A full description of SOCOL-AERv1 can be found in , so here we will only summarize the main aspects of the model. The model originated from the SOCOLv3 chemistry–climate model , which consists of the middle atmosphere version of the global circulation model (GCM) European Centre/Hamburg 5 (MA-ECHAM5) and the chemistry model MEZON . SOCOLv3 includes 39 hybrid vertical levels ranging from the Earth surface up to 0.01 hPa (80 km). The model is an atmosphere-only model prescribing global sea surface temperatures and sea ice coverage with observed data from the Hadley Centre . The quasi-biennial oscillation is produced in the model by relaxing the simulated zonal winds in the equatorial stratosphere to observed wind profiles .

The chemistry module in SOCOL-AERv1 includes a comprehensive range of stratospheric chemical reactions and a simplified set of tropospheric reactions: of the atmospheric hydrocarbons, only methane photochemistry is included. introduced online sulfur chemistry and sulfate aerosol microphysics to the SOCOL model, based on the two-dimensional sulfate aerosol model AER . The model considers eight gaseous sulfur species: OCS, CS2, H2S, DMS, methanesulfonic acid (MSA), SO2, sulfur trioxide (SO3), and H2SO4. Sulfate aerosol particles are resolved in 40 size bins, ranging in radius from 0.39 nm to 3.2 µm, with sequential bins doubling in volume. Chemical reaction rate coefficients and absorption cross sections of all reactions, including sulfur reactions, follow the recommendations by . In the aqueous phase, sulfur is described as S(IV) and S(VI) without further speciation. Aqueous oxidation of S(IV) by ozone (O3) and hydrogen peroxide (H2O2) is calculated by the model using the scheme by . The aqueous production flux of S(VI) is added to the atmospheric sulfate aerosol tracers with the flux to each bin proportional to the bin volume.

The microphysical scheme of SOCOL-AERv1 considers the nucleation , composition , growth through H2SO4 condensation, evaporation , coagulation , and sedimentation of sulfate aerosol . SOCOL-AERv1 employs a crude altitude-varying lifetime approach for tropospheric wet removal of sulfur species, with H2SO4 and MSA having a mean column lifetime of 5 d and SO2 having a mean lifetime of 2.5 d . Dry deposition of SO2, MSA, H2SO4, and sulfate aerosol is modeled assuming a deposition velocity of 1 cm s-1 at the ground. The model is run with operator splitting so that dynamical quantities are recalculated every 15 min, whereas the chemistry, aerosol microphysics, and radiation schemes are called every 2 h. Twenty sub-time-steps are used for the aerosol microphysical scheme, yielding an aerosol microphysical time step of 6 min.

The model's boundary conditions that we use for the year 2000 time-slice simulations are identical to . SO2 is emitted from anthropogenic and biomass burning sources according to a gridded emission inventory for the year 2000 and from continuous volcanic degassing . DMS fluxes are calculated online using a wind-driven parametrization and a climatology of sea surface DMS concentrations . As in , 1 Tg S yr-1 of CS2 is emitted between the latitudes of 52∘ S and 52∘ N. The mixing ratios of H2S and OCS are fixed at the surface to 30 pptv and 500 pptv , respectively.

To ensure comparability of results with the new development runs for this paper, we have rerun the source code from in two experiments. As opposed to the simulations in , we output the sulfur cycle burdens and fluxes as accumulated rather than instantaneous quantities to reduce the influence of diurnal cycling on the 12-hourly output of the model. To test the effect of horizontal resolution on the atmospheric sulfur cycle we ran one simulation at T31 resolution (∼3.75∘×3.75∘ in latitude and longitude, SHENG31) and one simulation at T42 resolution (SOCOL-AERv1).

In SOCOL-AERv1, the sulfate aerosol is resolved in wet radius bins. Uptake and evaporation of H2O during transport-induced changes in relative humidity and temperature cause shifts in the sulfate mass distribution with respect to wet aerosol radius, the coordinate variable. In SOCOL-AERv1, this process was treated by rescaling the number of sulfate aerosol particles so that each bin would have the correct H2SO4 weight percent. Although this procedure guarantees the conservation of the total number of H2SO4 molecules, it does not conserve the aerosol number density. To amend this, SOCOL-AERv2 resolves the sulfate aerosol distribution in dry radius bins, similar to the approach of other sectional models e.g.,. Dry radius bins can also be described as aerosol H2SO4 mass bins.

The new dry radius bins range from 0.39 nm to 3.2 µm, corresponding to 2.8 to 1.6×1012 molecules of H2SO4 per particle (assuming a H2SO4 density of 1.8 g cm-3), with molecule number doubling between bins. Since aerosol microphysics schemes and heterogeneous chemistry on sulfate aerosol require wet aerosol volume and H2SO4 weight percent, we calculate these quantities for each bin online, based on the grid cell temperature and relative humidity. This change in the dimension variable of SOCOL-AER necessitated several changes to the sulfate condensation and coagulation schemes to ensure that the transfer of aerosol from bin to bin is based on molecular fluxes rather than aerosol volume fluxes. For calculation of aerosol radiative properties, a new look-up table was produced as a function of relative humidity and temperature. To ease interpretation of the output, the outputted aerosol bins of SOCOL-AER are rebinned to the previous wet volume binning approach.

In the CONSERVE simulation, corrections were made to the aerosol microphysics scheme in SOCOL-AER, mainly to improve aerosol mass conservation. In the scheme calculating H2SO4 condensation and evaporation, the equation for the “effective” mean free path of H2SO4 molecules in air was corrected to agree with Eq. (6) from . An additional constraint was added in the H2SO4 condensation scheme such that the flux of H2SO4 from the gas phase must equal the flux of H2SO4 into the particle phase. This improves mass conservation in cases when H2SO4 is depleted below the saturation vapor pressure within one time step. Furthermore, the aerosol sedimentation scheme in SOCOL-AERv1 was not applied within boundary layer levels and sedimenting aerosol from the model level above the boundary layer was artificially removed. In the CONSERVE simulation this is amended: sedimenting aerosol from the model level above the boundary layer is added to the layer below. had implemented several forced mass conservation checks on the total (gas-phase and aerosol) H2SO4 burden in each grid cell. If the total burden had changed by more than 0.1 % during aerosol microphysics, H2SO4 aerosol and gas-phase mixing ratios would be scaled to agree with the total H2SO4 burden before microphysics calculations. These forced mass corrections were found to be unnecessary after the above improvements to the microphysics scheme, and therefore they were removed from SOCOL-AERv2.

Since the publication of , improvements have been made to the SOCOL model in preparation of the coordinated simulations within the Chemistry Climate Model Initiative (CCMI), mainly related to the improvement in tropospheric chemistry processes . Many of these improvements have been merged into SOCOL-AERv2 and have upgraded the representation of chemistry in our model, in particular in the troposphere.

In SOCOL-AERv1, as well as SOCOLv3 , ozone-depleting substances (ODSs) were transported in three families (short-lived Cl, long-lived Cl, and Br) to save computational cost. With modern supercomputers this treatment is no longer necessary and the ODS species are transported individually. The individual treatment of ODS species avoids a repartitioning of the family members, based on simplified age-of-air estimates, after each transport step. The chemistry scheme was expanded in the CCMI simulation, as described in . We included the Mainz Isoprene Mechanism (MIM-1) in SOCOL-AER. This scheme considers the degradation of isoprene and necessitates the addition of 14 organic species and 44 chemical reactions to SOCOL-AER . Additional CO emissions were added to the model to account for the effect of oxidation of nonmethane volatile organic compounds (NMVOC) emitted from anthropogenic, biogenic, and biomass burning sources. Lightning NOx is now calculated interactively based on cloud-top height and grid cell scaling factors from satellite observations . A cloud modification factor approach was implemented to account for the effect of clouds on photolysis rates. We derived a new look-up table of photolysis rates averaged over two solar cycles (22 years) from a comprehensive reconstruction of total and spectral solar irradiance (NRLSSI) by , which was used in the CCMI REF-C1 experiment. Additional heating through Hartley and Huggins bands of ozone has also been implemented into SOCOL-AER. As documented by , N2O5 hydrolysis on tropospheric aerosols is now included in SOCOL-AER. Methanesulfonic acid (MSA) chemistry is solved in the explicit scheme instead of the implicit Newton–Raphson scheme since otherwise the chemical solver does not properly converge. Reaction rates have been updated or added from the NASA JPL data evaluation no. 18 .

In the previous simulations, to allow for rapid boundary layer mixing, emissions of chemical species were immediately dispersed over the four lowermost model levels (∼1 km altitude), species with prescribed mixing ratios (including OCS and H2S) were dispersed over the six lowermost levels (∼2 km altitude), and dry deposition of species occurred out of the four lowermost model levels. While such a coarse approach was sufficient for stratospheric applications, it is inadequate for deposition flux and tropospheric lifetime calculations. Instead of emitting the species in multiple lower layers, SOCOL-AERv2 emits only in the first model layer (∼70 m), from which the species are mixed via the model's boundary layer parametrizations. The BNDLAYER simulation tests specifically the effect of using only one model layer for emission and prepares the model for revised dry deposition boundary conditions.

We implemented the interactive dry deposition scheme described in in SOCOL-AERv2, replacing the simple prescribed constant deposition velocities of SOCOL-AERv1. The new treatment is based on the DRYDEP scheme in the EMAC model . Dry deposition velocities are calculated using an interactive resistance-based approach which considers surface properties, the solubility and reactivity of each gas tracer, and the radius and density of aerosol tracers . Effective Henry’s law constants for near-neutral pH and reactivity of gas tracers are taken from . These improvements are tested in the DRYDEP simulation.

An interactive wet deposition scheme was added to SOCOL-AER, based on the SCAV submodule in the EMAC model . Grid scale variables from ECHAM5 such as liquid and ice water contents, cloud cover, convective and large-scale rain and ice formation and precipitation fluxes, and the convective upward mass flux are used by the wet deposition scheme. Since our model does not include a comprehensive cloud aqueous chemistry mechanism, we implemented the EASY2 version of the SCAV submodule with a constant pH of 5 for cloud water and rain water. The constant pH of 5 is within the wide range of pH values (3.6–7) measured by several hill cap cloud field campaigns . Scavenging coefficients for gas-phase species are calculated based on Henry’s law equilibrium constants. Scavenging of aerosol is based on a radius-dependent calculation of nucleation and impaction scavenging. During cloud evaporation, all scavenged gas-phase species are released to the atmosphere in their original species, whereas evaporating scavenged sulfate aerosol species are transferred to the largest aerosol size bin. The wet deposition scheme is applied to SO2, gaseous H2SO4, and sulfate aerosol, as well as other gas chemical tracers such as O3, HNO3, N2O5, H2O2, etc. The WETDEP simulation includes this new interactive wet deposition scheme instead of the fixed wet deposition lifetimes used in SOCOL-AERv1.

In the SO2 aqueous chemistry subroutine of SOCOL-AERv1, the pH of clouds is prescribed vertically according to so that pH equals 3 from the surface to 600 hPa and 4.5 above 600 hPa. However, this paper reported modeled pH within a single cumulus cloud, where liquid water content increased with height. This pH distribution is therefore not applicable to the whole atmosphere. Although in the interactive wet deposition scheme a constant cloud pH of 5 is used (Sect. ), aqueous-phase sulfur chemistry is more sensitive to the choice of pH and therefore a more detailed pH distribution was applied. We use an approximation of the modeled cloud pH from for the revised aqueous chemistry routine. Between the surface and 600 hPa, north of 20∘ N a cloud pH of 5.2 is used and south of 20∘ N a cloud pH of 4.2 is used. Above the 600 hPa level, a uniform pH of 3.5 is used.

In SOCOL-AERv1, the SO2 oxidized in the aqueous cloud phase is released as aerosol. With the new interactive wet deposition scheme, it is possible to transfer the oxidized SO2 directly to the scavenged aerosol flux in cloud water. The wet deposition routine is called at each dynamical time step (15 min), while the aqueous-phase chemistry was called at each chemical time step in SOCOL-AERv1 (2 h). To transfer the oxidized SO2 flux to the wet deposition scheme directly, it was both logical and technically simpler to synchronize these two processes. In the AQCHEM simulation, the above changes were added to SOCOL-AER and the aqueous-phase chemistry is called at each dynamical time step.

Section – complete the description of improvements in developing SOCOL-AERv2 with one exception, namely how SO2 oxidation is calculated in clouds in the mixed-phase temperature regime. This is important because the S(IV) to S(VI) conversion only occurs in the liquid phase in the model. Therefore, in the final development simulation (SOCOL-AERv2) we wanted to investigate whether the aqueous SO2 reaction was hampered by the model's representation of the liquid fraction in mixed-phase clouds. It has recently been discussed in the literature that many general circulation models (GCMs) underpredict the supercooled liquid fraction (SLF) observed by satellite products . The modeled liquid fraction in SOCOL-AERv1 underestimates the fitted CALIOP satellite measurements from throughout most of the mixed-phase cloud temperature range (Fig. S1 in the Supplement). In the SOCOL-AERv2 run, we correct for the influence of the underestimated supercooled liquid fraction on SO2 aqueous chemistry. The ECHAM5 calculated liquid water content (LWC) and ice water content (IWC) are added together and inputted into the aqueous-phase chemistry subroutine as total water content (TWC). If the grid cell temperature (T) is in the mixed-phase cloud regime (-38 to 0 ∘C), we calculate the observed supercooled liquid fraction (SLF) from the fitted sigmoid function from : 1SLFHu=1+exp⁡-f(T)-1,2f(T)=5.3608+0.4025T+0.08387T2+0.007182T3+2.39×10-4T4+2.87×10-6T5, where T is the air temperature in degrees Celsius (∘C). The determined SLF can is used to correct LWC in the aqueous chemistry subroutine, i.e., LWC=SLFHu×TWC.

We ran two additional simulations to probe whether the remaining disagreement between observations and SOCOL-AERv2 could be caused by overestimated cross-tropopause fluxes of SO2 and sulfate aerosol. In ICE-OX, the aqueous-phase oxidation of SO2 was allowed to occur in ice water as well as liquid water. Increased oxidation of SO2 in the upper troposphere reduces its cross-tropopause flux. In AER-SCAV, the scavenging coefficient of aerosol particles on ice clouds was increased by a factor of 20 from 0.05 to 1. This enhances the removal of sulfate aerosol in the upper troposphere.

Since the SHENG31 simulation was rerun for this study, several quantities differ slightly in SHENG31 compared to (e.g., 114 vs. 109 Gg S of stratospheric sulfate aerosol). The differences in the quantities could be caused by the switch in output format from instantaneous 12-hourly values to mean 12-hourly values. However, the changes are minor and the overall picture for the sulfur cycle remains unchanged. Refining the horizontal resolution to T42 in SOCOL-AERv1 does not result in substantial changes for the tropospheric and stratospheric aerosol burdens.

The change from wet radius to dry radius binning reduces the tropospheric aerosol burden and increases the stratospheric aerosol burden in DRYRAD (Table ). The increased stratospheric aerosol burden can be explained by a decrease in the effective aerosol radius, leading to a longer stratospheric lifetime. The decrease in tropospheric aerosol burden occurs mainly around the Northern Hemisphere midlatitudes, where anthropogenic emissions of SO2 are high and thus sulfate particles can grow through condensation. In the DRYRAD version of the model the wet particle radius is no longer restricted to 3.2 µm; accounting for the uptake of water the maximum radius can reach well above 10 µm. The possibility of larger particle formation can lead to enhanced sedimentation velocities and therefore reduced aerosol lifetimes.

The corrections in the sedimentation and H2SO4 condensation schemes do improve the mass conservation of sulfur species. The tropospheric sulfate aerosol burden increases by 4 %, mainly due to the correction of the artificial removal of particles sedimenting from the model level above the boundary layer level. This artificial loss due to sedimentation represents a ∼3 Tg S yr-1 sink since the outputted total sulfur deposition increases by this amount from the DRYRAD to the CONSERVE simulations. Furthermore, in the DRYRAD simulation the total sum of tropospheric aerosol influxes and outfluxes result in an imbalance of 3339 Gg S yr-1, which corresponds to about 8 % of the source flux of tropospheric sulfate aerosol. In the CONSERVE simulation, this imbalance is reduced to 63 Gg S yr-1, i.e., around 0.1 % of the aerosol source flux. These improvements to the model provide more confidence to the outputted sulfur cycle fluxes, which will be used to study the sulfur budget in Sect. .

Including the expanded chemistry set and updates from the CCMI version of SOCOLv3 in SOCOL-AER leads to altered distributions of gas-phase species in the troposphere. The relevant change for the tropospheric sulfur cycle is increased mixing ratios of H2O2, causing increased aqueous conversion of SO2 to S(VI). For this reason, the CCMI simulation shows a 19 Gg S lower SO2 burden and a 10 Gg S larger sulfate aerosol burden in the troposphere than the CONSERVE simulation. Larger OH mixing ratios in the upper troposphere and lower stratosphere (UTLS) reduce the SO2 lifetime, causing 5 Gg lower SO2 and 2 Gg higher sulfate aerosol burdens in the stratosphere. These chemical changes also lead to differences in the Pinatubo simulation, to be discussed in Sect. .

In BNDLAYER the boundary layer conditions are only implemented for the lowest level of the model. The confinement of the boundary layer conditions to one model level reduces the burdens of SO2 and sulfate aerosol in the troposphere and stratosphere. This is a strong effect with reductions of the tropospheric aerosol burden by 40 % and the stratospheric aerosol burden by 20 % in BNDLAYER. The first cause is the reduction in effective S emissions into the atmosphere since H2S is prescribed to be 30 ppt in only one model level instead of six model levels. Assuming steady-state conditions over the 5-year averaging period, the 8.5 Tg S yr-1 decrease in total sulfur deposition (Table ) corresponds to an 8.5 Tg S yr-1 decrease in the sulfur emissions. Another cause for the SO2 and aerosol burden decrease is that SO2 is emitted close to the surface in BNDLAYER, leading to less dispersion of SO2 in the atmosphere and enhanced dry deposition close to emission regions. The shorter SO2 lifetime reduces its atmospheric burden, as well as reducing the conversion of SO2 to H2SO4 and subsequent sulfate aerosol formation.

The correct treatment of the lowermost model levels remains difficult and is model dependent. Owing to their coarse resolution, CCMs cannot resolve the transport of chemical species by rapid boundary layer convection and turbulence. This leaves the boundary layer parametrizations in SOCOL-AER imperfect and the number of model levels that should be included in the emission boundary conditions uncertain. For the subsequent simulations we use the single-level boundary layer treatment.

The implementation of interactively calculated dry deposition velocities, compared to the previously included constant dry deposition velocities, results in much longer dry deposition lifetimes for both SO2 and sulfate aerosol. SO2 dry deposition velocities decrease more drastically over land than over ocean in the DRYDEP simulation (Fig. ). Over land, the SO2 dry deposition velocity is smaller than 1 cm s-1, which was the original value set in SOCOL-AERv1. The only locations where SO2 dry deposition velocities are greater than 1 cm s-1 are above certain parts of the ocean, due to the high solubility of SO2 in waters at near-neutral pH. The dry deposition velocities of SO2 agree well with the distribution simulated by the EMAC model . The resultant longer SO2 dry deposition lifetime increases the tropospheric SO2 burden, the conversion of SO2 to aerosol, and consequently the tropospheric aerosol burden. In addition, dry deposition velocities of sulfate aerosol decrease globally compared to the assumed constant deposition velocity in SOCOL-AERv1 (1 cm s-1), leading to longer aerosol lifetimes with respect to dry deposition. Due to augmented transport of tropospheric SO2 and primary sulfate aerosol from the troposphere, the stratospheric aerosol burden increases by 22 to 128 Gg S. The changes in DRYDEP largely compensate the changes in BNDLAYER, for which emissions were confined to a single model level.

When the constant wet deposition lifetimes for sulfur species are replaced with interactively calculated wet removal in the WETDEP simulation, the SO2 wet deposition flux is reduced from 20.1 to 0.3 Tg yr-1, revealing an overestimation in the approach of SOCOL-AERv1. With the elimination of the wet deposition sink for SO2, the tropospheric SO2 burden increases by around 60 % and the total (aqueous + gas phase) conversion flux of SO2 to S(VI) increases by around 40 %. In , the mean wet deposition lifetime for SO2 was selected as 2.5 d following the two-dimensional AER model. However, the AER model includes the 2.5 d lifetime for SO2 to account for aqueous oxidation of SO2, which is not explicitly modeled by AER . As SOCOL-AERv1 already includes a mechanism for aqueous oxidation of SO2 by H2O2 and O3 in clouds, this resulted in double counting of the loss of SO2 by aqueous oxidation in previous simulations. The aerosol wet deposition maps and the relative difference between the DRYDEP and WETDEP simulations are shown in Fig. . The inclusion of an interactive wet deposition enhances sulfate aerosol deposition in areas with high precipitation and suppresses it in drier regions. Sulfate deposition is reduced over polar regions, the eastern part of ocean basins, and the Sahara (lower precipitation regions), and is enhanced in the tropics and midlatitude storm tracks (higher precipitation regions). The reductions in sulfate deposition fluxes above Greenland and Antarctica are notable since SOCOL-AERv1 overestimated the magnitude of polar sulfate deposition fluxes compared to ice core measurements, which are used as proxies for past volcanic eruptions . Calculating a global aerosol wet deposition lifetime with respect to wet deposition (lifetime is tropospheric aerosol burden divided by aerosol wet deposition flux), DRYDEP has an aerosol wet deposition lifetime of 4.9 d and WETDEP has a lifetime of 5.1 d. Therefore, there is not a large change in the global aerosol wet deposition lifetime; however, the spatial distribution of the wet deposition sink has shifted. In WETDEP the tropospheric column wet deposition lifetime of sulfate aerosol varies from 2 d in the northern midlatitude storm tracks to more than 3 years over the southwestern United States. The introduction of interactive wet deposition to SOCOL-AER has the largest impact of any step on the stratospheric sulfate burden. Driven by the longer SO2 wet deposition lifetime, the stratospheric sulfate aerosol burden climbs by around 60 % to 202 Gg S. As will be discussed in Sect. , this value is much higher than the inferred stratospheric burden from SAGE II data for background nonvolcanic conditions. To improve the agreement with observations, we focus on a possible underestimation of the sulfate aqueous chemistry flux since the unintended double counting of this flux led to good agreement of SOCOL-AERv1 with stratospheric observations .

In the AQCHEM simulation we amended the cloud pH distribution for aqueous chemistry, reduced the aqueous chemistry time step to 15 min, and directly transferred oxidized S(IV) to the scavenged sulfate aerosol in the wet deposition scheme. This increases the aqueous oxidation flux of S(IV) to S(VI) by around 50 %. The enhanced aqueous conversion of SO2 to sulfate aerosol leads to increased aerosol formation in the lowermost troposphere, where deposition is efficient. This results in smaller tropospheric burdens of both SO2 and sulfate aerosol, meaning that there is also less transport of tropospheric S to the stratosphere. The stratospheric aerosol burden decreases by 18 % from 202 to 165 Gg S. From separate sensitivity studies (not shown), we find that the shorter aqueous chemistry time step is the main cause of the increased aqueous flux. investigated the sensitivity of sulfate aqueous chemistry to different settings and also found that reducing the aqueous chemistry time step increases the conversion of S(IV) to S(VI). This is because the Henry’s law equilibration rate and aqueous oxidation is fast so with shorter time steps more SO2 can be dissolved in cloud droplets and converted to S(VI).

Because of the underprediction of the SLF (Fig. S1) and oxidation of SO2 occurring only in liquid water in SOCOL-AER, the oxidation of SO2 is likely underestimated in the upper troposphere, leading to a too intensive transport of SO2 to the stratosphere. Therefore, in the SOCOL-AERv2 simulation we increased the supercooled liquid fraction to agree with the SLF–temperature relationship observed by CALIOP . This increase in SLF enhances the SO2 oxidation rate in the middle and upper tropospheric mixed-phase clouds, reducing the cross-tropopause SO2 flux by around 10 %. However, the impact on the stratospheric aerosol burden is minor, with only a reduction of 6 Gg S (-4 %) compared to the AQCHEM simulation. Therefore, the underestimation of the SLF does not play a major role in SOCOL-AER's stratospheric sulfur cycle. However, the amount of SO2 oxidation in the upper troposphere may be affected by other processes, e.g. by oxidation on ice surfaces. This will be discussed further in Sect. .

compared the modeled stratospheric sulfate aerosol burden to the value calculated by the SAGE-4λ method . In this method, extinctions measured by the SAGE II satellite product are used to estimate the stratospheric aerosol size distribution, which can then be used to determine the aerosol burden. The background stratospheric aerosol burden derived from SAGE-4λ almost exactly matched the burden simulated by SOCOL-AERv1. Since that time, a new SAGE II retrieval has been published as part of the GloSSAC database . A new method (SAGE-3λ) has been used to calculate the aerosol size distribution from the GloSSAC database. In this method, the surface area density and mass density of very small particles, which are invisible to the satellite extinction measurements, are added to the lognormal size distributions derived from the GloSSAC data. The stratospheric aerosol burden derived from SAGE-3λ for the volcanically quiescent period 2000–2004 is 165±11 (±σ) Gg S. This aerosol burden is about 40 % larger than the stratospheric burden calculated from SAGE-4λ, 117±8 Gg S. (Note that this value differs slightly from the value reported in , 112.5 Gg S, possibly due to different assumptions about the tropopause height.) The addition of small aerosol particles derived from OPC measurements contributes 18 Gg S to the SAGE-3λ. The rest of the increase from SAGE-4λ to SAGE-3λ can be attributed to the new retrieval methods.

The stratospheric aerosol burden simulated by SOCOL-AERv2, 160 Gg S, agrees well with the SAGE-3λ-derived burden of 165 Gg S. However, evaluating a model's performance with the stratospheric aerosol burden is not straightforward since both SAGE-3λ and SAGE-4λ are themselves derived products and not direct measurements. The retrieval of size distributions from measured SAGE II wavelengths is uncertain, as can be seen when comparing the change between SAGE-3λ and SAGE-4λ stratospheric burdens. In addition, the MERRA climatological tropopause height was used to calculate the stratospheric burden for the SAGE-3λ and SAGE-4λ products. However, for SOCOL-AER's burden, the WMO-defined (World Meteorological Organization) tropopause height from the model was used . Differences between the tropopause heights used in different calculations can play a big role in the derived burden since the majority of the aerosol burden is located in the lower stratosphere. For example, if the tropopause height from SOCOL-AER instead of MERRA is used, the stratospheric burdens derived from SAGE-3λ and SAGE-4λ are around 7 % smaller. For these reasons we will evaluate SOCOL-AER with the extinctions measured directly by SAGE II of version GloSSACv1.0, in addition to the derived burdens.

Figure  shows the comparison of annual mean SOCOL-AERv1 and v2 extinctions with SAGE II at the Equator and 45∘ N for 525 and 1020 nm. Below 20 km at the Equator, SOCOL-AERv2 shows higher extinctions at both wavelengths, which match better with the SAGE II observations. However, in the lowest 1–3 km of the stratosphere, organics are a nonnegligible fraction of the overall aerosol burden and therefore can contribute to the aerosol extinction observed by SAGE II. If anything, SOCOL-AER as a sulfate aerosol-only model should underestimate the extinction at these altitudes, although to what extent is unknown. Since SOCOL-AERv2 matches or overestimates the SAGE II extinctions in the lowermost stratosphere, SOCOL-AERv2 may have too high sulfate aerosol concentrations in the lower stratosphere. Between 20 and 25 km SOCOL-AERv2 overestimates the SAGE II extinctions, while SOCOL-AERv1 matches observations. Between 25 and 30 km both model versions overestimate the SAGE II extinctions. The model versions are within observed variability between 30 and 35 km; however, above 35 km they tend to underestimate the extinction, possibly because of meteoritic dust, which is the major contributor to extinction in the upper stratosphere . The comparison at 45∘ N is similar to the equatorial comparison with SOCOL-AERv2 overestimating the observed aerosol extinctions below 20 km and otherwise showing similar behavior to SOCOL-AERv1.

Since the overestimation of SOCOL-AERv2 in the lower stratosphere originates from the introduction of interactive deposition schemes, it possibly stems from too fast cross-tropopause transport of primary sulfate aerosol and/or SO2, whereas the better agreement of SOCOL-AERv1 may be fortuitous due to the double counting of the SO2 oxidation flux in the wet-deposition scheme. SOCOL-AERv2 is the version that is more physically consistent in its representation of the tropospheric sulfur cycle. However, several outstanding issues remain in SOCOL-AERv2's representation of sulfate aerosol extinction below 20 km at 45∘ N and between 20 and 30 km at the Equator.

We also compare the SOCOL-AER simulations with in situ OPC measurements from Laramie, USA, and Lauder, New Zealand (Fig. ). Since the publication of , the counting efficiencies of OPC channels as a function of radius have undergone important revisions . In Fig. , we apply the measured counting efficiencies for the channels r>0.15, r>0.25, and r>0.30 µm from to the SOCOL-AER size bins (counting efficiencies were not measured for other channels). In this manner, we can calculate the number density that an OPC instrument would measure given a simulated size distribution.

SOCOL-AERv2 simulates higher number densities of condensation nuclei (CN, r>0.01 µm) above 25 km, matching the shape of the observed curve better than SOCOL-AERv1. The transport of polar H2SO4-rich air to midlatitudes during the breakup of the polar vortex may lead to the high number densities of CN above 25 km in the measurements . The improved agreement in SOCOL-AERv2 is due to the implementation of dry radius binning and the improvement in sulfur mass conservation, which enable the model to capture the increased transport of CN to midlatitudes during late winter and spring. SOCOL-AERv2 also displays a kink at the tropopause for particle channels larger than r>0.15 µm, which appeared after the addition of interactive wet deposition. In the interactive wet deposition scheme, the scavenging efficiency of particles depends on radius, which leads to stronger removal of larger aerosol particles in the troposphere. Lauder OPC measurements may also show a similar kink at the tropopause for the larger particle channels; however, it is difficult to verify this given the large variability in the measurements (Fig. ).

Otherwise, both model versions show similar levels of agreement with the OPC measurements. All four channels larger than r>0.25 µm have too high number densities compared to observations at Laramie, with the agreement becoming even worse with altitude. At Lauder the agreement of the largest three channels (r>0.30 µm) is better. attributed the worsening agreement of larger aerosol particles with altitude to either numerical diffusion in the sedimentation scheme or an overestimate in the speed of the Brewer-Dobson circulation, a known artifact in the SOCOL model .

There has been an ongoing debate in the literature regarding the magnitude of the cross-tropopause SO2 flux and its relative importance in establishing the Junge layer . The debate has been fueled by a lack of in situ measurements in the UTLS region and the high temporal and spatial variability in UTLS SO2. Figure  compares the tropical UTLS SO2 measured by two aircraft campaigns with two annual mean satellite products, MIPAS , and ACE-FTS , averaged during volcanically quiescent periods. The two in situ measurements and the ACE-FTS satellite product all show SO2 mixing ratios of 5 to 10 pptv around the tropical tropopause (∼17 km). MIPAS-observed SO2 is around 24 pptv at 17 km, substantially higher than the other observations.

The annual means of SOCOL-AERv1 and v2 agree with MIPAS-observed SO2 and overestimate the three other observation sets at the tropopause, simulating SO2 mixing ratios between 20 and 30 pptv at 17 km. MIPAS satellite observations of SO2 under nonvolcanic conditions are uncertain, which may explain the systematic offset between MIPAS SO2 measurements and the other observation sets . On the other hand, in situ measurements lack the spatial and temporal coverage of satellites, which reduces their comparability with global models. More aircraft campaigns will be invaluable for determining the background level of UTLS SO2. If anything, the currently available observations suggest that SOCOL-AER's cross-tropopause SO2 transport might be too high. In Sect.  we will investigate the consequences of an overestimated UTLS SO2.

The wet deposition scheme in SOCOL-AERv2 is coupled to the climate model’s cloud and precipitation fields, whereas in SOCOL-AERv1 constant wet deposition lifetimes are applied. SOCOL-AERv1 therefore simulates too large deposition fluxes in dry regions and too small deposition fluxes in wet regions compared to SOCOL-AERv2 (Sect. ). To verify the SOCOL-AERv2 wet deposition fluxes in both dry and wet regions, we compare simulated and observed sulfate deposition fluxes over 3 orders of magnitude in Fig. . The presentation is logarithmic since using linear axes would give too high a weight to large deposition fluxes, obscuring biases at the lower range of deposition fluxes.

SOCOL-AERv1 indeed overestimates low deposition fluxes (<1 kg S ha-1), corresponding to sites in drier areas (<50 cm yr-1 precipitation). For both time periods (2000–2002 and 2005–2007), SOCOL-AERv2 improves the agreement with observations compared to SOCOL-AERv1 (R2=0.61 and R2=0.69 for SOCOL-AERv2 vs. R2=0.51 and R2=0.58 for SOCOL-AERv1). The fraction of stations where the model is within a factor of 2 of observations (f2×) also improves slightly for both measurement periods in SOCOL-AERv2. The variability in simulated wet deposition fluxes, shown by the ensemble standard deviation bars in Fig. , increases in SOCOL-AERv2 because wet deposition is coupled to modeled precipitation. Due to the internal variability in modeled precipitation in a free-running climate model, multiple-ensemble simulations as well as long-term deposition measurements are required when comparing models with observations. Overall, SOCOL-AERv2 matches the measurements better than SOCOL-AERv1, especially for sites with low and high deposition fluxes.

Nevertheless, there are remaining biases in the deposition fields of SOCOL-AERv2, e.g. high biases in many North American sites compared to the WMO observations (Fig.  and Table ). Since the model's deposition scheme is coupled to precipitation fields, inaccuracies in the modeled precipitation distribution can lead to incorrect deposition fluxes. We calculated the model's precipitation biases compared to the WMO database for each station. The bias in precipitation depth in SOCOL-AERv2 correlates with the bias that we find for sulfate deposition fluxes (Spearman's correlation coefficient, ρ=0.5, Fig. S4). This finding suggests that some of the model biases can be explained by errors in precipitation fields rather than errors in the wet deposition scheme. Both versions of SOCOL-AER match the observations better in the period 2005–2007 rather than 2000–2002. Since there are no large differences in the precipitation biases between these periods, this improvement could be related to more accurate SO2 emission maps for the 2005–2007 period. One known issue with the CEDS anthropogenic SO2 inventory is that the emissions from the western United States are overestimated compared to the eastern United States . SOCOL-AERv2 also shows higher deposition biases in the western United States. Since errors in emission inventories and model precipitation fields impact the evaluation of the deposition field, it is difficult to attribute errors to the deposition scheme itself.

Table  compares the performance of SOCOL-AERv2 to past model intercomparison studies, including Photocomp , ACCMIP , HTAP I , and HTAP II . These intercomparison projects used observational data from the same networks as in the WMO database to evaluate their results. However, the analysis periods for these intercomparison projects differed from this study for both the simulations and observations (Table S1), which can contribute to the differences in the results. SOCOL-AERv2 shows similar levels of agreement with observations as the previous model intercomparison studies in the European and East Asian regions. The model biases, correlation coefficients, and fraction of values within ±50 % of measurements fall within or very close to the range of the intercomparison projects. In North America, SOCOL-AERv2 correlates similarly with observations (Pearson correlation coefficient, R=0.8); however, biases and the fraction within ±50 % are worse than the past intercomparison projects. As mentioned above, the North American deposition fluxes may be affected by inaccuracies in our model's precipitation fields and/or errors in the anthropogenic SO2 emission inventory. In addition, there are several factors that advantage the model-intercomparison projects compared to the SOCOL-AER runs. Firstly, we have compared ranges of the multimodel means and not the individual model values from the intercomparison projects, which likely have a wider spread and individually worse performance. Secondly, model resolution can play an important role in the comparison between observations and simulations and SOCOL-AER was run at a relatively coarse resolution (2.8∘×2.8∘) compared to many of the models used in the intercomparison project. Finally, three of the intercomparison projects (Photocomp, HTAP I, and HTAP II) were based on offline chemistry-transport models that are run with observed meteorology. On the other hand, SOCOL-AER is used in free-running mode, producing five ensemble members that are subsequently averaged. SOCOL-AER, and its parent climate model ECHAM5, include precipitation biases that impact the simulation of deposition. Considering these aspects, the performance of SOCOL-AERv2 compares well with state-of-the-art sulfate wet deposition models.

Dry deposition fluxes compiled by the WMO assessment are based on North American stations from the Canadian Air and Precipitation Monitoring Network (CAPMoN) and the US Clean Air Status and Trends Network (CASTNET). Dry deposition fluxes are not measured directly but are inferred through surface-based measurements of gas and particle concentrations and estimates of their dry deposition velocities . The estimation of dry deposition velocities is uncertain; the SO2 dry deposition velocities calculated by the CAPMoN network are around 50 % higher than those of the CASTNET network . The inferred dry deposition fluxes are therefore less reliable for comparisons with models than the measured wet deposition fluxes.

Figure  displays the comparison between SOCOL-AER versions and the total sulfur (sum of SO2 and aerosol) inferred dry deposition fluxes from North American measurement networks. Despite the systematic bias between the CAPMoN and CASTNET networks, we calculate the power regression, f2×, and the R2 value based on the combined dataset of both networks. We take this approach as it is unclear which network's dry deposition velocity calculation is more accurate . SOCOL-AERv2, with its new interactive dry deposition scheme, shows a similar correlation with the observations as SOCOL-AERv1. However, SOCOL-AERv2's improved deposition scheme simulates much more realistic slopes of the correlation lines and higher fractions of model results within a factor of 2 of observations. The improved agreement of SOCOL-AERv2 is likely caused by the better spatial representation of SO2 dry deposition velocities in the interactive scheme. The modeled dry deposition fluxes can also be affected by the new wet deposition scheme since enhanced sulfur removal through wet deposition leaves less sulfur available for dry deposition, and vice versa. Similar to the wet deposition comparison, the model performs better in 2005–2007 compared to 2000–2002, suggesting that the North American emission inventories may be biased in the earlier time period. Additional comparisons for the SO2 and aerosol dry deposition fluxes with observations show better agreement for SOCOL-AERv2 than SOCOL-AERv1 (Fig. S5 and S6).

Compared to past model-intercomparison projects for total sulfur dry deposition, SOCOL-AERv2 simulates a lower bias and a higher fraction of model values within ±50 % of the observation sites (Table ). The agreement nevertheless remains poor with only 19 % to 28 % of the modeled total dry deposition fluxes within ±50 % of the observations. Aerosol dry deposition biases are larger in SOCOL-AER compared to past model intercomparison projects. However, since SO2 dominates the dry deposition flux (compare Figs. S5 and S6), the reduced biases in the SO2 deposition fluxes in SOCOL-AERv2 leads to overall lower total sulfur dry deposition biases. It is difficult to conclude whether the observations should actually be the target for the model in this case since dry deposition fluxes are inferred values with inherent uncertainties. As observational networks improve their parametrizations for deriving the dry deposition flux, they will become more reliable standards with which to compare modeled results. However, the similar, if not better, agreement of SOCOL-AERv2 compared to sulfur dry deposition from model-intercomparison studies adds confidence to the implemented dry deposition scheme.