qa is strongly tied to the imaginary part of the sulfate refractive index at 0 % relative humidity (nHess; Appendix B) (Hess et al., 1998). The proportionality to xeff is denoted in Fig. 13 by the linear increase in Qa(λ) with increasing Reff; the dependence on the imaginary part of nHess is reflected in the unchanging pattern in absorption magnitudes for all datasets and times. Generally speaking, Qs is characterized by changes in the wavelength and is more sensitive to aerosol size fluctuation (Figs. 10 and 9), while Qa shows changes in the absorption efficiency and is less sensitive to aerosol size fluctuation.

In Fig. 13, the linear dependence of Qa on Reff means that an individual particle in the tropics has more absorption capacity than the midlatitudes across the whole period, and the observations will show more absorption than the models. This is explained by Reff in these two regions shown at the top of each panel. For example, the smaller modeled Reff at 41° N leads to a modeled Qa that is 15 %–30 % lower than that of WOPC through 1992 (Fig. 13c–f).

Because the same refractive index is used across all models and observational datasets, the differences in Qa are due only to differences in aerosol size. However, this is a simplifying assumption for the modeled Qa values due to their explicit calculation of the soluble aerosol refractive index (ns) in the stratosphere based on aerosol water and sulfate content (Eq. B4). E3SM simulates a stratosphere with unrealistically low-stratospheric water vapor (Keeble et al., 2021; Christiane Jablonowski, personal communication, 2024), which results in aerosols that are mostly sulfate (Fig. S18) with a refractive index similar to nHess (Appendix B). Higher water vapor in CESM2-WACCM means that the assumption of nHess in the calculation of Qa does not account for the volume weighting of the hydrated aerosol refractive index (Appendix B). When interstitial stratospheric water and sulfate are used to calculate a volume-weighted ns using nHess and nwat, Qabs at λearth is smaller than that reported with only nHess by ∼ 14 %–20 % over the 41° N band and by ∼ 13 %–18 % over 20° S–20° N (Table S3). This is due to a smaller-magnitude imaginary refractive index for water at this wavelength.

It is unclear whether injecting volcanic H2O would help offset the stratospheric dry bias in E3SM. Abdelkader et al. (2023) showed that the injection of H2O for a 20 km Pinatubo-like injection increases sulfate mass and stratospheric AOD by ∼ 5 %, but at the colder temperatures in the lower stratosphere almost all of this water vapor freezes and sediments out. Retention of water vapor in the stratosphere depends on injections at higher altitudes where temperatures are warmer. Given that E3SMv2-SPA already tends to produce higher sulfate burdens compared to other simulations (Fig. 1), it is possible that the enhanced sulfate aerosol mass attributed to the addition of water vapor in the plume would bias the aerosol sulfate content to be high compared to observations, even as it would improve upon the aerosol size. Furthermore, the lower injection height of our simulations (20 km) and a cold-point tropopause that is too cold in E3SMv2 (Christiane Jablonowski, personal communication, 2024) would aid in the rapid removal of most of the injected water, reducing the effect of the water injection on aerosol properties.