Figure shows the evolution of observation-derived and model-calculated stratospheric aerosol burdens in units of Tg of sulfur globally integrated (panel a) and in the tropics (panel b). The High-Resolution Infrared Radiation Sounder (HIRS) measured the aerosol vertical column and derived total aerosol mass with about 10 % uncertainties. HIRS includes tropospheric and stratospheric aerosols together . In contrast, the limb-occultation measurements of SAGE II allow aerosols in the troposphere and stratosphere to be distinguished from one another. In this work the SAGE-II-derived total aerosol mass is represented by two data sets. The first one, the SAGE-4λ method used within the Chemistry–Climate Model Initiative (CCMI), employs all four SAGE wavelengths with overall about 30 % uncertainties for non-gap-filled data and higher uncertainties in data gaps filled by lidar station data. The second data set was recently compiled for phase 6 of the Coupled Model Intercomparison Project (CMIP6; ) using the SAGE-3λ method, which is similar to SAGE-4λ but refrains from employing the less reliable channel at 385 nm, thus considering only three SAGE wavelengths. Directly after Pinatubo the SAGE-3λ data set uses additional satellite and ground-based data for gap filling. More information about the SAGE-3,4λ composites can be found in a recent paper by .

During the first year after the Pinatubo eruption, the aerosol mass in both SAGE-II-based data sets is noticeably lower than in HIRS data. This is likely related to the saturation effects of SAGE II as a limb-occultation instrument during this period . The SAGE-3λ composite provides significantly larger burdens than its predecessor due to additional data used in a gap-filling procedure , but still much lower than HIRS. After this period, when the atmosphere becomes sufficiently transparent, SAGE II measurements are expected to provide more accurate aerosol extinctions. In contrast, the HIRS-derived mass becomes less reliable with time, when the aerosol cloud spreads to higher latitudes with lower values that are close to the noise level of the technique . This suggests trusting the HIRS data up to mid-1992 and the SAGE data afterwards . Note, however, that the updated SAGE-II-based data set now also provides values closer to HIRS from mid-1992 to early 1993 and considerably larger values later in 1993.

The global stratospheric aerosol burden calculated by REF (grey shaded area representing 2σ ensemble spread) agrees well with the HIRS data peaking around 5.4 Tg at the end of 1991. Later, REF agrees well with the SAGE-4λ composite, while the updated SAGE-3λ has a generally larger burden. Qualitatively similar results are found for the tropics. Recent modeling studies by and showed very similar time series of the global aerosol burden with initial emissions of 10 and 14 Tg of SO2, respectively. These studies, another work by , and the present study fail to reproduce the pronounced step-like evolution of the burden seen in HIRS and SAGE-3λ, showing a smoother decrease instead. overestimated the HIRS peak burden even with 10 Tg of SO2 emitted, but obtained this step-like behavior. explained it by variability in the background aerosols related to the summer increase in photolysis, but they also noted that their background values are significantly larger than in the other models and observations. Besides instrumental uncertainty, another reason for the complicated shape of the observational curves seen in Fig.  could be the seasonal variability of the stratospheric circulation that is known to be underestimated in ECHAM5 and LMDZ , which are core GCMs of the sectional models SOCOL-AER and LMDZ-S3A, respectively.

Panels (c) and (d) of Fig.  show deviations (%) from REF in all experiments. Our experiment with lower emission (REF12, 12 Tg of SO2 instead of 14 in REF, but otherwise unchanged plume characteristics) shows lower burdens of up to 14 % globally and 17 % in the tropics, which is therefore even farther than REF from the latest SAGE-II-derived estimates after mid-1992. The results of the sensitivity runs noQBO, noRAD, and noRADnoQBO are presented by the red curves. During the first few months after the Pinatubo eruption, the aerosol mass loading in the tropical reservoir is maintained by the competition between sedimentation and enhanced tropical upwelling due to the radiative heating of volcanic aerosols with the QBO in a strongly descending easterly phase . Therefore, deactivation of each of these processes leads to a stratospheric burden decrease mostly located in the tropics. About 1 year after the eruption the global aerosol burden in noQBO and noRAD is approximately 15 % lower than in REF. The experiment noRADnoQBO shows a cumulative effect up to -30 % around 1993. Gravitational sedimentation becomes a dominant removal process when particles grow sufficiently large after the Pinatubo eruption. With effective radii of 0.5 µm or more these particles sediment efficiently. The burden calculated by UPWIND mostly lies within ±10 % with respect to REF. This upwind scheme was shown to have a large numerical diffusion smearing the aerosol layer out in both the up and down directions . This results in a slightly lower mass during 1–1.5 years after the eruption (effect of the downward diffusion) and a slightly larger mass later on (upward transported aerosols stay longer in the stratosphere). Although this diffusion effect is of numerical origin, for our model it increases the stratospheric lifetime of aerosols and leads to a better agreement with SAGE-3λ after 1993. The aerosol burden calculated by COAG, which differs from REF by a higher coagulation efficiency, shows a more rapid decay rate of the global volcanic aerosol burden compared to REF and the measurements. The difference to REF maximizes in late 1993 at approximately -33 %, which is in agreement with other studies also looking at the van der Waals forces effects .

Figure shows comparisons of the optical particle counter (OPC) measurements operated above Laramie, Wyoming 41∘ N, 105∘ W; against our model experiments. The model was sampled as monthly mean values averaged over a region of ±5∘ latitude and longitude around Laramie. Panel (a) shows the effective aerosol radius averaged over 14–30 km. The effective radius calculated by REF generally lies within the observational uncertainty. However, compared to the observational mean, it is biased high under quiescent conditions and biased low during the volcanically perturbed period. COAG shifts the effective radius up compared to REF, which improves the agreement with observations after 1992, but worsens it earlier. Differences of other experiments reflect the burden of the aerosol behavior shown in Fig. , illustrating that less mass present in the stratosphere generally also leads to smaller sizes.

Panels (b)–(c) of Fig.  show cumulative number distributions for two OPC size channels (R>0.15 µm and R>0.5 µm) in August 1991, May 1992, and March 1993 representing different stages of the volcanic aerosol cloud. We use months with at least two soundings to obtain a useful approximation of day-to-day variability. Aerosol number densities at the altitudes of the maximum concentrations are well reproduced by REF for both large and small particles. Higher altitudes, however, are not so well reproduced, with modeled number densities being up to 3 orders of magnitude too high for bigger particles at certain levels. However, at these high altitudes OPC measurements are themselves uncertain, often having to rely on only one or two channels (plus the concomitant condensation counter measurement). Even larger deviations from the OPC measurements are found for the UPWIND experiment, which clearly has too many particles, especially large ones, in the middle stratosphere all the way to the upper edge of the stratospheric aerosol layer, highlighting the importance of a sedimentation scheme with low numerical diffusivity. Experiments with radiatively decoupled aerosols, noRAD and noRADnoQBO, illustrate the importance of the enhanced upwelling, even in midlatitudes, by showing more large particles staying at the lower levels.

To analyze the global mean size distributions, in Fig.  we show the ratio of aerosol optical depth (AOD) at 565 and 940 nm for the column above 18 km calculated from SAGE-II-derived composites (blue curves) and from model results. These ratios are inversely related to the particle size: a smaller ratio corresponds to larger particles. In the early phase of the Pinatubo eruption, a large number of small particles are formed, which coalesce very quickly as shown by the very sharp drop in the AOD ratio, falling below 1.25 in observations. Afterwards, the small AOD ratio stays almost constant for approximately 1 year. Around late 1993 the ratio starts to return to higher values because the large particles continuously sediment out of the stratosphere and smaller particles nucleate in the air entering the stratosphere in the tropics. REF predicts smaller particles than derived from SAGE II during the early phase after the eruption, and only in 1993 does it start to agree well with the satellite observations. In contrast, due to the enhanced coagulation, COAG produces larger particles (smaller AOD ratios) than REF and shows better agreement with SAGE II during the 4 years following the eruption. The model run UPWIND with a simplified upwind scheme for sedimentation is initially close to REF but reveals overestimation of the particle sizes compared to REF after 1993. This is related to a larger aerosol burden (Fig. ), which enables further coagulation. Our experiment with the reduced emission (REF12) further illustrates this effect by showing that weaker emission leads to slightly smaller sizes over the whole lifetime of the volcanic aerosol cloud.

In general, the model in its reference configuration slightly underestimates the mean particle radius. The agreement with observations is much better if a more detailed coagulation is used. However, as seen in panels (b)–(c) of Fig. , the model in all configurations also has problems in reproducing altitudes higher than 25 km. Comparison of the model to both in situ OPC measurements and the satellite-based global composites SAGE-3λ and SAGE-4λ reveals the same effects of individual experiments. The main difference between the two comparisons is seen during the pre-eruption time, as the model shows larger particles than OPC and smaller particles than SAGE, which can be attributed to the local bias of model parameters.

Figure shows the latitudinal evolution of volcanic material as modeled and measured AOD in the visible part of the solar spectrum, which also represents the main direct climate forcing, since it defines the amount scattered back to space solar irradiance responsible for global cooling. In addition to SAGE II, we used data from the Advanced Very High Resolution Radiometer (AVHRR) satellite instrument, which makes observations over global oceans . Modeled and SAGE-3,4λ AODs are obtained by vertically integrating the extinctions above the tropopause. We removed latitudes not observed by AVHRR for each month from the other data sets and subtracted background values from observations and calculations. Aerosol optical depths derived from SAGE II and AVHRR significantly disagree both in magnitude and spatial distribution. SAGE-3,4λ shows much smaller AOD in the tropics in 1991 and not so strong a southward plume as seen in AVHRR at the end of 1991, part of which is influenced by the high-latitude Cerro Hudson eruption in August 1991. The northern hemispheric plume in 1992 is also more pronounced in the AVHRR data. Figure  shows the same AOD values, but averaged over the non-masked regions in Fig.  over the globe and the tropics. The main difference between AVHRR and SAGE is that AVHRR shows a higher AOD peak in 1991 (2 times higher in tropics) similar to the faster increase in early aerosol burden of HIRS (Fig. ). However, AVHRR reveals a much faster decay, so starting from late 1992 SAGE-II-derived AOD is much larger than measured by AVHRR.

Modeling results are closer to AVHRR before mid-1992 and to SAGE-II-derived data later. REF shows weaker south- and northward plumes in Fig. , but nicely captures the initial increase in the tropics seen by AVHRR. The lifetime of the initial tropical cloud is also well captured compared to AVHRR, except for a small increase in early 1992. Similarly to the burden shown in Fig. , starting from mid-1992 the model results are closer to SAGE-4λ than to SAGE-3λ. The experiment REF12 shows lower AODs that are closer to AVHRR globally but at the same time it also provides a weaker initial increase in 1991. The experiment without QBO shows that less mass is maintained in the tropics compared to REF, and therefore more mass is transported southward in 1991 following the Brewer–Dobson circulation. The experiment with increased coagulation efficiency (COAG) shows a faster decay of initial AOD increase. UPWIND has slight changes but mostly lies within the uncertainties of REF. Similarly to the size evolution discussed in the previous section, in general the details of all modeling experiments are also qualitatively consistent with those shown for the burden in Fig. .

Lower tropical stratospheric warming after major eruptions is one of the key features of volcanic influence on climate e.g.,. It is a forcing for the thermal wind balance, a mechanism through which volcanoes can affect high-latitude tropospheric circulation. This warming is also an important indicator for the aerosol mass distribution in the stratosphere because it is mostly caused by the infrared absorption of volcanic aerosols, which does not critically depend on aerosol particle size . The difficulty of a correct representation of post-volcanic stratospheric warmings is a known issue of global models. Key factors are, besides uncertainties in aerosol distributions, model dynamics and radiative transfer, which in turn also depend on many factors such as spatial and spectral resolution, the presence and quality of interactive chemistry, and others .

Figure compares zonal mean tropical temperature anomalies computed by SOCOL-AER in the lower stratosphere after the Pinatubo eruption with the ERA-Interim and MERRA reanalyses. Anomalies are calculated by subtracting the climatological annual cycle averaged over 1986–2013 for reanalyses and over 1991–1995 of the noRADnoQBO experiment for all other model experiments. Although the noRAD experiment has no aerosol radiative effect, we have also added it to Fig.  so that everything between the noRAD line and other lines can be attributed to the radiative effect of volcanic aerosols. By mid-1993 this effect is mostly gone and then all model experiments are in line with reanalyses. Since the lower tropical stratosphere is a dynamically very active region, the model also shows a large ensemble spread in the stratospheric temperature signal so that all numerical experiments and observations generally fall into this variability. While the temperature anomalies in the reanalyses differ by up to 1 K, the ensemble mean of REF (black curve) overestimates the warming both at 30 and 70 hPa by 1–2 K in late 1991 and mid-1992. The SOCOL-AER scenarios show some differences with respect to each other. While the experiment with reduced emissions (REF12) shows better agreement with reanalyses at both levels, this apparent improvement comes with clear deteriorations in other quantities, such as too-small particle sizes (Fig. 3). The scenario with enhanced coagulation efficiency COAG is warmer at 70 hPa early in 1992, which is related to the increased sedimentation of larger particles to lower altitudes. The results of the UPWIND scenario show a smaller warming than REF, which reflects the larger vertical spread of the aerosol mass due to enhanced diffusion, leading to faster aerosol removal from the lowermost stratosphere.

To further understand the model results, we plotted the vertical aerosol mass distribution in the tropics for REF and the SAGE-3,4λ composites in Fig. . We did not plot the vertical mass distributions from other experiments because they are all very similar to REF relative to SAGE data. There are small differences between experiments that are consistent with the previous analysis; i.e., the UPWIND mass is more vertically diffused, while COAG results show a faster decay of the whole aerosol cloud and therefore slightly more mass present at lower levels. The main difference of all SOCOL-AER experiments to the SAGE-II-derived data is the presence of a large amount of aerosol mass in 1991 in the lowermost stratosphere, i.e., below approximately 60 hPa, which is not consistent with the SAGE-II-based composites, in particular SAGE-3λ. Potentially the SAGE-II-derived data can be still influenced by the known problems in observing the lower stratosphere, which became opaque for limb-occultation instruments in 1991 . This is partly confirmed by comparison of SAGE-II-derived data with HIRS and AVHRR in previous sections. Recently, analyzed the stratospheric warming after Pinatubo using SOCOLv3, which has the same dynamical and chemical cores as SOCOL-AER, but with prescribed aerosols from the SAGE-4λ and SAGE-3λ composites (dashed and dotted blue curves in Fig. ). While our SOCOL-AER-based REF simulation overestimates the temperature response at 70 hPa in 1991, both SOCOLv3 simulations driven by the SAGE-II-based data sets are biased low compared to the reanalysis temperatures (Fig. b). From a purely radiative point of view neglecting dynamical feedbacks, this suggests that the correct aerosol mass loading below 60 hPa lies between our REF simulation and SAGE-II-derived data.

At higher altitudes, i.e., around the level of maximum aerosol loading, all SOCOL-AER simulations and the SOCOLv3–SAGE-4λ results show a linear relation between aerosol mass and the resulting warming, while the SOCOLv3–SAGE-3λ results show a different behavior: despite having the largest aerosol mass among all considered cases, the simulated temperature response is smallest (Fig. a). Even considering potential dynamical effects e.g.,, the SAGE-3λ-based results are surprising. This encouraged to reassess their results, and they noticed an issue with the spectral integration of the SAGE-3λ extinctions. The effect of this spectral integration issue on the comparison between SAGE-3λ, SAGE-4λ, and SOCOL-AER will be investigated and discussed further in an upcoming study.

The response of ozone to major volcanic eruptions is subject to a plethora of dynamical and radiative stratospheric feedbacks, including changes in heterogeneous chemistry. Previously, it was shown that even the sign of the total ozone response after a volcanic eruption depends on the stratospheric halogen loading e.g.,. Volcanic eruptions can in principle also contribute to stratospheric chlorine, which further affects ozone e.g.,, but there was no significant increase in stratospheric chlorine observed after Pinatubo . and pointed to the hemispheric asymmetry of the midlatitude ozone response to Pinatubo due to modified ozone transport from the tropics. Figure  compares monthly mean midlatitude ozone (30–60∘ for both hemispheres) from SOCOL-AER simulations with the total ozone column from the combined record SBUV Merged Ozone Data Set version 8.6; and with the lower stratospheric (20–70 hPa) ozone mixing ratio from the merged satellite composite SWOOSH Stratospheric Water and Ozone Satellite Homogenized data set;. Anomalies are obtained by subtracting monthly means for 1991–1995.

Compared to SBUV, SOCOL-AER does show a decline in ozone column; however, it underestimates it in the Northern Hemisphere (NH) and overestimates it in the Southern Hemisphere (SH). REF12, COAG, and UPWIND generally fit into the ensemble spread of REF. REF also shows an ozone increase in 1991 in the SH discussed by and , but in late 1991 a similar increase is shown by the model in the NH, which is not seen in SBUV data. The noRAD and noQBO results show that parts of these ozone increases in the SH and NH are due to heating by aerosols in the tropics and due to QBO, respectively, and both of these peaks disappear in the noRADnoQBO experiment. This hints that SOCOL-AER dynamics do not adequately respond to perturbations in the tropics given that QBO is prescribed and post-eruption warming is well captured, at least by the REF12 experiment (Fig. ). In order to check this, we performed another experiment with the dynamics nudged to ERA-Interim reanalysis data with the rest of the settings kept as in REF. We used the same nudging procedure as described in . The nudged experiment also shows some differences compared to SBUV, but in general reproduces its behavior much better, thus suggesting some problems in the model's dynamics and good performance of the model's chemistry and aerosol microphysics. Comparison of SOCOL-AER ozone with the SWOOSH composite of stratospheric satellite measurements leads to the same conclusions for the lower stratosphere.