2024 Volume 58 Issue 5 Pages 169-183
A 1D model of the CS2 reaction network with the addition of the photo-oxidation pathway has been developed and quantitatively studied. The reaction pathway analysis focusing on the sulfur element was applied to determine the importance of the photo-oxidation pathway in the atmospheric CS2 sink resulting in a 15.8% of sulfur in the CS2 reaction network passes through the photo-oxidation pathway under a global average solar radiation conditions and ranging from 8.1% to 18% depending on the irradiance intensity. The concentration of COS and SO2, the main products of CS2 atmospheric oxidation, changed slightly from the sulfur cycle developed with the updated CS2 reaction network. 7.4% of the COS comes from the new pathway and a total of 40.9% of COS comes from the conversion of CS2. A sulfur budget for the main species in the sulfur cycle was constructed, and the CS2 lifetime was estimated to be 2–3 days. The newly added photo-oxidation pathway plays an moderate role in the CS2 reaction network and has a high variability under specific geochemical conditions. The results of this report should be taken as an incentive for 3D climate-chemistry models to account for local COS sources.
Carbon disulfide (CS2) is a common atmospheric trace gas mainly distributed in the troposphere. The oxidation of CS2 accounts for 30–75% of the global carbonyl sulfide (COS) budget (Chin and Davis, 1993; Khalil and Rasmussen, 1984; Toon et al., 1987; Whelan et al., 2018). COS is the most abundant sulfur compound present in the atmosphere with a lifetime more than one year (Mopper et al., 2015), which is eventually transported to the upper atmosphere and then converted to stratospheric sulfur aerosol (SSA) via sulfur dioxide (SO2) oxidation (Crutzen, 1976; Weisenstein et al., 1997). SSA shields solar infrared radiation and when produce in large amounts by episodic stratospheric volcanic eruptions significantly affects global temperatures. SO2 is also an oxidation product of CS2 mostly in the lower atmosphere, which directly participates in the formation of acid rain (Sze and Ko, 1980), harming plants and animals (Hajer, 2002). An early study by Chin and Davis (1993) showed that anthropogenic sources account for 60% of total CS2 emissions, Lee and Brimblecombe (2016) reported that industrial production and transportation are the main contributions to atmospheric CS2. Additionally, based on field measurements and simulation studies extending over several decades (Bandy et al., 1981; Khalil and Rasmussen, 1984; Lennartz et al., 2020, 2021) show that consequence of anthropogenic activities a year-on-year emissions increase is unfolding and the fate of this additional emissions need to be understood.
CS2 is rapidly depleted in the lower atmosphere and above 5–6 km is hardly detected suggesting that ground-based sources and rapid atmospheric removal (Bandy et al., 1981). Current understanding expounds that the main CS2 sink is through the oxidation with OH radicals to produce COS and SO2 as the oxidized products (Khalil and Rasmussen, 1984). A previous model study suggests that the OH-oxidation pathway shares 75–88% of CS2 global removal (Khan et al., 2017). In addition, the calculated atmospheric residence time by Khalil and Rasmussen (1984) range from a few days to half of a month, varying according to the extent of pollution and human activities.
The UV absorption spectrum of CS2 shows two distinct highly structured bands (Burkholder et al., 2020). The strong absorption band extending from 185–230 nm denotes the CS2 photolysis reaction and has been included in previous CS2 model studies (Khan et al., 2017; Kjellström, 1998; Weisenstein et al., 1997). However, due to the presence of UV-absorbing gases in the air, such as oxygen and ozone, the UV light with wavelength shorter than 320 nm can hardly reach the surface, resulting in the CS2 photolysis reaction barely occurring in the troposphere. Meanwhile, the weaker absorption band extending from 290–380 nm excites the CS2 molecule (the excited state is expressed as CS2* in this study) and triggers a photo-oxidation pathway, producing the same products as the OH-oxidation pathway through a series of oxidation reactions (Wood and Heicklen, 1971). Although the CS2 absorption cross-sections that induce the photolysis reaction are three orders of magnitude larger than the cross-sections of the photo-excitation reaction (Grosch et al., 2015), CS2 can hardly reach the upper atmosphere, resulting in the CS2 photolysis being irrelevant in the atmospheric sulfur cycle. Consequently, CS2 photochemistry has been neglected in the previous sulfur cycle model studies (Brühl et al., 2012; Kremser et al., 2016; Mills et al., 2017; Sheng et al., 2015; Weisenstein et al., 1997). The solar radiation at different altitudes was calculated using a 1D chemical transport model PATMO (Planetary ATMOspheres) (Danielache et al., 2023), which compares favorably with reference data (Kerr and Fioletov, 2008; McLinden et al., 2002). Figure 1 shows that the atmospheric absorption is very weak for irradiance with wavelength longer than 320 nm, indicating that long-wavelength solar radiation can reach the ground and provide enough photons for the CS2 photo-excitation reaction to occur in the lower atmosphere. Several studies have been conducted to detect the fluorescence of CS2 under long-wavelength radiation (Brus, 1971; Lambert and Kimbell, 1973), and the photo-oxidation pathway was elaborated as a potential atmospheric COS source (Wine et al., 1981). However, there are no quantitative studies to elucidate the role of new reaction pathways in the reaction network of CS2 and the contribution to atmospheric COS.
a) Solar irradiance at different altitudes using the opacity values calculated from the PATMO (Planetary ATMOSphere). The daytime-weighted method is applied to counteract the spatial-temporal variation in the 1D model and to represent the global averaging solar irradiance level. The yellow line representing the high-resolution CS2 UV absorption spectrum (Li et al., 2024) shows sufficient cross-sections with solar irradiance at surface. b) Solar irradiance at surface calculated by PATMO model fits the reference value (Kerr and Fioletov, 2008; McLinden et al., 2002). Errors may arise from different sources of solar irradiance at the top of atmosphere (TOA).
The reaction pathway analysis (also known as reaction flux analysis) is a commonly used method to identify the dominant chemistry by post-processing a microkinetic model (Agarwal et al., 2022; Grcar et al., 2003; Hossler et al., 2006; Pfaendtner and Broadbelt, 2008; Salami et al., 2017; Salciccioli et al., 2011). This study applies the reaction pathways analysis to the CS2 reaction network following the sulfur atom to quantify the influence of the CS2 photo-oxidation pathway on the atmospheric sulfur cycle. A revised atmospheric CS2 reaction network with the addition of the photo-oxidation pathway is introduced and evaluated in a 1D model PATMO.
The chemistry of atmospheric CS2 has been incorporated into the 1D chemical transport model PATMO, which has been proven reliable for atmospheric chemistry simulation (Avila et al., 2021) and is designed to handle photochemistry with high-resolution absorption spectra (Danielache et al., 2023). This study employs a model structure that starts from the ground in 1 km units as one layer, totaling sixty layers, which coupled with a line-by-line radiative transfer calculation reproduces the attenuation phenomenon of solar irradiance after entering the atmosphere, and giving accurate data on solar irradiation for photochemical calculations at different altitudes. The photochemistry in this study applies a spectrum with a wavelength resolution of 4440 equally spaced energy beams covering the 180 to 400 nm band. More details of the photochemical calculation in the model can be found in the work of Danielache et al. (2023).
To compensate for the 1D model’s typical inability to account for spatial-temporal variation, we choose the daytime-weighted method by setting the zenith angle θ at 60° and solar constant I(∞, λ) at half to counteract the cyclical fluctuations of solar irradiance from the annual cycle and the diurnal cycle. More studies on radiative-convective equilibrium (Manabe and Strickler, 1964; Manabe and Wetherald, 1967; Ramanathan, 1976), the exoplanetary climate (Wordsworth et al., 2010), and the estimates of the global radiative forcing caused by aerosols and clouds (Fu and Liou, 1993; Zhang et al., 2013) showed that the agreements on using the daytime-weighted adjustment to reduce the solar radiation bias in the 1D model simulation.
In this report an ideal atmospheric condition was assumed where the sky is clear with no clouds, aerosols, dust, pollutants, or any material that can cause Mie scattering. Local meteorological information is necessary for a more realistic approach to this type of phenomena, additionally a generalized global average of hydrometeors such as cloud, rain, and snow droplets would be an artificial if not an unrealistic set of conditions for the model. Estimated Rayleigh scattering cross-sections (Bates, 1984; Bucholtz, 1995; He et al., 2021; Thalman et al., 2014) is at least four orders of magnitude smaller than that of CS2 in the UV band, the influence of Rayleigh scattering on CS2 reactions is negligible. On this report only the direct solar radiation attenuated by the absorption of photochemically relevant molecules is considered for light intensity calculation. By taking a clear sky condition and an atmosphere without Rayleigh scattering approach the results produced in this report suggest an upper limit to the photo-oxidations pathway. An assessment of the validity of this assumption is presented in Fig. 1 where calculated solar fluxes at low altitudes are compared to solar flux measurements made by Kerr and Fioletov (2008) and discussed in detail in the additional information section.
In this study, the main sulfur species that contribute to the sulfur cycle are removed from the photochemical model by combining rainout with surface deposition, dry deposition, and gravity settling of aerosols. The chemical species removed by this process are COS, CS2, H2S, SO2, CH3SCH3 (DMS), and stratospheric and tropospheric aerosols. Rainout and surface deposition account for water-soluble gases according to their solubility. The calculation of rainout rates was based on the parametrization of Giorgi and Chameides (1985), where the cleaving mechanism of airborne rain droplets is calculated according to the Henry constant of each sulfur species. Solubility parameters used by Giorgi and Chameides (1985) are corrected for chemical reactions of the dissolved species within raindrops. This chemical correction to the gas-liquid phase equilibrium is known as the effective Henry constant (Heff). The surface deposition rate at which the effective deposition velocity for each gas is calculated as the addition of atmospheric resistance and resistance of the ocean’s surface layer. This parameterization (Lee and Schwartz, 1981; Liss, 1971; Slinn, 1978) requires calculated rainout rates where effective Henry constant (Heff) is the key factor in determining how fast a chemical species is removed out of the atmosphere.
Dry deposition generally accounts for removing gases and particles from a surface due to gravity (sedimentation). In this study, it is applied only to the sulfur gases mentioned above. The dry deposition flux Fd (molecule cm–2 s–1) is calculated based on the reported dry deposition velocity vd (cm s–1) following the expression:
| (1) |
Where the number density ni (molecule cm–3) of species i is approximated by the following expression under steady-state conditions (Seinfeld and Pandis, 2016):
| (2) |
Where τi (s) is the estimated lifetime, Pi and Ri (molecule cm–3 s–1) are respectively the rates of production and removal for all species i being added to the model.
The formation of SSA above 13 km is based on the scheme proposed by Hamill et al. (1977), where the aggregated nuclei are formed when the ratio between molecular H2SO4 partial pressure and water vapor pressure is larger than 1. The gravitational deposition velocity was taken from Kasten (1968) with a curve parameter (r) value equal to 0.33 μm for SSA.
This study focuses on the chemical transformation of sulfur species, and therefore the atmospheric profiles of common gases in the model, which are N2, O2, O3, OH, O, CO2, CO, HO2, H2O, and NO2, are set at steady state conditions (Hu et al., 2012; Krueger and Minzner, 1976; Turco et al., 1979). Temperature, pressure, and molecular diffusion coefficient at each layer is set as a constant parameter according to Hu et al. (2012) and Krueger and Minzner (1976). The vertical transport of gaseous species occurs by the eddy diffusion coefficient which are derived from the work of Massie and Hunten (1981).
The simulation period is set to 10 years to ensure the gas mixtures have enough time to diffuse into the upper atmosphere to participate in the reactions, and each species can achieve a steady state from production and removal processes.
CS2 has strong regional and near-surface distribution characteristics (Bandy et al., 1981), indicating active sinks in the CS2 reaction network. The main reaction channels are illustrated in Fig. 2, where, despite the dry deposition, the main sink of CS2 comes from the competition between the OH-oxidation and photo-oxidation pathways. The complete CS2 reaction network is listed in Table A1 and A2. More details of these two pathways are discussed below.
The main reaction pathways of CS2 in the atmosphere. Each sulfide reactant represents a node in the reaction network. Despite the dry deposition occurring at the surface, the main competition is between the OH oxidation pathway and the photo-oxidation pathway, and both pathways produce the same end-oxidation products COS and SO2. The figure does not include branching reactions with reaction rate less than 1% with respect to the total reaction rates at the same reaction network node.
Experiments have been carried out to confirm the existence of CS2 fluorescence under UV light with a wavelength over 300 nm (Brus, 1971; Lambert and Kimbell, 1973), implying the transition from ground
R28: CS2 + ℏν → CS2*
R1: CS2* + O2 → CS2 + O2
R2: CS2* + N2 → CS2 + N2
The latest high-resolution UV absorption spectrum for CS2 at 298 K is from the work of Grosch et al. (2015) and made available through the MPI-Mainz UV/Vis Spectral Atlas database (Keller-Rudek et al., 2013). However, cross-section data at wavelengths longer than 350 nm are still unreliable. Instead, we use the suggested absorption cross-section in the 290–350 nm region from Burkholder et al. (2020) for the R28.
The end-product analysis experiments reported by Wood and Heicklen (1971) revealed the existence of the CS2 photo-oxidation pathway. They deduced the rate coefficient ratio between O2 oxidation and quenching reactions that kR3/kR1 ≈ 0.05. The CS2* oxidation reaction produces CS and SO2 according to:
R3: CS2* + O2 → CS + SO2
The CS radical then undergoes the following four reaction pathways:
R10: CS + O → S + CO
R11: CS + O2 → COS + O
R12: CS + O2 → SO + CO
R13: CS + O3 → COS + O2
Considering the atmospheric concentration of O2 is many orders of magnitude higher than that of O(3P) and O3, R11 and R12 are the main competing oxidation channels. Richardson (1975) presented evidence that the rate coefficient ratio kR11/kR12 > 10 via a fast-flow study. A more precise determination based on the work of Black et al. (1983) suggested the rate coefficient for R11 as 2.9 × 10–19 cm3 molecule–1 s–1.
The SO radical generated by R12 is further oxidized to SO2 through the following three reaction channels:
R18: SO + O2 → SO2 + O
R19: SO + O3 → SO2 + O2
R20: SO + OH → SO2 + H
R18 dominates due to the relatively high atmospheric content of O2. The rate coefficient uses Burkholder et al. (2020), which takes the average of values computed by Black et al. (1982) and Schurath and Goede (1984) and presents them in the form of the Arrhenius expression as 1.6 × 10–13 exp(–2280/T).
OH-oxidation pathwayThe OH oxidation pathway produces the same end-oxidation products as the photo-oxidation pathway. The two initial reactions are given below:
R4: CS2 + OH → COS + SH
R5: CS2 + OH → SCSOH
Experimental evidence shows that R4 proceeds very slowly as a direct bimolecular process at 298 K and 1 atm (Iyer and Rowland, 1980; Wine et al., 1980). An upper limit of 2 × 10–15 cm3 molecule–1 s–1 for kR5 (298K) was suggested by Burkholder et al. (2020).
R5 dominates the initial reaction in the OH-oxidation pathway, and it has been observed that the existence of O2 has an accelerating effect (Barnes et al., 1983; Hynes et al., 1988; Jones et al., 1982). Moreover, several experiments demonstrated the R5 reaction process that the adduct formation followed by the adduct decomposition in competition with the long-lived adduct oxidation reaction R6 (Hynes et al., 1988; Murrells et al., 1990):
R6: SCSOH + O2 → COS + HSO2
The molecule structure configuration of the adduct SCSOH follows theoretical studies, which provided evidence that the formation of the S-adduct SCS-OH was followed by adding O2 to the carbon atom in the initial step. A subsequent step appears to be the transfer of an O(3P) atom to the sulfur-bearing hydroxyl group, leading directly to the formation of COS and HSO2 as shown in R6 (McKee and Wine, 2001; Zhang and Qin, 2000). A more recent density functional theory calculation of the energy and intermediate molecule structures provided theoretical support for the priority production of the S-adduct in atmospheric conditions (Zeng et al., 2017).
The negative temperature-dependent rate coefficient was determined in the experiment by Hynes et al. (1988) experiment and the effective kR5 was suggested as (1.25 × 10–16 exp(4550/T))/(T + 1.81 × 10–3 exp(3400/T)) cm3 molecule–1 s–1. Besides, the subsequent adduct oxidation kR6 = 2.8 × 10–14 cm3 molecule–1 s–1 takes the suggestion value from Burkholder et al. (2020). The molecule rearrangement step for the adduct is simplified and not included as an independent reaction in this study considering that the effective rate coefficient is used.
The HSO2 generated in R6 will be oxidized rapidly through R26 as shown below:
R26: HSO2 + O2 → SO2 + HO2
That Lovejoy et al. (1990) found the formation of SO2 and HO2 are equal and near unity in the experiment. His later work showed that the 18O atom in the 18OH reactant is transferred predominantly (90 ± 20)% to the SO2 product, indicating the S-O bonded SCS-OH adduct formation and the preservation of the S-O bind in the steps leading to SO2 formation as described in R26 (Lovejoy et al., 1994). The rate coefficient data takes the suggestion from Burkholder et al. (2020) as kR26 = 3.0 × 10–13 cm3 molecule–1 s–1.
To determine the dominant reaction pathway among different oxidation channels of CS2 and its intermediates, we performed a reaction pathways analysis based on the model-derived reaction rates which are in molecule cm–3 s–1 units and describe the change in number of molecules per unit of volume and time. Using the reaction nodes and edges in the reaction network, this quantitative analysis method reveals the mechanism of the detailed CS2 oxidation pathways. For the reaction rate at a particular sulfide reactant node in the reaction network as shown in Fig. 2, we used the concept of local consumption to illustrate the percentage of sulfur atoms from the reactant to each product. The equation is shown as follows:
| (3) |
Where
The local consumption condition at the node of the initial reactant CS2 is shown in Fig. 3, that at the surface, 88.8% of CS2 molecules participate in the photo-excitation reaction R28 to produce the excited state CS2*, only 5.4% of CS2 molecules participate in the OH-addition reaction R5 to form the relatively long-lived S-adduct SCSOH, and 5.8% of CS2 are removed by dry deposition. With increasing altitude, the ratio of CS2 participating in the photo-excitation reaction reaches its maximum of 95.5% at 3 km, gradually decreasing to 88.7% at 10 km. The result shows that the photo-excitation reaction in the photo-oxidation pathway dominates in the initial reactions of the CS2 reaction network.
Local consumption situation of CS2 initial reactions at each height in 1–10 km.
However, most excited state CS2* molecules formed by photo-excitation reactions are quenched back to the ground state collision with N2 and O2 molecules (Wine et al., 1981). Fig. 4 shows the local consumption situation at the node of CS2* between 1 and 10 km, about 99% of excited CS2* molecules are quenched to the ground state through R1 and R2, and only 1% of CS2* molecules are further oxidized through reaction R3 to form CS radical and SO2. The highly reactive intermediate CS2* is in a pseudo-steady state of the CS2-CS2* equilibrium where CS2* is consumed virtually as rapidly as they are formed and consequently exists at very low concentrations. The ratio of overall flux for CS2 removal was close to the experimental results by Colman and Trogler (1997). However, more quantitative studies are still needed considering the limits and errors of instrumental measurements at low CS2 concentrations.
Local consumption situation at the node of CS2* at each height in 1–10 km.
The CS radical formed from the CS2* oxidation reaction R3 is further oxidized through several reaction channels, where R11 and R12 play a major role, consuming about 90% and 9% of the sulfur, respectively. However, the result is based on the reaction coefficients inferred from previous studies using the product ratio method (Black et al., 1983; Richardson, 1975) and more accurate and targeted experiments are needed. In conclusion, the photo-oxidation pathway gives a product ratio COS:SO2 ≈ 9:11 as shown in Fig. 5. Meanwhile, in the OH-oxidation pathway, R4 is too slow to occur in the atmosphere and R5 dominates as the initial reaction of the OH-oxidation pathway that forms the S-adduct SCSOH. The following oxidation reactions, R6 and R26, are fast and produce COS and SO2 in the ratio of 1:1.
Reaction rates ratio in OH oxidation and photo-oxidation pathway in CS2 reaction network.
A comparison of reaction rates between the S-adduct SCSOH oxidation reaction R6 and excited state CS2* oxidation reaction R3 at different altitudes was conducted to determine the proportion of sulfur passes through the two oxidation pathways. This is in consideration of the fact that most of the CS2* returns to the ground state and that the oxidation reactions of both intermediates are irreversible, meaning that once the sulfur atoms passe through the intermediate reactions R3 and R6, it will eventually be involved in the formation of the end-oxidation products COS and SO2. The red line in Fig. 6 illustrates the proportion of sulfur element that passes through the photo-oxidation pathway under the global average solar radiation condition. The figure also shows that about 15% of the sulfur element is involved in the photo-oxidation pathway at the surface. This ratio reaches its peak at 3 km, about 18%, and gradually decreases to 7% at 10 km. For a vertical distribution, a concentration-weighted average of 15.8% of the sulfur element passes through the photo-oxidation pathway.
The percentage of CS2 involved in the photo-oxidation pathway with respect to OH oxidation pathway at each altitude in 1–10 km.
The above results are all based on solar irradiance using the daytime-weighted method (Cronin, 2014), representing the global average irradiance level of about 342 W m–2. The annual mean solar irradiance received at different latitudes on Earth varies approximately from 160 W m–2 in the Arctic area to 400 W m–2 in the tropic area (Liou, 2002). To investigate the ratio of CS2 oxidized through the photo-oxidation pathway under different solar irradiance conditions, we also performed a reaction pathway analysis for each solar irradiance condition, and the results are shown as the black and blue line in Fig. 6. As expected, more sulfur enters the photo-oxidation pathway under stronger solar irradiance conditions. At low latitudes in the tropic region where sunlight is strongest on average, about 17% of the surface oxidized CS2 passes through the photo-oxidation pathway to produce COS and SO2, and this proportion reaches about 21% at 3 km. Even in the polar regions at high latitudes, where the average annual solar irradiance is less than half the global average, about 8% of CS2 is involved in the photo-oxidation pathway at the surface, again peaking at about 10% at 3 km altitude. All these results show that the photo-oxidation pathway shares an important proportion in the atmospheric removal of CS2. Taking the concentration-weighted method as above, at low latitudes with the highest sunlight radiation (400 W m–2) and high latitudes with the lowest sunlight radiation (160 W m–2), about 18% and 8.1% of the CS2 passes through the photo-oxidation pathway in the two main sink pathways of CS2, respectively.
Effect of photo-oxidation pathway on atmospheric COSThe introduction of the photo-oxidation pathway to the CS2 reaction network changes the original product balance according to the reaction pathway analysis above. To investigate the effect of the CS2 photo-oxidation pathway in the atmospheric sulfur cycle, we add the CS2 reaction network to the sulfur cycle with the schematic diagram as illustrated in Fig. 7 which includes the emission of major sulfur species in the atmosphere, the oxidation processes between sulfur substances, the generation of sulfate aerosols as well as its removal from the atmosphere by deposition processes where the description is mentioned above. The newly added CS2 photo-oxidation process is shown in the box to illustrate its place in the sulfur cycle. The emission and deposition data are listed in Table 1. The complex organic species oxidation processes of DMS in the atmosphere were simplified under the scheme presented by Weisenstein et al. (1997), and only the conversion of DMS to SO2 was used since the other minor product MSA is irrelevant to this study. Table A3 and A4 list the new reactions that are added to the CS2 reaction network to complete the sulfur cycle.
The schematic diagram of the reproduced atmospheric sulfur cycle in this study with the addition of the CS2 photo-oxidation pathway.
Emission rates and deposition velocities of the sulfur compounds
| Species | Emission (Tg year–1) | Dry deposition (cm s–1) | Henry’s constant (mol/L atm–1) |
|---|---|---|---|
| COS | 1.3 | 9.5 × 10–3 | 0.02 |
| CS2 | 1.2 | 4.48 × 10–2 | 0.05 |
| SO2 | 105.4 | 1 | 4000 |
| H2S | 7.72 | 1.7 × 10–1 | 0.1 |
| DMS | 65.57 | 1.48 × 10–1 | — |
| SSA | — | — | 5 × 104 |
Emission rates (Lee and Brimblecombe, 2016; Watts, 2000; Zhong et al., 2020) and deposition velocities of CS2 and its end-oxidation products COS and SO2 (Belviso et al., 2013; Burkholder et al., 2020; Lee and Brimblecombe, 2016; Seinfeld and Pandis, 2016) are prepared for CS2 reaction network. Dry deposition of CS2 and SO2 is calculated from reference lifetime data (Lee et al., 2011; Seinfeld and Pandis, 2016). Emission rates (Lee and Brimblecombe, 2016; Watts, 2000) and deposition velocities (Cope and Spedding, 1982; Judeikis and Wren, 1977) for H2S and DMS are added for complete sulfur cycle calculation. The effective Henry’s constant for SO2 is suggested by Giorgi and Chameides (1985), and the rest uses recommended data from Burkholder et al. (2020).
The model reproduced the vertical distribution of CS2, COS, and SO2 in the atmosphere as shown in Fig. 8. The modeled CS2 concentration at the first layer (1 km) is 2.69 pptv, which is within the estimated range in the free troposphere of less than 3 pptv (Bandy et al., 1981). The CS2 concentration decreases rapidly with increasing altitudes and is below 0.01 pptv over 10 km. The modeled COS concentration at the surface is 521.62 pptv which compares favorably with tropospheric field measurements of about 500 pptv (Carroll, 1985; Glatthor et al., 2017; Maroulis et al., 1977; Remaud et al., 2023; Torres et al., 1980), and when it rises to the stratosphere, the photolysis reaction rapidly depletes COS resulting in a sharp decrease in concentration. Natural and anthropogenic emissions cause high variability in SO2 concentration (Garland, 1977; Seinfeld and Pandis, 2016), modeled SO2 is 288.4 pptv at the surface which is within the estimated range of tropospheric background values of 20–1000 pptv (Jacobson, 2005). With increasing altitude, the SO2 concentration decreases faster than the measured values without volcanic influence of about 20 pptv (Höpfner et al., 2015), and when it comes to the upper atmosphere over 35 km, the simulated SO2 concentration is lower than the measured data of about 110 pptv (Rinsland et al., 1995). The uncertainty is most likely associated with the photodissociation process of molecule H2SO4 prior to the formation of SSA. In this report the SSA formation scheme is based on a simple approximation and the origin of SO2 in the upper stratosphere is not fully understood since the current wisdom suggest that is produced by H2SO4 photodissociation and yet there are no reports of strong ultraviolet absorption spectra. Trace sulfur species DMS, H2S, and H2SO4 at surface are calculated as 71 pptv (40–110 pptv, Maroulis and Bandy, 1977), 20 pptv (5–300 pptv, Jacobson, 2005), and 60 pptv (5–70 pptv, Seinfeld and Pandis, 2016), respectively. The vertical distribution of SSA is also within a reasonable range compared to the reference (Toon et al., 1979). We thus conclude that the overall results are reasonable.
The vertical distribution of sulfur compounds in the reproduced sulfur cycle. The solid and dashed lines indicate the concentration results with and without the addition of the CS2 photo-oxidation pathway, respectively. The field measurements and calculation estimations of CS2 (Bandy et al., 1981), COS (Carroll, 1985; Glatthor et al., 2017; Maroulis et al., 1977; Remaud et al., 2023; Torres et al., 1980), SO2 (Höpfner et al., 2015; Jacobson, 2005; Rinsland et al., 1995), DMS (Maroulis and Bandy, 1977), H2S (Jacobson, 2005), H2SO4 (Seinfeld and Pandis, 2016), and SSA (Toon et al., 1979) match the results in this study.
The vertical distribution of CS2, COS, and SO2 concentrations before and after the addition of the CS2 photo-oxidation pathway are also compared in Fig. 8. At surface height, the concentration of CS2 decreases by 12% when the photo-oxidation pathway was added. Even after the CS2 photo-oxidation pathway was added COS mixing ratios remained unchanged. That is expected since a 12% difference of a few ppt of mixing ratio will not significantly affect background levels of 500 ppt of COS. These results are for CS2 emissions rates of 1.22 Tg S y–1 as reported by Lee and Brimblecombe (2016) which are annual average emissions of all known natural and anthropogenic sources. Industrial locations with high anthropogenic activities would create scenarios in which CS2 emissions that are oxidized by a combination of ultraviolet light and OH radicals providing a COS distribution different from a scenario with a unique oxidation pathway.
A schematic diagram of the sulfur budget for the entire atmosphere regardless of altitude is shown in Fig. 9, where each sulfur gas burden is presented in the square boxes in Gg of sulfur units. The arrow line represents the net sulfur fluxes of surface emissions, deposition processes such as dry and wet deposition, gravitational settling for the case of aerosols and chemical exchange in Gg of sulfur per year units. The simplified aerosol formation mechanism assumes that all formed SSA with a single curve parameter (r) value equal to 0.33 μm. A realistic approach to the chemical transformation of H2SO4 into aerosols would include coagulation intermediates and formation of aerosols of different masses and settling velocities. Additionally chemical species closely related to the formation mechanisms of aerosols such as SO3 are not rigorously treated and therefore calculated concentrations for minor sulfur species might have discrepancies with the real atmosphere. Aerosol related processes will not be further discussed since the main purpose of aerosol-related sulfur species removal in this study is to achieve the model’s mass balance.
Schematic diagram of the sulfate budget for the entire atmosphere regardless of altitude in this study. Each of the three solar irradiance conditions, global average (342 W m–2), arctic regions (160 W m–2), and tropical regions (400 W m–2), is shown in the figure.
The result in this study shows that under global average solar irradiance condition (342 W m–2), surface emissions of 1025.82 Gg of sulfur per year to the global CS2 burden (7.05 Gg S), and the presence of branching reactions in the photo-oxidation pathway results in about 1.5% more sulfur from CS2 to SO2 (486.73 Gg S yr–1) than to COS (479.79 Gg S yr–1). Considering sources different from COS emissions (693.33 Gg S yr–1), the contribution from CS2 oxidation accounts for about 40.9% of COS sources, and the result verifies that CS2 is an important precursor of COS. Under global average solar irradiance level (342 W m–2) applying conditions of daytime-weighted method as described above, about 15.8% of sulfur that CS2 contributes to COS comes from photo-oxidation reaction, which means that about 6.5% (40.9% × 15.8%) of sulfur to the COS comes from the photo-oxidation pathway, and this implies that the CS2 photo-oxidation pathway cannot be ignored. Nevertheless, SO2 has significant surface emissions (52700 Gg S yr–1) and sources from other chemical conversions other than CS2 oxidation are much more significant making variability on CS2 a minor effect on SO2. When latitude decreases and average solar irradiance increases, more CS2 is involved in photo-oxidation reactions from the arctic regions (160 W m–2) to the tropical regions (400 W m–2) and leads to a decrease in the global burden of CS2 by about 10%. Meanwhile, more COS and SO2 are also involved in photolysis reactions, resulting in a decrease of about 4‰ in the global burden of COS and about 0.2‰ in the global burden of SO2. Moreover, the CS2 lifetime in the troposphere is about 2 to 3 days from model estimation, consistent with estimations reported by Khan et al. (2017).
In this study, we have constructed a 1D model of the CS2 reaction network and extended it to a sulfur cycle. The daytime-weighted zenith angle and solar constant are applied to counteract the spatial-temporal variation and simulate the global average solar radiation. Modeled sulfur-bearing species concentrations reproduced field measurements or other model estimations. From the reaction pathway analysis, we found that the overall reaction rates for photo-oxidation and OH-oxidation pathways are on the same order of near-magnitude that 15.8% of CS2 are involved in the photo-oxidation pathway under global average solar irradiance condition. Depending on the local solar radiation intensity, this proportion ranges from 8.1% to 18%. The sulfur budget of the sulfur cycle in this study is determined and it is concluded that the addition of the CS2 photo-oxidation pathway has a relatively minor change (1.5%) on the product ratio between COS and SO2. Nevertheless, the significant proportion of the CS2 photo-oxidation pathway in the CS2 sink makes the photo-oxidation pathway play an important role in the CS2 reaction network.
Code for modeling CS2 reaction network is available at https://github.com/PatrickYLi/PATMO/tree/2022_CS2_v1, and code for modeling modern atmospheric sulfur cycle with the addition of CS2 reaction network is available at https://github.com/PatrickYLi/PATMO/tree/2022_STD_v5.
Non-photochemical reactions and related intermediates associated to the CS2 oxidation pathways
| No. | Reaction | Rate Constant | References |
|---|---|---|---|
| 1 | CS2* + O2 → CS2 | 2.5 × 10–11 | Brus (1971); Lambert and Kimbell (1973) |
| 2 | CS2* + N2 → CS2 | 2.5 × 10–11 | Brus (1971); Lambert and Kimbell (1973) |
| 3 | CS2* + O2 → CS + SO2 | 1.25 × 10–12 | Wood and Heicklen (1971) |
| 4 | CS2 + OH → COS + SH | 2 × 10–15 | Burkholder et al. (2020) |
| 5 | CS2 + OH → SCSOH | (1.25 × 10–16 exp(4550/T))/(T + 1.81 × 10–3 exp(3400/T)) | Burkholder et al. (2020) |
| 6 | SCSOH + O2 → COS + HSO2 | 2.8 × 10–14 | Burkholder et al. (2020) |
| 7 | CS2 + O → CS + SO | 3.2 × 10–11 exp(–650/T) | Burkholder et al. (2020) |
| 8 | CS2 + O → COS + S | 2.72 × 10–12 exp(–650/T) | Burkholder et al. (2020) |
| 9 | CS2 + O → S2 + CO | 9.6 × 10–13 exp(–650/T) | Burkholder et al. (2020) |
| 10 | CS + O → S + CO | 2.7 × 10–10 exp(–760/T) | Burkholder et al. (2020) |
| 11 | CS + O2 → COS + O | 2.9 × 10–19 | Burkholder et al. (2020) |
| 12 | CS + O2 → SO + CO | 2.9 × 10–20 | Burkholder et al. (2020) |
| 13 | CS + O3 → COS + O2 | 3.0 × 10–16 | Burkholder et al. (2020) |
| 14 | S + O2 → SO + O | 1.6 × 10–12 exp(100/T) | Burkholder et al. (2020) |
| 15 | S + O3 → SO + O2 | 1.2 × 10–11 | Burkholder et al. (2020) |
| 16 | S + OH → SO + H | 6.6 × 10–11 | Burkholder et al. (2020) |
| 17 | S2 + O → S + SO | 1.6 × 10–13 | Hills et al. (1987); Singleton and Cvetanović (1988) |
| 18 | SO + O2 → SO2 + O | 1.6 × 10–13 exp(–2280/T) | Burkholder et al. (2020) |
| 19 | SO + O3 → SO2 + O2 | 3.4 × 10–12 exp(–1100/T) | Burkholder et al. (2020) |
| 20 | SO + OH → SO2 + H | 2.6 × 10–11 exp(330/T) | Burkholder et al. (2020) |
| 21 | SH + O → SO + H | 1.6 × 10–10 | Burkholder et al. (2020) |
| 22 | SH + O2 → SO + OH | 4.0 × 10–19 | Burkholder et al. (2020) |
| 23 | SH + O3 → HSO + O2 | 9.0 × 10–12 exp(–280/T) | Burkholder et al. (2020) |
| 24 | HSO + O2 → SO2 + OH | 2.0 × 10–17 | Burkholder et al. (2020) |
| 25 | HSO + O3 → SO2 + SH | 1.0 × 10–13 | Burkholder et al. (2020) |
| 26 | HSO2 + O2 → SO2 + HO2 | 3.0 × 10–13 | Burkholder et al. (2020) |
Photochemical reactions of CS2
| No. | Reaction | References |
|---|---|---|
| 27 | CS2 + hv → CS + S |
180–194 nm: Chen and Robert Wu (1995) 194–205 nm: Sunanda et al. (2015) 205–275 nm: Grosch et al. (2015) |
| 28 | CS2 + hv → CS2* |
275–370 nm: Burkholder et al. (2020) 370–400 nm: No data |
| 29 | SO + hv → S + O |
180–260 nm: Danielache et al. (2014) 260–400 nm: No data |
Additional non-photochemical reactions that completes the complete sulfur cycle
| No. | Reaction | Rate Constant | References |
|---|---|---|---|
| 30 | COS + OH → CO2 + SH | 1.1 × 10–13 exp(–1200/T) | Burkholder et al. (2020) |
| 31 | COS + O → CO + SO | 2.1 × 10–11 exp(–2200/T) | Burkholder et al. (2020) |
| 32 | H2S + OH → H2O + SH | 6.1 × 10–12 exp(–75/T) | Burkholder et al. (2020) |
| 33 | H2S + O → OH + SH | 9.22 × 10–12 exp(–1803/T) | Burkholder et al. (2020) |
| 34 | H2S + H → H2 + SH | 8 × 10–13 | Burkholder et al. (2020) |
| 35 | H2S + HO2 → H2O + HSO | 3 × 10–15 | Burkholder et al. (2020) |
| 36 | SO2 + HO2 → OH + SO3 | 1 × 10–18 | Burkholder et al. (2020) |
| 37 | SO2 + O3 → O2 + SO3 | 3 × 10–12 exp(–7000/T) | Burkholder et al. (2020) |
| 38 | HSO3 + O2 → HO2 + SO3 | 1.3 × 10–12 exp(–330/T) | Burkholder et al. (2020) |
| 39 | SO2 + O → SO3 | 1.80 × 10–33(T/300)2 | Burkholder et al. (2020) |
| 40 | SO2 + OH → HSO3 | 3.30 × 10–31(T/300)–4.3 | Burkholder et al. (2020) |
| 41 | SO3 + H2O → H2SO4 | 1.2 × 10–15 | Burkholder et al. (2020) |
| 42 | H2SO4 → SO2 + 2OH | 1.2 × 10–15 | Burkholder et al. (2020) |
| 43 | CH3SCH3 + O → SO2 | 1 × 10–11 exp(410/T) | Weisenstein et al. (1997) |
| 44 | CH3SCH3 + OH → SO2 | 1.2 × 10–11 exp(–260/T) | Weisenstein et al. (1997) |
| 45 | CH3SCH3 + OH → SO2 + CH4O3S | 3.04 × 10–12 exp(350/T) | Weisenstein et al. (1997) |
Additional photolysis reactions that complete sulfur cycle
| No. | Reaction | References |
|---|---|---|
| 46 | COS + hv → CO + S |
180–185 nm: No data 185–195 nm: Limão-Vieira et al. (2015) 195–260 nm: Hattori et al. (2011) 260–300 nm: Limão-Vieira et al. (2015) 300–400 nm: No data |
| 47 | SO2 + hv → SO + O |
180–189.5 nm : Danielache et al. (2008) 189.5–225 nm: Endo et al. (2015) 225–239 nm: Wu et al. (2000) 239–400 nm: Bogumil et al. (2003) |
| 48 | O3 + hv → O2 + O |
180–230 nm: Burkholder et al. (2020) 230–400 nm: Malicet et al. (1995) |
| 49 | O2 + hv → 2O |
180–181 nm: Kockarts (1976) 181–235 nm: Ogawa (1971) 235–400 nm: Bogumil et al. (2003) |
| 50 | SO3 + hv → SO2 + O |
180–330 nm: Burkholder et al. (2020) 330–400 nm: No data |
| 51 | H2S + hv → SH + H |
180–260 nm: Wu and Chen (1998) 260–370 nm: Grosch et al. (2015) 370–400 nm: No data |
We would like to thank the editors and anonymous reviewers for their help and advice. We also appreciate Anni Pu for her contribution to the hand-drawn graphical abstract. This study does not have real or perceived financial conflicts of interests for any author. This research was funded by JSPS KAKENHI (grant numbers 22H05150 and 20H01975).
