The SAGE III/ISS instrument is the latest successor of the previous SAM II (Stratospheric Aerosol Measurement), SAGE I, SAGE II and SAGE III Meteor-3M satellite experiments and aims at the investigation of the stratosphere and upper troposphere. Its mission started in June 2017 with its measurements still ongoing at the time of writing. On board the ISS, which has an orbital inclination of 51.6∘ and orbits Earth in about 92 min, the instrument performs lunar and solar occultation measurements. Only the latter are used in this work. Due to the platform's orbit SAGE III/ISS observes roughly 15 sunrise and 15 sunset events in 24 h. Sunrise and sunset measurements are taken at different latitudes, and these latitudes oscillate roughly between 70∘ N and 70∘ S with a period of around 2 months .

Through the measurement of the solar radiation attenuated by atmospheric constituents the SAGE III/ISS data set provides information on gases like ozone and water vapor as well as on aerosol. Aerosol extinction coefficients are provided at nine spectral channels between 384 and 1544 nm on a 0.5 km grid from Earth's surface up to 45 km altitude. The spectral resolution of the first eight channels between 384 and 1020 nm, which are all covered by a CCD array, is 1–2 nm. The 1544 nm channel is detected by an indium gallium arsenide (InGaAs) infrared photodiode and has a bandwidth of about 30 nm. In this work, version 5.21 of the SAGE III/ISS level 2 data is used .

Advantages of using aerosol extinction data from the SAGE III/ISS satellite solar occultation measurements are firstly that there is no need to make assumptions on the particle size distribution (PSD) to retrieve the extinction coefficients in the first place. Secondly, the Sun provides a strong signal, benefitting the signal-to-noise ratio of the data product. Data are provided with a high vertical resolution. Additionally, since the measurements of every sunset or sunrise event are calibrated with corresponding direct solar irradiance measurements between 100 and 300 km, the data set is relatively unaffected by changes in the instrument over time. On the other hand the spatial and temporal coverage is low compared to, e.g., satellite limb measurements. This is because in a single day only around 30 profiles are obtained and only a narrow latitude range is covered. Still, compared to ground-based measurements, an almost global coverage is possible within 1–2 months. Therefore, an analysis of the spatial and temporal evolution of quantities derived from the SAGE III/ISS measurements is feasible (see Sects.  and ) .

The method that was used for the retrieval of the stratospheric aerosol particle size from the SAGE III/ISS data set has been described in detail in . Therefore, the size distribution parameter retrieval method employed will only be described briefly here.

A monomodal log-normal shape of the size distribution for stratospheric aerosol is assumed, which is expressed mathematically as follows: 1n(r)=dN(r)dr=N02π⋅r⋅ln⁡σ⋅exp⁡-ln⁡2(r/rmed)2ln⁡2σ, with N0 being the total number density, rmed being the median radius and σ being the distribution width of the particle size distribution. These parameters needed to be retrieved.

The aerosol is assumed to be composed of a solution of 75 % H2SO4 and 25 % H2O. Furthermore, stratospheric aerosol is assumed to be spherical in shape; thus the Mie theory can be applied. The possible values of the parameters to be retrieved are assumed to lie between 1 and 1000 nm for the median radius and 1.05 and 2.0 for the distribution width.

Before their use in the retrieval process, the extinction coefficients provided in the SAGE III/ISS data set were smoothed over altitude using a 1–2–1 smoothing scheme, aligning the version 5.21 data set with that of version 5.1, where a similar smoothing of the data was inherent. Two extinction ratios using a total of three wavelengths (449 nm : 756 nm and 1544 nm : 756 nm) are used to retrieve the median radius and the distribution width σ. Using a Mie code these extinction ratios were calculated for all combinations of a median radius value between 1 and 1000 nm in 1 nm increments and a distribution width value between 1.05 and 2.0 in steps of 0.1. The real parts of the refractive indices at the wavelengths used were calculated from using Lorentz–Lorenz corrections. These corrections have been described by and were necessary to obtain refractive indices at typical lower-stratospheric temperatures. The results of the Mie calculations are then used as a lookup table, since a given combination of the median radius and σ can be related to a specific combination of the calculated extinction ratios at 449 nm : 756 nm and 1544 nm : 756 nm. Forming extinction ratios at the same wavelengths from the SAGE III/ISS extinction coefficient data set, both size distribution parameters can then be retrieved by means of interpolation using the lookup table. More details are provided in .

The effective radius which is used for the comparison to the model simulations in Sect.  is calculated from the median radius and distribution width with the following relation: 2reff=rmed⋅exp⁡52⋅ln⁡2(σ).

Also, an accuracy parameter a as defined by , which is calculated from the distance between the curves of the lookup table and the error bars of the extinction ratios calculated from the SAGE III/ISS extinction coefficients, is used to exclude noisy data in the retrieved quantities shown in this work.

The simulations of the Raikoke and Ulawun volcanic eruptions (see Sect. ) were performed using MAECHAM5-HAM. ECHAM5 , a general circulation model, was used in its middle atmosphere (MA) version, with a horizontal resolution of about 1.8∘. It has a spectral truncation at wavenumber 63 (T63), with 95 vertical layers up to 0.01 hPa (about 80 km). To achieve realistic wind and transport conditions, a nudging of the large wavenumbers of the model to ERA5 reanalysis data was performed .

The aerosol microphysical model HAM is interactively coupled to ECHAM. HAM includes the simulation of the oxidation of sulfur and sulfate aerosol formation, including nucleation, accumulation, condensation and coagulation processes. Above the tropopause, a simple stratospheric sulfur chemistry was considered using prescribed chemical species of OH, NO2 and O3. In the simulations, the sulfate aerosol is radiatively active for both shortwave and longwave radiation and coupled to the radiation scheme of ECHAM. The model setup and the setup of the distribution width is described in and , respectively. The parametrization of nucleation processes has been updated according to , which slightly increased particle nucleation in the model.

For the comparison of model to observations data in Sect.  the emitted SO2 masses of the 2019 Raikoke and Ulawun eruptions were estimated from TROPOMI (TROPOspheric Monitoring Instrument) measurements on board of the Sentinel-5 Precursor satellite. The data product used in this study assumes the SO2 profile as a 1 km thick box filled with SO2 and centered at 15 km altitude. We defined a grid with a latitude–longitude resolution of 0.1∘ × 0.1∘ from 30∘ N to 30∘ S and 110∘ E to 100∘ W. For the June and August 2019 eruptions of Ulawun, only SO2 total vertical column data with a solar zenith angle less than 70∘ and with values less than 1000 mol m-2 were used. The vertical columns were multiplied by the SO2 molar mass in order to obtain an SO2 mass loading in units of grams per square meter. Different thresholds of either 0 or 0.05 g m-2 were applied to distinguish the volcanic signal from the background. The data were averaged for each grid segment, and the SO2 mass in units of grams was determined for each segment. Since some orbits spatially overlap, 14 consecutive orbits were bundled into a batch that covered approximately 24 h and averaged for each grid segment of the batch. The SO2 mass in all grid segments of a batch were summed up to finally receive the total SO2 mass per batch. Depending on the threshold, estimates for the SO2 mass were 0.12–0.16 Tg for the June 2019 eruption and 0.18–0.2 Tg for the August eruption. The SO2 mass emitted by the Raikoke eruption in June 2019 was calculated using no threshold with no restriction on the solar zenith angle but with the requirement that the quality value needs to be larger than 0.5. This is described in more detail in and resulted in an SO2 mass estimate of 1.37 Tg.

In Fig. , the effects of the Ambae eruptions on the stratospheric aerosol layer can be seen.

In the first row of plots the closest to background conditions before the two main eruptive phases in April and July 2018 are shown, namely monthly averages for March. Nevertheless, the number density and the extinction coefficient are already enhanced. For the Northern Hemisphere this can be attributed primarily to the Canadian wildfires of 2017, which was the burning season with the largest area burned in British Columbia since beginning of the recording . However, there is also a signal in the Southern Hemisphere with enhanced number densities and extinction coefficients and low median radius values. This signal first showed up in the Southern Hemisphere in October 2017 (not shown). This is more of a mystery but could be a consequence of several smaller tropical volcanic eruptions in late 2017, which, to our knowledge, did not directly inject SO2 above the tropopause. These include the Tinakula (10.4∘ S) eruption on 21 October, whose ash and gas plume reached up to 10.7 km altitude ; the Agung (10.4∘ S) eruption on 21 November, with an ash plume reaching 9.1 km ; and Ambae's (15∘ S) first two, less explosive eruptive phases, which lasted from 22 September to 6 October 2017 and from 21 October to 7 December 2017 . Since these are all tropical volcanoes, it is conceivable that some of the sulfur precursor gases emitted could have been transported into the lower stratosphere across the tropical tropopause layer (TTL) .

The second row of plots in Fig.  depicts the month of June. Here, the effects of the third eruptive phase can be seen, which lasted from mid-March to mid-April 2018. This third eruptive phase was explosive enough to inject SO2 directly into the lower stratosphere, with the largest injection period occurring on 6 April. In the third row, which shows monthly means for September 2018, the impacts of the fourth and most active eruptive period of Ambae in July are visible. In July the largest amount of SO2 was emitted, with 0.35–0.4 Tg SO2 .

The extinction coefficient and the number density both show a distinct enhanced layer in the lowermost stratosphere above the tropopause that stands out from the much lower values at higher altitudes, where the signals of the Canadian wildfires and the unknown perturbation in the Southern Hemisphere in 2017 still relax more towards background conditions. This enhanced layer can be seen in June after the third eruptive phase, but it becomes much stronger after the July eruptions. As described before, both hemispheres are affected by the eruptions .

The most notable and surprising signal, though, is the strong decrease in the median radius and absolute distribution width in that same enhanced layer above the tropopause, mostly below 20 km altitude. This means that the particle size distribution (PSD) shifts towards smaller aerosol radii, while also becoming more narrow. Therefore the Ambae eruptions seem to have led to a domination of a large number of smaller aerosol droplets in the lowermost stratosphere. It is also remarkable that the PSD stays in this configuration of on average very small aerosol particles for many months, as in January the signal is still very clear, although already diminished. These findings will be discussed more in depth in Sect. . Over time, an interesting layering emerges in the tropics that is best visible in January 2019 (lowermost row), where a layer of larger values of the median radius and absolute distribution width resides at roughly 21 km altitude with very small average aerosol sizes above and below.

In Fig.  the PSD parameter evolution for the eruptions of Raikoke and Ulawun in the summer of 2019 are depicted. In the first row, an average over the time between 1 to 20 June is shown, i.e., before the Raikoke and Ulawun eruptions on 22 and 26 June, respectively. This is the closest to background conditions before this phase of volcanic activity. At this point, the effects of the Ambae eruptions in the year before have diminished strongly, although the extinction coefficient is still slightly enhanced throughout the main Junge layer.

In August, after the June eruptions of Raikoke and Ulawun and after the second Ulawun eruption on 3 August, an increase in the extinction coefficient over both the Northern and Southern Hemisphere occurred, as expected. The signal is much stronger in the Northern Hemisphere, since the Raikoke eruption emitted more SO2 (around 1.37 Tg) than both Ulawun eruptions together (around 0.44 Tg combined).

However, regarding the PSD parameters a unique pattern emerges, where Ulawun and Raikoke had opposite effects. Over the broad Raikoke area and in the lowermost stratosphere below roughly 15 km, the median radius, absolute distribution width and number density increase from June to August. In contrast, in the Southern Hemisphere values of the median radius and absolute distribution width show a strong decrease. This goes along with an especially strong increase in the number density in the Southern Hemisphere. This means that the Southern Hemisphere is dominated by a high number of very small aerosol particles below roughly 20 km, which notably stay small until the end of the year, similar to the effects of the Ambae eruptions in the previous year. The average aerosol size stays small at least until November 2019. In January 2020 the signal is covered by emissions stemming from the Australian wildfires of 2019–2020, which were unprecedented in the destruction caused and in the area affected by high-severity fire . The PSD parameters affected by these wildfires in the last row of plots are not reliable though, since the assumptions on the shape of the size distribution as well as on the refractive indices of the aerosol made in the retrieval of this work may not be realistic for these conditions.

Although the Raikoke eruption emitted around 15 Tg of ash , it was only detectable in the atmosphere for a few days and roughly 90 % of it was removed from the atmosphere within 48 h . Therefore, it is unlikely to play a big role in the retrieval data presented in Fig. . Nevertheless, the signals visible in the Northern Hemisphere may not be attributable to the Raikoke eruption alone, since there also have been two different severe wildfire events in the Northern Hemisphere in 2019 that were strong enough to reach the stratosphere . It is still not clear if and to what extent there was interaction between smoke and the sulfate aerosol plume originating from the Raikoke eruption. Therefore it cannot be excluded that smoke might have played a role in the aerosol size increase retrieved in the volcanic period displayed in the Northern Hemisphere.

In Fig. , the period of volcanic activity before and after the La Soufrière eruptions between 9–22 April 2021 is depicted.

The first explosive eruptions happened on 9 April throughout the day with the ash plume reaching up to 8 km. Explosive activity on 10 and 11 April led to ash plumes rising up to 16 km in altitude. In the following days more volcanic activity was observed, although plume heights did not exceed 12 km anymore . Based on TROPOMI measurements, La Soufrière emitted roughly 0.4 Tg of SO2.

The patterns in the PSD parameters as well as in the extinction coefficient that emerge are very similar to those observed for the period of the Ambae eruptions in 2018 (Fig. ). The aerosol cloud spreads over both hemispheres, visible in an increase in the number density and extinction coefficient in the lowermost stratosphere slowly affecting higher altitudes over time. Notably, there again is a strong decrease in median radii and absolute distribution widths after the La Soufrière eruptions in both hemispheres in the same altitude region. Both parameters stay very low due to the eruptions at least until January 2022. A slow rising of the enhanced aerosol layer in the tropics from around 20 km altitude in June 2021 up to around 23 km in November 2021 can be observed in all PSD parameters. On 15 January the Hunga Tonga–Hunga Ha'apai eruption happened, which was very unusual in many ways and introduced perturbations into the stratosphere which are not shown or discussed here .

In the simulations, SO2 masses that are vertically resolved in three altitude levels are injected into the lower stratosphere at the locations of the Raikoke and Ulawun volcano at the time of each of the eruptions. Consequently, the evolution of the particle size distribution of the forming sulfate aerosol is calculated. Multiple model runs were performed with varying input parameters. The relevant parameters used for the best model run, which is used in this work, are shown in Table . The SO2 mass injected into the stratosphere for the second eruption of Ulawun is taken from , and parameters for the other two eruptions come from our own SO2 mass estimation using the TROPOMI data set. Like in the SAGE III/ISS retrieval the stratospheric aerosol is assumed to be composed of sulfuric acid and water only. In order to start the Raikoke and Ulawun simulations with background conditions comparable to the observations, the simulation is started from a 10-year simulation on 1 January 2018. By doing that, the Ambae eruptions are included in the run. If the Ambae eruptions were not included, the simulated atmosphere would end up too “clean” in June 2019, before the Raikoke and Ulawun eruptions, and therefore not be comparable to observations.

In the model simulations ash is included, but there is no interaction with the sulfate aerosol; i.e., no mixed ash–sulfate aerosol is calculated. Regarding the aerosol particle size, ECHAM uses a modal model. Four log-normal distributions are considered, which are called, sorted from smaller to larger radii, the nucleation mode, Aitken mode, accumulation mode and coarse mode. Each of these modes has a fixed distribution width σ and a median radius that can change within certain value ranges. The number densities within the individual modes change as well, as a result of the calculated microphysical processes like the nucleation, condensation and coagulation rates.

Here, the extinction coefficient at 550 nm is compared between the observational SAGE III/ISS data and the ECHAM simulations. In the SAGE III/ISS solar occultation level 2 data set the extinction coefficient is not provided at 550 nm directly. To address this, a third-order polynomial was fitted to the extinction spectra using the six most reliable wavelength channels of the data set, i.e., 449, 521, 756, 869, 1021 and 1544 nm, to retrieve extinction coefficients at 550 nm that can then be used for comparison.

In Fig. , zonal averages of the extinction coefficient at 550 nm are depicted for the time before the volcanic eruptions (left column), i.e., between 1 and 20 June 2019, and for August of 2019 (right column). The panels in the upper row show the data that were calculated from the SAGE III/ISS measurements, while the panels in the lower row depict results from the ECHAM simulations. As explained in Sect. , the spatial and temporal sampling of SAGE III/ISS is limited. Therefore, to acquire actually comparable temporal and spatial coverage between the observational and model data set, we applied the sampling of the SAGE III/ISS measurements to the model output. In other words, only profiles from the ECHAM simulations for locations and times were included, where SAGE III/ISS measurements happened on the same day within 1∘ of longitude and 2.5∘ of latitude. As in Sect.  this means that data in different latitude bins correspond to different days within the month depicted. The tropopause height shown was provided in the SAGE III/ISS level 2 data set, taken from the MERRA-2 (Modern-Era Retrospective analysis for Research and Applications) reanalysis data. The blue line marks a 1 km interval above this calculated tropopause height, above which it is unlikely that the measurements are affected by clouds or include tropospheric air in general.

The background conditions in prevolcanic June 2019 are reproduced very well by the ECHAM simulations, both in magnitude of the values and in the spatial patterns emerging, aside from an enhanced extinction between 40∘ N and 60∘ N below 14 km in the SAGE III/ISS data. This perturbation may be smoke from the two larger wildfires that reached the lowermost stratosphere, which is not included in the model. For August 2019, in general the ECHAM simulations could reproduce the observations as well, although in the SAGE III/ISS data the perturbations of the extinction coefficient partly reach higher altitudes in the northern latitudes. Both the model and observations show a strong increase in the extinction, with a much stronger effect over the latitudes near Raikoke.

The effective radius is the area-weighted mean radius of the size distribution . It is a useful quantity since with it a particle size distribution can be expressed using only one parameter. Furthermore, it can be used to compare PSDs of different shapes. This is necessary in this case, since our SAGE III/ISS retrieval data set includes monomodal log-normal size distribution, while in the ECHAM model output, the PSD is expressed in terms of four individual log-normal modes. The effective radius reff from the ECHAM simulations, representing these four modes, is calculated in the following way: 4reff=∫r3n(r)dr∫r2n(r)dr=m3m2, where m3 is the third moment and m2 is the second moment of the particle size distribution.

The effective radii retrieved from the SAGE III/ISS observations in Fig. a and b show an increase over the Raikoke area from June to August 2019 in the lowermost stratosphere roughly between 40 and 60∘ N. Most notably, there is a large reduction in the effective-radius values over the Ulawun area (around 5∘ N to 35∘ S) over the same time span, analogous to the reduction in the median radius and absolute distribution width that was discussed before in Sect. . This reduction in average particle size persists at least until November 2019 (see Appendix). In Fig. c, the effective-radius temporal anomaly, i.e., the difference between Fig. b and a, is depicted, which makes it clear where the effective radius increased and where it decreased from June to August. Over the Raikoke area an increase in the effective radius by up to 87 nm is found, and in the tropics and southern subtropics there is a decrease by up to 123 nm. It has to be noted that part of the Raikoke plume has been missed because of the limited spatial coverage of the SAGE III/ISS measurements, since a substantial part of the plume was transported further north than 60∘ N .

The lower row of panels in Fig.  is analogous to the upper row but shows the ECHAM simulations for the same time frames. For the background conditions (Fig. d) effective radii in the lowermost kilometer above the tropopause are much lower than in the SAGE III/ISS retrieval data. Apart from this effective radii are close to the observations. In August, the qualitative pattern of high values in the lowermost stratosphere over Raikoke and low values over the broad Ulawun region is reproduced by the model. Also in Fig. f, which again shows the temporal anomaly, the absolute increases and decreases in the regions affected by the volcanic eruptions mostly match the observations well. The effective-radius increase over the Raikoke area in the lowermost stratosphere is stronger in the model, which is because of the low effective radii in this region in the model's background. The smaller effective radii in Fig. e and the region of decrease in Fig. f reach further into the Northern Hemisphere than in the observations.

Starting in September 2019, the model and observations start to diverge: effective radii stay very low over the tropics and southern subtropics in the SAGE III/ISS retrieval data until December of 2019, before the Australian wildfires cover the signal in January 2020. In contrast, the model calculates strong particle growth in the months after August, with effective radii increasing far beyond the background at higher altitudes. This suggests that the MAECHAM5-HAM model can be used to learn about the stratospheric aerosol evolution and its underlying mechanisms in the short term after volcanic eruptions. In the longer term, however, the comparison reveals differences which may point towards the microphysical evolution in the model. Identifying the cause of this discrepancy between the model and observations is difficult. Possible causes could in principal be an overestimation of coagulation by the model, a lack of interactive OH chemistry in the model, deviations in dynamics e.g., due to smaller vertical advection in ECHAM compared to other models;, or biases in the observational data set or the retrieval algorithm. To investigate this, comparisons with different models need to be conducted.