Modelling the atmospheric 34 S-sulfur budget in a column model under volcanically quiescent conditions

. We investigated the sulfur isotope budget of atmospheric carbonyl sulﬁde (COS) and the role of COS as a precursor for stratospheric sulfate aerosols (SSA). Currently, the sulfur isotopic budgets for both SSA and tropospheric COS are unresolved. Moreover, there is some debate on the signiﬁcance of COS on SSA formation. With the use of an atmospheric column model, we model the isotopic composition of COS to resolve some of the uncertainties in its budget. We attempt to constrain the 5 isotopic budget ( 32 S and 34 S) of COS in the troposphere and the stratosphere. We are able to constrain the model results to match the observed COS isotopic signature at the surface, which has recently been measured to lie between δ 34 S = 10– 14 permil ( h ). When we propagate this composition to SSA, we match the isotopic signal of SSA that was measured in volcanically quiescent times at 18 km as δ 34 S = 2.6 h . Our results show that COS becomes isotopically enriched during destruction in the stratosphere, and this enriched isotopic signal of COS propagates through SO 2 to sulfate, creating strong 10 positive isotopic gradients of both SO 2 and sulfate in the lower stratosphere. Sensitivity tests indicate that the enriched sulfur in the stratosphere is mostly sensitive to COS photolysis,

air masses arriving at the measurement location (Hattori et al., 2020). Air masses from the continent were more prominent in winter and the atmospheric COS measured was depleted i.e. with a smaller δ 34 S value (Hattori et al., 2020). According to Davidson et al. (2021) the anthropogenic signature of COS was estimated at about 8 , and the oceanic COS at about 15 .
The oceanic measurements were a composite of direct COS emissions (13 ), and oxidation from CS 2 (16 ) and CH 3 SCH 3 (20 ) (Davidson et al., 2021). Lastly, Baartman et al. (2021) measured a mean δ 34 S of 15.9 in the Netherlands, concluding 5 that anthropogenic COS emissions in this region are small. Overall, it is expected that anthropogenic COS is likely to be more satellite observations. Based on balloon measurements, Leung et al. (2002) and Colussi et al. (2004) suggested relatively large, positive isotope effects for COS photolysis with fractionations of +73.8 ± 8.6 and +67 ± 7 , respectively and postulated that this would result in highly enriched sulfate in the stratosphere, leaving a pool of depleted COS. 20 Little information is available concerning fractionation during uptake by the biosphere. Using the binary diffusion theory Angert et al. (2019) calculated a fractionation of -5 , implying an enrichment of atmospheric COS in 34 S. Recent measurements on one plant species (Scindapsus Aureus branch) place it at -1.9 (Davidson et al., 2021).
Regarding the isotopic signature of SSA, the final product of COS photolysis, only one study exists that measured the corre- 25 sponding isotopic signature of SSA δ 34 S. For non-volcanic SSA in the stratosphere, a value of +2.6 ±0.3 between 18-19km was reported by Castleman et al. (1974).
From the above considerations, it is clear that the COS budget and the corresponding sulfur isotopic budgets are still far from being completely understood. In order to bridge this gap, we present a model study that aims to simulate the full atmo- 30 spheric budget of sulfur, including its isotopes. By using available observations of concentrations and isotopic composition, we explore the following questions: 1. What is the COS contribution to SSA?
2. How can isotopic information help constrain the sulfur budget?
3. What are the largest uncertainties in the COS isotopic budget?
In this pioneering study, we use a 1-D column model, with the full atmospheric sulfur chemistry to explore the fate of sulfur in the atmosphere. We describe how the budgets are calculated, and study the isotope profiles of COS, SO 2 and sulfate in order to understand the profiles of the sulfur isotopic composition in the atmosphere. In Section 2 we discuss the methodology, in particular the 1D model set up (Section 2.1) for the sulfur chemistry, including the sulfur isotopologues (Section 2.2). We 5 also discuss how we calculate the atmospheric budget for COS, SO 2 and sulfate and the COS isotopic budget (Section 2.3), followed by a description of the sensitivity analyses we performed (Section 2.4). In Section 3, we present the aforementioned budgets and sensitivity analyses, followed by a discussion in Section 4 on the uncertainties in the model and the COS budget.

Methodology
In this section the set-up of the 1-dimensional column model is described. We explore how the model is equipped to simulate 10 the full sulfur chemistry in the atmosphere. This includes a brief description on how the radiative transfer through the atmospheric column is modelled to obtain height-dependent photolysis frequencies. We then discuss the set-up that includes sulfur isotopologues as separate species, from which isotopic ratios of atmospheric sulfur are derived. The budget analysis of the sulfur S gases (COS, SO 2 , and sulfate) in the atmosphere is then discussed, as is the budget calculation of the sulfur isotope delta (δ 34 S) for these gases. Lastly, we describe the sensitivity analysis we carried out in our model, in order to encompass 15 some of the uncertainties and unknowns of the COS isotopic budget.

Model description
We use the 1-dimensional column model PATMO (Planetary ATMOSpheres), which simulates the Earth's atmosphere up to 60 km. The model is based on the KROME code (Grassi et al., 2014) and the discretization follows Hu et al. (2012) and Rimmer and Helling (2016). The code is presented in Ávila et al. (2021) and will be further explained in Danielache et al. (2022, in 20 prep). At the surface, sulfur gases are emitted into the lowest 1 km grid cell of the model. To this end, emissions of COS, CS 2 , H 2 S, SO 2 , CH 3 SCH 3 are converted from teragrams of sulfur per year (Tg S yr -1 ) to molecules cm −3 s −1 , in the lowest model layer. COS and CS 2 emissions are obtained from Whelan et al. (2018), Zumkehr et al. (2017) and Suntharalingam et al. (2008).
However, the COS budget as reported in the literature is not closed. We include therefore a missing source in our emissions as well, in order to reach a steady state that matches the available observations. The emission rates for the other S gases are 25 taken from Watts (2000), Khalil and Rasmussen (1984), Lee and Brimblecombe (2016) and Georgii and Warneck (1999). In the Supplement we provide a brief description of model performance, especially the mass balance, as well as a more extended model set up.
We include deposition of sulfur gases by dry and wet deposition and aerosol sedimentation. Dry deposition includes the uptake 30 of COS by soils and the biosphere (Whelan et al., 2018), and takes place in the lowest model layer. Wet deposition represents the removal of S-gases by precipitation. Wet removal of species is restricted between the surface and 12 km. Details on the  (Giorgi and Chameides, 1985) that are used for the calculation of wet deposition velocities. The effective rainout lifetime is plotted in the Supplement ( Figure S2).  Turco et al. (1979) The temperature and pressure profiles of the atmosphere are prescribed, as are the profiles of the other relevant atmospheric gases: the major atmospheric gases such as N 2 , O 2 , H 2 O, CO 2 and CO. Also prescribed are the profiles of important oxidants namely OH, O 3 , HO 2 and O 3 P, and data are taken from 1976 US standard profiles (Krueger and Minzner, 1976), and bench-5 marked against the present-day Earth atmosphere following Hu et al. (2012).
In every 1 km thick layer, the model resolves time-dependent bimolecular, termolecular, and bidirectional chemical reactions using the DLSODES solver for ordinary differential equations (Hindmarsh, 1983) of the form shown in Equation (1). 10 where n i,j is the number density (molecules cm -3 ) of species i in layer j, P is the corresponding chemical production rate (molecules cm -3 s -1 ), n·L is the chemical destruction rate (molecules cm -3 s -1 ), and φ is the vertical transport flux (molecules cm -2 s -1 ) (Hu et al., 2012). The vertical flux has a turbulent eddy diffusion component and a molecular diffusion component along the vertical (z-axis) (Hu et al., 2012). However, the molecular diffusion (O 10 -3 cm 2 s -1 ) is much smaller than the eddy diffusion in the 60 km of the atmosphere we simulate. Hence the vertical mixing is described as: Here, K j is the turbulent eddy diffusion coefficient (cm 2 s -1 ), as presented in Supplementary Figure S1. The N j is the total density in layer j, and the f i,j is the mixing ratio = n i,j /N j . For K, empirical values from Massie and Hunten (1981) were used that range from 10 5 cm 2 s -1 close to the surface and in the upper stratosphere to 10 3 cm 2 s -1 in the lower stratosphere. The default K values were multiplied by a factor of 2 to ensure that the stratospheric COS turnover (determined by transport and stratospheric photolysis) amounts to about 40 Gg S yr −1 , as reported in the literature (Brühl et al., 2012)). Most of the COS transport to the stratosphere takes place in the tropics in the upward branch of the Brewer-Dobson circulation, and we expect that higher eddy diffusion coefficients are needed in our model to match the transport of COS to the stratosphere.
The full chemical reaction scheme and the photochemistry that is solved in PATMO are shown in Table 2, Table 3 and Ta-5 ble 4. Stratospheric sulfur chemistry is driven by photochemical reactions that depend on the amount of ultraviolet radiation that reaches each layer. Rather than the full radiative transfer, we only consider direct solar radiation that is attenuated by absorption of ultraviolet light, caused by species aloft. Since stratospheric photolysis is our main focus, we restrict the calculations to UV radiation only (Bian and Prather, 2002).
The solar flux (photons cm −2 s −1 nm −1 ) is attenuated by absorption using the Beer-Lambert equation: where θ is the solar zenith angle. I λ (∞) is the spectral irradiance at the top of the atmosphere, which is attenuated by the overhead optical depth (τ z ) that is calculated as: (z top − z) represents the total thickness from the top of the atmosphere to altitude z (in cm). In our model the z top is 60 km.

15
The τ takes into account the number density n (molecules cm −3 ) and wavelength-dependent, UV absorption cross-sections, σ λ (cm 2 molecule −1 ) of molecule i. Subsequently, τ is summed over all the relevant species in the model (O2, O3 and all the S gases).
Using spectral information at height z, photolysis frequencies (s -1 ) are calculated from the actinic flux I (λ) , absorption cross 20 section σ and quantum yield q according to: We calculate the height-dependent photolysis, where the wavelength integral runs over the range 180-400 nm. This spectral range is relevant for the photo-dissociation reactions included in the model, namely all the sulfur species, O 2 and O 3 . The entire integral is multiplied by 1/2 to take the diurnal cycle into account and the solar zenith angle is set at 57.3°to represent the mean 25 planetary angle (Hu et al., 2012). We solve the integral by numerical integration with a spectral resolution dλ of 0.05 nm. For COS, the spectral resolution should not significantly change the isotopic effect due to its broad spectrum.
Our aim is to analyse the steady state solution, in which sources, sinks, and transport of S-compounds are in equilibrium. 10 To this end, we simulate 60 years and check if the simulation has converged (Supplement Figure S5). We find that the slowest timescale is in the stratosphere, where transport is slow, and photolysis frequencies depend critically on the overhead burdens of UV-absorbing S-gases.

Sulfur isotopologues
Our simulations include different isotopologues of all the sulfur gases as separate molecules. Sulfur has 4 stable isotopes 15 ( 32/33/34/36 S). Isotopic ratios are usually reported relative to an international standard ratio: where x stands for 32, 33, 34 and 36, and x R stands for the isotopic ratios ( 32/33/34/36 S) of samples and standards; sulfur isotope ratios are reported relative to the Vienna Canyon Diablo Triolite (VCDT) in permil ( ).
formed. In this test the isotopologues of S are emitted per natural abundance (VCDT) and all the reaction rates are assumed the same for each isotope. We found that the numerical noise of the model is negligible and hence we conclude that the model is suitable for modelling isotopologues (Supplementary Figure S3 and discussed further in Danielache et al. (2022, in preparation)).

5
Since most measurements are available for 32 S and 34 S, we will concentrate on these isotopologues and the corresponding δ 34 S values. 32 S and 34 S have natural abundances of 95.02% and 4.25% respectively. In the model, sulfur gases are emitted to the atmosphere with an assumed δ 34 S source signature. We prescribe some of the reported source signatures to the emissions of 32 S and 34 S, respectively. These signatures are listed in Table 5.
10 For the isotopic signature of COS emission we use 10.5 , an effective emission signal derived from Davidson et al. (2021).
This study reports anthropogenic COS to have a signal close to 8 and direct oceanic COS to be closer to 13 . Although the contribution of anthropogenic versus marine sources is debated, we consider a 50-50 split as derived in Angert et al. (2019). Davidson et al. (2021) also measured oceanic CS 2 isotopic signatures to be around 16 , but the anthropogenic signature is 15 unknown. With the assumption that the anthropogenic signature of CS 2 is the same as that of COS (8 ), and assuming that 70% of the CS 2 emission is anthropogenic (Angert et al., 2019), we use an effective emission signature of 10.4 for CS 2 (Chin and Davis, 1995). Lastly, Davidson et al. (2021) measured oceanic CH 3 SCH 3 with a signal of 20 , which we use in our model.
Chemical, physical, and biological processes may fractionate, which implies that a process proceeds sightly faster or slower 20 for one isotopologue compared to the other. In this paper, we only consider fractionations for 34 S. Fractionation often arises due to mass differences, and symbols α and are used to describe differences in rate coefficients k: Values of are often reported in . A negative value of implies that the light isotopologue reacts faster. The dominant sink of COS is uptake by the biosphere through the stomata of leaves (Berry et al., 2013). We impose an bio of -1.9 for the 25 dry deposition process as measured by Davidson et al. (2021), implying that the lighter isotopologue diffuses slightly faster [1] at 18 km, these are in fact height-dependent, see Supplementary Figure S3   [2]  [3] (Harris et al., 2012) and is therefore taken up preferentially by plants. Chemical reactions may also fractionate. We include fractionations for the following reactions: COS + O 3 P , COS + OH  and SO 2 + OH as in Table 6. The fractionation for COS + OH  is height-dependent. For COS + O( 3 P) , fractionation is height independent. Note that the SO 2 + OH reaction has a positive 34 (Harris et al., 2012). Not much is known about the fractionation that is associated with CS 2 and CH 3 SCH 3 oxidation, therefore we currently assume no fractionation.

5
The photolysis frequencies are calculated using Equation (5). For COS, we use the cross-sections from Hattori et al. (2011), resulting in height-dependent as presented in the Supplementary Figure S4. Values reported in the literature vary considerably, ranging from +73 to -10.5 (Leung et al., 2002;Lin et al., 2011). Most studies expect this to be small, but whether the values are negative or positive is still debated Yousefi et al., 2019). 10

Budget calculation
As we run the model to steady state, the change in concentration over time is below a threshold value at the end of the simulation, i.e. the sources and sinks are in balance with the imposed transport and radiation processes. Using the steady state assumption, the steady state mass balance equation for COS, SO 2 and sulfate (H 2 SO 4 and SO 4 ) in the atmosphere is calculated as: in which chemical loss, transport and deposition are defined as negative contributions, and C is the amount of S-compound in each layer, or integrated over the troposphere, stratosphere, or global atmosphere (i.e. the budget equation is in steady state in each layer). To separate the troposphere from the stratosphere, we define two boxes. Although the wet removal in the troposphere ends at 12 km, we consider the 12-16 region (Upper Troposphere/Lower Stratosphere (UTLS)) a part of the troposphere  Figure S1). Hence, for the budget, we define the troposphere as the sum of the lower 16 boxes (0-16 km), and the stratosphere as the remainder (16-60 km). The flux contributions are calculated in Gg S yr −1 or Tg S yr −1 .
The same steady state approximation is used to derive a δ 34 S budget. This assumes, as before, that the δ 34 S value of all 5 compounds in all layers has reached steady state. We develop the following isotopic δ budget equation: The step-by-step derivation of this equation is given in Supplement S3. In this equation, δ and α values are given as absolute values (Equation (7)). In the chemical production term, α y represents the possible fractionation due to a yield difference (See Supplement S3.3), while α k and α l are the ratios of the rate constants (Equation (7)). δ A is the atmospheric signature of the 10 chemical compound, δ E is the emission signature, and δ pre is the signature of the precursor S molecule, δ n is the signature of the compound in a neighbouring layer. 32 E is the amount emitted of the more abundant isotope (Tg S yr −1 ). 32 C A is the atmospheric abundance of the compound in question in the layer. 32 P is the amount produced (in Tg S yr −1 ) of the more abundant isotope. 32 C n is the amount of the compound in a neighbouring layer (Tg S). 32 L is the loss rate for the abundant isotope (yr −1 ). k t is a transport timescale in yr −1 (see Supplement S3) . We present the δ budget contributions in yr −1 . A 15 similar concept was used in Tans et al. (1993) and Van Der Velde et al. (2018) for carbon isotopes.

Sensitivity analyses
To assess the uncertainties in our calculations, we perform a number of sensitivity studies. There is relatively little information from isotope measurements, hence we want to assess how sensitive our simulations are for some key model parameters. 20 In our "BASE" simulation, photolysis frequencies of COS are based on radiative transfer calculations, which results in a negative fractionation (see Supplementary Figure S4), but with some dependence on altitude. To test the influence of the uncertain cross sections, we include sensitivity simulations with prescribed fractionation. In the literature, the photolysis fractionation has been reported as both positive (which would result in isotopically lighter COS in the stratosphere) or negative (vice versa).
Hence, we include simulations where we impose a positive (J COS + xx ) for the COS photolysis reaction and a negative and we utilise -10.5 , to take into account the negative value for COS photolysis. We also include a run with no photolysis fractionation.
atmospheric COS. CS 2 contains 2 S atoms, and currently it is unclear how the δ 34 S signature of CS 2 will propagate to COS (Zeng et al., 2017). We also impose a yield of 0.83 towards COS on this reaction based on Stickel et al. (1993). The fast reaction of CS 2 + OH completely converts CS 2 to COS and a SO 2 precursor. Hence, in order to account for a yield fractionation the yield needs to be adjusted just for the 34 S reaction. We impose more (less) 34 S towards COS and in turn making atmospheric COS heavier (lighter). We include a yield fractionation of 6 , and we implement this fractionation by shifting the yield to 5 either 0.835 or 0.825 towards COS and 1.165 or 1.175, respectively towards the SO 2 precursor, (see R3 Table 2).
In order to understand the significance of COS for SO 2 and SSA in the model, we also include a simulation without COS.
With this we study the effect of COS on the SO 2 and sulfate signatures, especially in the stratosphere, and highlight the importance of COS for SSA formation.  The BASE biosphere fractionation from Davidson et al. (2021) was taken as -1.9 . In order to study the importance of this biosphere fractionation (BIO), we include a simulation with no biosphere fractionation ( BIO = 0 ), and another with biosphere fractionation of -5 , as calculated by Angert et al. (2019).

Vertical profiles
25 Figure 1 shows the steady state vertical profiles for COS, SO 2 and sulfate, resulting from the BASE simulation. In the top panels the mixing ratios are plotted. For COS, the tropospheric mixing ratio amounts to 527 ppt, close to the 500 ppt observed for tropospheric COS (Montzka et al., 2007). In the stratosphere, the COS profile decays rapidly due to photolysis, and at 40 km altitude there is almost no COS left. In the SO 2 profile, there is a significant decrease in the troposphere with height, as SO 2 oxidation and wet deposition are prominent in the troposphere. Above the SO 2 minimum around 20 km, a slight enhancement 30 towards the top of the atmosphere is observed (note the logarithmic scale). COS is the major source of SO 2 in this region, but SO 2 is quickly oxidized to sulfate. Higher up in the stratosphere, sulfate photolyses back to SO 2 , hence there is an equilibrium between SO 2 and sulfate. For sulfate that is produced from SO 2 , we clearly model a Junge layer (as labelled) in the stratosphere, and 2.6 for stratospheric sulfate (Castleman et al., 1974) with a peak of about 320 ppt at 20-25 km.
The lower panels in Figure 1 show the simulated δ 34 S profiles in steady state. The COS isotopic signal is about 14 in the troposphere, very close to the measured 13.9 reported by Davidson et al. (2021), and within the range measured by Hattori et al. (2020). In the stratosphere, COS gets increasingly enriched in 34 S with height. This is due to COS removal by 5 photolysis. The prescribed negative 34 , which removes the lighter COS faster, leads to a continuous isotope enrichment of COS in the stratosphere. The simulated δ 34 S value reaches 58 at 40 km, though at this height there is hardly any COS left in the stratosphere. For SO 2 δ 34 S = 3 at the surface, reflecting the source signature of the emitted SO 2 ( Table 5). As we continue up the troposphere, the SO 2 isotopic signature is increasingly depleted, largely due to the inverse kinetic effect during OH oxidation (Table 6). As a result, the heavier isotope reacts away faster, leaving a pool of lighter SO 2 in the troposphere. At 17 km, the SO 2 signature reaches a value of almost -22 , however very little SO 2 is found at this height; it is converted to sulfate. In the stratosphere, COS becomes the major source of SO 2 . As a result, a progressive enrichment of SO 2 is observed towards 40 km, reflecting the isotopically enriched COS precursor. Similarly, the sulfate isotopic signature largely follows the 5 signal of SO 2 . Sulfate is enriched with respect to its precursor SO 2 , due to heavier S reacting favourably away from SO 2 in the OH oxidation reaction ( = +8.9 , see Table 6). Once COS photolysis becomes significant, the sulfate signal also becomes more isotopically enriched. Between 18-19 km, the modelled sulfate signal falls between 2-3 , matching very well with the 2.6± 0.3 measured by Castleman et al. (1974). However, it is important to note that the sulfate δ 34 S in the stratosphere has a strong vertical gradient, which also vary with latitude. At about 40 km the signal is strongly enriched compared to 20 km 10 altitude, with a δ 34 S of almost 15 .
It is interesting to observe that all the modelled sulfur compounds get enriched with height in the stratosphere. In the Supplement Section 4 we present the total S budget in the atmosphere. Total S gets increasingly enriched in the stratosphere due to to the gravitational settling term of sulfate, which is the main sink of S in the stratosphere (Supplementary figure S9). Grav- 15 itational settling removes S that is relatively light compared to the signature of total S. SO 4 is ≈ 10 at 30 km (Figure 1) compared to ≈ 15 for total S at 30 km (Supplementary figure S6). The positive tendency in the δ budget (Equation (9)) is compensated by a negative tendency of transport to bring lighter COS to the stratosphere. in our model. This value includes direct sources of COS from oceans, anthropogenic, biomass burning and also includes an unidentified flux of 276 Gg S yr -1 . This gap in the COS budget is smaller compared to Berry et al. (2013) mainly due to updated anthropogenic emissions (Campbell et al., 2015;Zumkehr et al., 2017;Whelan et al., 2018;Ma et al., 2021).

COS Budget
The total chemical production amounts to 436.6 GgS yr -1 , and is a combination of CS 2 and CH 3 SCH 3 oxidation. As we utilise the 83% yield from Stickel et al. (1993), we get about 278.6 GgS yr -1 from CS 2 oxidation. From CH 3 SCH 3 oxidation we prescribe a contribution of 158 GgS yr -1 of COS, similar to Ma et al. (2021). We note here that CH 3 SCH 3 oxidation to COS is considered feasible only in very pristine, low NOx conditions. However, as marine CH 3 SCH 3 emissions are very large, we assume some COS formation, albeit with a very small yield of 0.7% (Barnes et al., 1994(Barnes et al., , 1996Albu et al., 2006).

5
The largest COS sink is uptake by the biosphere, which removes about 930.2 Gg S yr -1 in our model, in line with Berry et al. (2013). Note the deposition rate was adjusted such that the COS mixing ratio (527 ppt in the model) matches atmospheric observations (Kettle, 2002;Montzka et al., 2007). COS oxidation (mainly by OH) to SO 2 accounts for 84.1 Gg S yr -1 . This number is on the lower end of other studies that have modeled the OH sink to be between 82-116 Gg S yr -1 (Kettle, 2002;10 Montzka et al., 2007;Ma et al., 2021).
The tropospheric lifetime, which is the tropospheric burden divided by the removal rate of COS (dry deposition, oxidation and net transport to the stratosphere), in our model is 2.2 years, which lines up well with the 2-3 years calculated in literature (Brühl et al., 2012). 15 Due to the long lifetime of COS in the troposphere, a net amount of 40 Gg S yr -1 is moved to the stratosphere comparable with the estimate by Sheng et al. (2015) of 40.7 Gg S yr -1 . In the stratosphere, COS is photolysed to SO 2 and then further converted to SSA. The calculated stratospheric burden of COS is 130 Gg S, which is only 5.4% of the tropospheric burden. 20 We calculate the stratospheric lifetime, defined as the stratospheric burden of COS divided by the stratospheric chemical destruction, to be about 3.3 years. The lifetime defined as total atmospheric burden divided by stratospheric loss amounts to 60.2 years, consistent with literature estimates (Sheng et al., 2015;Brühl et al., 2012) In the next section we explore the full stratospheric sulfur budget, to investigate the importance of COS for SSA formation.   Table 8 shows the stratospheric sulfur budget for COS, SO 2 and sulfate. As we saw in the previous section, about 40 GgS yr -1 of COS enters the stratosphere, which is oxidised to SO 2 and sulfate. About 12 GgS yr -1 of SO 2 also enters the stratosphere which is also transferred to sulfate. Hence, about 52 GgS yr -1 of sulfate is produced in the stratosphere. COS thus accounts for 77% of the SSA formation.

5
In the troposphere, sulfate is quickly removed due to efficient wet removal. As the eddy transport in the model depends on the gradient, the removal of sulfate in the troposphere and production of sulfate in the stratosphere leads to a sulfate (eddy-driven) transport of 13 Gg S yr -1 towards the troposphere. An additional 39 GgS yr -1 is lost to the troposphere due to gravitational settling of sulfate aerosol; this is related to the gravitational deposition rate which is prescribed per layer. For completeness, we provide the tropospheric budgets of SO 2 and sulfate in the Supplement (Supplementary Table 1). We exclude the quick cycling 10 between sulfate and SO 2 that occurs in the upper atmosphere (> 40 km, (Brühl et al., 2012)), since these processes have little impact on the COS budget. Table 9. Carbonyl sulfide (COS) δ 34 S budget in the troposphere (below 16 km) and stratosphere (above 16 km) in permil per year ( yr -1 ).

Isotopic Budget of COS
Negative numbers imply that the process depletes atmospheric COS, whereas positive numbers imply enrichment of atmospheric COS.  Table 9 shows the isotopic contributions to the atmospheric signal of COS δ 34 S, calculated according to Equation (9). We found that a 60 year simulation is sufficient to reach steady state for the isotopes as well (See Supplement, Figure S6). In the tro- 15 posphere, the processes of emission and chemical production deplete the atmospheric CO 34 S signal. The emission has a larger depleting effect, since the emission signal is 10.5 , while the atmospheric signal is around 14 , following Equation (9).

Process
Hence, emission introduces relatively light COS in the atmosphere, causing it to be depleted by -0.95 yr -1 . However, due to varying emission signatures, contrasting emission signals are expected over the oceans versus regions influenced by anthropogenic emissions (Hattori et al., 2020;Davidson et al., 2021;Baartman et al., 2021). We carried out a sensitivity simulation 20 with different emission signals that we discuss in Section 3.5.
Chemical production has a slightly depleting contribution (0.02 yr -1 ), which depends on the signature of the two COS precursors and the fractionation during oxidation. CS 2 , which is emitted at 10.4 , leads to depleted atmospheric COS while CH 3 SCH 3 , which is emitted at 20 , enriches atmospheric COS.
Chemical loss has an enriching effect on COS, since the fractionation of all the oxidising reactions are negative. This means that the lighter isotope reacts away faster, leaving behind more enriched atmospheric COS (α l < 1 in Equation (9)). In the troposphere this enrichment is about 0.11 yr -1 . In the stratosphere, chemical loss through photolysis leads to a strong en-5 richment (1.96 yr -1 ). Figure 1 shows that the stratospheric COS indeed gets quite enriched. Note, however, that photolysis fractionation in the stratosphere is currently very uncertain. We therefore carry out a sensitivity test with different photolysis fractionations that are discussed in Section 3.5.
Transport to the stratosphere has an enriching effect on the tropospheric COS, though this effect is quite small (0.07 yr -1 ).

10
It has a larger, albeit a depleting effect on the stratospheric COS since lighter COS from the troposphere is mixed into heavier stratospheric air (1.96 yr -1 ).
Lastly, dry deposition is a large sink for COS. The measured fractionation for this process is negative (Davidson et al., 2021).
Hence, biospheric uptake leads to a more enriched pool of atmospheric COS, enriching it by 0.79 yr -1 . Close to strong COS 15 uptake regions, one would therefore expect to measure 34 S-enriched COS.

Sensitivity Analysis
In this section, we study the uncertainties that are present in the COS isotopic signature and its associated fractionations, and how the subsequent sulfate δ 34 S signature are affected by these uncertainties. Figure 2 shows the sensitivity of the COS photolysis fractionation (J ) and a case with no COS in the model. The outcome 20 of a positive for the photolysis reaction of COS (J = + 73 -blue, from Leung et al. (2002)) shows that the COS becomes strongly depleted in the stratosphere, compared to the base case (dashed black line). The heavier S moves faster to SO 2 and sulfate. Since COS oxidation in the stratosphere leads to a strong enrichment in the oxidation products SO 2 and sulfate, the sulfate at 18 km becomes too enriched (> 5 ) compared to Castleman et al. (1974)'s measurements. The 0 fractionation (peach) case leads to sulfate that is slightly more enriched than the measured values, but remains still very close to the mea- 25 surements. The negative (J = -10.5 -red from Lin et al. (2011)) shows that SO 2 and sulfate are enriched, but remain very similar to the base case. In conclusion, a small, negative is required to reproduce the SSA isotopic measurement of Castleman et al. (1974). A similar conclusion was drawn by Hattori et al. (2011) and Schmidt et al. (2012).
The case with no COS in the model (No COS -lighter blue) clearly shows that without COS as precursor, SO 2 and sul- 30 fate in the stratosphere would be strongly depleted in δ 34 S and would not match the measurements reported by Castleman et al. (1974). This illustrates that the COS abundance and the COS photolysis fractionation control the 34 S isotopic signature of SSA. Figure S10 shows the mixing ratios of COS, SO 2 and sulfate in a no COS case versus with COS present. While a small peak in sulfate in at 15 km is observed when there is no COS present, there is significantly less SSA formed compared to when COS is present. Stratospheric SO 2 is also less when there is no COS in the model.
The next sensitivity scrutinises the oxidation of CS 2 to COS. As CS 2 oxidation is a large source of COS (about 64% of total COS produced, see Table 7), a fractionation during this reaction would have significant effect on the COS isotopic signature.
In Section 4, we will discuss the considerations of isotopic fractionation in this oxidation pathway. Figure 3 shows the impact 5 of adjusting the yield on the subsequent δ 34 S signature for COS, SO 2 and sulfate. When the yield towards CO 34 S is lowered (pink), more of the lighter S ends up in the COS product. This is because less of the heavy S is ending up in COS and more in SO 2 , while the yield for the 32 S remains the same. Only in the stratosphere this signal propagates to SO 2 and sulfate, which get also slightly less enriched due to the lighter COS precursor. In contrast, when the yield is increased (purple line), the heavier S propagates towards COS, and to stratospheric SO 2 and sulfate. 10 The top panel of Figure 4 shows the sensitivity of the subsequent δ 34 S signature for COS, SO 2 and sulfate to biosphere uptake fractionation ( BIO -green). For the biosphere, we show a fractionation range between 0 and -5 , compared to -1.9 in our base scenario. As expected, no fractionation leads to lower δ 34 S values and a fractionation of -5 leads to higher δ 34 S values. This range of fractionations encapsulates the sulfate measurements well. The effect on COS is small but there is 15 a much more significant effect on SO 2 and sulfate in the stratosphere, depending on whether COS is more or less enriched. The bottom panel of Figure 4 shows the sensitivity to the emission signature of COS at emission (E COS -blue). Not surprisingly, results show that the more enriched the COS signature, the more enriched the SO 2 and sulfate will be in the stratosphere. Since the range of the emission signatures (from 8-14 ) is rather small, the effect is only a shift of about 1 for SO 2 and sulfate.
Again, for COS this signal appears throughout the atmosphere, while for SO 2 and sulfate, the effect is only observed in the 5 stratosphere, where COS photolysis is the main source of SSA. Similarly to the biosphere case, the effect on COS is clear but there is a larger effect on SO 2 and sulfate in the stratosphere, because the COS is either more or less enriched.
Overall, this set of sensitivity simulations very clearly shows that COS is a source of stratospheric SO 2 and sulfate. The COS isotopic signature in the troposphere is important for the isotopic signatures of stratospheric SO 2 and sulfate. In the troposphere, while the COS δ 34 S is different in each sensitivity test, the SO 2 and sulfate δ 34 S only respond in the stratosphere. 10 This is especially the case when COS photolysis becomes significant, particularly above 16 km. The dominating factor that determines the δ 34 S signature of SSA is, therefore, the fractionation associated with COS photolysis.

Discussion
Severe gaps in knowledge exist concerning the sulfur isotopic budget in the atmosphere. In this study, we explored the sulfur budgets and δ 34 S budgets for COS, SO 2 and sulfate in an attempt to integrate current knowledge of the system and performed  showing a case of -5 , as calculated by (Angert et al., 2019). The blue lines in the lower panel show the sensitivity of the model to different emission signatures, with cyan at 8 , having a larger contribution from anthropogenic sources, and the darker blue at 14 , more in line with marine measurements (Hattori et al., 2020;Davidson et al., 2021).
some sensitivity analyses to explore the uncertainties.
Firstly, it is important to realise that we use a horizontally-averaged column model. With such a modelling instrument, it is not possible to capture regional variability. A full 3D simulation of an isotope-enabled model is needed to indicate what horizontal gradients in COS isotopologues are to be expected, specifically in the troposphere. For instance, above a forest, which 5 acts as a sink for COS, we expect that measurements will be enriched in δ 34 S. It should be realized that the very small trend of +0.79 yr -1 derived for dry deposition of COS (Table 9) represents a global average, and larger deviations are expected in the real atmosphere, in particular close to the surface.
A 1D column model also misses the atmospheric Brewer-Dobson circulation with upwelling motions in the tropics and down-10 welling in the higher/polar latitudes (Sheng et al., 2015). In our model we have a one-way net flux that always works counter gradient, which misses these effects due to the regional dynamics of the atmosphere. When modelling a two-way flux, it is estimated that about 90% of COS flows back to the troposphere (Sheng et al., 2015;Kremser et al., 2016). Yet, we are able to adjust the transport such that a net COS loss in the stratosphere is calculated that is comparable to Sheng et al. (2015).
Moreover, this study, for the first time, propagates the S-isotopic composition from S-emissions to SSA, and couples this to a (isotopic) mass-balance approach.
Secondly, much of the remaining uncertainties stem from the fact that the COS budget and its isotopic signature are not 5 well constrained. The budget of COS is currently not closed, with missing sources that are still being studied. There are many hypotheses. Literature ranges from missing oceanic or anthropogenic sources, an overestimate of biosphere uptake, or missing chemical pathways (Whelan et al., 2018;Ma et al., 2021). While we do include the CH 3 SCH 3 pathway in our model, which is often not considered in other models, we also include a missing source in our emission to reach the required mixing ratio of COS in the troposphere. Figure 4 shows that more anthropogenic (marine) emissions lead to more depleted (enriched) COS 10 δ 34 S.
The δ 34 S isotopic signature of COS in the atmosphere is being investigated and recent studies expect the atmospheric signature to be between 9.7-14.5 (Kamezaki et al., 2019;Angert et al., 2019;Hattori et al., 2020;Davidson et al., 2021).
Moreover, current knowledge about fractionation to COS is mixed, ranging from the almost no information about COS pro-15 duction from CS 2 (discussed in more detail below), to the plethora of different values that have been calculated and measured for stratospheric COS photolysis. Understanding the photolysis fractionation would also help in constraining the COS isotopic signature in the stratosphere. The sensitivity test (Figure 2) highlights that a large, positive photolysis fractionation as posited by Leung et al. (2002) is not compatible with the SSA δ 34 S measurements. 20 As discussed above, CS 2 oxidation is a major COS precursor that produces 280 Gg S yr -1 of COS. Stickel et al. (1993)  bonds to 32 S, which would result in the 34 S atom ending up in COS. Hence, depending on which step is rate-determining, the produced COS could either be enriched or depleted compared to its CS 2 precursor. According to Zeng et al. (2017), the formation of the SCS−OH adduct is rate-determining. This scenario represents a yield that is lower towards COS (0.825 in the sensitivity analysis) and hence would result in depleted COS δ 34 S, as seen in Figure 3. The CH 3 SCH 3 reaction pathway is also included in this study as a COS source. Despite the low yield, it still amounts to a significant source of COS due to the large amount of CH 3 SCH 3 emitted. Whether this pathway does elicit some COS above pristine conditions is still highly uncertain, and it remains to be seen how this might affect the isotopic signature of COS. A recent study measured enriched CH 3 SCH 3 emissions over the oceans, with an expectation that CH 3 SCH 3 led to COS formation (Davidson et al., 2021). We utilise this enriched CH 3 SCH 3 (20 ) in our model, and it leads to an enriched COS pool in the 5 atmosphere. Hence, over oceans not only do we expect emission of enriched COS, but also enriched COS from the CH 3 SCH 3 pathway. Modelling studies have postulated CH 3 SCH 3 oxidation as a missing source for COS (Lennartz et al., 2017;Ma et al., 2021).
Thirdly, the SSA 34 S signature that we use as a constraint for our model, is based on a study performed in the 1970s (Castleman 10 et al., 1974). Our modelled sulfate profiles in the stratosphere show large gradients. There is therefore an obvious need for more measurements. Measurements of atmospheric COS isotopes, fractionation factors for COS photolysis, and the sulfate signal in the stratosphere and in volcanically quiescent periods would all provide valuable information.
Finally, in this paper we addressed only a steady state solution. The model was run for 60 years in order to achieve a steady 15 state approximation for the S-isotopologues. The model can also be used to study transient, sporadic phenomena like volcanic eruptions. In a future study we intend to add emissions from a volcanic eruption to the stratosphere and then model the timedependent removal of the sulfur species. Large, Plinian eruptions may add substantial amounts of sulfur to the stratosphere.
This sulfur is then moved around the globe and after a few years is deposited at the Earth surface. Sulfate measurements in polar ice show an anomalous, mass independent S-signature, which is considered to be a result of radiation effects due to a 20 thick SO 2 plume (Baroni et al., 2007;Savarino et al., 2003;Gautier et al., 2018Gautier et al., , 2019. These anomalous signals in 33 S and 36 S can be also modeled with PATMO, as we also include these isotopologues in our chemistry scheme. The needed sulfur chemistry framework is already present, as are the multi-frequency radiation calculations that are needed to resolve the SO 2 self-shielding that is expected in a volcanic plume (Ono et al., 2013;Lyons, 2007;Endo et al., 2015). This will be explored in future work, in which we intend to study the effects of self-shielding on S-isotopologues of SO 2 in volcanic plumes (Lyons,25 2007; Ono et al., 2013;Hattori et al., 2013).

Conclusion
Using a 1D column model we analysed the sulfur isotopic budget for a non-volcanic, modern day atmosphere. We modelled the isotopes of COS, SO 2 and sulfate in the atmosphere. To analyse the contributions to the isotopic composition of sulfur species in steady state, we derived their δ budget equations and analysed the main processes that contribute to the modeled 30 isotopic composition. We clearly demonstrate that COS is an important precursor for SSA during non-volcanic periods. We calculate that 77% of sulfur in SSA comes directly from COS. Concerning the 34 S isotopic signals, oxidation and photolysis in the stratosphere lead to a pool of enriched COS, which is transferred to SO 2 and SSA. In the troposphere, oxidation of SO 2 leads to isotopically depleted SO 2 , but in the stratosphere SO 2 gets more enriched due to SO 2 production from COS photolysis.
Hence, there is a large gradient in the SO 2 δ 34 S profile in the lower stratosphere. In the stratosphere, the enriched isotopic signal is carried from COS to SO 2 and finally to sulfate. The modeled sulfate in the lowest part of the stratosphere matches well with the observations from Castleman et al. (1974) (δ 34 S = 2.6 ) in volcanically quiescent times, at 18 km. The sulfur budget, and especially the isotopic budget of sulfur is, however, still not very well understood, with significant uncertainties Baartman, S. L., Krol, M. C., Röckmann, T., Hattori, S., Kamezaki, K., Yoshida, N., and Popa, M. E. (2021). A gc-irms method for measuring sulfur isotope ratios of carbonyl sulfide from small air samples. Open Research Europe, 1(105):105. Barnes, I., Becker, K., and Patroescu, I. (1994). The tropospheric oxidation of dimethyl sulfide: A new source of carbonyl sulfide. Geophysical