In the present study, a detailed investigation and evaluation of SO2 simulated by the global EMAC model integrated within the Modular Earth Submodel System (MESSy) framework , is undertaken. The EMAC model is a comprehensive global CCM that represents physical and chemical processes in the troposphere and middle atmosphere, along with their interactions with the land surface, ocean systems, and human-induced changes such as emissions and land-use . The second version of the Modular Earth Submodel System and the 5th generation European Center Hamburg general circulation model ECHAM5, make up the EMAC model used in this study. The physics-related submodels within the MESSy framework have been adapted from the physics routines of ECHAM5 . Only the spectral dynamical core, the flux form semi-Lagrangian (FFSL) large scale advection scheme , the time integration loop, and the Newtonian relaxation methods retain their original structure from the ECHAM5 base model.

The results analysed here stem from the RD1SD-base-01 EMAC simulation that has been performed under the CCMI-2022 protocol . Here, the emissions of SO2 and other sulfur species are calculated by the submodels OFFline EMISsions (OFFEMIS, formerly called OFFLEM) for prescribed emission fluxes , and AIRSEA (calculating the air-sea exchange of chemical species ). Details about the emission setup used here are described in a separate subsection (Sect. ).

Chemical reactions in the gas phase are computed by the submodel Module Efficiently Calculating the Chemistry of the Atmosphere MECCA,, while the Scavenging Submodel for Regional and Global Atmospheric Chemistry Modeling (SCAV) simulates the aqueous phase kinetics and scavenging processes in the atmosphere . The dry deposition of gases and aerosols is calculated by the dry deposition submodel (DDEP, formerly called DRYDEP) , and aerosol sedimentation is calculated by the aerosol sedimentation submodel SEDI,. The sampling along sun-synchronous satellite orbits submodel (SORBIT) to sample model results on-line along orbits of sun-synchronously orbiting satellites, as described by , has been applied to facilitate a direct comparison between simulated Vertical Column Density (VCD) of trace gases such as SO2, with observations from satellite instruments.

The RD1SD-base-01 EMAC simulation results analysed in this study cover the years 1979 to 2019. The simulation was performed at a resolution of T42L90MA with output of results every 5 h of the simulated period. The spectral resolution (triangular truncation) T42 corresponds to a quadratic Gaussian horizontal grid of roughly 2.8° × 2.8° in both, longitude and latitude coordinates, and L90 denotes 90 vertical layers (with a median lowest level height of 60 m) between the surface and the uppermost model layer centered around 0.01 hPa . For the RD1SD-base-01 simulation, the gas phase chemistry is calculated throughout the entire atmosphere using the Mainz Isoprene Mechanism (MIM1) based on . This mechanism accounts for hydrocarbons up to 4 carbon atoms, along with isoprene (5 carbon atoms). SO2 in the gas phase is oxidized by the hydroxyl-radical OH or direclty photolysed. The major sink, however, is by transition into the aqueous phase, mainly cloud water, and further oxidation in the liquid phase. Since gaseous SO2 is not released on evaporation of cloud and rain droplets, the sulfur contents is in these cases transferred into a so-called residual (res) pseudo-aerosol tracer SO4res,cs with characteristics of a coarse mode soluble (cs) aerosol. This tracer is treated as aerosol tracer, e.g. by the sedimentaion submodel (SEDI), by the dry deposition submodel (DDEP), and by the wet scavenging submodel (SCAV). The details of the gas phase and liquid phase chemistry are documented as supplemantary material. Other aerosol effects were prescribed in both, the troposphere and the stratosphere, to consider their impact through heterogeneous chemistry and radiative forcing . To allow for a direct comparison of the simulation results, in particular chemical tracers, between the simulated and observational data, the RD1SD-base-01 simulation was operated in “specified dynamics” (SD) mode, for which the prognostic variables temperature, divergence, vorticity and the logarithm of surface pressure were “nudged” by Newtonian relaxation towards the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA5; ). The model dynamics of the SD simulations are then aligned with the observed dynamics, aiming a good reproduction of real meteorological situations.

Sulfur emissions of both, anthropogenic and natural sources, need to be taken into account. The following prescribed emission inventories were used:

Throughout this study the Coupled Model Intercomparison Project Phase 6 (CMIP6) inventory is selected as the standard inventory for global EMAC simulations, since it was recommended by the experimental protocol for participation in the CCMI-2022 model intercomparison initiative . The CMIP6 inventory has a horizontal resolution of 0.5° × 0.5° and it primarily combines bottom-up inventories to provide emission data for climate models. Bottom-up inventories involve estimating emissions based on detailed data about specific sources and activities, such as energy consumption and industrial processes. The CMIP6 inventory contains historical emissions from 1850 to 2014, provided by the Atmospheric Chemistry and Climate-Model Intercomparison Project (ACCMIP) developed by . The historical data are then combined with the shared socioeconomic pathways (SSPs) for projected future emissions from the IPCC Sixth Assessment Report AR6,. The SSPs used within the CMIP6 inventory provide a range of future scenarios based on varying levels of greenhouse gas emissions and societal changes, such as SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7, SSP4-6, and SSP5-8.5 . These SSPs present different emission scenarios, in order to explore different future climate outcomes based on varying levels of greenhouse gas emissions and societal changes. For the RD1SD-base-01 simulation the SSP2-4.5 scenario has been used to prescribe trace gases emissions, including SO2 emissions after 2014. The SSP2-4.5 is a middle-of-the-road scenario with moderate emissions, leading to a radiative forcing of 4.5 Wm2 by 2100 .

Volcanic sulfur emissions from both, continuously degassing and explosive volcanoes are represented by an inventory of the Aerosol Inter Comparison (AeroCom) project as a zonal mean climatology . Volcanic sulfur is emitted as 97.5 % SO2 and 2.5 % SO4. The data are based on the bottom-up Global Emissions Inventory Activity (GEIA) for the years 1750 and 2000 . Continuously degassing sulfur in the AeroCom inventory is equally distributed over the grid points with GEIA volcano locations and amounts to a multi-annual total emission of 12.6 Tg(S)yr-1 (Teragrams of Sulfur per year) over all the years . The height of these emissions is defined in the upper third of the volcano altitudes, simulating the degassing processes that occur predominantly at the volcano flanks. Explosive volcanic emissions are quantified at approximately 2 Tg(S)yr-1 over all the years. This estimation is based on the Aerosol Index (AI) provided by the Total Ozone Mapping Spectrometer (TOMS) satellite sensors . The emissions data are distributed evenly across grid boxes that include volcanoes, which were active in the last century . It is important to note that these emissions are treated as being continuously released rather than episodic, due the fact that only about one-third of such emissions occur during violent explosive events . Furthermore, these emissions are typically defined to occur between 500 and 1500 m above the peaks of the volcanoes, to accurately represent their dispersal in the atmosphere. The injection height, time resolution and the sulfur flux of the different volcano types are listed in Table .

In addition to the prescribed emissions, sulfur from oceanic Dimethyl Sulfide (DMS_airsea) and from Carbonyl Sulfide OCS are calculated using the submodels AIRSEA (for gas exchange between air and sea) and TNUDGE for Newtonian relaxation towards prescribed mixing ratios, respectively.

Since the concentration simulated by the model is affected by the prescribed emissions, it is important to understand the differences between the used CMIP6 emission inventory and other emission inventories. In this study, the Emissions Database For Global Atmospheric Research (EDGAR) emission inventory is used for this comparison (See Sect. ). Same as for the CMIP6 inventory, EDGAR is also considered a bottom-up inventory, but with a finer horizontal resolution on grid-maps at 0.1° × 0.1°. EDGAR is developed using a bottom-up approach combining internationally available statistics on activity data with emission factors derived from scientific literature and guidelines (e.g., IPCC) . The data is available as yearly and monthly mean and is emitted into 7 vertical tropospheric levels (0, 20, 92, 184, 324, 522 and 781 m), as described by . Version 5.0 of EDGAR (EDGAR5) contains solely historical data about anthropogenic emissions from different sectors such as fossil fuels, agricultural waste burning, ships and roads, starting from 1970 till present. Other emissions from large scale biomass burning, forest fires and sources from land-use forestry are excluded . Here, the EDGAR 5.0 and the EDGAR8 inventories are used for inter-comparison to provide an estimate of the uncertainty of the magnitude and variability of SO2 emissions over time from the CMIP6 emission inventory.

In their studies, and address the tropospheric sulfur budget within their atmospheric chemistry models for the year 1990. used the STOCHEM-Ed model, which is a global three-dimensional Lagrangian Chemistry-Transport Model (CTM), while the IPCC Third Assessment Report (IPCC AR3, ) incorporates the average results from 11 distinct models providing a comprehensive overview of the global tropospheric sulfur budget. Since the RD1SD-base-01 EMAC simulation covers the years 1979 to 2019, we directly compare the year 1990, which is used in both references. Note that in , sulfur anthropogenic emissions were presented as a single sector, unlike the detailed breakdown presented in our study, which categorizes the prescribed emissions into sectors such as fossil fuels, aircraft and shipping emissions, among others. Additionally, the models in both studies applied an interactive aerosol model, unlike the EMAC model for the RD1SD-base-01 simulation. Therefore, some sulfur species present in have not been considered in the EMAC model, such as the Methane Sulphonic Acid (MSA) and vice versa (such as OCS).

For a clear comparison of the processes used by with those in EMAC, Table  provides the values for both, the prescribed emission and the deposition rates, for the year 1990. Despite discrepancies arising from the applied emission inventories between EMAC and the literature, as well as differences in used chemical reactions and physical processes, this comparative analysis reveals a good agreement between our model results and existing literature.

Consequently, the magnitudes of sulfur emissions across different sectors are consistent between EMAC and the compared models. The total emissions from EMAC align perfectly with those reported in the IPCC AR3, with a slight difference of about 1 Tg(S)yr-1 in EMAC. Regarding the STOCHEM-Ed model, the EMAC simulation utilises larger sulfur emissions by approximately 12 %, related to the applied emission inventories. This overall good agreement in magnitude is also apparent in the deposition rates. In EMAC, the deposited sulfur through wet and dry processes is 93.79 Tg(S)yr-1 compared to 95.3 and 96.5 Tg(S)yr-1 for the STOCHEM-Ed model and the IPCC AR3, respectively. The remaining deposited sulfur from sedimentation is present only in EMAC and not in the cited literature.

This evaluation highlights the validity of the EMAC model in comparably capturing sulfur emission and deposition rates, despite minor differences in the chemical species and mechanisms used by the compared models. This discrepancy is attributed to the sulfur emissions inventories utilized as input for the models, which play an important role in shaping both, sulfur mixing ratios and deposition processes. Further refinement and validation of these emissions inventories may help to improve the models performance in representing the tropospheric sulfur cycle.

A comprehensive analysis of the global distribution and discrepancies of SO2 VCDs as derived from the RD1SD-base-01 EMAC simulation and from TROPOMI/Sentinel-5P satellite observations for the year 2019 is performed. Figures  and  show the monthly spatial distribution of SO2 VCDs, with EMAC results on the left and TROPOMI data on the right.

Overall, both datasets display low SO2 VCDs (< 0.5 DU) over regions like Western Europe, Africa, and Australia. However, notable discrepancies appear in areas such as Southern Italy, Northeast China, India, Central America, and Papua New Guinea, where EMAC simulates persistently higher values (> 1 DU) compared to TROPOMI (< 0.5 DU) throughout most of the year, except in June and July. In August, elevated TROPOMI signals over Papua New Guinea are caused by the Ulawun eruption .

In June and July, TROPOMI detects higher SO2 over northern latitudes, particularly following the June 2019 Raikoke volcanic eruption in Russia . These enhanced signals are absent in the EMAC simulation due to the omission of such episodic volcanic emissions in the CMIP6 inventory.

To disregard the missing volcanic SO2 emissions from Raikoke and Ulawun in the EMAC simulation, a 10 months average excluding June and July 2019 is used for the comparison with TROPOMI observations. The resulting differences in SO2 VCDs are shown in Fig. .

The comparison between EMAC simulations and TROPOMI observations reveals significant discrepancies in Northeastern China, India, Southern Italy, and at localized sources in the Southern Hemisphere, where EMAC consistently overestimates SO2 VCDs by 1.5 to 2 DU.

Conversely, a better agreement (0.1–0.5 DU differences) is found in Fig.  over Western Europe, the USA, Africa, Australia, and most of South America, where SO2 emissions are relatively low. The most significant differences arise in regions with large anthropogenic emissions or active volcanoes, such as Etna (Italy), Mt. Fuji (Japan), Ulawun (Papua New Guinea), Nevado Ojos del Salado (Chile), and Kunlun (Tibetan Plateau). Elevated SO2 VCDs in Beijing and India highlight the impact of industrial emissions.

To ensure accurate comparisons, different SO2 sources require appropriate TROPOMI product types and Averaging Kernels (AKs). For instance, AK_15km is used to assess the impact of explosive volcanic eruptions (e.g., Raikoke, Ulawun) on SO2 emissions and deposition, as detailed in Sect. . For anthropogenic and outgassing volcanic emissions, a relative comparison of SO2 VCD magnitudes is performed, without directly assessing the absolute emitted and deposited SO2 mass from individual point sources.

The differences between the AKs and the corresponding VCDs are explained in detail in Appendix .

TROPOMI detected significant SO2 signals in June and July 2019, which were not visible in the EMAC RD1SD-base-01 simulation due to the lack of eruptive events in the applied emission inventories (Fig. ). The Raikoke (48.29° N, 153.25° E) and Ulawun (5° S, 151° E) eruptions injected volcanic SO2 into the stratosphere, increasing stratospheric Aerosol Optical Depth (sAOD) across both hemispheres . Raikoke, the largest SO2 injection into the Upper Troposphere and Lower Stratosphere (UTLS) since Nabro (2011), released about 1.5 ± 0.2 Tg SO2 , while TROPOMI estimated 0.14 Tg (SO2) from Ulawun in June and 0.2 Tg (SO2) in early August .

To investigate the effects of these two eruptions, we performed additional sensitivity simulations (June–December 2019, initialized with results end of May 2019 of the RD1SD-base-01 simulation), in which the volcanic SO2 emissions were taken into account with the submodel TREXP . Two different SO2 vertical emission profiles (named StratProfile and VolRes1.5, respectively, adopted from ) were utilized for the Raikoke eruption. In EMAC, the StratProfile has been applied in the RD1SD-raik-02 (raik-02) sensitivity simulation, whereas the VolRes1.5 injection profile was used in the RD1SD-raik-03 (raik-03) simulation. In both simulations the SO2 release is approximately 1.5 Tg SO2 (1.57 for raik-02 and 1.5 for raik-03) into the atmosphere, the only difference lies in the vertical distribution. In raik-02 (StratProfile profile from ), 69 % of the volcanic SO2 mass (1.09 Tg) is emitted into the stratosphere, with the primary peak occurring at 12–13 km altitude. In contrast, for raik-03 (equivalent to the VolRes1.5 profile in ), only 43 % of the SO2 mass (0.64 Tg) is emitted into the stratosphere, with the primary peak located around 10 km altitude in the upper troposphere. Additionally, raik-04 is based on the setup from raik-02 with additional emissions stemming from the Ulawun volcano. Table  lists the set-ups applied in all sensitivity simulations.

For a detailed study focusing solely on the SO2 mass burden originating from volcanic eruptions, the results of the RD1SD-base-01 reference simulation have been subtracted from the sensitivity simulations. This approach isolates the SO2 mass specifically attributable to volcanic activity from other anthropogenic or outgassing volcanic emissions, thereby enabling a more precise analysis of its impact. Figure  illustrates the SO2 mass emitted at different altitudes in both simulations. The altitude of the SO2 emissions significantly influences their atmospheric distribution and dispersion patterns, impacting their climate effects, lifetime, and oxidation rates .

The combined SO2 mass in the troposphere and stratosphere represents the total SO2 mass burden from the Raikoke eruption. This mass burden is then compared with the global SO2 mass burden derived from the TROPOMI/Sentinel-5P satellite after the Raikoke eruption and until mid-July 2019 (see Fig. ). The raik-02 simulation (black line), which assumes a larger emission of SO2 into the stratosphere, aligns more closely with TROPOMI's derived SO2 data than the raik-03 simulation (orange line), in which a larger proportion of SO2 is released into the troposphere.

Both simulations accurately capture the SO2 mass burden peak at approximately 1.8 Tg. The peak values of the EMAC simulated Raikoke SO2 mass are slightly larger than the total emissions presented in Table , due to the application of AK_15km to the EMAC results. Moreover, raik-02 (black curve) shows a better long-term agreement with TROPOMI estimates than raik-03 (orange curve), however both consistently remaining within the estimated uncertainty range (as derived by ). For TROPOMI, uncertainties of SO2 in the stratosphere are approximately ± 30 % of the retrieved VCDs . Conversely, the raik-03 simulation exhibits a more rapid decline of the SO2 mass in the stratosphere, compared to the TROPOMI data after the Raikoke eruption, suggesting a faster removal of SO2 from the atmosphere, with an exception for the first two days after the SO2 mass peak, where raik-03 agrees better with the measurement based estimates than raik-02.

The discrepancies between TROPOMI SO2 based estimates and EMAC simulation results can be attributed to the vertical injection profiles (which might deviate from reality) or to the rate of sulfur removal from the atmosphere. suggest that additional injections are required after the initial Raikoke plume to accurately replicate the observed SO2 mass, underscoring the complexity of modeling volcanic SO2 emissions and their interactions in the atmosphere. To address these differences, a sensitivity simulation labeled raik-04 (green curve in Fig. ) was conducted. It is based on the setup of the raik-02 simulation, chosen because it best matches the temporal evolution of TROPOMI derived SO2 mass, but additionally includes emissions from the Ulawun volcano in the Southern Hemisphere. The Ulawun eruptions on 26 June 2019, at 12:00 UTC and 3 August 2019 at 12:00 UTC were taken into account, with each eruption lasting 6 h. During the first eruption, 0.14 Tg of SO2 was injected at altitudes between 16 and 19 km in the model. For the second eruption, 0.2 Tg of SO2 was emitted at altitudes between 11 and 15 km. As shown in Fig. , these adjustments improved the temporal evolution of SO2 mass, slowing the decline in the raik-04 simulation following the Ulawun emission injections on 26 June due to the increased SO2 mass in the stratosphere.

During the Raikoke eruption and up to 29 June 2019, all simulations consistently show a continuous decrease of the SO2 mass. TROPOMI data indicates a decline rate of approximately 0.08 Tg(SO2)d-1, which is slower than the decline simulated by the EMAC model. The raik-03 simulation shows a decline rate of around 0.14 Tg(SO2)d-1, indicating a lower SO2 mass compared to TROPOMI. Conversely, the raik-02 simulation exhibits a slower decline rate of 0.1 Tg(SO2)d-1. However, raik-04 aligns most closely with TROPOMI, with a decline rate of 0.09 Tg(SO2)d-1. This closer match can be attributed to the additional Ulawun emissions injected into the stratosphere on 26 June 2019, which increases the mass of SO2 in the atmosphere. Note that for the first two days following the SO2 mass peak, TROPOMI observations indicate a rapid decline rate of approximately 0.15 Tg(SO2)d-1. This rate aligns most closely with the raik-03 simulation, where a significant amount of SO2 is emitted at lower altitudes, resulting in a decline rate of 0.14 Tg(SO2)d-1. In contrast, the raik-02 and raik-04 simulations, which involve the majority of SO2 being emitted into the stratosphere, exhibit a slower decrease of about 0.12 Tg(SO2)d-1. Between 29 June and 15 July 2019, all EMAC simulations show a decrease similar to TROPOMI, at a rate of approximately 0.05 Tg(SO2)d-1.

Over the period from 22 June to 15 July 2019, raik-04 aligns most closely with TROPOMI observations, by simulating about 3 % lower SO2 mass than TROPOMI over the entire period. raik-02 indicates a mean relative difference of 10 %, while raik-03 simulates lower values than TROPOMI with a mean relative difference of 25 % due to differences in the decline rate and SO2 vertical injection profile. The fact that all EMAC simulations fall within the 30 % uncertainty range of the SO2 total column in TROPOMI provides confidence that EMAC correctly captures the main processes required to represent SO2 oxidation and deposition.

To summarize, this analysis shows the capability of all sensitivity simulations, to reproduce the TROPOMI measured peak after the Raikoke and Ulawun eruptions. Furthermore, the consistent decay rates between TROPOMI data and sensitivity simulations, particularly raik-04 (which encompasses both, the Raikoke and Ulawun eruptions in the stratosphere), as well as accounting for the deposition of most of the initially emitted SO2 mass within EMAC, further underline the model's realism in capturing the intricate processes of SO2 emission, oxidation, and deposition associated with volcanic eruptions. Nevertheless, over extended durations, various factors such as simulated wind patterns, radiative heating effects, and mixing dynamics can introduce deviations between model results and real-world observations. These complexities highlight the ongoing challenges in achieving complete concordance between model simulations and empirical data over prolonged temporal scales.

EMAC SO2 emissions from both, anthropogenic and outgassing (non-eruptive) volcanic sources, are derived from prescribed emission inventories, specifically CMIP6 and the AeroCom Project, respectively. Each of these emission inventories is based on distinct assumptions that may not accurately reflect the actual emitted SO2 masses and injection heights. Consequently, only a relative comparison of SO2 hotspots (i.e. with large SO2 emissions) and background regions between the EMAC model results and TROPOMI observations is feasible. Therefore, for the comparison discussed in this section, only the ratios and the relationship between EMAC results and retrieved TROPOMI SO2 VCDs are investigated.

Table  lists the ratios between SO2 VCDs simulated with the EMAC model compared to those retrieved from TROPOMI, around specific outgassing volcanoes, presented as a yearly mean for 2019. The table indicates that EMAC SO2 VCDs are generally larger than TROPOMI values over volcanic regions. Note that, when comparing the satellite data to model results folded with the AKs, COBRA data are subject to an uncertainty of approximately 27 % to 32 % on the retrieved SO2 column, mainly due to instrumental noise .

The comparison reveals notable discrepancies between the SO2 VCDs over several volcanic regions, with EMAC-to-TROPOMI ratios of approximately 7 for Etna, 6 for Tajumulco, and 5 for Mt. Fuji. In contrast, a lower ratio of about 2.5 is observed over Nevado Ojos del Salado. Notably, these differences are out of the error margin of the satellite measurements, which typically ranges between 27 % and 32 %.

These differences are attributed to the volcanic emission inventory used within the EMAC model. The larger ratios derived for the first three volcanoes could be attributed to both, the SO2 emission masses and the emission heights. In the AeroCom inventory , the Etna, Tajumulco, and Mt. Fuji volcanoes are considered not only as outgassing, but also explosive volcanoes. The top of Etna is approximately 3300 m, Tajumulco about 4000 m, and Mt. Fuji about 3700 m, with emissions reaching up to around 4500 m (577 hPa). This indicates explosive volcanic activity, with emissions ranging from the “top of the volcano + 500 m” to “top of the volcano + 1500 m”, as detailed in Sect. . Conversely, the volcano in Chile is categorized solely as an outgassing volcano, thus showing the lower ratio between EMAC results and TROPOMI retrievals. Continuously outgassing volcanoes, within the used model setup, emit from “the height of the volcano × 0.67” up to the height of the volcano.

For anthropogenically influenced regions, the EMAC results also shows larger SO2 VCDs compared to those from TROPOMI, but with smaller ratios in most regions compared to volcanic areas. Figure  shows a geographical map depicting the selected areas which have been investigated quantitatively, and Table  lists the ratio of EMAC SO2 VCDs to TROPOMI VCDs in these SO2 background and hotspot regions. In background regions, a specific area in central Africa (coordinates: 12° N, 15° E to 2° N, 27° E, respectively) and the South Atlantic Ocean (coordinates: 20° S, 20° W to 30° S, 5° W) reveal small discrepancies between the SO2 VCDs (10 %–20 %). Larger differences are derived in anthropogenically influenced regions: Europe (1.6 factor, 60 % difference), the USA (1.8 factor, 80 % difference), and India (2.5 factor, 150 % difference). In Northeastern China the factor is 3.2 (220 % difference), while in Southeastern China it is 2 (100 % difference).

The regional discrepancies of SO2 VCDs between EMAC and TROPOMI can be attributed to the large SO2 emissions in these regions, originating from the CMIP6 emission inventory, as well as to their different original spatial resolutions. EMAC, with a coarse resolution of 300 km × 300 km, averages emissions over larger areas, potentially underestimating localized SO2 peaks from sources like volcanoes or power plants. In contrast, TROPOMI/Sentinel-5P, with a much finer resolution of 3.5 km × 7 km, captures fine-scale variations. This difference might lead to discrepancies, especially in regions with strong emissions, since the emissions in the model become instantaneously diluted by spreading the emitted mass over the model grid-boxes. For instance, in areas like India and China, where large SO2 emissions take place, the ratios between EMAC and TROPOMI are larger, while background regions such as Africa show minimal differences in 2019, falling within TROPOMI's uncertainty range. In regions like Europe, the USA, and Southeastern China, which have lower SO2 emissions than China and India for example, there is a better agreement between the two datasets.

Since TROPOMI only provides total VCD values, a detailed analysis of the vertical profile between both datasets is not possible. Therefore, it is difficult to ascertain whether the differences originate near the surface or higher up in the atmosphere. To address this, a comparison of the simulated SO2 concentrations at the Earth's surface is conducted in the next section.

For the United States, sulfur species simulated with EMAC near the Earth's surface (i.e. the lowermost grid box) are compared with observation data obtained from the CASTnet network. As detailed in Appendix , CASTnet provides surface-level observations, including monthly and yearly mean SO2 concentrations in µgm-3, and sulfur wet deposition fluxes in kg(S)ha-1yr-1. The SO2 concentrations and sulfate amounts in precipitation samples are measured, whereas the dry deposition fluxes are simulated based on a multi-layer model.

Figure  shows the SO2 concentration measured at the CASTnet sites (right panel, as mentioned above aggregated onto the model grid) and the EMAC simulated concentration (left panel). In both cases, 20 year averages are calculated. It is important to note that the EMAC results are only shown for grid boxes, where observational stations are located, which explains the presence of “empty boxes” in the EMAC model results. The figure indicates that Eastern USA sites exhibit larger SO2 concentrations compared to the sites in the Western region in both datasets. This disparity is attributed to the higher density of SO2 emission sources in the Eastern USA compared to the Western part. This is also reported by and .

As shown in Fig. , CASTnet (right panel) measures approximately 7 µgm-3 at some individual sites in the Eastern USA, with other Eastern sites showing very low SO2 concentrations of about 0.5 µgm-3. On the left panel in Fig. , the RD1SD-base-01 simulation driven by the CMIP6 inventory indicates that SO2 concentrations at some individual Eastern sites are lower than those reported by CASTnet. However, on average, EMAC results show overall consistent SO2 concentrations between 1.5 µgm-3 and a maximum of about 5.5 µgm-3 at Eastern sites. In the Western region, both datasets show lower SO2 concentrations, averaging around 1 µgm-3 across all sites. However, the RD1SD-base-01 simulation results in larger SO2 concentrations reaching up to 3 µgm-3 at some Western sites.

Figure  shows the comparison between both, the RD1SD-base-01 simulation results and CASTnet SO2 concentrations as well as sulfur deposition fluxes across different regions in the USA. Specifically, SO2 concentrations and sulfur deposition fluxes from Western sites (Fig. a and c, respectively), and from Eastern sites (Fig. b and d, respectively), are shown. The comparison involves calculating the annual mean of SO2 concentration in µgm-3 and of sulfur deposition fluxes (wet and dry deposition) in kg(S)ha-1yr-1, averaged over Eastern, and Western USA sites, respectively. For both, surface SO2 concentration and sulfur deposition flux, the RD1SD-base-01 simulation driven by the CMIP6 emission inventory effectively captures the decline in both regions of the USA for the period 2000–2019. As shown in Fig. , the model tends to simulate larger surface SO2 concentrations than CASTnet by a factor of 2 in the Western region over the 20 year period (Fig. a), while showing approximately a factor of 1.2 larger SO2 concentrations over the Eastern USA (Fig. b). For the western USA, EMAC shows decreasing surface SO2 concentrations after 2000, which brings the simulated results into better agreement with the observations over time (see Fig. a). The large standard deviation derived from the datasets are attributed to the extensive dispersion of sulfur sources across a broad geographical area.

In the Eastern and Western USA, the largest part of sulfur removal occurs via wet deposition. This is effectively simulated by EMAC in agreement with CASTnet observations. For the calculation of deposition flux within the RD1SD-base-01 simulation, the deposited sulfate and SO2 were converted to a sulfur equivalent. In Fig. d, EMAC shows a lower sulfur deposition flux over the Eastern USA, for wet deposition (10 % lower EMAC values compared to CASTnet) and larger values for dry deposition (30 % larger EMAC values compared to CASTnet) over the 20 year period. In the Western USA, EMAC also simulates a 5 % lower sulfur wet deposition flux compared to CASTnet over the entire 20 year period (Fig. c). Here, EMAC does not show lower values over all the time range, but indicates larger wet sulfur deposition between 2002 and 2008. For the sulfur dry deposition flux (orange lines), EMAC shows a factor of 2 larger values over the entire 20 year-period compared to CASTnet.

analysed the wet-deposition of SO4-2 for urban and suburban site classes separately, whereas we did not distinguish different sites and analysed the total sulfur deposition. Thus, the results are not directly comparable. Nevertheless, see their Figs. 2D and 5D estimated for the year 2000 a wet deposition rate (urban stations) of approx. 20 kg(SO4-2)ha-1, equivalent to 6.7 kg(S)ha-1yr-1. For 2018, they derived a wet deposition rate of 5 (rural) to 7.5 (urban) kg(SO4-2)ha-1yr-1, equivalent to 1.7 to 2.5 kg(S)ha-1yr-1, respectively. These numbers agree, given the limitations of this comparison, with our results for the eastern USA (see Fig. d, blue area). derived for the USA a decrease of the total sulfur depostion from 5.3 kg(S)ha-1 in 2002 to 1.8 kg(S)ha-1 in 2017 (see their Fig. S14b). These total fluxes are lower than the wet deposition fluxes derived by and than our results, but the derived trends are consistent.

Since the concentration simulated by the model is directly affected by the prescribed emissions, it is important to assess potential uncertainties of the applied emission inventory (CMIP6). For this, we present the comparison with the EDGAR5 (see Sect. ), and the EDGAR8 emission inventories. The temporal evolution of sulfur emissions in Tg(S)yr-1 from the CMIP6 emission inventory (orange lines in Fig. e and f) is compared with those from the EDGAR5 (black lines in Fig. e and f) and the EDGAR8 emission inventory (green lines in Fig. e and f). This comparison highlights the discrepancies and potential biases between the different emission inventories, which would be reflected in model results, if based on the alternative inventory. For the calculation of sulfur emissions, the emissions from SO2 were also converted to sulfur equivalent. The anthropogenic emissions (particularly from fossil fuels, ship, road, and aircraft sectors) from both emission inventories are calculated as a yearly area integral over the Western USA region (see Fig. e), and over the Eastern USA region (see Fig. f). Both regions are shown in Fig. , where the red and blue boxes represent the selected Eastern and Western USA regions, respectively.

For the western USA (Fig. e), the CMIP6 inventory has 50 % larger sulfur emissions than the EDGAR5 inventory between 2000 and 2015, and 60 % larger sulfur emissions than the EDGAR8 inventory between 2000 and 2019. The picture is different for the Eastern USA (Fig. f), where the CMIP6 inventory indicates 10 % less sulfur emissions than the EDGAR5 inventory between 2000 and 2015, and more or less the same sulfur emissions compared to the EDGAR8 inventory over the entire time range. The differences between the emission inventories, particularly the larger anthropogenic sulfur emissions in CMIP6 compared to those in EDGAR5 and EDGAR8 over the Western USA, are a major factor contributing to the larger SO2 concentrations simulated by EMAC compared to those observed at the CASTnet in Western USA (see Fig. a). Consequently, using the EDGAR5 or the EDGAR8 emission inventory over the Western USA would likely result in smaller SO2 concentrations in the EMAC model, thereby reducing the bias between the CASTnet measurements and the EMAC results in that region.

For the final year of the study, 2019, the used CMIP6 emission inventory used for the RD1SD-base-01 simulation leads overall to a larger SO2 concentration by a factor of approximately 1.6 compared to the CASTnet measurements.

In Europe, 48 observational stations from the EMEP database are analyzed, as detailed in Appendix . First, the spatial distribution of SO2 concentration over Europe from both datasets, is shown in Fig. . EMAC results are only shown for grid boxes where observational stations are located, which explains the presence of “empty boxes” in the EMAC model results. Here, EMAC (left panel) shows the largest SO2 concentrations (between 4 and 8 µgm-3) over central East Europe, with lower SO2 concentrations (between 0.3 and 3 µgm-3) over sites in the United Kingdom and Western Europe. On the other side, EMEP measures one very large SO2 concentration (about 7.5 µgm-3) over a grid box situated in Serbia, while showing lower SO2 concentrations at the remaining sites (between 0.2 and 3.3 µgm-3).

Furthermore, Fig.  illustrates the decline of SO2 concentration across Europe, which is well captured by EMAC throughout the 20 year period (top left panel in Fig. ). Consequently, the temporal reduction in sulfur loss due to wet deposition is also accurately represented by EMAC (top right panel in Fig. ). However, the used CMIP6 emission inventory tends to produce larger SO2 concentrations within the RD1SD-base-01 simulation compared to observational data within the European domain (top left panel in Fig. ). Specifically, SO2 surface concentrations from the model show a gradual decline between 2000 and 2012, with an annual decrease rate of 0.11 µgm-3, whereas ground-based observational data indicate a slower reduction rate of 0.04 µgm-3yr-1 during the same period. After 2012, both, model results and observational datasets, exhibit a more pronounced acceleration in the decline of SO2 concentration, with rates of approximately 0.22 and 0.12 µgm-3yr-1, respectively.

Over the entire 20 year period, EMAC driven by the CMIP6 emission inventory consistently shows larger annual mean surface SO2 concentrations in Europe by a factor of approximately 1.8 compared to the EMEP dataset. Specifically, EMAC indicates larger SO2 concentrations relative to observational data by a factor of 2 between 2000 and 2012, and with a lower factor of approximately 1.5 between 2012 and 2019. Regarding sulfur wet deposition flux, EMAC also simulates consistently larger values than observed by EMEP by a factor of 1.3 over the entire 20 year period. Notably, a consistency is observed in the decline rates of both datasets, characterized by a yearly mean decrease of about 0.05 µgm-3 throughout the duration from 2000 to 2019. This trend, calculated by linear regression, is comparable to the trend of -0.067 µgm-3 derived by see their Table S3 for the perios 2000–2019, which has been derived with a different method and based on a slightly different number of stations. Despite the differences in SO2 concentration and sulfur deposition flux, it is noteworthy that the model exhibits a good alignment with observational data, as shown in the temporal progression of both, SO2 concentration and sulfur deposition flux.

Similar to the study of sulfur emissions over the USA (see Sect. ), the prescribed CMIP6 emission inventory in Europe used for the RD1SD-base-01 simulation, shows differences in the temporal evolution of emitted sulfur compared to the EDGAR5 and EDGAR8 emission inventories (see the low panel of Fig. ). Here, the anthropogenic sulfur emissions (particularly from fossil fuels, ship, road, and aircraft sectors) from all emission inventories are calculated as a yearly area integral between 2000 and 2019 (2015 for EDGAR5) over a region in Europe. The chosen region is marked by a blue box, as shown in Fig. . In the lower panel of Fig. , an identifiable reduction of anthropogenic sulfur emissions across Europe is evident throughout the temporal evolution of both emission inventories. Specifically, the sulfur emissions in the CMIP6 inventory are about 20 % larger than those from the EDGAR5 and EDGAR8 inventories over the available time frames over Europe. This implies that using the EDGAR5 or EDGAR8 emission inventory would result in 20 % less SO2 being emitted in the model. Consequently, using the EDGAR5 or EDGAR8 emission inventory in Europe would likely result in lower SO2 concentrations and therefore lower sulfur wet deposition fluxes in the EMAC model, thereby reducing the bias between the EMEP measurements and the EMAC results.

For the final year, 2019, the used CMIP6 emission inventory used for the RD1SD-base-01 simulation leads to a larger EMAC SO2 concentration by a factor of approximately 1.45 compared to EMEP measurements.

For East Asia, a comprehensive investigation of SO2 and its associated processes, particularly within China, is imperative due to the substantial contribution of Chinese SO2 emissions, which account for 64 %–71 % of the total emissions across Asia . However, as described in Appendix , it is complicated to find representative monitoring stations providing continuous, long-term datasets of measured SO2 concentrations and sulfur deposition fluxes. Consequently, only 5 stations in Southeastern China and 9 over Japan from the EANET network have been selected for the present study. This selection was based, as for the previous networks in the USA and Europe, on the availability of long-term measurements (2000 to 2019 for this study) providing both, measured SO2 concentration in µgm-3 and wet deposition sulfur fluxes in kg(S)ha-1 in EANET. The geographical distribution and SO2 concentrations of selected stations in both, EMAC and EANET datasets at sites situated in China and Japan are shown Fig. .

Here, both, EMAC and EANET datasets, indicate larger SO2 concentrations at sites situated in China compared to those in Japan. As shown on the right panel of Fig. , EANET measures large SO2 concentrations with a maximum of about 12 µgm-3 at three sites in China, while showing lower SO2 concentrations ranging between 1 and 3 µgm-3 at the sites in Japan. On the left panel of Fig. , the EMAC results show overall more consistent SO2 concentrations with one site in China showing around 12 µgm-3, while SO2 concentrations at the other sites in China and Japan range between 2 and 8 µgm-3.

and reported a significant increase of SO2 emissions in China during the early 2000s, a trend confirmed by CMIP6, EDGAR5 and EDGAR8 emission inventories, as depicted in the lower panel of Fig.  (SO2 emissions were converted to sulfur equivalent). This rise of sulfur emissions is also reflected in the SO2 concentrations and the wet deposition sulfur fluxes, as illustrated in the same figure (top left and top right panels, respectively). EMAC indicates an overall increase of SO2 concentration and the deposited sulfur from 2000 till 2014. However, data from EANET reveals a different trend. According to the EANET network, SO2 concentration increased until 2006 at a rate of 0.7 µgm-3yr-1. On the other side, the deposited sulfur also increased until 2006 at a rate of 0.035 kg(S)ha-1yr-1. Afterwards, a decline of SO2 concentration by 0.5 µgm-3yr-1 and of the wet deposition sulfur flux by 0.4 kg(S)ha-1yr-1 until 2014, was measured.

Following 2014, numerous reports from environmental agencies and satellite observations have consistently indicated a significant decrease of China's SO2 emissions. Studies by and have highlighted that SO2 emissions in China experienced a sharp decline post-2014, nearly vanishing by 2020. This reduction of SO2 emissions after 2014 is also noticeable in the time evolution of sulfur emissions from the CMIP6 inventory utilized in this study (lower panel in Fig. ). From 2014 to 2019, a reduction exceeding 50 % has been documented across the China-Japan region, with sulfur emissions decreasing from about 22 to 12 Tg(S)yr-1 in the CMIP6 emission inventory. This decline of sulfur emissions notably influences the SO2 concentration and the wet deposition sulfur flux over that region. Consequently, a remarkable reduction, from about 5.5 µgm-3 of SO2 concentrations in 2014 to approximately 3 µgm-3 by 2019, is detected (see the upper left panel in Fig. ). Additionally, a good agreement is also evident between EMAC results and EANET measurements regarding the evolution of the deposited sulfur. Here, the wet deposition sulfur flux from both datasets indicate a decrease from 9 kg(S)ha-1 in 2014 to 5.8 kg(S)ha-1 in 2019 (see the upper right panel in Fig. ). This is an average decline of 0.53 kg(S)ha-1yr-1 between 2014 and 2019 based on station data in South China and Japan. reported a China nationwide average decline rate (2013–2023) of -0.244 kg(S)ha-1yr-1 and furhter showed that the trends in South and Central China are larger (negative) than this average (see their Fig. 2). Thus, our results can be considerd to be consistent. In addition, found “no clear increase or decrease trends in the S deposition amounts throughout the 15 year period” (2003–2017) at 8 stations in Japan. This is also in line with our results (Fig. , top right panel) due to the large standard deviations and because the overall decline is largely driven by emission reductions over China.

In contrast to Europe and the USA, a comparative analysis of SO2 concentration and of the wet deposition sulfur flux between the RD1SD-base-01- simulation results and measurements in China and Japan reveals noticeable differences in their temporal evolution. The RD1SD-base-01 simulation results based on the CMIP6 inventory consistently exhibits lower SO2 concentrations than EANET between 2000 and 2012, with a factor of approximately 1.5. Subsequently, larger SO2 concentrations from EMAC of approximately 15 % are detected in the years between 2012 and 2019. This pattern extends to the wet sulfur deposition temporal evolution, where EMAC consistently simulates lower values than EANET from 2000 until 2014, with a factor of approximately 1.6. However, from 2014 onwards, EMAC exhibits a reversal in trend, indicating larger values than EANET measurements by approximately 8 % until 2019.

In the lower panel of Fig. , the anthropogenic emissions from, the used CMIP6 emission inventory, the EDGAR5 and EDGAR8 emission inventories are calculated as a yearly area integral over a region covering China and Japan. The chosen region is marked by the blue box shown in Fig. . Again, the emissions from SO2 were converted to sulfur equivalent.

In 2019, the used CMIP6 emission inventory used for the RD1SD-base-01 simulation leads to a SO2 concentration of 3.6 µgm-3 compared to 2 µgm-3 measured by the EANET network, giving a bias of 1.6 µgm-3 and a ratio of 1.8.