The oxidation of SO2 in the gas phase has been extensively studied by numerous researchers (Baulch et al., 1984; Kerr, 1984; Atkinson and Lioyd, 1984; Calvert and Stockwell, 1984; Graedel, 1977; Atkinson et al., 1997). In this study, the oxidation of SO2 is described using comprehensive reaction mechanisms shown in Table S1. The mechanisms can also be simplified as follows: SO2g+OH→HOSO2,HOSO2+O2→SO3+HO2,SO3g+H2O(g)+M→H2SO4aq+M,HOSO2+OH(g)+M→H2SO4aq+M.

SO2 is dissolved into hygroscopic sulfuric acid (H2SO4), which is formed in the gas phase, via a partitioning process and reacts with the aqueous-phase oxidants (e.g., H2O2 and O3) to heterogeneously form H2SO4. The chemical species that were treated by the partitioning process include SO2, NOx, O3, OH, HO2, H2O2, HCOOH, CH3OOH, HNO3, CH3O2, HONO, CH3COOH, and HCHO. In the model, the partitioning process is approached using the gas–particle partitioning coefficient Kaq,SO2 (m3µg-1) based on aerosol mass concentration. Kaq,SO2 is derived from Henry's law constant of SO2 (KH,SO2=1.2 mol L-1 atm-1 at 298 K) (Chameides, 1984), Kaq,SO2=KH,SO2RTρaq, where R is the ideal gas constant (J K-1 mol-1) and ρaq (g cm-3) is the density of the particle, which is calculated using an inorganic thermodynamic model (E-AIM II) (Clegg et al., 1998; Wexler and Clegg, 2002; Clegg and Wexler, 2011) based on humidity and inorganic composition. The partitioning process of SO2 on inorganic aerosol (Inaq, µg m-3) is expressed as SO2g+Inaq→SO2aq+Inaqkabs,SO2,aq(m3µg-1s-1),SO2aq→SO2gkdes_SO2,aq(s-1), where kabs,SO2,aq (m3µg-1s-1) and kdes,SO2,aq (s-1) are the uptake rate constant and the desorption rate constant, respectively, and are calculated as follows: kabs,SO2,aq=fabs,aqωSO2faq,S_M4,kdes,SO2,aq=kabs,SO2,aqKaq, where faq,S_M (5×10-4, m2 µg-1) is the coefficient to convert the aerosol mass concentration (µg m-3) to the surface area concentration (m2 m-3) for particle size near 100 nm. fabs,aq is the coefficient for uptake process and ωSO2 is the mean molecular velocity (m s-1) of SO2 and can be calculated as follows: ωSO2=8RTπMW, where MW is molecular weight (kg mol-1). In our model, fabs,aq was set at 2×104 in Eq. (2) to have fast partitioning process. Table S2 summarizes the characteristic time that is estimated for diffusion, partitioning, and the reactions of major species with OH radicals in gas, aqueous, and dust phases. In general, the characteristic time (s) of a partitioning process (order of 10-7 s) is much faster than gas-phase oxidation (order of 106 s), aqueous-phase oxidation (order of 103–104 s), and dust-phase oxidation (order of 102–103 s at presence of 200 µg m-3 of dust particles). The mass concentration (µg m-3) of inorganic seeded aqueous phase above the efflorescent relative humidity (ERH) is also dynamically calculated for the SO42-–NH4+–H2O system. Colberg et al. (2003) semiempirically predicted ERH by fitting to the experimental data based on the ammonia-to-sulfate ratio in the SO42-–NH4+–H2O system. AMAR model utilizes these parameterizations to predict ERH dynamically. Ammonia is inevitable in our chamber study and mainly acts as a carryover from previous chamber experiments. Thus, H2SO4 is fully or partially neutralized by ammonia.

The AMAR model implements aqueous-phase chemistry that occurs in inorganic salted aqueous aerosol (SO42-–NH4+–H2O system without dust) to form SO42-aq and NO3-aq. We employed the preexisting aqueous-phase kinetic reactions involving SO2 (Liang and Jacobson, 1999) and NOx chemistry (Liang and Jacobson, 1999; Hoyle et al., 2016). Thus, our simulation inherits all the possible uncertainties embedded in the original kinetic data.

The SO2 dissolved in the aqueous phase is hydrolyzed into H2SO3 and dissociates to form ionic species (HSO3- and SO32-). SO42-(aq) is formed by reactions of the sulfur species in oxidation state IV ((S(IV)aq) with OH(aq), H2O2(aq), or O3(aq) (Table S1). The dissolved HONO can also dissociate to form NO2-aq and result to NO3-aq. Each chemical species in S(IV)aq has a different reactivity for oxidation reactions. The distribution of chemical species is affected by aerosol acidity, which is controlled by humidity and inorganic composition. Hence, the formation of sulfate is very sensitive to aerosol acidity. For example, most of the S(IV) is consumed by H2O2 at pH < 4, whereas most of it is consumed by O3 at pH > 4. Some strong inorganic acids, such as sulfuric acid, influence aerosol acidity. In AMAR, aerosol acidity ([H+]) is estimated at each time step by E-AIM II (Clegg et al., 1998; Wexler and Clegg, 2002; Clegg and Wexler, 2011) corrected for the ammonia-rich condition (Li et al., 2015; Beardsley and Jang, 2016; Li and Jang, 2012) as a function of inorganic composition measured by a particle-into-liquid sampler coupled with ion chromatography (PILS-IC). When the ammonia-to-sulfate ratio is greater than 0.8, the prediction of [H+] is corrected based on the method described by Li and Jang (2012). At high NOx levels, NO2-aq competes with S(IV)aq for the reaction with OH(aq), O3, or H2O2 (Table S1) (Ma et al., 2008). However, the HONO concentration becomes high at high NOx levels and enhances SO2 oxidation in the inorganic-salt seeded aqueous phase due to the formation of OH radicals via photolysis of HONO.

In an adsorptive mode, water molecules suppress partitioning of SO2 because they compete for adsorptive sites with tracers (Cwiertny et al., 2008). However, the formation of the sulfate associated with ATD increased with increasing RH as shown in Table 1, suggesting that gas–dust partitioning is more likely operated by absorption on the multilayer coated dust with water molecules. ATD contains hygroscopic inorganic salts that form the thin water film on the surface of ATD particles when the salts are deliquescent (or above ERH). Some salts such as magnesium sulfate and calcium sulfate can be hydrated even at low humidity (Beardsley et al., 2013; Jang et al., 2010). Gustafsson et al. (2005) reported that ATD particles showed a substantially high affinity to water compared to pure CaCO3 particles. In their study, the water content of ATD particles, which was measured using the thermogravimetric method, ranged from two monolayers to four monolayers based on the BET surface area between 20 and 80 % relative humidity. This water layer influences gas–dust partitioning of atmospheric tracers such as SO2 and NO2. The gas–dust partitioning constant (Kd,SO2, m3 m-2) of SO2 is defined as Kd,SO2=[SO2]d[SO2]gADust(m3m-2), where Adust (m2 m-3) is the geometric surface concentration of ATD dust particles and is calculated by multiplying the dust mass concentration (µg m3) by a geometric surface-mass ratio (fdust,S_M) of ATD particles (3.066 × 10-6, m2 µg-1). The SO2 absorption and desorption processes for the dust phase are expressed as SO2g+ADust→SO2d+ADustkabs_SO2,dust(m3m-2s-1),SO2d→SO2gkdes_SO2,dust(s-1), where kabs_SO2,dust (m3 m-2 s-1) and kdes_SO2,dust (s-1) are the absorption rate constant and the desorption rate constant, respectively. At equilibrium, the absorption rate (R7) equals the desorption rate (R8). Thus, Kd,SO2 can be expressed as Kd,SO2=kabs_SO2,dustkdes_SO2,dust(m3m-2). The Kd,SO2 value at 20 % RH is set at 1.63 (m3 m-2) based on the literature data (dust particles at 20 % RH) (Adams et al., 2005; Huang et al., 2015). The characteristic time to reach to equilibrium is very short (Sect. 3.1.1). In kinetic mechanisms, kads_SO2,dust was set at 1.7×103 m3 m-2 s-1 for dry particles (20 % RH) using the same approach as Eq. (2). The resulting characteristic time for kads_SO2,dust is 10-6 s. The characteristic time of the reaction of SO2 with an OH radical (106 molecules cm-3) is about 106–107 s in gas phase and 105–106 s in both aqueous phase and dust phase.

To consider the effect of temperature on Kd,SO2, the temperature dependency of kdes_SO2,dust (Eq. 6) is derived from the Henry's constant (Chameides, 1984). Kd,SO2 (Eq. 5) is also influenced by aerosol water content (Zuend et al., 2011) as well as the dissociation of H2SO3, which is operated by aerosol acidity ([H+]) and an acid dissociation constant (KaSO2) (Martell and Smith, 1976). Thus, kdes_SO2,dust is expressed as kdes_SO2,dust=1×109exp⁡-3100T/Fwater1+KaSO2H+(s-1). KaSO2 is 0.013 (mol L-1) at 298 K (Martell and Smith, 1976). The influence of the dissociation of inorganic acid on Kd,SO2 is accounted for by the term (1+KaSO2H+) in Eq. (7). The estimation of [H+] is treated in the same ways as aqueous chemistry (Sect. 3.1.3).

In order to estimate Kd,SO2 at different RH, Fwater (coefficient of the mass fraction of water to dust particles) was introduced into the model. The hygroscopic property of mineral dust dynamically changes because dust can be substantially modified by direct reaction of some of its components (e.g., CaCO3) with inorganic acids such as H2SO4 and HNO3. When dust forms Ca(NO3)2, dust becomes more hygroscopic. Nitrate salts deliquesce at very low RH (17 %) (Krueger et al., 2003, 2004). CaSO4 is, however, relatively hydrophobic. Nitrate salts exist only when sulfate concentrations is very low. In the model, Fwater is associated with the hygroscopic property of indigenous dust (first term in Eq. 8), the inorganic nitrates formed from the reaction of absorbed HNO3 with dust (second term), and the inorganic sulfate (SO42-–NH4+–H2O system, third term). Fwater=exp⁡4.4RH+3.7fdust,S_Mexp⁡4.4RHNO3-(d_salt)ADust+fdust,S_MMin,waterADust, where Min,water is the water concentration (µg m-3) associated with inorganic sulfate and calculated using E-AIM II. Both NO3-(d_salt) and Min,water are normalized by the mass concentration of ATD particles ([Dust], µg cm-3). Fwater is first determined using chamber simulation of SO2 heterogeneous oxidation (first and third terms in Eq. 8) (D1–D3 in Table 1) under varied RH levels and extended to SO2 oxidation in the presence of NOx (Exp. 14 April 2017 in Table 2). Among temperature, RH, and aerosol acidity, the most influential variable is RH due to the variation in Fwater (see sensitivity analysis in Sect. 5).

Typically, autoxidation of SO2 is an oxidation process via the reaction of absorbed SO2 (Reactions R7 and R8) with an oxygen molecule. In the model, [SO42-]auto is defined as the sulfate resulted from any oxidation reactions (autoxidation in open air and oxidation with ozone) of SO2 without UV light (Fig. 1). In autoxidation, the reaction of SO2(d) with the oxygen molecules is treated as the first-order reaction (assuming the concentration of oxygen is constant as 2 × 105 ppm). SO2d⟶O2(g)SO42-dkauto=5×10-6(s-1) Under dark conditions, the formation of sulfate is mainly sourced from autoxidation of SO2. For comparison with other studies, we estimate the reactive uptake coefficient (γSO42-,auto) of SO2 onto ATD dust in the absence of ozone and NOx (Fig. 2). γSO42-,auto=4Kd,SO2kautoωSO2, γSO42-,auto is proportional to Kd,SO2, and influenced by humidity (Eq. 7).

The reactive uptake of SO2 on particles is traditionally treated as a first-order process (Ullerstam et al., 2003; Li et al., 2007). Such an approach is appropriate for simple autoxidation mechanisms, but not for the complex heterogeneous photooxidation of SO2. In the AMAR model, the heterogeneous photooxidation of SO2 is approached in three steps: (1) the formation of an ecb-–hvb+ pair via photoactivation of dust particles, (2) the formation of OH(d) via the reaction of an ecb-–hvb+ pair with a water or oxygen molecule, and (3) the reaction of absorbed SO2 with the resulting OH(d) (second-order reactions) (Table S1).

The photoactivation of dust particles and the recombination reaction of an electron–hole pair (e_h) are added into the model. Dust⟶hυDust+e_hke_hj=jATD,e_h⟶energykrecom=1×10-2(s-1), where ke_hj is the photoactivation rate constant to form ecb-–hvb+ pairs and krecom is the reaction rate constant of recombination (heat radiation) of an electron and a hole. The value of krecom is set at a large number to prevent the accumulation of electron–hole pairs. The formation of OH(d) is expressed as e_h+O2(g)⟶OH(d)kOH,O2=1×10-22exp(2.3RH)(cm3molecules-1s-1), where kOH,O2 is the reaction rate constant to form OH(d) and is first estimated using indoor chamber data (L1–L3 in Table 1) at RH 20, 55, and 80 % and then regressed against RH. The study by Thiebaud et al. (2010) reported the recombination of OH(d) near to TiO2 surfaces. In our model, the mechanistic role of the catalytic formation of the electron–hole pairs (Reaction R10) and their recombination (Reaction R11) compensates the formation and the self-reaction of OH radicals.

In Reaction (R10), ke_hj is the operational rate constant for the photoactivation of dust particles and is dependent on the photolysis rate constant, jATD (s-1). Like the typical photolysis of a gaseous molecule, the photocatalytic production of ecb-–hvb+ pairs is linear to both the actinic flux (I(λ), photons cm-2 nm-1 s-1) originating from the light source and the photocatalytic property of dust particles. The value of jATD is determined by I(λ), the absorption cross section (σ(λ), cm2 µ g-1), and the quantum yield (ϕ(λ)) of dust conducting matter at each wavelength range (λ, nm), j[ATD]=∫λ1λ2Iλσλϕλdλ. In the model, σ(λ) is the light absorption needed to activate dust-phase semiconducting metal oxides (excitation from a ground energy level to a conducting band), and ϕ(λ) is the probability of yielding the ecb-–hvb+ pair in the dust phase. Both σ(λ) and ϕ(λ) cannot be directly measured because of complexity in the quantity of photoactive conducting matter in dust particles and the irradiation processes of the ecb-–hvb+ pair. In order to deal with σ(λ)×ϕ(λ), we calculated the mass absorption cross section of dust particles (MACATD, m2 g-1), which was determined using the absorption coefficient of ATD particles (bATD, m-1) with the particle concentration (mATD, g m-3): MACATD=bATDmATD. In Eq. (11), bATD can be calculated from the absorbance of dust filter sample (AbsATD, dimensionless) measured using a reflective UV–visible spectrometer (Fig. S3): bATD=AbsATDAfVln, where A=7.85 × 10-5 (m2) is the sampled area on the filter and V (m3) is the total air volume passing through the filter during sampling. In order to eliminate the absorbance caused by filter material scattering, a correction factor (f=1.4845) is obtained from a previous study (Zhong and Jang, 2011) and coupled into Eq. (12). The preliminary study showed that the effect of aerosol scattering on the babs values of the aerosol collected on the filter was negligible. Further, Bond (2001) reported that particle light scattering does not significantly influence spectral absorption selectivity. The MACATD of dust particles originates from photocatalytic conducting matter (e.g., TiO2) as well as light-absorbing matter (e.g., gypsum and metal sulfate). Thus, the MACATD spectrum is adjusted using the known TiO2 absorption spectrum (Reyes-Coronado et al., 2008) and applied to σ(λ) × ϕ(λ) (Fig. S3). The resulting σ(λ) × ϕ(λ) spectrum is applied to Eq. (10) to calculate jATD (Reaction R10).

SO2 is oxidized by OH(d) on the surface of ATD particles as follows: SO2d+OH(d)SO42-dkphoto=1.0×10-12(cm3molecule-1s-1), where kphoto is the reaction rate constant of SO2 with OH(d) and is estimated from gas-phase Reaction (R1). Combining Eq. (4), (5), Reactions (R11) and (R15), the reactive uptake coefficient (γSO42-,photo) of SO2 on ATD particles under UV light can be written as γSO42-,photo=4Kd,SO2kphotoOHd+kautoωSO2, where γSO42-,photo is the constant at a given concentration of OH(d) (for a given light source, dust concentration, and humidity) (Reactions R10 and R12). Figure 2 illustrates γSO42-,photo values at three different RHs, which were obtained using indoor chamber data. γSO42-,photo is significantly influenced by both UV light and humidity. For example, γSO42-,photo is 1 order of magnitude higher than γSO42-,auto at low NOx levels (< 5 ppb), and γSO42-,photo increased from 2.0 × 10-5 to 1.24 × 10-4 when the RH changed from 20 to 80 %.

The gas–dust partitioning coefficient of ozone is scaled using Kd,SO2 and the ratio of the Henry's law constant of SO2 (KH,SO2, Eq. 1) to that of ozone (KH,O3=1.2 × 10-2 mol L-1 atm-1 at 298 K) (Chameides, 1984), Kd,O3=Kd,SO2KH,O3KH,SO2=7.7×10-7Fwaterexp(2700T)(m3m-2). The partitioning process is also treated by the absorption–desorption kinetic mechanism as shown in Reactions (R7) and (R8) (Table 3: partitioning). Ozone can decay catalytically in the dust phase, forming an oxygen molecule and surface-bound atomic oxygen (Usher et al., 2003; Chang et al., 2005). The formed atomic oxygen reacts with SO2(d) to form sulfate (Ullerstam et al., 2002; Usher et al., 2002): SO2d+O3d⟶SO42-d+O2kauto,O3=2×10-11(cm3molecules-1s-1). In the presence of 300 µg m3 of ATD particles and 60 ppb of ozone, the concentration of O3(d) is estimated as 2.4 × 107 molecule cm-3. Under this condition, the characteristic time of the autoxidation by ozone (Reaction R14) is 2 × 103 s and is much faster than the autoxidation by oxygen (Reaction R9, 2 × 105 s). At nighttime, in the presence of ozone, the autoxidation of SO2(d) yields a significant amount of sulfate.

Under UV light, ozone is also involved in the production of the surface oxidants (O3-, HO3 radicals, and OH radicals) that further promote heterogeneous oxidation of SO2. O3(d) acts as an acceptor for ecb-–hvb+ and forms OH(d). e_h+O3d⟶⚫OHd+O2kOH,O3=1×10-12(cm3molecules-1s-1)

The gas–dust partitioning coefficient of NO2 (Kd,NO2) is treated as the same approach with ozone, using Kd,SO2 and the ratio of KH,SO2 (Eq. 1) to the Henry's law constant of NO2 (KH,NO2=1.2 × 10-2 mol L-1 atm-1 at 298 K) (Chameides, 1984). Kd,NO2=Kd,SO2KH,NO2KH,SO2=1.5×10-6Fwaterexp(2500T)(m3m-2) The absorbed NO2 first reacts with ecb-d or ⚫O2-d on the dust surface (Reaction R10) and forms HONO(d) (Ma et al., 2008; Liu et al., 2012; Saliba and Chamseddine, 2012; Saliba et al., 2014). In AMAR, the formation of HONO(d) is simplified into e_h+NO2d⟶HONOdke_h,NO2=6×10-12(cm3molecules-1s-1). HONO(d) is further decomposed through photolysis and yields OH(d): HONOd⟶hv⚫OHd+NOkHONOj=jHONO(s-1). The photolysis rate constant of HONO(d) is treated with the one for gaseous HONO (j[HONO]). Similar to autoxidation of SO2 (Sect. 3.2.2), NO2(d) autoxidizes to form nitrate: NO2d⟶O2(g)NO3-dkauto,NO2=6×10-5(s-1). NO2 reacts with OH(d): NO2d+OHd→NO3-dkphoto,NO2=1×10-10(cm3molecules-1s-1). kauto,NO2 and kphoto,NO2 was determined using the simulation of outdoor chamber data (Exp. 14 April 2017 in Table 2). The estimation of the gas–dust partitioning coefficients of HONO (Kd,HONO) (Becker et al., 1996) and HNO3 (Kd,HNO3) (Schwartz and White, 1981) was approached using the similar method for SO2 (Table 3). N2O5 forms nitrate via a reactive uptake process as shown in Table 3 (partitioning Reaction 11).