Exploring DMS oxidation and implications for global aerosol radiative forcing

Abstract. Aerosol indirect radiative forcing (IRF), which characterizes how aerosols alter cloud formation and properties, is very sensitive to the preindustrial (PI) aerosol burden. Dimethyl sulfide (DMS), emitted from the ocean, is a dominant natural precursor of non-sea-salt sulfate in the PI and pristine present-day (PD) atmospheres. Here we revisit the atmospheric oxidation chemistry of DMS, particularly under pristine conditions, and its impact on aerosol IRF. Based on previous laboratory studies, we expand the simplified DMS oxidation scheme used in the Community Atmospheric Model version 6 with chemistry (CAM6-chem) to capture the OH-addition pathway as well as the H-abstraction pathway and the associated isomerization branch. These additional oxidation channels of DMS produce several stable intermediate compounds, e.g., methanesulfonic acid (MSA) and hydroperoxymethyl thioformate (HPMTF), delay the formation of sulfate, and hence, alter the spatial distribution of sulfate aerosol and radiative impacts. The expanded scheme improves the agreement between modeled and observed concentrations of DMS, MSA, HPMTF, and sulfate over most marine regions based on the NASA Atmospheric Tomography (ATom), the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA), and the VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx) measurements. We find that the global HPMTF burden, as well as the burden of sulfate produced from DMS oxidation are relatively insensitive to the assumed isomerization rate, but the burden of HPMTF is very sensitive to a potential additional cloud loss. We find that global sulfate burden under PI and PD emissions increase to 412 Gg-S (+29 %) and 582 Gg-S (+8.8 %), respectively, compared to the standard simplified DMS oxidation scheme. The resulting annual mean global PD direct radiative effect of DMS-derived sulfate alone is −0.11  W m−2. The enhanced PI sulfate produced via the gas-phase chemistry updates alone dampens the aerosol IRF as anticipated (−2.2 W m−2 in standard versus −1.7 W m−2 with updated gas-phase chemistry). However, high clouds in the tropics and low clouds in the Southern Ocean appear particularly sensitive to the additional aqueous-phase pathways, counteracting this change (−2.3 W m−2). This study confirms the sensitivity of aerosol IRF to the PI aerosol loading, as well as the need to better understand the processes controlling aerosol formation in the PI atmosphere and the cloud response to these changes.



Introduction
The IPCC AR5 (Myhre et al., 2013) and the recent preliminary release of AR6 (https://www.ipcc.ch/report/sixth-assessment-report-cycle/) indicates that atmospheric aerosol 55 particles are a dominant source of uncertainty in global climate forcing. Aerosols interact with incoming and outgoing radiation directly (via scattering and absorption) and indirectly (via changing cloud properties and lifetime). In particular, the aerosol indirect radiative forcing (IRF) via interactions with clouds is driven by the fractional enhancement of aerosol burden from a preindustrial (PI;1850) atmosphere to a present-day (PD; 2000) one, with a cleaner PI atmosphere producing a larger IRF 60 (Menon et al., 2002). Carslaw et al. (2013) confirm that the estimated uncertainty in aerosol IRF is dominated by uncertainty in natural aerosols. It is therefore critically important to accurately determine the formation of natural aerosols and their radiative impacts in both PD and PI atmosphere.
Though the crucial role of DMS oxidation as a source of natural aerosols has been acknowledged for decades, its oxidation mechanisms are still not well understood (Barnes et al., 2006;Hoffmann et al., 75 2016). Global/regional models often simplify the DMS oxidation processes for the sake of computational costs. For example, the Community Atmosphere Model with chemistry (CAM-chem) includes only the oxidation of DMS by OH and NO3 radicals, directly producing SO2, which further oxidizes to produce sulfate (Emmons et al., 2020;Lamarque et al., 2012). This simplification ignores 80 some potentially important reaction intermediates and pathways. For instance, previous studies suggest that BrO contributes up to 30% of the DMS sink in remote MBL (Boucher et al., 2003;Breider et al., 2010;von Glasow and Crutzen, 2004;Khan et al., 2016). MSA has been found to form efficiently via the multi-phase OH-addition DMS oxidation pathway followed by reaction with OH(aq) to form sulfate aerosol in the MBL (von Glasow and Crutzen, 2004;Milne et al., 1989;Zhu et al., 2006). Recently,85 both theoretical and laboratory studies have proposed that a pristine environment favors the Habstraction reaction when DMS is oxidized by OH, generating methylthiomethylperoxy radicals (MSP: CH3SCH2OO), which further undergoes a series of rapid intramolecular H-shift isomerization reactions, yielding a stable intermediate hydroperoxymethyl thioformate (HPMTF: HOOCH2SCHO) (Wu et al., 2015;Berndt et al., 2019). Recent in situ measurements report HPMTF concentrations that are on 90 average 50% of DMS concentrations in the MBL during the day, but can exceed DMS concentrations at times, confirming the importance of the isomerization branch for capturing the fate of oxidized DMS (Veres et al., 2020;Vermeuel et al., 2020).
The lifetimes of stable intermediates from DMS oxidation can be up to days. As a result, these intermediates can delay the formation of DMS-derived sulfate, affecting not only the spatial distribution 95 of sulfate aerosols but also the effective sulfate yield from DMS as unreacted sulfate precursors may be subject to physical removal through wet or dry deposition. Thus, neglecting these intermediates could lead to misrepresentation of the spatial distribution of sulfate aerosol loading and limit our ability to accurately determine aerosol radiative forcing.
Here, we implement a more detailed multi-generational and multi-phase chemical mechanism 100 to describe DMS oxidation within the Community Atmosphere Model version 6 with chemistry (CAM6-chem) (Emmons et al., 2020) -the atmosphere component of the Community Earth System Model version 2.1 (CESM2.1) (Danabasoglu et al., 2020). The expanded chemistry captures the formation of stable intermediates such as MSA and HPMTF alongside SO2. We perform multiple sensitivity tests to investigate how the uncertainty in modeling the newly confirmed HPMTF could 105 influence the DMS chemistry and the resulting atmospheric sulfate burden. The model results are compared against an array of in situ observations. Finally, we examine how the natural aerosol background from DMS oxidation simulated with the modified model impacts estimates of aerosol radiative forcing. 110 2 Model description CESM2.1 consists of model components that quantitatively describe the atmosphere, land, seaice, land-ice, rivers, and ocean (Danabasoglu et al., 2020). Fluxes and state variables are exchanged through a coupler to describe the co-evolution of these earth system components. Here, we run with a coupled atmosphere (CAM6-chem) and land (Community Land Model, CLM5) and use prescribed data 115 for the remaining earth system components. In particular, sea surface temperature (SST) and sea ice conditions (Hurrell et al., 2008), as well as the mixing ratios of greenhouse gases (Meinshausen et al., 2017) are all fixed to present-day conditions. Following similar practices in previous studies (Gettelman, 2015;Gettelman et al., 2019), this configuration aims to constrain the potential environmental feedbacks such that the aerosol effects (on atmospheric composition, cloud, and radiation) are due to 120 the change in emissions and chemistry only.

Model configuration
In this work, CAM6-chem is run in an online configuration with free dynamics at 1.9º ´ 2.5º (latitude by longitude) horizontal resolution and 32 vertical layers (surface to 3 hPa or ~45 km), with a model timestep of 30 minutes. The default chemistry scheme is Model of Ozone and Related chemical 125 Tracers with representations of both tropospheric and stratospheric chemistry (MOZART-TS1) (Emmons et al., 2020) with a Volatility Basis Set (VBS) scheme specifically for the gas-phase intermediate semi-volatile organic precursors of secondary organic aerosols (SOA) (Tilmes et al., 2019). The DMS chemistry is described in further detail in Sect. 2.3. Aerosols are simulated using the Modal Aerosol Model with four modes (MAM4) (Liu et al., 2016) coupled with Model for Simulating Aerosol 130 Interactions and Chemistry (MOSAIC) (Zaveri et al., 2008(Zaveri et al., , 2021Lu et al., 2021), for sulfate (SO4 2-), ammonium (NH4 + ), nitrate (NO3 -), primary organic matters (POM), SOA, sea salt, and mineral dust.
MAM4 classifies aerosols into three size-dependent modes (Aitken, accumulation, and coarse) with an additional primary carbon mode for handling the aging of fine POM and black carbon (BC). Size distributions of aerosols in each mode are assumed to be log-normal with fixed geometric standard 135 deviations and varying mode dry or wet radius depending on particle number and changes in total dry or wet volume (Liu et al., 2012). MAM4 defines the cut-off size ranges of 0.015-0.053 µm for aerosol in Aitken mode, 0.058-0.27 µm for accumulation mode, and 0.80-3.65 µm for coarse mode. Dynamic partitioning of H2SO4, HNO3, HCl, and NH3 to each mode, related particle-phase thermodynamics, as well as water content and pH of interstitial aerosols, are computed using the MOSAIC module (Zaveri 140 et al., 2008(Zaveri 140 et al., , 2021Lu et al., 2021). Further details describing the dry and wet deposition, aerosol optical properties, radiative transfer, and aerosol-cloud microphysics are described in Supplementary   Information; these processes are all based on the standard CAM6-chem.
We perform four sets of simulations for the PD and PI atmospheric conditions with the standard and our modified chemical schemes. Details of the runs are tabulated in Table 1. Each run is performed 145 for 10 years with the first year as spin-up and averages over the latter nine years are presented in our results.   Table 4, Table 5, Table 6, and Table 7.
1850-level MOD_RE_2000 TS1 with the new gas-phase and aqueous-phase reactions in Table 4, Table 5, Table 6, and  Table 4, Table   5, and  (Wang et al., 2019b), acetone (Wang et al., 2020), and organohalogens (e.g. CHBr3 and CH2Br2) (Wang et al., 2019c). OASISS employs a two-layer framework that considers transfer velocities both through air and through water (kair and kwater) (Johnson, 2010): 155 where k (m s -1 ) is the overall transfer velocity.  (Jeffery et al., 2010), which is a function of surface wind speed, with an additional adjustment for the diffusivity of still air (Mackay and Yeun, 1983). kwater is based on Nightingale et al. (2000), which considers sea surface temperature and salinity. Lastly, fcice is the fraction of sea-ice coverage in each grid cell, such that DMS emission is suppressed from sea-ice covered surfaces. 165 On average, the global annual-total marine EDMS is 21.5 Tg-S yr -1 in [STD_2000].
Meteorological variability has little impact on the interannual variability of emissions (<±4%). Our EDMS is higher than the 18 Tg-S yr -1 from the model default inventory (Kettle and Andreae, 2000), but lower than the 28 Tg-S yr -1 reported in the original model study by Lana et al. (2011) and within the range of 11-28 Tg-S yr -1 simulated by GEOS-Chem, TOMCAT-GLOMAP and other models (Lennartz 170 et al., 2015;Spracklen et al., 2005;Hezel et al., 2011). The estimation of EDMS is sensitive to the choice of sea-surface DMS climatology; Chen et al. (2018) (Guenther et al., 2012). CAM6-chem assumes that 2.5% by molar of sulfur emitted from the Energy & Industry sector is already in the form of primary sulfate aerosols (in accumulation mode). Volcanic emissions are fixed at the same level in both PI and PD simulations. Emissions from continuously outgassing volcanos are constant (97.5% as SO2 and 180 2.5% emitted as primary sulfate aerosols) based on the GEIA inventory (Andres and Kasgnoc, 1998).  Table 2. We use the same emissions for other species as the standard CMIP6 simulations (Emmons et al., 2020).

Expanded DMS Oxidation Scheme
The standard CAM6-chem contains three gas-phase DMS oxidation reactions ( Table 3) (Barth et al., 2000;Emmons et al., 2010). These reactions simplify the DMS oxidation chemistry by treating only gas-phase reactions and producing SO2 directly, neglecting the role of multiphase chemistry and other key chemical products and intermediates found in chamber and field studies (e.g., Hoffmann et 195 al., 2016;Wu et al., 2015). We note that the second reaction does not conserve sulfur. Table 3. The three DMS oxidation reactions in the standard CAM6-chem.

References
DMS + OH → SO2 (H-abstraction) 9.60 × 10 -12 -234 (Emmons et al., 2010) DMS + OH → 0.5SO2 + 0.5HO2 (OH-addition) See note a (Emmons et al., 2010) DMS + NO3 → SO2 + HNO3 1.90 × 10 -13 520 (Emmons et al., 2010)  To improve the representation of DMS oxidation in CAM6-chem, we add a suite of new reactions that describe the chemical evolution from DMS to SO2, and ultimately, sulfate via the Habstraction and OH-addition pathways.   (Table 4, Table 5, Table 6, and Table 7). Key relatively long-lived species (DMS, MSA, 205 HPMTF, SO2, and sulfate) with lifetimes of >0.5 days are highlighted in bold. The blue shadings denote species and reactions in the aqueous phase in interstitial aerosols and cloud droplets. DMS (highlighted in green) can undergo O-atom addition (rightward path) or H-abstraction (upper paths). The Habstraction channel further diverts into the isomerization branch (top path) and the MSA-producing branch. SO2 is the dominant product of most gas-phase pathways while MSA is formed mainly via the 210 aqueous-phase oxidation of DMS. Oxidation of SO2 to sulfate or sulfuric acid is handled by the CAM6chem standard chemistry. The resultant particulate MSA and sulfate (highlighted in red) are key species with important radiative impacts.

The H-abstraction Pathway 215
The H-abstraction reactions of DMS with OH or Cl generate MSP, which then either reacts with NO or RO2 forming of MSA and H2SO4, or undergoes consecutive intramolecular H-shift reactions (isomerization), yielding HPMTF and SO2. Hence, we group these two serial reactions into two branches, namely the MSA-producing branch and the isomerization branch. The reactions of the MSAproducing branch are tabulated in Table 4. These reactions are largely based on Hoffmann et al. (2016), 220 who combined the chemical mechanism from the Master Chemical Mechanism version 3 (MCM v3) (Saunders et al., 2003) and other laboratory and computational studies. The reactions in the isomerization branch are detailed in Table 5. Here, we use the only currently available temperature dependent isomerization rate of MSP (kiso) of 0.04 s -1 at 293K estimated by Veres et al. (2020). This new kiso is slower than the previously determined values of 0.23 s -1 at 295K (Berndt et al., 2019) to 2.1 225 s -1 at 293K (Wu et al., 2015), delaying the formation of HPMTF. A recent chamber experiment estimates an intermediate kiso value of 0.12 s -1 at 293K (Ye et al., 2021). We investigate the impact of the uncertainty in kiso, in Sect. 3. The only chemical loss process of HPMTF in our model is oxidation by OH at a rate of 1.11 × 10 -11 cm 3 molecule -1 s -1 as recommended by Vermeuel et al. (2020), which is an experimentally determined OH-oxidation rate of MTF (a structurally similar proxy to HPMTF) by 230 Patroescu et al. (1996). Oxidizing HPMTF at this rate was shown to match better with recent measurements (Vermeuel et al., 2020) than the 1.4 × 10 -12 cm 3 molecule -1 s -1 suggested by a computational study (Wu et al., 2015). Recent studies (Veres et al., 2020;Vermeuel et al., 2020) suggest that cloud uptake is another important sink of HPMTF; we include a series of sensitivity tests based on [MOD_2000] to address the uncertainty in the HPMTF budget arising from this potential loss process. 235 Vermeuel et al. (2020) report that using a cloud uptake rate (kHPMTF+cloud) at 5 × 10 -3 s -1 results in a better match of diurnal variability of HPMTF with their local measurements. Due to the lack of detailed measurement, we use this kHPMTF+cloud and a substantially slower hypothetical value at 5 × 10 -5 s -1 for our sensitivity tests.

Gas-phase Reactions
where T is air temperature. Table 6 summarizes the new gas-phase reactions in the OH-addition pathway of DMS oxidation.

Gas-phase reactions of the OH-addition Pathway
We update the gas-phase reactions in the model to consider the oxidation of DMS by not only OH and 245 NO3 but also BrO, O3, and Cl as recommended or reported in previous studies, e.g., Barnes et al. (2006), Hoffmann et al. (2016), and Chen et al. (2018). The new reactions producing dimethyl sulfoxide (DMSO: CH3SCH3O), methanesulfinic acid (MSIA: CH3SOOH), and MSA intermediates, are added to the model as new advected chemical tracers which undergo not only chemical production and loss but also transport and deposition. MSA and SO2 are terminating products of these new gas-phase OH-250 addition pathway reactions, which is consistent with various modeling studies, e.g., Pham et al. (1995), Spracklen et al. (2005), and Chen et al. (2018). All oxidants (OH, O3, H2O2, BrO, and HOBr) are simulated online by the standard gas-phase chemistry scheme of CAM6-chem.

Aqueous-phase reactions of the OH-addition Pathway
We also introduce new aqueous-phase reactions of the OH-addition pathway as shown in Table   7. Table 7. Aqueous-phase DMS oxidation (OH-addition pathway) implemented into CAM6-chem in this study.

Global sulfur budget and distribution in present-day
The global burden of DMS in [MOD_2000] is 50 Gg-S. It is 38% lower than the standard run, 280 [STD_2000], but remains within the range of 9.6-140 Gg-S from other studies (Faloona, 2009;Kloster et al., 2006). Figure 2 shows the reduction is mainly over the Southern Ocean and is attributable to faster chemical losses via DMS+BrO and DMS(aq)+O3(aq) (Figure 3)  Hemisphere mid-latitudes, where the outflow of nitrogen oxides (NOx) -precursors of atmospheric NO3 -from land are substantial (Miyazaki et al., 2012). DMS oxidation by NO3 contributes <10% over most marine environments in the Southern Hemisphere. Previous studies estimate that the global contribution of OH and NO3 to DMS oxidation range ~50-70% and 15-30%, respectively (Berglen, 305 2004;Boucher et al., 2003;Khan et al., 2016;Chen et al., 2018).
Oxidation by BrO is responsible for 11% of global DMS removal, which falls midway within the previously estimated range of 8-29% (Boucher et al., 2003;Khan et al., 2016;Chen et al., 2018).
Regionally, its importance can be up to 50-60% over the high latitudes in the Southern Hemisphere, which is close to a previous box model experiment (Hoffmann et al., 2016). 310 DMS+O3 is the only multi-phase DMS oxidation reaction in this study, accounting for 8% (aqueous-phase) and 0.4% (gas-phase) of global DMS depletion. The oxidation rates via these reactions estimated by Boucher et al. (2003) were 6% and 3% of the total DMS sink calculated, respectively. Our lower gas-phase DMS+O3 reaction rate could be due to the inclusion of the BrO oxidation, which is missing in their study. Regionally, the fractional contribution of aqueous-phase DMS+O3 to DMS 315 oxidation can be up to 20-30% over high-latitude oceans, which is on the upper end of the range of 5-30% high-latitude DMS losses previously reported (von Glasow and Crutzen, 2004;Chen et al., 2018).
Lastly, the Cl oxidation reactions via either the addition or abstraction channels contribute equally (0.3% each, globally) to the chemical removal of DMS, which is consistent with the proposal of (Atkinson et al., 2004). Our estimated values are much lower than the 4% found in a global model 320 study (Chen et al., 2018) and the 8-18% from box-model studies (von Glasow and Crutzen, 2004;Hoffmann et al., 2016).
We note that recent studies (e.g., Wang et al., 2021b) have shown that large discrepancies in Cl and BrO are found within the same models and/or sets of measurements. Further investigation of how uncertainties in the representation of the halogen cycle feed back onto DMS chemistry is hence 325 warranted. The global atmospheric sulfur burden is increased by 41 Gg-S (or 4.1%) from [STD_2000] to 335 [MOD_2000] (Figure 4 and Table S1). Approximately half (23 Gg-S) of this increment is associated with the recovery of the missing sulfur associated with the OH-addition reaction in the standard chemistry (the second reaction in Table 3), which does not conserve sulfur. The remaining total sulfur burden increase is attributable to the extended chemistry scheme. As discussed above, the DMS burden in [MOD_2000] is lower than [STD_2000] by 38% due to faster oxidation. This oxidation produces 340 intermediates with a wide range of lifetimes. The addition of intermediates with relatively long physical lifetimes (to dry and wet deposition only) of HPMTF (1,300 days) and MSA (8.5 days) delays the formation of SO2 (2.6 days) and sulfate (4.4 days) compared to the standard reactions in [STD_2000], which increases the export of sulfur-containing intermediates. Gg-S in a previous CAM6-chem study (Tilmes et al., 2019) and is within the estimates (420-660 Gg-355 S) from studies using other models (e.g., Heald et al., 2014;Chen et al., 2018). The new DMS chemistry has increased the global sulfate burden by 47 Gg-S (or 8.8%) from the baseline value of 535 Gg-S in [STD_2000]. The statistically significant increases in sulfate resulting from the expanded chemistry are mostly found over the tropical and sub-tropical oceans in the Southern Hemisphere (Figure 5). There is no strong seasonality in the additional sulfate produced from our expanded chemistry. We estimate 360 that the sulfate burden attributable to DMS increases by 41% from 126 Gg-S in [STD_2000] to 178 Gg-S in [MOD_2000]. Most of this increase in sulfate burden (72%) comes from the expansion of the gas-phase chemistry with a minor additional contribution from the aqueous-phase chemistry. In a sensitivity test where the isomerization branch reaction (  The spatial distribution of the product branching ratios of DMS oxidation is shown in Figure 6. 375 In addition to depositional removal, HPMTF converts into SO2 while SO2 and MSA are then oxidized to form sulfate. We estimate that 33% of the annual-total DMS oxidation will yield HPMTF. This is comparable to the observationally constrained estimates from ATom-3 and ATom-4 flight campaigns, that ~30-40% DMS was oxidized to HPMTF along their flight tracks (Veres et al., 2020). High HPMTF production is typically seen in the summer MBL, coinciding with the HPMTF hotspots over tropical 380 oceans as shown in Figure S2. To address the uncertainty in the production and loss of HPMTF as discussed in Sect. 2.3, we run several sensitivity tests using five combinations of kiso and kHPMTF+cloud values based on [MOD_2000]. Table S2 and Figure S5 summarize the key results of these sensitivity tests. Compared to [MOD_2000], we find that using a faster kiso of 0.12 s -1 at 293 K (Ye et al., 2021) increases the global annual-total isomerization rate of MSP by 5.6% while the global burden of HPMTF 385 increases by 4.1%. Increasing the isomerization rate has little impact on the burden of sulfate from DMS (increase of only 4.0%). We also evaluate the importance of cloud uptake of HPMTF with two hypothetical values of kHPMTF+cloud at 5 × 10 -3 s -1 (Vermeuel et al., 2020) and 5 × 10 -5 s -1 . At these rates, cloud uptake becomes an important sink of HPMTF, responsible for 68-69% and 28% of total HPMTF losses respectively. The corresponding global burdens of HPMTF are substantially lowered by 85-86% 390 and 52%. For simulation with cloud uptake loss, the burdens of HPMTF and sulfate are much less sensitive to our choice of kiso due to the rapid loss of HPMTF to cloud uptake. In these sensitivity simulations, the sulfur contained in HPTMF is assumed to be removed from the system once taken up by cloud, thus reducing the sequential formation of SO2 and sulfate (by up to 8 %). considering HPMTF, SO2, and MSA as terminating products estimated from their annual-total production rates. 400 MSA is a key intermediate generated from the OH-addition channel of the multi-phase DMS oxidation, especially, over remote marine atmosphere. Our result shows that aqueous-phase MSA formation accounts for most of MSA production as commonly reported (von Glasow and Crutzen, 2004; Barnes et al., 2006;Zhu et al., 2006;Hoffmann et al., 2016;Chen et al., 2018). In [MOD_2000], the 405 global MSA burden is 7.5 Gg-S, which is smaller than the range of 13-40 Gg-S from previous model studies (Pham et al., 1995;Chin et al., 1996Chin et al., , 2000Cosme et al., 2002;Hezel et al., 2011;Chen et al., 2018). In [MOD_2000], most MSA is formed over the Southern Ocean ( Figure S3). The lifetime of MSA is 0.6 days globally, shorter than the 5-7 days previously proposed (Chin et al., 1996(Chin et al., , 2000Cosme et al., 2002;Hezel et al., 2011;Pham et al., 1995), likely because we include the aqueous-phase 410 OH-oxidation to sulfate which is a significant loss process for MSA. This oxidation accounts for ~76% of removal in [MOD_2000], followed by cloud uptake (18%).   (Wang et al., 2019a(Wang et al., , 2021a. ACE-ENA provides high timeresolution in-situ measurements of MSA and sulfate aerosol in the lower troposphere (Zawadowicz et al., 2021). We note that the model-measurement comparisons are not exact, given that our simulations are performed using free-running dynamics and thus are not paired to the meteorological year of 430 measurements. We therefore sample monthly mean values from the model at the location of the observations to provide qualitative comparisons.

2021)
Most DMS resides in the lower troposphere (Figure 7). Annual-mean surface DMS from 435 [MOD_2000] ranges from 40-300 ppt over much of the ocean, but can exceed 320 ppt over the Southern Ocean and northeastern Pacific, regions with high DMS emissions. DMS concentrations of ~25-125 ppt were observed at Cape Grim, Australia in 1990-1993(Ayers et al., 1995. Sciare et al. (2000) report hotspots that are not simulated by the model (Figure 8(a)). During VOCALS-REx the ship-based measurements (BROWN) recorded a range of near-surface DMS from 18 ppt to 111 ppt, while the 450 airborne measurements (C130) reveal a vertically decreasing trend of DMS mixing ratios, from 33 ppt at ~500 m to 2.0 ppt at ~2 km (Figure 8(b)). Modeled surface DMS falls in the range of the ship measurements. Compared to the aircraft observations, simulated DMS is biased high at the surface and declines more abruptly, which may indicate biases in vertical mixing or cloud processing. DMS concentrations are slightly lower in the simulation with updated chemistry [MOD_2000], but follow 455 the same vertical profile. We disaggregate the ATom observations into three regional groups, namely Pacific, Atlantic, and Southern Oceans as in Figure 8(a). DMS concentrations were measured by two instruments during ATom (WAS and TOGA, the former generally reported higher values); both are compared with model values in Figure 8(c). Observed DMS concentrations during ATom are substantially lower than measured during VOCALS, and lower than any region simulated by the model.  is generally larger than the average 2:1 ratio observed during ATom (Veres et al., 2020), suggesting that the model may underestimate the DMS-to-HPMTF conversion rate or overestimate the HPMTF loss. Our model predicts that OH-oxidation to SO2 is dominant in the removal of HPMTF while dry and wet deposition are negligible. The addition of cloud uptake (discussed in Sect. 2.3.2) can dramatically decrease HPMTF concentration (by up to >73% when assuming moderate cloud uptake 495 rate of 5 × 10 -5 s -1 ), resulting in a better model-observation agreement in the lower troposphere over the Southern Ocean but low biases over the Pacific and Atlantic (Figure 9). In light of the DMS biases of Figure 8, this irreversible cloud uptake may over-correct the HPMTF concentrations.

505
Our simulation shows that the gas-phase MSA formation is small compared to aqueous-phase formation, in line with previous work (Barnes et al., 2006;von Glasow and Crutzen, 2004;Zhu et al., 2006;Hoffmann et al., 2016;Chen et al., 2018;Hoffmann et al., 2021). Near the sea surface, simulated gas-phase MSA is < 0.03 ppt even in Southern Hemisphere summer, while recent ship-based measurements reported concentration ranging from 1.4-25 ppt (Yan et al., 2019). The model also 510 substantially underestimates gas-phase MSA (<0.001 ppt) when compared to a wintertime site measurements in Germany (0.5-10 ppt) (Stieger et al., 2021). and Atlantic, the model underestimates MSA at mid-and low altitudes. Over the southeastern Pacific, the measured submicron MSA from VOCALS-REx ranged from 50-80 ng m -3 at lower altitudes (<1 km) (Wood et al., 2011) while the location-matched simulated MSA was considerably lower (6-15 ng m -3 ). Above Graciosa Island in the north Atlantic, ACE-ENA-observed MSA ranged from 10-20 ng m -3 at the lower troposphere (<1 km) and gradually reduced to ~5 ng m -3 in the mid-troposphere (2-5 520 km) (Zawadowicz et al., 2021), whereas the model estimates a negligible amount of MSA (<0.5 ng m -3 ) near the Azores, as a result of limited DMS emissions in that region (as reflected by low DMS concentrations in Figure 2). Outside of the Southern Ocean, the mean simulated concentration of MSA is underestimated compared to all observations, which suggests that the MSA-forming branches of DMS oxidation (H-abstraction where MSP reacts with NO, or multi-phase OH-addition reactions of 525 DMS) may be under-represented in our simulations, or that the loss of MSA (by reaction with OH , the reaction rate for which is still highly uncertain (Milne et al., 1989;Zhu et al., 2006;Chen et al., 2018)) may be overestimated. generally agree well with measurements from ATom ( Figure S6). Our model also performs well at the surface when compared against VOCAL-REx and ACE-ENA, but is biased high above 1 km, likely reflecting biases in anthropogenic sulfate exported from continental regions.

Global sulfur budget and distribution in the pre-industrial era 540
As seen under PD conditions, the formation of intermediates expands the overall lifetime of sulfur-containing species in the PI atmosphere, thereby increasing the natural sulfate aerosol background. A summary of the burdens and lifetimes of the sulfur-containing species from the PI simulations is given in Table S1. The DMS burden in PI from [MOD_1850] is 84% larger than its PD counterpart due to slower oxidation which prolongs the atmospheric lifetime. Oxidation by OH via the 545 H-abstraction (38% of total DMS oxidation in [MOD_1850]) and the OH-addition channels (27%) are still the primary loss pathways of DMS ( Figure S7). DMS+NO3 becomes less important (23% in PD vs. 6.0% in PI) given reduced sources of NOx, resulting in a lowered DMS-to-SO2 conversion rate at 27%, compared to 47% in [MOD_2000] (Figure S8). Reduced NOx also limits the reaction rates of MSP+NO, thereby favoring the isomerization pathway (92% of total loss of MSP in PD vs. 96% in PI). 550 Hence, the conversion of DMS to HPMTF becomes more important (39% of total DMS oxidation in PI), leading to a doubling of the HPMTF burden in the PI compared to PD. The addition pathway producing MSA becomes more dominant over the tropical ocean via oxidation by OH and the high latitudes by DMS+BrO, raising the MSA burden by 59% compared to PD. Lastly, the expanded DMS oxidation chemistry increases the PI global annual-mean sulfate burden by 29% from 319 Gg-S 555 [STD_1850] to 412 Gg-S ([MOD_1850]) (Figure 5), of which 57% is derived from DMS, significantly larger than the 31% in PD, confirming that DMS is a relatively more important source of sulfate in PI.
Similar to PD, the majority (66%) of this additional sulfate in the PI is produced via the expanded gasphase oxidation pathways and this addition is largely aseasonal. The absolute burden of sulfate produced from DMS oxidation is higher in the PI (236 Gg-S) compared to the PD (178 Gg-S). 560

Global Radiative Impacts of Updated DMS Chemistry
Changes to particle-phase sulfate and MSA due to the expanded DMS chemistry, as described above, may alter both aerosol-radiation and aerosol-cloud interactions. Given that particulate MSA is not included in the current CAM6-chem aerosol scheme, to account for its radiative impacts, we assume 565 MSA interacts with radiation like sulfate optically by implementing an artificial rapid conversion of MSA to sulfate. These two adjusted cases are aliased as [MOD_RE_1850] and [MOD_RE_2000] respectively. Details of this implementation are described in Supplementary Information.

Direct Radiative Effect (DRE)
Following the recommendation in Ghan (2013), we focus our analyses on the shortwave (SW) 570 DRE. The PD global annual-mean sulfate DRE modeled with [MOD_RE_2000] and [STD_2000] are -0.32 W m -2 and -0.31 W m -2 , respectively, which are slightly less negative than previous estimations of -0.36 W m -2 to -0.42 W m -2 (Heald et al., 2014;Myhre et al., 2013;Yang et al., 2017). The global annual-mean cloud fraction in the model is 77% while the all-sky DRE is 59% of the estimate of clearsky DRE. The more frequent cloudiness in CAM6-chem may explain the lower DRE compared to the 575 AeroCom II models, which report a typical all-sky to clear-sky ratio of 1:2 (Myhre et al., 2013). The DMS-associated sulfate DRE in PD is -0.11 W m -2 in [MOD_RE_2000], which is slightly stronger than the value of -0.074 W m -2 in a CAM5-chem study using the standard DMS oxidation chemistry (Yang et al., 2017)  ). The sulfate DRE is not sensitive to HPMTF cloud loss given that this loss has a modest impact on the sulfate burden in our simulations. Our new DMS chemistry has strengthened the PD sulfate direct cooling by 0.01 W m -2 or 4% of the contribution attributed to DMS relative to [STD_2000].
The rise in sulfate burden from PI to PD driven by anthropogenic emissions occurs mainly over 585 the land in the northern hemisphere; this impact is much larger than the increase in sulfate produced by the expanded DMS chemistry (Figure 11). The zonal extrema of PD sulfate burden, aerosol optical depth (AOD), and DRE are collocated around 30ºN (Figure 11). The larger difference in sulfate load in the southern tropics (30ºS to 0ºN) due to the new DMS oxidation reactions also translates to a larger DRE difference in those latitudes ( Figure S9).

Impacts on Aerosol-cloud Interactions and Indirect Radiative Forcing (IRF)
While the central estimate of the IRF of aerosols from the AR5, which reflects constraints from selected satellite and GCM analyses, is -0.45 W m -2 , the IRF estimated by the majority of models reported in AR5 (see Figure 7-19 of ) ranges from -1.0 to -2.5 W m -2 . This 600 suggests that aerosol-cloud interactions may be substantially overestimated by the majority of models; an overly pristine pre-industrial may contribute to this (Menon et al., 2002;Carslaw et al., 2013). We anticipate that the increase in PI sulfate following the expansion of DMS chemistry (Figure 11a) may dampen the IRF in our simulations. We evaluate IRF by calculating changes in the SW cloud radiative effects (DCRE) from PI to PD conditions, following previous studies (Gettelman et al., 2019;Ghan, 605 2013). Our estimates of IRF encapsulate not only the Twomey and the Albrecht effect (Twomey, 1977;Albrecht, 1989), but also cloud feedbacks in response to meteorological changes driven by different sulfate aerosol loadings. For instance, our simulations do not fix air temperature and wind fields. Deeper mixing and stronger turbulence may affect cloud microphysics and limit/promote the precipitation efficiency of clouds, and hence alter cloud lifetime (Gettelman and Sherwood, 2016). These cloud 610 feedback mechanisms are still poorly constrained and contribute to the uncertainty in CRE estimations in both PI and PD eras.
The global-mean DCRE estimated by differencing [STD_2000] and [STD_1850] is -2.2 W m -2 , comparable to a previous study using CAM6 (Gettelman et al., 2019) which reported SW DCRE of -2.1 W m -2 with CMIP6 emissions. They also showed that under CMIP5 emissions the magnitude of the 615 SW DCRE drops to -1.4 W m -2 , closer to the AR5 range. Our expanded DMS chemistry leads to a modest (~5%) strengthening in the simulated IRF (-2.3 W m -2 ). However, due to the high variability of the cloud effects, these differences, both in the global values and the zonal means shown in Figure   12c are not statistically significant. The strengthening of the IRF is opposite in sign to the expected response to the increase in PI sulfate. Carslaw et al. (2013) describe how cloud albedo is much more strongly sensitive to CCN in the PI, suggesting that higher PI aerosol burden may decrease the cloud response to anthropogenic increases. Figure 13 illustrates the change of SW CRE and sulfate burden from multiple simulations from PI to 625 PD. Counter to expectations, we find that the SW CRE is more sensitive to each unit increment of sulfate burden (steeper slope) when the PI aerosol burden is higher (in [MOD_RE], shown in dark red) compared to our baseline simulations ([STD], shown in blue). Figure S10 shows that the of PI-to-PD change in CCN and cloud properties are also more sensitive to the change in sulfate burden in This sensitivity may also be related to the spatial distribution in the change in DMS-derived sulfate burden. Figure 12 shows that the increase in sulfate burden from PI to PD is stronger in the 635 marine atmosphere, as expected. In a sensitivity test, [GAS_RE], where only the gas-phase reactions of the new DMS oxidation scheme are enabled but not the aqueous-phase reactions (with the exception of aqueous phase oxidation of SO2), produces a less negative IRF of 1.7 W m -2 . Figure S11 illustrates that this sensitivity simulation follows the anticipated response, with an increase in PI sulfate decreasing the change in liquid water path (LWP) from PI and PD (particularly in low clouds) and thus dampening 640 the IRF, indicating the important climate implications of marine stratocumulus clouds (Wood, 2012).
Contrasting [MOD_RE] and [GAS_RE] reveals that the introduction of the aqueous-phase pathway contributes to large changes in the PD-PI sulfate co-located with high clouds over the tropics and low clouds over the Southern Ocean. Though the change in sulfate in both regions produce stronger regional cooling IRF, this appears to be the result of two different processes. In the tropics, decreases in sulfate 645 in the presence of high clouds modify ice nucleation (Gettelman et al., 2010), leading to increased ice water path (IWP) and strengthened cloud cooling over the tropical oceans. Over the Southern Ocean, decreases in sulfate attributable to the aqueous-phase chemistry are associated with even higher LWP in low clouds, further exaggerating the local cooling IRF compared to the gas-phase only simulation.
Even though the amount of sulfate produced by the aqueous-phase pathway is relatively small (~8% of 650 DMS-derived sulfate), it appears to have a disproportionate impact on clouds and the estimate of aerosol IRF, suggesting a strong sensitivity of cloud properties to the spatial distribution of natural marine sulfate. More work is needed to better understand this response. [GAS_RE] (yellow) which only includes the expanded gas-phase reactions is also shown. Arrows indicate changes from PI (tails) to PD (heads). Horizontal and vertical error bars span the 1-s 660 variabilities of burden and SW CRE in the simulations, respectively.

Conclusions
We expand the chemical mechanism in CAM6-chem to better describe DMS oxidation in the atmosphere, determine the formation of the intermediate sulfur products, and estimate the aerosol 665 radiative implications under the PI and PD periods.
Uncertainty in our estimate of sulfate response to the new DMS chemistry is largely associated with estimated reaction rates. Some rate constants for the multiphase reactions are obtained from a limited set of box-model and laboratory studies which have not been validated with field measurements.
For example, our rate constant for MS -(aq)+OH(aq) from Zhu et al. (2003) is 4.7 times smaller than 670 another lab study (Milne et al., 1989), potentially leading to a higher global tropospheric MSA burden by ~30% (Chen et al., 2018). As discussed in Sect. 3.2, it is likely that our model overestimates the concentration of particulate MSA and underestimate gaseous MSA when compared with in situ measurements (e.g., ATom, and Yan et al. (2019) in the Southern Ocean. This could result in an overestimate of sulfate given that gas-phase MSA is expected to have a longer lifetime than particulate 675 MSA and H2SO4 vapor (Berresheim, 2002). Our comparisons with observations also suggest that emissions of DMS, in particular a likely overestimate over the Southern Ocean, play an important role in dictating the regional loading of secondary oxidation products; the climate response to these changes should be further investigated.
This study included a relatively new chemical mechanism for the formation and loss of HPMTF. 680 The rate of isomerization of MSP (kiso) controls the production of HPMTF. The analyses reported here are based on a theoretically calculated value of kiso (0.04 s -1 at 293K) (Veres et al., 2020), which is slower than previously experiment-and model-based estimates of 0.23-2.1 s -1 (Wu et al., 2015;Berndt et al., 2019). We find that a faster kiso (0.12 s -1 at 293K based on Ye et al. (2021) has a negligible impact on the HPTMF burden (+4.1%) and resulting sulfate formation. However, the HPMTF burden is quite 685 sensitive to the loss of HPMTF due to cloud uptake (kHPMTF+cloud), which was recently suggested as a particularly important sink of HPMTF in the MBL (Veres et al., 2020;Vermeuel et al., 2020). These large changes suggest that further field measurements are needed to better understand the cloud uptake process of HPMTF and the resulting formation of in-cloud sulfur products.
In this study, we dramatically expand the DMS oxidation mechanism within an Earth System 690 Model. Doing so increases the global sulfate burden by 8.8% in PD, and 29% in PI. While we anticipated that a larger PI burden of sulfate would dampen the aerosol IRF, our simulations instead suggested that the role of aqueous phase chemistry, though modest in terms of the sulfate burden, confounds this effect. In a simulation with only updated gas phase chemistry, the higher PI burden decreases the magnitude of the IRF as anticipated (-2.2 W m -2 in standard chemistry vs. -1.7 W m -2 695 with updated gas-phase chemistry). However, high clouds in the tropics and low clouds in the Southern Ocean appear to be particularly sensitive to the sulfate produced via the aqueous phase pathway, counteracting the effect of the additional sulfate formed via the gas-phase pathways (net -2.3 W m -2 ).
These large differences confirm the high sensitivity of aerosol indirect effects to the natural aerosol background, while revealing complex cloud responses to aerosol produced in different geographical 700 regions via different pathways. More work is needed to understand these responses (e.g., better understanding of cloud responses to aerosols formed in the aqueous phase, observational constraints on the cloud uptake process of HPMTF via both laboratory and field measurements). While our new chemistry increases computational costs by ~15% (in core-hours/simulation-year), this study suggests that a detailed description of the chemical oxidation of DMS and its products, and particularly the 705 chemistry relevant to pristine conditions, is needed to accurately represent the abundance of natural sulfur species in the marine atmosphere and changes in natural aerosol burden over time.
contribution to the modeling of this study. This material is based upon work supported by the National 730 Center for Atmospheric Research, which is a major facility sponsored by the NSF under Cooperative Agreement No. 1852977. The high-performance computing was conducted on Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We also thank Andy Neuman, Alan Bandy, Barry J.
Huebert, and Stephen R. Springston for their contribution to the measurements used in this study. ACE-735 ENA data were obtained from the Atmospheric Radiation Measurement (ARM) User Facility, a U.S. DOE Office of Science user facility managed by the Biological and Environmental Research Program.