Changes in stratospheric aerosol extinction coefficient after the 2018 Ambae eruption as seen by OMPS-LP and ECHAM5-HAM

Stratospheric aerosols are an important component of the climate system. They not only change the radiative budget of the Earth but also play an essential role in ozone depletion. Most noticeable those effects are after volcanic eruptions when SO2 injected with the eruption reaches the stratosphere, oxidizes and forms stratospheric aerosol. There have been several studies, where a volcanic eruption plume and the associated radiative forcing were analyzed using climate models. Besides, volcanic eruptions were studied using the data from satellite measurements; however, studies combining both models and 5 measurement data are rare. In this paper, we compared changes in the stratospheric aerosol loading after the 2018 Ambae eruption observed by satellite remote sensing measurements and by a global aerosol model. We use vertical profiles of aerosol extinction coefficient at 869 nm retrieved at IUP Bremen from OMPS-LP (Ozone Mapping and Profiling Suite Limb Profiler) observations. Here, we present the retrieval algorithm as well as a comparison of the obtained profiles with those from SAGE III/ISS (Stratospheric Aerosol and Gas Experiment III onboard International Space Station). The observed differences 10 are within 25% for the most latitude bins, which indicates a reasonable quality of the retrieved limb aerosol extinction product. The volcanic plume evolution is investigated using both: monthly mean aerosol extinction coefficients and 10-day averaged data. The measurement results were compared with the model output from ECHAM5-HAM. In order to simulate the eruption accurately, we use SO2 injections estimates from OMPS and OMI for the first phase of eruption and TROPOMI for the second phase. Generally, the agreement between the vertical and geographical distribution of the aerosol extinction coefficient from 15 OMPS-LP and ECHAM is quite remarkable, in particular, for the second phase. We attribute the good consistency between the model and the measurements to the precise estimation of injected SO2 mass and height as well as through nudging to ECMWF reanalysis data. Additionally, we compared the radiative forcing (RF) caused by the increase of the aerosol loading in the stratosphere after the eruption. After accounting for the uncertainties from different RF calculation methods, the RFs from ECHAM and OMPS-LP agree quite well. We estimate the tropical (20° N to 20° S) RF from the second Ambae eruption to be 20 about -0.13 W/m. 1 https://doi.org/10.5194/acp-2020-749 Preprint. Discussion started: 5 August 2020 c © Author(s) 2020. CC BY 4.0 License.

2008) being on-orbit, nowadays there is a very limited number of space-borne missions, which can be used to retrieve stratospheric aerosol information. At the time of writing, only the Optical Spectrograph and InfraRed Imager System (OSIRIS) (Llewellyn et al., 2004), the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) (Vernier et al.,  (Seftor et al., 2014). To retrieve information on stratospheric aerosols, only measurements from LP can be used.
OMPS-LP registers solar radiance scattered by the atmosphere. Unlike SCIAMACHY and OSIRIS, OMPS-LP does not use a diffraction grating; instead, a prism disperses the light on a two-dimensional CCD (charge-coupled device) detector, which registers the radiance simultaneously from all altitudes from 290 to 1000 nm with the spectral resolution from 1 nm to 30 nm 100 depending on the wavelength (Jaross et al., 2014). The LP has three vertical slits; however, we use only the measurements from the central slit because of remaining pointing and stray-light issues on the side ones. Each slit registers vertically 105 pixels with a 1.5 km instantaneous field of view of each detector pixel. The radiances are registered with a vertical sampling of 1 km at the tangent point. The lowest and the highest registered altitudes vary depending on the latitude and season; nevertheless, the altitude span from 5 to 80 km is constantly covered (Jaross et al., 2014). 105 As it can be inferred from its name, initially, OMPS was designed to obtain ozone products, and in the instrument design, the UV-Vis parts of the spectrum were prioritized. As the prism dispersion is non-linear, the spectral resolution of the measurements at the wavelength longer than 500 nm degrades exponentially, reaching about 30 nm at 1000 nm. This results in the situation that the usual stratospheric aerosol extinction wavelength 750 nm, used by, e.g., SCIAMACHY and OSIRIS  is not suitable for use as OMPS-LP measurements around this wavelength are affected by the O 2 -A absorption band. 110 Thus, for the stratospheric aerosol extinction retrieval, instead of 750 nm, we use the measurements at 869 nm (with a spectral resolution of 22 nm), because the spectral interval from 830 to 900 nm is absorption free.
Even though some aspects of our algorithm have been briefly described in Arosio et al. (2018) and Malinina (2019), here, we provide a consolidated summary. The OMPS V1.0.9 Ext 869 retrieval algorithm was adapted from the SCIAMACHY V1.4 algorithm  and uses the same regularized iterative approach. However, here, we use the first-order Tikhonov 115 regularization with the parameter value of 50 to smooth spurious oscillations in the level 1 V2.5 data. Based on the information provided by NASA, the signal-to-noise ratio (SNR) is set to 500 for all the tangent altitudes.
In V1.0.9, Ext 869 is retrieved on a 1 km grid from 10.5 to 33.5 km, with the measurement at 34.5 km being used as the reference. Additionally, the effective Lambertian albedo is simultaneously retrieved using the sun-normalized spectrum at 34.5 km.
The retrieval is done under the assumption of stratospheric aerosols being spherical sulfate droplets (75% H 2 SO 4 and 25% 120 H 2 O) with 0% relative humidity and unimodal lognormal particle size distribution. In this distribution the median radius (r med ) is equal to 0.08 µm and σ=1.6; the particle number density a priori profile is chosen in accordance with Extinction Coefficient retrieval, the Ext 869 values higher than 0.1 km −1 are considered to be cloud contaminated and thus are filtered. Here we want to highlight, that we increased our threshold extinction value for the identification of cloud contamination (Malinina, 2019), because the previous threshold was filtering some profiles with increased aerosol loading.

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Stratospheric Aerosol and Gas Experiment (SAGE) III on the International Space Station (ISS) started operating in early 2017 as a continuation of the SAM-SAGE data record. SAGE-III/ISS provides solar and lunar occultation, as well as limb-scatter measurements (Cisewski et al., 2014); however, for now, for stratospheric aerosol extinction coefficient retrievals, only solar occultation measurements are used. The principle of solar occultation is to measure solar irradiance attenuated by the Earth's atmosphere between the Sun and the instrument during each sunrise and sunset. The solar occultation measurements are self-135 calibrating, and unlike limb instruments, for the Ext retrieval, no assumptions on the aerosol particle size distribution are needed, thus, making occultation measurements rather precise. SAGE-III/ISS provides continuous measurements from 280 to 1040 nm with spectral resolution from 1 to 2 nm depending on the wavelength, which are registered on a 808×10 pixel CCD. Additionally, there is an infrared photodiode centered at 1550 nm (McCormick et al., 2019, and references therein). According to Cisewski et al. (2014), the aerosol extinction coefficients 140 provided by NASA have 0.75 km vertical resolution. In the official NASA product, aerosol extinctions are provided in 0.5 km steps from 0 to 45 km. Due to the ISS orbit, the measurements are performed from 70°N to 70°S. It should be noted here that occultation measurements are very sparse in comparison to limb measurements. This is because for one orbit a solar occultation instrument can register one sunrise and one sunset, while a limb instrument does not have these limitations. For example, OMPS-LP provides 180 measurements per orbit, which drastically increases geographical sampling.

Comparison
The OMPS-LP Ext 869 was originally retrieved to improve the ozone product (Arosio et al., 2018); however, it can also be used to evaluate the changes in stratospheric aerosol loading after volcanic eruptions and biomass burning events (Malinina, 2019). Here, it should be noted that there are three other OMPS aerosol extinction products. Two of them are the official NASA Ext 675 products V1.0 (Loughman et al., 2018) and V1.5 (Chen et al., 2018). Moreover, at the University of Saskatchewan, as 150 a part of the ozone retrieval, a tomographic Ext 750 product was obtained (Bourassa et al., 2019). All four Ext products were retrieved at different wavelengths and using different approaches. Thus, their inter-comparison will be challenging and will contain uncertainties, e.g., associated with Ångtröm exponent calculations.
In order to evaluate the quality of our Ext 869 , it was compared with the SAGE III/ISS solar occultation product. There are several advantages to this comparison. Firstly, SAGE III is an independent data set; thus, the OMPS instrumental uncertainties 155 (e.g. scattering angle dependency) will not influence the comparison, as it would be with be the case for the other OMPS products. Secondly, SAGE III is an occultation instrument, which means that its Ext profiles are rather precise and independent of the aerosol PSD assumption, as, e.g., OSIRIS.
Another advantage of the comparison with SAGE III is the same measurement wavelength. Both, OMPS-LP and SAGE III provide measurements at 869 nm, so aerosol extinction does not need to be recalculated assuming an Ångström exponent. Even 160 though the spectral resolution of the instruments at this wavelength is different (1.5 nm in SAGE III versus 30 nm in OMPS-LP), it does not influence the aerosol extinction coefficient strongly because the wavelength interval from 830 to 900 nm is absorption free.
For the comparison, individual profiles from the 07 June 2017 until the 31 August 2019 were used. The profiles were collocated using the following criteria, the difference between the profile's coordinates should be less than 2.5°in latitude, 165 10°in longitude and 24 hours in time. Overall, there are 19264 collocated measurements used for this comparison. For SAGE III data, the same as for OMPS, the aerosol extinction values higher than 0.1 km −1 were filtered out. Additionally, the SAGE III Ext 869 values were excluded, if the uncertainty provided by NASA is higher than 50%. We did not filter negative Ext 869 because this would bias the comparison.
The mean relative differences between OMPS and SAGE III Ext 869 are presented in Fig. 1 in 20°latitude bins. For most of 170 the altitudes in all latitude bins, the relative difference is within 25%. In the tropical and mid-latitudes, the only exceptions are the altitudes below 18 km, where despite filtering, the influence of clouds is still present. The largest differences are observed in high latitudes (40°to 80°in both hemispheres), in particular, at the altitudes above 24 km. For example, at about 28 km altitude, the differences reach up to 60% in these latitude bins.
Generally, the above-described differences are similar to the relative differences between SCIAMACHY V1.4, OSIRIS v5.07 and SAGE II v7 Malinina, 2019). Additionally, Chen et al. (2019) showed that the differences seen between OMPS Ext 675 V1.5 and SAGE III product have the same shape and order of magnitude. Rieger et al. (2018) studied precisely the reasons for the seen differences. Since the OMPS V1.0.9 algorithm is very similar to the SCIAMACHY V1.4 algorithm used in that study, and since the OMPS and SCIAMACHY have very similar geometries, the same explanations as Rieger et al. (2018) are appropriate. Thus, the most important sources of errors in limb retrievals arise from the uncertainly 180 assumed aerosol loading at the reference tangent altitude as well as the unknown aerosol particle size distribution parameters.
The latter factor mostly affects the high latitudes where the viewing geometries are close to forward and backward scattering.
Based on our comparison and the results from the other limb-occultation instrument studies, it can be concluded that our OMPS V1.0.9 Ext 869 is of sufficient quality to be used for scientific purposes. The shaded areas show ± 1 standard deviation.

OMPS-LP aerosol extinction climatology 185
In order to study the aerosol extinction coefficient evolution after a volcanic eruption, the OMPS V1.0.9 product has to be averaged in some fashion. We have created two level 3 products, which are monthly and 10-day averaged Ext 869 . Both products were put onto a regular grid with 2.5°latitude and 5°longitude steps.
An example of zonal monthly mean Ext 869 averaged in 30°latitude bins for the whole OMPS operation period is presented in Fig. 2. In this figure, the volcanic eruptions and a relevant biomass burning event are shown with grey triangles with numbers.

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The information on the volcanic eruptions is presented in Tab. 1. We show only Ext 869 within 60°in both hemispheres because, as it was pointed out in Sec. 3, the aerosol extinctions above these latitudes are associated with larger uncertainties.  Furthermore, the main scope of this paper is to study the tropical Ambae eruptions; thus, we do not focus our attention on aerosol loading in the high latitudes.
Analysis of Fig. 2 shows that there is a certain increase of Ext 869 in the very beginning of OMPS operation in the Northern

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Hemisphere latitude bins. This is associated with the eruption of Nabro (13°N) in the middle of 2011. Additionally, one can see an increase of Ext 869 some time after eruptions from Table 1 and from Canadian Wildfires of 2017 (number 5 in Fig. 2 and Table 1). The degree of the enhancement, as well as the time lag between the eruptions, seen in the latitude bands, are  2015); Malinina et al. (2018). Additionally, the annual seasonality in both tropics and mid-latitudes is related to two factors. First, there are some yearly changes in stratospheric aerosol loading (Hitchman et al., 1994;Bingen et al., 2004). But for the limb viewing instruments, the more important factor is the seasonality in solar scattering angle, which leads to artifacts 210 of the retrieval predominately in the extratropical regions (see e.g. Rieger et al., 2018).

Aerosol extinction coefficient evolution after Ambae eruption as seen by OMPS-LP
As it was already highlighted in the introduction, Ambae was one of the largest eruptions of the last decade but has not been a focus of scientific or public interest. The eruptive period, which lasted over a year, had two explosive phases when SO 2 was injected into the stratosphere (the exact information on SO 2 mass estimation can be found in Sec. 6.1). The first emission was 215 smaller, and the perturbation in Ext 869 did not reach the altitudes above 21 km (see Fig. 2 (a) and (b)). The second emission was considerably larger; it perturbed Ext 869 up to 23.5 km in the tropics and up to 22 km in the extratropical regions. Although, to better evaluate the plume evolution, we will further analyze 10-day averaged Ext 869 .
The evolution with time and altitude of 10-day mean Ext 869 averaged over longitudes at 18.5 and 20.5 km is presented in panels (a) and (b) of Fig. 3. Foremost, it should be noted that the increase of Ext 869 in February -May 2018 in the latitudes 220 above 25°N at 18.5 km and above 7°N at 20.5 km is related to the disappearing plume from the Canadian Wildfires of 2017.
The first small increase in Ext 869 associated with the April Ambae eruption appears at 18.5 km in the first week after the injection. The more significant increase is observed in early May 2018. At the time, the plume is located around 10-25°S and stays there until late June. In June, the increase in Ext 869 starts to spread to the south, reaching 35-45°S in July 2018.
At 20.5 km, the increase after the first SO 2 release is rather negligible. Nevertheless, there is still an area with the increased 225 aerosol loading below 20°S from the beginning of May.
In late July 2018, at the fourth phase of the eruption, Ambae injected another portion of ash and SO 2 . Almost at the same time, Ext 869 increases at 18.5 km directly at the source. In about two weeks, the volcanic plume starts to spread both northwards and southwards and is located between the equator and 35°S in early September, reaching 45°N in November -December 2018. The southern border of the plume at 18 km is harder to identify because it mixes with the aerosol from the 230 previous SO 2 release. However, an increased aerosol loading is observed to the south of 35°S in September and intensifies At 20.5 km, the plume appears in mid-September 2018 at around 10°S, spreads northwards and southwards from that moment on, reaching its maximum in November. It is located in between 30°S and 35°N in mid December 2018. Again, at the southern border of the plume, there is an area of increased Ext 869 , which is related to both eruptions.

Estimation of SO 2 injection
In order to simulate the Ambae eruptions, as a first step the amount of SO 2 emissions and injection altitude should be determined. Although there are methods to retrieve SO 2 mass and altitude from nadir measurements, it is well known these methods do not allow to distinguish, if SO 2 was released into the stratosphere or into the upper troposphere (see e.g. Carboni et al., To assess the Ambae SO 2 burden and plume location, combined OMI (Ozone Monitoring Instrument) (Fioletov et al., 2011) and OMPS-NM (Carn et al., 2015) data were used for the April eruption. Yet for the July eruption, data from TROPOMI 245 (TROPOspheric Monitoring Instrument) was taken into consideration. We do not use the same SO 2 satellite product for both eruptive episodes because of two reasons. First, the TROPOMI data with a fine grid and extensive coverage is publicly available from the early May 2018, thus missing the first eruption. Second, even though the combined OMI and OMPS-NM dataset temporally covers both eruption phases, it contains spatial gaps, which results in less precise SO 2 mass assessment. Thus, the current choice provides a trade-off between the spatial coverage and overall data availability.

Combined OMI and OMPS-NM dataset
For the first eruption, OMI SO 2 level 2 data with the assumption of an SO 2 distribution in the lower stratosphere (center of mass altitude of 18 km ) was used. Due to the OMI row anomaly, all rows > 21 (counting starts at 0) were excluded. The first ten rows were discarded in order to limit the across-track pixel width (Lu et al., 2013), so that only rows 10-21 were considered. Furthermore, the radiative cloud fractions less than 0.2 and a solar zenith angle less than 70°were 260 required. SO 2 total columns with large negative values below -1E30 DU were not included in the analysis. A threshold of 0.05 g/m 2 was introduced to distinguish the volcanic signal from the background. All satellite pixels that fulfilled the above requirements were averaged for each segment of the self-defined grid (see below). The SO 2 data was converted into units of g/m 2 and multiplied with the segment area to obtain the SO 2 mass in units of g for every grid segment. All orbits measured on one day were combined so that the SO 2 mass in each segment for a specific day was determined.

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OMPS-NM level 2 SO 2 data with the SO 2 column for the lower stratosphere (16 km) was used accordingly. Pixels at the edges of the swath were discarded, excluding rows < 2 and rows > 33 (counting starts at 0) (Fioletov et al., 2020;Zhang et al., 2017). Only data with a pixel quality flag equal to 0 and a solar zenith angle less than 84°were used. Again, a threshold of 0.05 g/m 2 was applied, and the SO 2 mass per day for each grid segment was determined as described above for the OMI data.
The daily OMI and OMPS data were projected on a self-defined grid from 10°N to 45°S and from 150°E to 140°W with 270 a resolution of 0.5°and averaged for each segment. The data was summed up over the entire grid to determine the total SO 2 mass for each day in this area. The results for the period from the beginning of March until the end of April 2018 are presented in the panel (a) of Fig. 4. The estimate for the day when SO 2 reached the stratosphere is marked with a red circle. Due to the large data gaps, this SO 2 mass is a minimum estimate for the SO 2 ejected during the eruption.
Before the 0.05 g/m 2 threshold was applied, the combined satellite measurements covered approximately 40-70% of the 275 self-defined grid.
The largest source of error for estimating the SO 2 emission is probably the choice of the assumed SO 2 profile because the vertical distribution of the SO 2 affects the air mass factor used for the retrieval of the vertical column densities.

TROPOMI dataset
The SO 2 mass emitted during the eruption of Ambae in late July of 2018 was estimated by analyzing SO 2 total vertical 280 columns from the TROPOMI instrument (Veefkind et al., 2012) on the Copernicus Sentinel-5 Precursor satellite for the time period from the 1 July 2018 to the 29 September 2018. This instrument allows for global daily coverage of SO 2 with a spatial resolution of 3.5 × 7 km.
A grid with a resolution of 0.1°in longitude and latitude, respectively, was defined from 10°N to 45°S and 150°E to 140°W.
The utilized sulfur dioxide total vertical columns assuming an SO 2 profile represented by 1 km thick box filled with SO 2 and 285 centered at 15 km altitude, in order to model conditions in an explosive eruption (Theys et al., 2017). Only vertical column densities with values less than 1000 mol/m 2 and a quality value greater than 0.5 were considered for the analysis (Pedergnana et al., 2018). The total vertical column was multiplied by the SO 2 molar mass to get the SO 2 mass loading in the units of g/m 2 .
Afterwards, a threshold of 0.05 g/m 2 was applied. The SO 2 mass loadings exceeding the selected threshold were averaged in each grid segment, and the result multiplied by the segment area in order to obtain the SO 2 mass in units of g for every The application of a threshold of 0 g/m 2 seems to suggest an SO 2 background of approximately 0.2 Tg that is not apparent in 300 Fig. 4, using a more restrictive threshold. Focusing only on the additional SO 2 entry, i.e. the difference between the maximum SO 2 and the background emission of 0.2 Tg, a total burden of approximately 0.4 Tg SO 2 was emitted applying a threshold of 0 g/m 2 . This result is comparable to the maximal SO 2 burden in Fig. 4.
Furthermore, the calculated maximum of emitted SO 2 mass strongly depends on the SO 2 data product used. As mentioned in Sec. 6.1.1, the vertical SO 2 distribution affects the air mass factor that is used to retrieve the vertical column densities.

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Assuming a threshold of 0.05 g/m 2 2 and an SO 2 profile with the SO 2 existing in a 1 km thick box at an altitude of 15 km, as discussed above, results in the maximal SO 2 mass of 0.36 Tg. This value increases to 0.57 Tg and even to approximately 1.6 Tg by assuming a 7 km profile and a profile from the TM5 model, respectively, emphasizing the importance of a reasonable assumption for the vertical SO 2 distribution.

Model experiment 310
The volcanic eruptions were modeled by MAECHAM5-HAM. ECHAM is a general circulation model (GCM) which was used in the middle atmosphere version of the GCM ECHAM5 (Giorgetta et al., 2006). The horizontal resolution was about 1.8 • , spectral truncation at wave-number 63 (T63) with 95 vertical layers up to 0.01 hPa. The large wave numbers of the model were nudged to ERA5 reanalysis data (Hersbach et al., 2018) to achieve realistic wind and transport conditions.
Interactively coupled to ECHAM is the aerosol microphysical model HAM (Stier et al., 2005), which calculates the oxidation 315 of sulfur and sulfate aerosol formation, including nucleation, accumulation, condensation and coagulation processes. A simple stratospheric sulfur chemistry is applied above the tropopause (Timmreck, 2001;Hommel et al., 2011). The sulfate is radiatively active for both SW and LW radiation and coupled to the radiation scheme of ECHAM. These simulations use the model setup described in Niemeier et al. (2009) and Niemeier and Timmreck (2015). Hereafter we refer to MECHAM5-HAM as ECHAM.
The experiment setup used the estimated SO 2 emissions from Sec. 6.1. We injected 0.12 Tg SO 2 at altitudes of 82 to 102 hPa 320 on the 6 April for four hours and 0.36 Tg SO 2 at altitudes between 74 and 90 hPa on the 27 July for 24 hours, starting at 18h UTC. The long eruption phase was chosen to take the observed series of eruptions into account. To slow down the oxidation of SO 2 due to the limited availability of OH in a volcanic cloud , the concentration of OH was limited in the first days after the eruption: Day 1 to 10 to 40% and day 10 to 20 to 60% of the prescribed OH. The sea surface temperature (SST) is set to a climatological value (Hurrell et al., 2008).

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In order to be consistent with OMPS-LP measurements, the output of ECHAM was interpolated to the same altitudinal grid as provided by OMPS-LP. ECHAM provides Ext at 550 and 825 nm, thus, for the comparison consistency, the simulated Ext was recalculated to 869 nm and afterwards the 10-day averages were calculated.

Aerosol extinction coefficient evolution after Ambae eruption as modelled by ECHAM
The simulated distribution of Ext 869 with time and latitude at 18.5 and 20.5 km is presented in panels (c) and (d) of Fig. 3.

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In these panels, it is seen that at 18.5 km the aerosol extinction coefficient starts to increase almost right after the first eruption and reaches its peak in May. The main part of the volcanic aerosol stays in the tropics between 30°S and the equator. A small amount of aerosol is dispersed meridionally right after the eruption. After the second eruption, at the end of July, the 13 https://doi.org/10.5194/acp-2020-749 Preprint. Discussion started: 5 August 2020 c Author(s) 2020. CC BY 4.0 License.
first aerosol is formed right after the eruption with Ext increasing slowly until it reaches the maximum in September. Most aerosol is located to the south of 10°N. In the last days of September, the plume is still very well pronounced and it starts to 335 spread meridionally, mostly southwards. By beginning of October Ext increases also in the Northern Hemisphere at 20°N, this increase spreads with the time to 40°in the late December. The plume starts to weaken in the beginning of November.
At 20.5 km the plume from the first eruption appears in late June. The plume at this altitude is quite weak and does not extend much over the latitudes. Basically, it is a small blob in between the equator and 10°S. The increase in Ext associated with the second eruption appears at 20.5 km in very late August, by the middle of September the plume intensifies and starts to 340 expand meridionally. It reaches its maximum by November, when the increase is seen from 10°N to 40°S. From that moment, the plume starts to slowly disappear. In late December, the Ext increase is seen from 30°N to 45°S. The Ambae plume from the July eruption looks even more similar in the model results and measurements. Not only the 350 plume appears at the same time at 18.5 km and is located at the same latitudes, but also both model and measurements show a wave-shape of the plume. The curvature in both plumes appears in mid September, however, in the OMPS-LP data, the plume is bending stronger to the north. It should also be noted that the ECHAM simulations show a more intensive and longer living plume at this altitude. Additionally, in the OMPS-LP data, in the second part of October, the aerosols move evenly northand southward, while in the ECHAM data, the plume is transported rather to the south. In ECHAM data at 20.5 km, the July 355 plume appears about two-three weeks earlier than in the OMPS measurements. Though the intensity of the modeled plume at this altitude is slightly weaker, the absolute differences are smaller than at 18.5 km. However, the horizontal distribution of the modeled plume is less consistent with the measurements. While the plume in ECHAM stays with the time at the same geographical location mostly in the Southern hemisphere, in the OMPS data, it has a C-shape around the equator.
It should be highlighted that even though there are some differences between the modeled and measured Ext, the consistency 360 is quite remarkable. There are two main factors which contributed to this particular agreement between OMPS and ECHAM, namely, rather precise SO 2 mass and height estimation as well as nudging of meteorological data. Thus, it is seen that the second plume, whose emission was estimated from TROPOMI data, was modeled more accurately. At the same time, our internal studies showed that the ECHAM SO 2 sensitivity plays a key role in the lifetime and distribution of the plume.
It is a well-known feature of ECHAM that the meridional transport is too strong, causing a relatively short lifetime of sulfate 365 (e.g. Niemeier et al., 2009), especially compared to results of other models (e.g. Marshall et al., 2018). Therefore, the nudging of the meteorological data provided a realistic transport pattern resulting in good agreement with OMPS-LP measurements.
However, the nudging database, the ERA5 reanalysis, is a model product as well. Thus, small differences to observations are rather possible, especially in the stratosphere. Additionally, the stratospheric aerosol layer is close to the ozone layer at 24 km.
ECHAM uses prescribed ozone and OH values, which do not change due to the presence of volcanic aerosol.

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Another way to assess the degree of consistency between the model and the measurements is to analyze the vertical distribution of Ext with the time (see Fig. 5). Since most of the plume stayed in the tropical region, for Fig. 5 the OMPS (panel (a)) and ECHAM (panel (b)) Ext were averaged between 20°S and 10°N. In this figure, it is again obvious that in the model the perturbation from the volcano reached the same altitudes. Additionally, it is seen that the plume was weaker for the April eruption. However, consistency for the second eruption is again striking. Not only the plume has the same overall shape, but 375 it is located at the same time coordinates, with the only exception of a slightly increased blob in the OMPS data at 19.5 km in November. Thus, vertical transport is slightly weaker in ECHAM, which explains some of the differences to the OMPS data in the horizontal cross-section at 20.5 km.
Here it should be highlighted again that the vertical lofting of the volcanic cloud is related to the BDC with an upward branch in the tropics. The patterns in Fig. 5 are a prime example of the stratospheric tape-recorder effect, noticed earlier. For 380 the model experiment, one should bear in mind that the absorption of terrestrial radiation by stratospheric aerosols causes an additional vertical updraft which enhances the BDC effect in the tropics (Niemeier et al., 2011).

Radiative forcing
In order to assess the RF from Ambae eruption, we analyzed the ECHAM RF output as well as the RF calculated from OMPS-LP measurements. For the latter, we use the empirical approximation given by Eq.
(1) as suggested by Hansen et al. (2005): where τ 550 is the stratospheric aerosol optical depth at 550 nm. Although originally proposed for the globally averaged model data, Eq. (1) was used for the RF assessment from the measurement results as well (see e.g. Solomon et al., 2011;von Savigny et al., 2015). As the focus of our study is on the additional RF after the tropical Ambae eruptions, we do not consider global 390 averages but limit the comparison to 20°S -20°N region.
To apply Eq.
(1) to the OMPS-LP data, we determined τ 550(869) by integrating the Ext 869 from instantaneous tropopause height to 33.5 km and then converted the result to 550 nm wavelength by using an Ångström exponent of 2.47, which is appropriate for the particle size distribution used in the Ext 869 retrieval (see Sec. 2). The tropopause height values were obtained for each single OMPS-LP measurement by using corresponding ECMWF-ERA5 temperature profiles. The WMO 395 definition of the tropopause based on the temperature lapse rate was implemented (WMO, 1957). Afterwards the τ 550 (869) values were averaged over 10-days period. For consistency, we also applied Eq. (1) to the ECHAM τ . Additionally, from all datasets mean tropical τ in the period from 01 April to 19 July 2018 was subtracted to remove the effects of background aerosol. Even though the chosen period contains the effects of the first weaker Ambae eruption, it is a common "cleaner" period available for all datasets and thus is considered to be optimal for the study.

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The normalized RFs are presented in Fig. 6. Here, the tropical all-sky RF, calculated as an anomaly to a control simulation In the discussion of Fig. 6, it is important to draw reader's attention to the offset between the ECHAM RFs calculated with Eq. (1) from τ 550 and τ 550(869) . After the second eruption, the difference reaches up to 70%. This difference is a prime example of the influence of assumed particle size distribution parameters on the RF calculations. For example, at the plume maximum, the difference is almost as large as the forcing, but it decreases while the stratosphere relaxes. Considering these discrepancies, 425 the respective similarities of the ECHAM τ 550(869) and OMPS-LP RFs (dashed blue and red lines), as well as ECHAM τ 550 and ECHAM output (solid blue and green lines), are remarkable. Here it should be noted that although there are obvious differences between the curves, they generally have quite good temporal correlation and capture the second eruption very well.
Combining the above mentioned facts, the following conclusion can be drawn. Even when applied to the tropical region rather than globally, the Hansen's formula given by Eq.
(1) provides a reliable approximation of RF with about 20% accuracy.

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In turn, the τ conversion to a different wavelength is a more significant source of uncertainty with a potential to increase the estimated RF by up to 70%. After accounting for those uncertainties, a very good agreement between the RF values from ECHAM and those from OMPS-LP is observed. For the particular Ambae eruption studied in this paper, we estimate the tropical radiative forcing caused by an increase in stratospheric aerosols to be about -0.13 W/m 2 .

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The distribution of aerosol extinction coefficients at 869 nm in the stratosphere after the 2018 Ambae eruption was compared using the data retrieved from the OMPS-LP observations and that modeled by ECHAM.
We present here the retrieval algorithm (V1.0.9) of stratospheric aerosol extinction coefficient profiles at 869 nm from the OMPS-LP instrument. The retrieval algorithm was adopted from SCIAMACHY V1.4 and shows similar results in comparison with solar occultation instruments. The comparison of OMPS V1.0.9 product with the aerosol extinction coefficient observa-440 tions from SAGE III/ISS showed that the mean relative difference is less than 25% for the profiles in between 40°S and 40°N.
In the higher latitudes, the difference is somewhat larger; it is less than 35% below 25 km but can reach about 60% at 28 km.
We also show the changes in the aerosol extinction coefficient after the 2018 Ambae eruption using monthly mean and 10day average data. Ambae caused one of the largest perturbations in the aerosol layer for the OMPS operating period. Volcanic aerosols rise over time to about 21 km in the tropics within the tropical pipe of BDC (the tape-recorder effect). Analysing 445 the 10-day average data, it has been seen that the plume from the first phase of the eruption was relatively weak and did not spread outside tropics. The second eruption in July was much larger, and the aerosols also spread to the mid-latitudes of both hemispheres.
The measurement data was compared with the model output from a global aerosol model (ECHAM). In order to simulate the Ambae eruption accurately, the injected SO 2 emission was estimated using combined OMPS and OMI data for the April 450 eruption (0.12 Tg) and TROPOMI data for the July eruption (0.36 Tg). The altitudinal distribution of the SO 2 was assessed using MLS profiles. Thus, the resulting simulation showed that the model and measurements agree well with each other. The main differences concern the intensity and the lifetime of the volcanic perturbation. While for the first eruption, ECHAM underestimated the strength of plume as well as the time it reached 20.5 km altitude; for the second eruption, the modeled plume reached higher altitudes about two to three weeks earlier, and the plume lived longer, being overall slightly weaker at 455 that altitude. Although the differences in the measured and modeled plumes exist, they are rather minor, and the consistency is remarkable. The good agreement is explained by the rather precise SO 2 injection mass and height assessment, as well as by the nudging of meteorological data.
We also compare aerosol radiative forcing (RF) caused by the increase in stratospheric aerosol loading from the second Ambae eruption in the tropics. While the time courses of RF for the ECHAM output and ECHAM and OMPS-LP recalculated well not only for the globally averaged aerosol optical depths but also for the tropical region. However, this approach suffers from the errors associated with the assumed particle size distribution for the datasets where the Ångtsröm exponent has to be used. We estimate the RF in the tropics after the second 2018 Ambae eruption to be about -0.13 W/m 2 .
In general, if the initial data (SO 2 mass, day and height of injection as well as meteorological data) is quite precise, the 465 models give a very good estimate of the plume distribution, and the calculation of the radiative forcing can be made for an isolated plume without additional assumptions. Overall, the best results can be achieved only by combining observational data and modeling capabilities. Thus, it is very important to unite the measurement and model community together, for example, as the research unit VolImpact does (von Savigny et al., 2020).
Code and data availability. OMPS-LP aerosol extinction coefficient at 869 nm data are available after registration at http://www.iup.unibremen.de/DataRequest/. ECHAM primary data and scripts used in the analysis and other supplementary information that may be useful in reproducing the authors model work are archived by the Max Planck Institute for Meteorology and can be obtained by contacting publica-tions@mpimet.mpg.de. Model results will be available under cera-www.dkrz.de soon.
Author contributions. EM initiated the study, provided OMPS-LP aerosol extinction coefficient product, compared it to SAGE-III/ISS, CT helped with literature survey; CvS and CT initiated and proposed the research unit, they and JPB led the project and revised the text.
Competing interests. The authors declare no competing interests.