The AER 2-D sulfate aerosol model participated in an international aerosol assessment , in which it was compared with satellite, ground lidar and balloon measurements, as well as with other 2-D and 3-D aerosol models, and subsequently recognized as one of the best existing stratospheric aerosol models with respect to SO2, aerosol size distributions and extinctions under both background and volcanic conditions. The model represents sulfuric acid aerosols (H2SO4/H2O) on the global domain from the surface to about 60 km with approximately 9.5∘ horizontal and 1.2 km vertical resolution. The model is driven by year-by-year wind fields and temperature from , which were derived from observed ozone, water vapor, zonal wind, temperature, planetary waves, and quasi-biennial oscillation (QBO). The model chemistry includes the sulfate precursor gases carbonyl sulfide (OCS), sulfur dioxide (SO2), sulfur trioxide (SO3), sulfuric acid (H2SO4), dimethyl sulfide (DMS), carbon disulfide (CS2), hydrogen sulfide (H2S) and methyl sulfonic acid (MSA). The model uses pre-calculated values of OH and other oxidants from . Photodissociation and chemical reactions are listed in and their rates are updated to . The particle distribution is resolved by 40 size bins spanning wet radii from 0.39 nm to 3.2 µm by volume doubling. Such a sectional approach was proven to be more accurate in representing aerosol mass/extinctions compared to prescribed unimodal or multimodal lognormal distributions . The sulfuric acid aerosols are treated as liquid binary solution droplets. Their exact composition is directly derived from the surrounding temperature and humidity according to . Microphysical processes in the model include homogeneous nucleation, condensation/evaporation, coagulation, sedimentation, as well as tropospheric rainout/washout. These processes determine the evolution of the aerosol concentration in each size bin and thereby the entire particle size distribution. Operator splitting methods are used in the model with a time step of 1 hour for transport, chemistry, and microphysics, and 3 min sub-steps for the microphysical processes that exchange gas-phase H2SO4 with condensed phase, and 15 min sub-steps for the coagulation process. For more detailed descriptions of chemistry and microphysics in the model we refer to .

We employ the coupled aerosol–chemistry–climate model SOCOL-AER in order to verify the consistency between a 2-D model forced with observed dynamics and a 3-D free-running model. SOCOL-AER couples the size resolved AER 2-D microphysical model into the chemistry-climate model SOCOL with interactive aerosol radiative forcing. In this study we use the T31 horizontal resolution (3.75∘ ×3.75∘) and 39 vertical levels (from surface to 0.01 hPa) with nudged quasi-biennial oscillation. Transport is calculated every 15 min, whereas chemistry, microphysics and radiation are calculated every 2 hours with 40 sub-steps (3 min) for the microphysics. This model has been well validated by comparing calculations with sulfur-containing gases, aerosol extinctions at different wavelength channels (from 525 nm to 5.26 µm), and aerosol size distributions from satellite and in situ observations. It has been used to study the global atmospheric sulfur budget under volcanically quiescent conditions and moderate volcanic eruptions such as the 2011 Nabro eruption. A detailed description of SOCOL-AER is presented by .

We have simulated the Pinatubo-like eruption by injecting SO2 directly into the stratosphere. In the 2-D model, the injection is immediately mixed zonally, and takes place in the latitude band 5∘ S–14∘ N, which is an approximation to the observed rapid zonal transport of the SO2 cloud derived from satellite measurements . The lack of zonal resolution is clearly a deficiency of our approach, but since SO2 removal/conversion rate (e-folding time) is sufficiently slow (τ∼25 days) and the zonal transport around the globe sufficiently fast (τ∼20 days) , a zonal-mean description is a reasonable approximation. Also, the spaceborne aerosol data are typically provided as zonal averages. We examined three cases of total mass, namely 14, 17 and 20 Mt of SO2. The injection height extends from near the tropical tropopause (17 km) to 30 km. The vertical mass distribution is then represented by MtotF(z) where Mtot is the SO2 mass magnitude in units of megaton (Mt) and F(z)=f(z)/∫zmin⁡=17zmax⁡=30f(x)dx (in km-1) is a vertical distribution function of altitude z∈[17km,30km] with a skew-normal distribution f(z) given by f(z)=22πσe-(z-μ)22σ2∫-∞αz-μσ12πe-x22dx.

Figure  shows a few examples of F(z). The location parameter μ depends on available model levels and determines the altitude where the maximum of the emitted SO2 cloud is located when there is no skewness. The skewness or asymmetry of the curve increases when |α| increases and vanishes when α=0 (normal distribution). A negative α drives the location of the maximum SO2 emission to lower altitudes, while a positive α to higher altitudes. The scale parameter σ indicates how much dispersion takes place near the maximum; that is, it determines the width or standard deviation of the asymmetric bell-shaped curve.

The four parameters Mtot, μ, σ and α enable representation of a substantial space of SO2 distributions, whose evolution is computed forward in time (taking into account the transport and comprehensive chemical and microphysical processes), in order to compare with satellite and in situ data. We simulate the following cases in detail: Mtot∈{14Mt,17Mt,20Mt},μ∈{16.79km+n×1.16km,n=0…11},σ∈{2km,3km,4km},α∈{-2,-1,0}, which results in 324 different scenarios. The choice of the boundaries for this set of scenarios is already based on exploratory simulations. For example, based on the results of our 2-D model, it does not make sense to consider total masses Mtot>20 Mt, since no choice of the other three parameters would allow to reconcile the model results with the observations. Similarly, skewness α>0 leads to more biased model results, because the skew towards higher altitudes cannot be offset by lower Mtot. In addition to the above 324 simulations, we consider another two scenarios, which are adopted in modeling studies of Pinatubo: (1) Box14Mt has a uniform (“Box”) profile, which is similar to and the simulation “CONTROL_HIGH” in , injecting the SO2 mass homogeneously along altitudes (shown in Fig. ); (2) SPARC20Mt is the reproduction of the Pinatubo simulation conducted in , which injects 20 Mt of SO2 and has a vertical profile “SPARC” shown in Fig. .

A selected list from the 326 2-D simulations is summarized in Table , in which the specific choice of the four parameters for each scenario is provided. The score and ranking of these scenarios are discussed later in the text.

Given the limitation of the 2-D approach, we further perform two 3-D Pinatubo-like simulations (R001 3-D and R153 3-D at the bottom of Table ) using the coupled aerosol–chemistry–climate model SOCOL-AER to check the consistency between 2-D and 3-D approaches. Note that the location parameters used in the 3-D runs differ slightly from the corresponding 2-D runs (i.e., R001 and R153) due to different vertical model levels between the two models.

To determine an optimal set of the emission parameters, we define four metrics (ScoreSO2, ScoreBurden, ScoreOPC and ScoreExt) based on these four measurements sets described above, and rank all of our 326 simulations by a weighted score (ScoreWt) of the four metrics (see Table ).

ScoreSO2 is calculated as the relative l2-norm (Euclidean norm) error with respect to the MLS measurements: ||XSO2,model-XSO2,MLS||/||XSO2,MLS||,

where X is a 1-D vector of SO2 mixing ratio in altitude (21, 26, 31, 36 and 41 km). The negative values of the MLS measurements are set to zero in the calculation.

ScoreBurden is the average of the relative l2-norm errors with respect to HIRS (July–December 1991) and SAGE-4λ (January 1992–December 1993): 12(||Bmodelt1-BHIRSt1||/||BHIRSt1||+||Bmodelt2-BSAGEt2||/||BSAGEt2||), where Bt1 is a 1-D (in time) vector of the aerosol burden for July–December 1991 and Bt2 for January 1992–December 1993.

ScoreOPC – We first calculate the relative l2-norm errors with respect to the OPC measurements: errOPC=||Nmodel-NOPC||/||NOPC||, where N is a 1-D vector of the cumulative particle number concentration in altitude (15–30 km). We then evaluate a quadratic mean (RMS): rmsOPC=RMS{errOPCr}, where r denotes four particle size channels (r>0.01 µm, r>0.15 µm, r>0.25 µm and r>0.5 µm). Finally, ScoreOPC is obtained by averaging rmsOPC from October 1991 to December 1992.

ScoreExt – The uncertainty of SAGE is generally better than ∼ 20 % for 525 nm and ∼ 10 % for 1020 nm (see Fig. 4.1 in ). Therefore, ScoreExt is weighted as one-third for 525 nm (ScoreExt525nm) and two thirds for 1020 nm (ScoreExt1020nm). We use the SAGE II observations between 18 and 30 km. The calculations for ScoreExt525nm and ScoreExt1020nm are similar to those in ScoreOPC. Latitude bands (50–40∘ S, 30–20∘ S, 5∘ S–5∘ N, 20–30∘ N and 40–50∘ N) take the place of the particle size channels. The temporal average is from January 1992 to December 1993.

Note that extinction coefficients in the lower stratosphere (18–23 km) have a much larger weight than those above 23 km because extinctions at 525 nm and 1020 nm at 18–23 km after the Pinatubo eruption (see Fig. ) are one to several orders of magnitude larger than those above 23 km. We calculate the score by the relative Euclidean norm, therefore the scores above 23 km have a relatively small weight.

The overall score ScoreWt is weighted as follows: 16.7 % of the SO2 score (ScoreSO2), 16.7 % of the OPC score (ScoreOPC), 33.3 % of the global burden score (ScoreBurden), and 33.3 % of the aerosol extinction score (ScoreExt). The choice of the weighting is discussed below.

MLS detected residual SO2 in the stratosphere approximately 100 days after the eruption. The uncertainty of ScoreSO2 is likely larger than ScoreBurden and ScoreExt due to uncertain OH fields. An assumed uncertainty in OH fields of 10 % e.g., translates into an uncertainty of 30 % in SO2 at ∼ 90 days after the eruption. Moreover, ScoreOPC also has less weight than ScoreBurden and ScoreExt because of the small temporal and spatial sample size of the balloon-borne OPC measurements, which are not conducted very frequently (a maximum of two measurements per month after the Pinatubo eruption) and located only above Laramie.

ScoreBurden uses the HIRS-derived data up to December 1991 and the SAGE-derived data afterwards. During the first 6 months after the Pinatubo eruption, the SAGE II instrument was largely saturated in the tropical region , and therefore the aerosol mass retrieved from SAGE II during this period very likely underestimates the initial loading significantly. The SAGE-4λ data set corrects for this deficiency by filling observational gaps by means of Lidar data. However, Lidar-derived extinctions are generally lower than SAGE II below 21 km , and are not located in the equatorial region (see Fig. 3.7 in ), where maximum mass loadings are expected. Therefore, SAGE II gap-filled data probably remain as a lower limit after the eruption. Conversely, HIRS measurements represent an upper limit since they account for the entire aerosol column including the troposphere. This may explain the considerable difference between SAGE II and HIRS during the first 6 months after Pinatubo (see Fig. ). After this period, the aerosol mass in the extratropics contributes more to the global value than that in the tropics because the volcanic cloud starts to spread out from the tropics in November 1991 (see Fig. 5 of ). HIRS loses its sensitivity at mid/high latitudes where there is a contribution from errors in the background signal . As shown in Fig. , a visible increase of the HIRS-derived global burden begins after December 1991, and the noises in HIRS become more pronounced after March 1992. On the other hand, SAGE II, as an occultation instrument, becomes more reliable when the stratosphere starts to be sufficiently transparent after December 1991, particularly in mid latitudes. Therefore, ScoreBurden uses the HIRS-derived data up to December 1991 and the SAGE-derived data afterwards, with an overall uncertainty of 20 %. ScoreExt uses the SAGE II measurements from January 1992 to exclude the most saturated phase of SAGE II.

Table  shows the scores of selected scenarios, sorted according to the weighted rank (“RankWt” in the next to last column). The rank computed by the arithmetic average of the four scores is also provided (“RankAvg” in the third column from the right). The top 20 scenarios reveal that the total injection mass (Mtot) is 14 Mt of SO2, 70–80 % of which is below 24 km, and its maximum is likely between 18–21 km with 3–4 km width (scale parameter σ). Location parameters μ larger than 21 km are skewed towards a lower altitude (negative α). These sort of vertical profiles provide a range for the parameters of the optimal vertical distribution: μ=20.66±1.79 km, σ=3.33±0.72 km and α=-0.8∓0.77. Two examples (scenarios R001 and R010 marked in Table ) are shown in Fig. . The ranking based on “RankAvg” differs slightly from “RankWt”; however the set of the best scenarios found in “RankAvg” is consistent with “RankWt” despite the distinct weighting schemes. The worst scenarios (“RankWt” ≥ 322) in Table  are those with 20 Mt SO2 injection mass and highest location parameters (μ=29.55 km). The scenarios such as Box14Mt and R153 rank much more poorly than the optimal scenarios, although their injection mass is the same, because their vertical profiles (shown in Fig. ) inject over 50 % mass above 23–24 km. The scenario R033 has the same vertical profile as R001, but injects 17 Mt SO2. SPARC20Mt emits 20 Mt SO2 and ranks at 214 in Table , although its vertical profile is close to the optimal scenarios (about 10–20 % more mass above 23 km). This implies that emitting above 17 Mt SO2 is very likely an overestimation.

The optimal vertical profiles found in Table  are generally consistent with the earlier volcanic plume studies of and . showed that the SO2 plume from the 1991 Pinatubo eruption originated at an altitude of ∼ 25 km near the source and descended to an altitude of ∼ 22 km as the plume moved across the Indian Ocean. suggested that initially SO2 from a co-ignimbrite eruption (such as Pinatubo) that was forced over a large area, may reach above 30 km but the majority of SO2 would then collapse or sink back to its neutral buoyancy height (15–22 km) (see Fig. 1 in their paper).

We discuss in detail nine scenarios (R001, R010, R017, R033, R153, Box14Mt, SPARC20Mt, R001 3-D and R153 3-D). R001 represents the overall optimal scenario. R010 ranks first in the ScoreExt and third in the ScoreBurden, as an example of scenarios with high rankings in the extinction and aerosol burden scores. R017 matches best the OPC measurement, but has poorer scores in the other criteria than R001 and R010. R086 has a vertical profile similar to R001 (see Fig. ), and agrees the best with the SO2 observations. However, this scenario fails to match other observations due to its abundant initial injection of 20 Mt SO2. R033 emitted 17 Mt SO2 with the same vertical profile of R001, and ranks third in the ScoreSO2 but poorly among other scores, which shows a performance similar to R086. Here we will focus on R033 for later discussion. R153 and Box14Mt (with RankWt 94) inject the same sulfur mass as in R001, but use different vertical profiles (maximum injection mass of R153 is located at ∼ 26 km). SPARC20Mt turns out to be a bad representation, which reproduces the previous simulation conducted in . The two 3-D scenarios R001 3-D and R153 3-D correspond to the 2-D scenarios R001 and R153, respectively. The scores of the 3-D runs are similar to the corresponding 2-D ones.

Figure  compares the modeled SO2 with MLS measurements in September 1991. The scenario R001 captures the measured SO2 profile, and only underestimates the measured maximum SO2 mixing ratio near 26 km by about 20 %. SO2 modeled by R033 agrees excellently (within 7 %) with MLS measurement. R010 produces about 20–30 % less SO2 near 26 km compared to R001, and significantly more above 30 km. This could be explained by the fact that R010 disperses slightly more SO2 above 24 km compared to R001. The SO2 vertical profile of R017 is shifted to lower altitudes compared with the observed values, likely due to its concentrated injection distribution near 19–20 km (see Fig. ). Box14Mt and R153 fail to match the observed profile. SPARC20Mt agrees with the observations under 28 km better than Box14Mt and R153, but largely overestimates the observations above. The common feature of R153, Box14Mt and SPARC20Mt is that their initial vertical distributions release much more SO2 above 24 km compared to R001, which is skewed towards lower altitudes, therefore retaining more than 90 % of emitted SO2 below 24 km (Fig. ). SO2 profiles simulated by the two 3-D simulations (dashed curves in Fig. ) are similar to the corresponding AER 2-D results, though SOCOL-AER predicts a lower maximum value and more readily distributes SO2 to higher altitudes, reflecting differences in OH and transport between the two models.

Figure  shows the evolution of the simulated stratospheric aerosol burden (megaton of H2SO4/H2O) compared to that derived from HIRS and SAGE-4λ . R001 matches the HIRS-derived maximum aerosol burden of 21 Mt (equivalently 15–16 Mt of sulfate mass without water) during the first few months after the eruption, and after month 14 agrees with the SAGE-derived burden (mostly within 20 %). In contrast, SPARC20Mt reaches a maximum burden of 32 Mt of H2SO4/H2O, which is ∼ 50 % more than the 21 Mt derived from HIRS. R033 emits 17 Mt of SO2 using the same vertical profile as R001, and peaks at 25 Mt of aerosol mass, about ∼ 30 % more than HIRS, whereas the uncertainty of HIRS is about 10 % . This means that the initial mass loading of 17 or 20 Mt of SO2 into the stratosphere is apparently too high. Scenarios using 14 Mt of SO2 show that the evolution of the aerosol burden is highly sensitive to different injection profiles. R010 initially distributes somewhat more SO2 above 24 km compared to R001, and shows a better decay rate of the aerosol burden. R017 emits SO2 mainly concentrated between 19–21 km, and its aerosol burden peaks similarly to R001, but declines more rapidly. R153 and Box14Mt inject about 60 and 40 % of their sulfur mass above 24 km, respectively, leading to a greater maximum aerosol burden and a slower decay rate of the burden than R001. R153 has even a slightly larger maximum aerosol burden than R033, though R033 has the larger initial SO2 mass loading. Together, these results reveal that the injection altitude and initial mass loading affect the lifetime of the volcanic aerosol. An increase in the distance of the volcanic plume above the tropopause will increase the lifetime of the volcanic aerosol due to a longer residence time for sedimenting particles and a slower pathway of the aerosol within the Brewer-Dobson circulation. On the contrary, a larger initial mass loading may offset a higher injection altitude because of faster sedimentation caused by larger particles.

The results of “R001 3-D” using the coupled aerosol–chemistry–climate model SOCOL-AER is consistent (mostly within 10 %) with the AER 2-D simulation R001. In contrast, the consistency between R153 and “R153 3-D” is less satisfactory. The maximum aerosol burden simulated by “R153 3-D” is within 10 % of R153, but the e-folding time of the aerosol burden in the 3-D simulation (“R153 3-D”) is significantly faster (13 vs. 15 months) than in the 2-D simulation (R153). This indicates that in addition to the initial mass loading and microphysics, model dynamics is essential to the decay of the volcanic aerosols. This difference between R153 (AER) and “R153 3-D” (SOCOL-AER) is possibly due to an insufficient rate of exchange of air between the troposphere and stratosphere in the AER 2-D model and/or a faster Brewer-Dobson circulation with respect to observations in the SOCOL (see the “tape recorder” in Fig. 8 of ).

Figure  shows comparisons between the optical particle counter (OPC) measurements operated above Laramie and model-calculated cumulative particle number concentrations in October and December 1991 for two size channels (r>0.15 µm and r>0.5 µm). Below 23 km, R001 reasonably matches the observations for r>0.15 µm, but less satisfactorily for r>0.5 µm. The number density from R010 is slightly higher than R001 above ∼ 24 km, which is consistent with the comparison between initial vertical profiles of R001 and R010 (see Fig. ). R017 agrees best with the observed number density, particularly above 24 km, because R017 emits very little SO2 above 22 km. R033 predicts slightly higher number concentrations than R001 due to its larger initial mass loading (17 Mt SO2), but shows in general similar results to R001. In contrast, the calculations from R153, Box14Mt and SPARC20Mt differ significantly from R001. Above 23 km, these three scenarios further overestimate the observations than R001 because their initial injection profiles release much more SO2 above 23 km compared to R001. Below 23 km, R153 substantially underestimates the observations in October 1991 as its injected mass locates mainly between 23–27 km, while Box14Mt shows better agreement with the observations (r>0.5 µm) below 18 km than R001, but largely underestimates the maximum near 21 km. SPARC20Mt is similar to R001 below 20 km since its initial mass loading (20 Mt SO2) compensates for the deficiency of its vertical mass injection profile in the lower stratosphere. The calculations from SOCOL-AER are generally consistent with the corresponding 2-D ones (R001 and R153). SOCOL-AER produces higher number concentration in October 1991 compared to the AER 2-D model. In December 1991, this difference between the 2-D and 3-D simulations shrinks, and “R001 3-D” further improves the agreement with the OPC measurements below 18 km for r>0.5 µm.

We compare the modeled 1020 nm extinctions with the gap-filled SAGE II version 7.0 (Fig. ). SAGE II data points with horizontal bars are actual SAGE II measurements and denote natural variabilities, while data points without bars are gap-filled from lidar ground stations, which have a higher uncertainty . Figure  shows comparisons in January (upper panel) and July (lower panel) 1992 for five latitude bands from left to right: 50–40∘ S, 30–20∘ S, 5∘ S–5∘ N, 20–30∘ N and 40–50∘ N.

In January 1992, all the simulations reproduce aerosol extinctions reasonably near 20 km (mostly within 50–100 % of observed aerosol extinctions). R001, R010 and R017 agree better with observed aerosol extinctions compared to the other 2-D simulations. R010 performs best in the lower stratosphere (where ScoreExt by definition has a large weight), while R017 matches the observations well above 24 km. R033 is generally 10–20 % larger than R001 due to its higher initial mass loading, although it has the same vertical profile as R001. SPARC20Mt has even larger values than R033 due to a 20 Mt of SO2 mass loading. Box14Mt and R153 largely overestimate the observed extinctions above 24 km. The 3-D simulation “R001 3-D” is superior to all the 2-D simulations, while “R153 3-D” performs worse than the 2-D simulations R001 and R033. Likewise, in June 1992, R001, R010 and R017 also do a better job than other 2-D simulations. The two 3-D simulations “R001 3-D” and “R153 3-D” are now both superior to all 2-D model results, although the differences between them start to shrink as the their aerosol burdens are now within 10 % from each other. Here the 3-D model shows a better extinction vertical profile likely because the 3-D model uses an improved numerical scheme based on for sedimentation, while the 2-D model uses an upwind scheme, which would cause artificial upward transport of particles to high altitudes . Evaporation of aerosol becomes important only above ∼ 32 km, therefore should play a minor role in explaining the discrepancy between the 2-D AER and 3-D SOCOL-AER. Overall, the results from SPARC20Mt, Box14Mt, R033 and R153 display a common deficiency, as they tend to overestimate aerosol extinctions in high altitudes above 24 km. Excessive mass loading (as in SPARC20Mt or R033) is one of the reasons. However, the shape of the initial mass vertical profiles appears to be at least as important as the initial mass loading. Box14Mt has 30 % less total mass loading than SPARC20Mt, but it shows even higher extinctions in high altitudes because it has 40 % of its mass injected above 24 km, while SPARC20Mt has only about 20 % of its mass there.

Figure  compares the modeled aerosol optical thickness (AOT) with the SAGE II measurements. The southward transport of the volcanic clouds observed by SAGE II is reasonably reproduced by the models. The best scenarios here are R001 and R010, whose SO2 injection profiles peak between 18–21 km and disperse the volcanic plume broadly (σ=4 km). In contrast, R017 with a narrow dispersion (σ=2 km) constricts the initial SO2 between 18–22 km, which leads to a faster decay of AOT than R001 and R010. R153 and SPARC20Mt distribute too many aerosols to high latitudes due to injecting SO2 excessively above 24 km. The impact of the initial SO2 vertical profile on the hemispheric dispersion of the volcanic clouds is more pronounced in the 3-D simulations as shown in the two bottom panels. These results show that spatiotemporal distribution of the volcanic aerosols is affected by initial injection profile of SO2 and the optimal parameters found in Table  would lead to better model results when compared to SAGE II observations.