Hydroxymethanesulfonate (HMS) has recently been
identified as an abundant organosulfur compound in aerosols during winter
haze episodes in northern China. It has also been detected in other regions
although the concentrations are low. Because of the sparse field
measurements, the global significance of HMS and its spatial and seasonal
patterns remain unclear. Here, we modify and add to the implementation of
HMS chemistry in the GEOS-Chem chemical transport model and conduct multiple
global simulations. The model accounts for cloud entrainment and
gas–aqueous mass transfer within the rate expressions for heterogeneous
sulfur chemistry. Our simulations can generally reproduce quantitative HMS
observations from Beijing and show that East Asia has the highest HMS
concentration, followed by Europe and North America. The simulated HMS shows
a seasonal pattern with higher values in the colder period. Photochemical
oxidizing capacity affects the competition of formaldehyde with oxidants
(such as ozone and hydrogen peroxide) for sulfur dioxide and is a key factor
influencing the seasonality of HMS. The highest average HMS concentration
(1–3 µgm-3) and HMS / sulfate molar ratio (0.1–0.2) are found in
northern China in winter. The simulations suggest that aqueous clouds act as
the major medium for HMS chemistry while aerosol liquid water may play a
role if its rate constant for HMS formation is greatly enhanced compared to
cloud water.
Introduction
Organosulfur (OS) compounds have been detected in secondary organic
aerosols (SOAs). The OS compounds affect the physicochemical properties of aerosols
such as hygroscopicity, acidity, and viscosity, and ultimately the climate
and health effects of aerosols (Surratt et al., 2007; Farmer et al.,
2010; Sorooshian et al., 2015; Estillore et al., 2016; Riva et al., 2019).
The identified OS compounds include organosulfates
(ROSO3-), sulfoxides
(RSOR′), sulfones
(RSO2R′), and sulfonates
(RSO3-)
(Brüggemann et al., 2020). Sulfonates include
methanesulfonate
(CH3SO3-,
deprotonated MSA, methanesulfonic acid) and hydroxyalkylsulfonates
(RCHOHSO3-)
(Song et al., 2019a). These classes
of OS compounds may differ widely in their formation mechanisms, concentration
levels, and spatiotemporal distributions. Organosulfates and MSA are the two
most studied OS species or classes (Bates et al., 1992; Huang et al.,
2017; Brüggemann et al., 2020). Organosulfates are primarily formed by
the reactive uptake of gas-phase epoxides on acidic sulfate particles
(Froyd et al., 2010; Surratt et al., 2010; Xu et al., 2015). The most
abundant organosulfate observed in ambient fine particulate matter
(PM2.5) is the isoprene-derived methyltetrol sulfate
(C5H11SO7-),
with an average concentration of 1.8 µgm-3 found during August
2015 in Atlanta, Georgia, USA (Hettiyadura et al.,
2019). MSA is produced primarily by the oxidation of biogenic dimethyl
sulfide (DMS, mainly from marine phytoplankton) and is likely the major
organosulfur species in many regions over the oceans (Chen et al., 2018;
Hodshire et al., 2019). The concentrations of aerosol-phase MSA in marine
environments range from tens to a few hundred ng m-3
(Phinney et al., 2006; Sciare et al., 2009; Huang et al., 2017).
Recently, high mass concentrations of hydroxymethanesulfonate (HMS,
CH2OHSO3-), the most abundant
hydroxyalkylsulfonate species commonly found in the atmosphere, have been
detected in winter in Beijing, China using an aerosol mass spectrometer by
Song et al. (2019a), using an
improved ion chromatography method by Ma
et al. (2020), and using a UHPLC-LTQ-Orbitrap mass spectrometry by
Wei et al. (2020). The mass spectrometry quantification of HMS
in ambient aerosols may be subject to the interference of other inorganic
and organic sulfur compounds, as suggested by
Dovrou et al. (2019). Another difficulty with
interpreting HMS in the observational record is the potential for HMS to
decompose during sample storage and analysis (Ma et al., 2020; Moch et al.,
2020). The average HMS concentration in the 2015/16 and 2016/17 winters in
Beijing was observed to be 1.9 µgm-3
(Ma et al., 2020). The highest daily
average HMS concentration reached 15 µgm-3, accounting for 6 %
of PM2.5 concentration (Ma et al.,
2020). Song et al. (2019a) argued
that HMS was likely the major organosulfur compound during winter haze
events in northern China. Prior to the two studies, only low levels of HMS,
with averages on the order of 0.01 µgm-3, had been observed in
the United States, Japan, and Germany (Dixon and Aasen, 1999; Suzuki et
al., 2001; Scheinhardt et al., 2014). More recently, Moch et al. (2020)
reported observational evidence for a ubiquitous presence of HMS across 160
locations in North America, Europe, and Asia. Most of the observations of
HMS reported by Moch et al. (2020) were unquantified, but mass
concentrations of up to 7.6 µgm-3 were reported for
Shijiazhuang, China and up to 0.6 µgm-3 for Singapore.
Our knowledge of the chemical mechanism for HMS stems largely from studies
in the 1980s when it was recognized as part of the aqueous sulfur chemistry
(Pandis and Seinfeld, 1989). Field measurements of cloud
water in the Los Angeles Basin showed the coexistence of H2O2 and
S(IV) that was much larger than expected based on the phase equilibrium with
gaseous SO2 (Richards et al., 1983). The
formation of HMS by the reaction of dissolved SO2 and HCHO was
postulated, and then proved, to explain the observed excess of S(IV)
(Munger et al., 1986). The laboratory experiments from several
groups determined the kinetics and thermodynamics of HMS reactions in
aqueous solutions (Boyce and Hoffmann, 1984; Deister et al., 1986; Dong
and Dasgupta, 1986; Kok et al., 1986; Olson and Fessenden, 1992). Briefly,
both formation and decomposition of HMS depend strongly on pH, i.e., the
hydrogen ion activity expressed on a logarithmic scale. HMS is resistant to
oxidation by H2O2 and O3 but reacts with hydroxyl radicals
(OH) in the aqueous phase. These studies suggested that the atmospheric
conditions favorable for the formation and stability of HMS involved
abundant gas-phase SO2 and HCHO, high aqueous water content, low
temperature, intermediate pH, and low photochemical activity.
The integration and reconciliation of data from field observations,
laboratory experiments, and chemical modeling are crucial for obtaining a
better understanding of how HMS is processed in the atmosphere. Moch et al. (2020) recently implemented in-cloud HMS chemistry into the GEOS-Chem
chemical transport model to explore its large-scale spatiotemporal
distribution. The HMS chemistry is heterogeneous in nature since the
reactions occur in the aqueous phase with reactants transported from the gas
phase (Jacob, 2000). Sometimes heterogeneous chemistry is
referred to as multiphase chemistry (Ravishankara, 1997). As
shown in Fig. 1, the overall heterogeneous reaction rates are controlled
not only by rate constants in the aqueous phase but also by mass transfer
limitations between the gas and aqueous phases (Jacob, 1986;
Ravishankara, 1997; Seinfeld and Pandis, 2016). In partly cloudy conditions,
heterogeneous reactions may also be influenced by the entrainment and
detrainment of air into and out from clouds (Holmes et
al., 2019). Building upon Moch et al. (2020), the current study designed and
conducted multiple GEOS-Chem global model simulations, in order to explore
the controlling factors and processes of the spatiotemporal distribution of
HMS, including cloud entrainment and gas–aqueous mass transfer limitations,
kinetics and thermodynamics of HMS chemistry, and the formation media of
HMS. The model is driven by the kinetic and thermodynamic data obtained from
available laboratory experiments. The simulated results are compared with
observations made in four field campaigns. Compared with the control
simulation that follows the parameterization in the standard GEOS-Chem
model, the default simulation improves treatments of entrainment and mass
transfer processes for heterogeneous cloud sulfur chemistry. Both aqueous
cloud droplets (Jacob, 1986; Olson and Hoffmann, 1989; Moch et al., 2018;
Moch et al., 2020) and aqueous aerosols (Song et al., 2019a; Ma et al.,
2020) have been suggested to provide the media for HMS reactions. However,
kinetic and thermodynamic data have been determined only in dilute
solutions, which are suitable for application in clouds. The lack of
corresponding data in concentrated solutions poses a key challenge to
modeling HMS chemistry for aerosol water. Therefore, following Moch et al. (2020) we assume that cloud water serves as the only medium in the control
and default simulations. The role of aerosol water is explored through
sensitivity simulations. Aerosol water chemistry also considers the
physiochemical processes in Fig. 1, allowing an evaluation of the importance
of the two aqueous media.
Schematic of physicochemical processes that control the
heterogeneous reaction of a molecule A (with another molecule B) in a model
grid cell. (Left). Entrainment and detrainment of air into and out
from clouds. The volume occupied by aqueous clouds in the grid cell is
represented by the cloud fraction (fc), which is provided by
the MERRA-2 meteorological reanalysis in this study. The cloud-free fraction
is thus 1-fc. Aqueous aerosols are assumed to be evenly
distributed in the grid cell. For aqueous cloud droplets and aqueous
aerosols, the same mass transport processes are considered and are shown in
the right panel. (Top Right). Gas-phase, interfacial, and
aqueous-phase mass transport limitations for the molecules A and B.
(Bottom Right). Concentration (C) profiles of A and B are a function
of radial distance (r) from the surface of a spherical particle. The
subscripts g and aq refer to gas and aqueous phases, respectively. The
concentrations are in arbitrary units and their scales are different for gas
and aqueous phases. The entrainment/detrainment processes for clouds have
been described in detail by Holmes et al. (2019). The
right panel is adapted from Fig. 4 in Ravishankara (1997).
This article is organized as follows. In the Methods section, we first
provide an overview of the aqueous chemical reactions for HMS, including its
formation, decomposition, and oxidation (Sect. 2.1). From existing
laboratory studies, we critically estimate the best values and uncertainties
of their rate constants. The general configuration of the GEOS-Chem model is
described in Sect. 2.2, including its version, simulation period, spatial
and temporal resolutions, meteorological field, chemical mechanisms, and
underlying emissions. A brief introduction of sulfur simulation in the
standard model is given in Sect. 2.3. The two major simulations in this
study, control and default, are described in Sect. 2.4 and 2.5,
respectively. Based on settings in the standard model, the control
simulation implements heterogeneous HMS chemistry using cloud as the only
aqueous medium (Moch et al., 2020). We find that the in-cloud SO2
titration by various reactants is inappropriately represented in the control
simulation, very likely leading to an overestimation of HMS formation. The
default simulation fixes this issue. Section 2.6 describes the sensitivity
simulations designed to investigate the key factors leading to uncertainty
in the modeled HMS levels. In the Results and discussion section, we first
show in Sect. 3.1 the spatial and seasonal distributions of HMS from the
default simulation and discuss the underlying factors. Differences in the
modeled HMS between the default and control simulations are presented and
discussed in Sect. 3.2. Section 3.3 demonstrates the key uncertain parameters
and processes in the HMS model identified from sensitivity simulations.
Sect. 3.4 compares the observations of HMS in four different regions with
these model results. The knowledge gained in this study and the remaining
gaps are summarized in Sect. 3.5. Finally, the conclusions are given in
Sect. 4.
MethodsKinetics and thermodynamics of HMS chemistry
Hydroxymethanesulfonic acid (HMSA, CH2OHSO3H) is a diacid
with pKa1<0 (Reaction R1) and pKa2∼12 (Reaction R2). Thus,
it primarily exists as HMS (CH2OHSO3-) in
tropospheric clouds and aerosols. In the aqueous phase, HMS is produced by
the nucleophilic addition of
HSO3- and
SO32- to the carbonyl C atom of
HCHO (Reactions R3–R6). As
SO32- is a much stronger
nucleophile than HSO3-, the rate
constant of HCHOaq+SO32-, k2,
is a few orders of magnitude higher than that of HCHOaq+HSO3-, k1, as shown in Table 1. HCHOaq refers to the free, unhydrated formaldehyde dissolved in the
aqueous phase, and maintains an equilibrium with its hydrated form,
CH2OH2
(methylene glycol). The equilibrium constant of Reaction (R7), Kh,
represents the extent of hydration (Eq. 1). Reactions (R1)–(R6) are all reversible and
can be summarized by Reaction (R8). SO2aqT is the sum of
SO2⋅H2O,
HSO3-, and
SO32- (Eq. 2). kf
(M-1 s-1) and kd
(s-1) represent the forward and backward reaction
(HMS formation and decomposition) rate constants of Reaction (R8) and
Keq (M-1) is its equilibrium constant
(Eq. 3). kf is a combination of k1 and
k2 weighted by the fractions of
HSO3- and
SO32- in
SO2aqT (Eqs. 4–6). Ks1 and Ks2 denote the first and second
dissociation constants for dissolved SO2 (Table 2). Figure 2 shows the
values of kf and kd obtained from the available
laboratory experiments as a function of pH (Blackadder and Hinshelwood,
1958; Sørensen and Andersen, 1970; Boyce and Hoffmann, 1984; Deister et
al., 1986; Dong and Dasgupta, 1986; Kok et al., 1986; Lagrange et al.,
1999). In general, we find a large discrepancy for kf and good
agreement for kd.
R1CH2OHSO3H↔CH2OHSO3-+H+R2CH2OHSO3-↔CH2O-SO3-+H+R3SO2⋅H2O↔HSO3-+H+R4HSO3-↔SO32-+H+R5HCHOaq+HSO3-⟷k1CH2OHSO3-R6HCHOaq+SO32-⟷k2CH2O-SO3-R7HCHOaq+H2O↔CH2OH2R8HCHOaq+SO2aqT↔HMS
ReactionRate expression (M s-1)Reference and noteSO2+HCHO→HMSRaq=kfHCHOaqSO2Taq=k1xHSO3-+k2xSO32-HCHOaqSO2Taqk1,high=7.9×102×exp-3000×1/T-1/298M-1s-1k2,high=2.5×107×exp-2500×1/T-1/298M-1s-1k1,low=3.2×102×exp-2700×1/T-1/298M-1s-1k2,low=3.8×106×exp-2500×1/T-1/298M-1s-1Boyce and Hoffmann (1984)HMS→SO2+HCHOkd=6.2×10-8×exp-11400×1/T-1/298+4.8×103×Kw/H+×exp-4700×1/T-1/298s-1Boyce and Hoffmann (1984); Deister et al. (1986)HMS+OH⟶O2HCHO+SO5-k3=2.7×108M-1s-1Olson and Fessenden (1992)SO2+O3→SO42-+O2Raq=k1xSO2⋅H2O+k2xHSO3-+k3xSO32-O3aqSO2Taqk1=2.4×104M-1s-1k2=3.7×105×exp-5530×1/T-1/298M-1s-1k3=1.5×109×exp-5280×1/T-1/298M-1s-1Seinfeld and Pandis (2016)SO2+H2O2→SO42-+H2ORaq=k4Ks1xSO2⋅H2OH2O2aqSO2Taq For cloud water, k4=7.45×107×exp-4430×1/T-1/298/1+13H+ M-2 s-1 For aerosol water, k4 is multiplied by an enhancement factor EF that is dependent on μb: EF=1.5,0<μb≤42.3exp2.4log10μb-1.2,μb>4Seinfeld and Pandis (2016); Liu et al. (2020); note aSO2+O2⟶Mn2+Fe3+SO42-Raq=k5H+-0.74Mn2+Fe3+SO2TaqpH<4.2Raq=k6H+0.67Mn2+Fe3+SO2TaqpH≥4.2k5=3.7×107×exp-8400×1/T-1/297×10-3μM-2s-1k6=2.5×1013×exp-8400×1/T-1/297×10-3μM-2s-1Shao et al. (2019); note bSO2+2NO2→SO42-+2HONORaq=k7NO2aqSO2Taqk7=1.4×105M-1s-1pH<5k7=8.4×10-3H+-1.444M-1s-15≤pH≤5.8k7=2×106M-1s-1pH>5.8Cheng et al. (2016); note cSO2+HONO→SO42-+12N2ORaq=k8H+0.5HNO2TaqSO2Taqk8=142 M-1 s-1Martin et al. (1981); note dSO2+HOBr→SO42-+HBrRaq=k9xSO32-HOBraqSO2Taqk9=5×109M-1s-1Troy and Margerum (1991); note e
The chemical reaction equations are used to indicate major reactants and
products and may not be balanced in terms of stoichiometry and charge.
xSO2⋅H2O=SO2⋅H2O/SO2Taq=H+2/H+2+Ks1H++Ks1Ks2a EF is obtained by fitting the experimental data shown in Fig. 2C in
Liu et al. (2020). μb is the
molality-based ionic strength (mol kg-1).
b The relationship between k and μ is: k/kμ=0=10bμ/1+μ≈10bμ, in which b is in range of
-4 to -2 (Shao et al., 2019).
ck7 is believed to be the lower limit (Cheng et
al., 2016).
dHNO2Taq
is the total dissolved HONO and NO2-.
ek9 is determined at 25 ∘C, μ=0.5 M.
We consider the reaction of HOBr and SO32- but not the one between
HOBr and HSO3-, which is included in the standard GEOS-Chem model.
The original lab experiments (Liu, 2002) seemed to be interfered by
Br2, a stronger oxidizing reagent which also reacts with
HSO3-. A recent study by Liu and Abbatt (2020)
suggested that the rate constant of HOBr and HSO3- was much lower
that of HOBr and SO32-.
HMS formation
Boyce and Hoffmann (1984) determined the following kinetic
parameters at ionic strength μ=1 M, pH from 0 to 3.5:
k1=7.9×102 M-1 s-1 and
k2=2.5×107 M-1 s-1 (both at 298 K). The
enthalpies of activation Δ‡H1
and Δ‡H2 were
25 and 20 kJ mol-1, respectively. These parameters were
calculated assuming Ks1=1.45×10-2 M and
Ks2=6.31×10-8 M, which were in fact for dilute solutions (μ≈0 M).
According to Boyce and Hoffmann (1984), application of the
Davies equation to correct for the ionic strength effects on
Ks1 and Ks2 yielded
k1=4.5×102 M-1 s-1,
k2=5.4×106 M-1 s-1 (both at 298 K),
Δ‡H1=22 kJ mol-1, and Δ‡H2=21 kJ mol-1.
Boyce and Hoffmann (1984) also used a higher Kh
of 1.8×103 than the value of
1.3×103 obtained in a more recent
study by Winkelman et al. (2002) (Table 2). We
further adjust the kinetics based on this recent Kh and obtain
k1=3.2×102 M-1 s-1 and
k2=3.8×106 M-1 s-1.
Equilibrium reactions.
ReactionConstant expressionReference and noteSO2g+H2O↔SO2⋅H2OH=1.3×exp3100×1/T-1/298Matm-1Sander (2015)SO2⋅H2O↔HSO3-+H+Ks1=1.3×10-2×exp2000×1/T-1/298 MSeinfeld and Pandis (2016)HSO3-↔SO32-+H+Ks2=6.6×10-8×exp1500×1/T-1/298 MSeinfeld and Pandis (2016)H2O↔OH-+H+Kw=1.0×10-14×exp-6710×1/T-1/298 M2Seinfeld and Pandis (2016)HCHOg↔HCHOaqH=2.5×exp3300×1/T-1/298Matm-1Song et al. (2019a)HCHOaq+H2O↔CH2OH2Kh=1.3×103×exp3800×1/T-1/298kh=2×105×exp-2900/Ts-1kdh=kh/Kh s-1Song et al. (2019a)O3g↔O3aqH=1.13×10-2×exp2500×1/T-1/298 M atm-1Sander (2015)H2O2g↔H2O2aqH=9.1×104×exp6900×1/T-1/298 M atm-1Sander (2015)H2O2aq↔H++HO2-K=2.2×10-12×exp-3730×1/T-1/298 MSeinfeld and Pandis (2016)NO2g↔NO2aqH=1.3×10-2×exp2500×1/T-1/298 M atm-1Sander (2015)HONOg↔HONOaqH=48×exp4800×1/T-1/298 M atm-1Sander (2015)HONOaq↔H++NO2-K=5×10-4×exp-1300×1/T-1/298 MSeinfeld and Pandis (2016)HOBrg↔HOBraqH=1.3×102Matm-1Sander (2015); note *OHg↔OHaqH=32×exp3700×1/T-1/298 M atm-1Sander (2015)
* The Henry's law constant of HOBr is very uncertain, ranging from 90 to
6000 M atm-1. HOBr can undergo acid
dissociation and has a pKa of 8.65 at 25 ∘C. We do not
consider its acid dissociation because it is only partially dissociated in
the interested pH range and because of the high uncertainty of its intrinsic
Henry's law constant.
Comparison of rate constants for the formation (panel
a, kf in M-1 s-1) and decomposition (panel b,
kd in s-1) of HMS from the available
laboratory studies. Data are shown as a function of pH. Unless otherwise
noted, rate constants are determined at or corrected to 25 ∘C and under
dilute conditions (μ<0.01 M). For a, b, c, g, and h, the solid
curves show the range of pH at which these experiments are performed, whereas
the dash curves indicate the extrapolated values. Other experiments (d, e,
k, m, n, and p) are performed at discrete pH and shown by symbols. (a) the high
kf is from Boyce and Hoffmann (1984) at μ=1 M. (b) the low kf is also from Boyce and
Hoffmann (1984) and corrected for μ and Kh. (c)
Lagrange et al. (1999): kf=Kh×0.73×xHSO3-+0.13×xSO32- M-1 s-1. (d)
Kok et al. (1986): the reported kf is
limited by the dehydration rate of CH2OH2, kdh, and is thus corrected
here. (e) is calculated using the kd and Keq
determined by Deister et al. (1986) and is also
corrected for kdh. The calculated kf values are
2.6×103, 2.2×104, and 9.1×104 M-1 s-1, respectively, at pH =
4, 5, and 5.6 in (d) and (e). For comparison, the extrapolation of the low
kf data (b) are 2.7×103, 2.4×104, and 9.3×104 M-1 s-1, respectively, at pH =
4, 5, and 5.6. (g) kd is calculated using the Keq
from Deister et al. (1986) and the low
kf from Boyce and Hoffmann (1984). (h)
Lagrange et al. (1999): kd=1.1×104×Kw/H+ at μ=1 M in the presence of
H2O2. (k) Kok et al. (1986) measured
kd of 4.8 × 10-7 and 3.5 × 10-6 s-1, respectively, at pH 4 and 5. (m) Dong and Dasgupta
(1986) measured Keq at pH 4 and μ= 0.05 M, which
translated to a kd of 4 × 10-7 s-1. (n)
Blackadder and Hinshelwood (1958): kd=1×10-5 s-1 at pH 5 and μ≈0.1 M. (p)
Sørensen and Andersen (1970): kd=8.5×10-2 s-1 at pH 9 and μ=0.1 M. For
comparison, values of kd calculated by (g) are 5.4 × 10-7, 4.9 × 10-6, and 4.8 × 10-2 s-1 at pH 4, 5, and 9, respectively.
Therefore, two sets of HMS formation kinetic data can be obtained from
Boyce and Hoffmann (1984) and are designated here as the high
and low rate constants, as shown in Table 1 and Fig. 2. The high rate
constants are the same as those used in Moch et al. (2020). The calculated
high and low kf differ by a factor of about 3 at pH < 2 and by a factor of about 6 at pH > 4. The low kf
agrees very well (within a factor of 1.1) with the results determined by
Kok et al. (1986) and Deister et
al. (1986) at higher pH 4, 5, and 5.6 (Fig. 2). The low kinetic data are
also closer to the rate constants from the recent quantum chemical
calculations by Zhang et al. (2019)
(k1=0.9 M-1 s-1,
k2=2×106 M-1 s-1, at 298 K). Consequently,
the low formation rate constants from Boyce and Hoffmann
(1984) are adopted for the default model simulation, while the high ones are
used in a sensitivity simulation. Lagrange et al. (1999)
proposed another value of kf which was about 1–4 orders of
magnitude smaller than the low kf from Boyce
and Hoffmann (1984) at pH > 4 (Fig. 2). The simulated HMS
concentration is negligible everywhere when applying the kf
from Lagrange et al. (1999) in the model, and thus, will not
be discussed further.
HMS decomposition
The most complete analysis of Keq was done by
Deister et al. (1986). We calculate the expression of
kd using the low kf from Boyce
and Hoffmann (1984) and Keq from Deister
et al. (1986) (Eq. 3 and Table 1). As shown in Fig. 2, kd estimated in this way agrees within a factor of about 2
with results from the other laboratory studies (Blackadder and
Hinshelwood, 1958; Sørensen and Andersen, 1970; Dong and Dasgupta, 1986;
Kok et al., 1986; Lagrange et al., 1999). Therefore, this expression of
kd is adopted in the default simulation, and its value is
doubled in a sensitivity simulation. If we use the high kf
from Boyce and Hoffmann (1984) and the Keq from
Deister et al. (1986), we will obtain a
kd that is several times higher than estimates from the other
studies. This may serve as circumstantial evidence in favor of the low
kf. Moch et al. (2020) uses a value of 3.6 × 103 s-1 for kd following Diester et al. (1986).
HMS oxidation
HMS is resistant to oxidation by H2O2 and O3 but can be
oxidized by OH in the aqueous phase (Martin et al., 1989; Olson and
Fessenden, 1992). Reaction (R9) produces HCHO and peroxysulfate radical
(SO5-) with a rate constant of
2.7×108 M-1 s-1 (Olson and Fessenden, 1992) (Table 1). This value is lower by a factor of about 4 than the results reported in
two earlier laboratory studies (Martin et al., 1989; Deister et al.,
1990). Olson and Fessenden (1992) argued that these two
studies were subject to artifacts and interferences from secondary
reactions.
HMS+OHaq⟶O2HCHOaq+SO5-+H2O
The second source of uncertainty in Reaction (R9) arises from estimating aqueous OH
concentrations. Aqueous OH is a short-lived species that can be transferred
from the gas phase and generated/scavenged in the aqueous phase. Its sources
and sinks, which are linked to photochemical processes (e.g., photolysis of
nitrate and peroxides), transition metal ions (Fenton reactions), and/or
reactions with halogen anions and organic matter, are not yet fully
understood (Tilgner and Herrmann, 2018). Currently, there exist
significant discrepancies between the modeled and measured OHaq levels. A comprehensive overview has
shown that OHaq from different model
studies ranges from 3 × 10-15 to 8 × 10-12 M
for cloud droplets and from 1 × 10-16 to 8 × 10-12 M for aqueous aerosols. On the other hand, data ranges
of the measured OHaq are 0.5–7 × 10-15 M for clouds and 0.1–6 × 10-15 M for
aerosols (Tilgner and Herrmann, 2018). On average, the modeled
OHaq is 2 orders of magnitude higher
than the measured values. This large gap is believed to result from the
limitations of both models and measurements. The bulk measurements of
OHaq may underestimate its
concentrations in real aerosols and clouds due to lack of replenishment of
important oxidations and OH precursors from the gas phase under the dark
conditions of sample storage and treatment (Tilgner and Herrmann,
2018). On the other hand, the multiphase models may significantly
overpredict OHaq because they only
partially consider the complex organic aqueous chemistry. The reasonable
estimates of OHaq in real aerosols and
clouds seem to be 1 order of magnitude lower than modeled concentrations
and 1 order of magnitude higher than measured levels (Tilgner
and Herrmann, 2018). Since GEOS-Chem does not have a detailed representation
of aqueous OH chemistry, we follow Moch et al. (2020) and simply estimate
OHaq using the modeled OHg and a pseudo Henry's law constant
HOH∗ (Eq. 7). In the default simulation,
HOH∗ is set to 4 × 10-20 M cm3 molecules-1. HOH∗ is more than
1 order of magnitude lower than its intrinsic Henry's law constant,
HOH (Table 2), reflecting our presumption that the various
organic and inorganic compounds in the aqueous phase act as a net sink for
OH radicals. A global mean OHg of
about 1 × 106 molecules cm-3 implies a mean OHaq of 4 × 10-14 M, 1 order
of magnitude higher than the mean of the above-mentioned measured OHaq. Moch et al. (2020) use a
value for HOH∗ of 1 × 10-19 M cm3 molecules-1 based on Jacob et al. (2005).
OHaq=OHg×HOH∗
The products of Reaction (R9) are HCHOaq and
SO5-. Interestingly, the net effect of
HMS formation (Reaction R8) and its subsequent oxidation (Reaction R9) is the oxidation of
SO2aqT by
OHaq, which thus represents an
indirect oxidation pathway for SO2. The sinks for
SO5- are mainly the reactions with
O2-, HCOO-, and itself
(Reactions R10–R12). The reaction of SO5- and
HSO3- is slow
(Jacob et al., 1989). The peroxymonosulfate radical
(HSO5-) produced by Reactions (R10) and (R11)
can oxidize HSO3- to sulfate
(Reaction R13) with a similar rate constant to
H2O2+HSO3-
(Betterton and Hoffmann, 1988). The sulfate radical
(SO4-) produced by Reaction (R12) is a very
strong oxidant and can react rapidly with
HSO3- and
SO32- (Reactions R14 and R15) as well as with
many other species such as Cl-,
NO2-, O2-,
HCOO-, and HO2
(Jacob, 1986). The rate constants for Reactions (R10)–(R15) can be
found in Jacob et al. (1989). It is convenient to define
the sulfate yield as the number of
SO42- ions produced due to each attack
of OHaq on HMS. If
SO5- reacts with
O2-/HCOO- (Reactions R10 and R11) and
the product HSO5- oxidizes
HSO3- (Reaction R13), the yield is 2.
If SO5- undergoes self-reaction (Reaction R12)
and the produced SO4- reacts with
HSO3-/SO32- (Reactions R14 and R15), a reaction chain is
triggered as the products include SO5-.
In certain conditions, the sulfate yield can reach 20 or more
(Jacob et al., 1989). However, as mentioned above, other
oxidizable species also compete for
SO4-, thereby terminating this chain
and leading to a sulfate yield of 1. In remote environments where SO2
is very low, HSO5- may be a
stable species, resulting in a sulfate yield < 1. Our low OHaq assumption implies the existence of
important oxidizable species, and therefore, the chain propagation is
limited. As in Moch et al. (2020) the sulfate yield is assumed to be 2 in
our simulations.
R10SO5-+O2-⟶H2OHSO5-+O2+OH-R11SO5-+HCOO-⟶O2HSO5-+O2-+CO2R12SO5-+SO5-→2SO4-+O2R13HSO5-+HSO3-→2SO42-+2H+R14SO4-+HSO3-⟶O2SO42-+SO5-+H+R15SO4-+SO32-⟶O2SO42-+SO5-
Phase equilibrium
The gas/aqueous phase equilibriums of HCHO (Reaction R16) and
SO2 (Reaction R17) are described by intrinsic Henry's
law constants, HHCHO and
HSO2, respectively (Table 2).
HCHOaq is subject to hydration and
the apparent Henry's law constant, HHCHO∗, is
much larger than HHCHO (Eq. 8).
SO2⋅H2O dissociates twice in the aqueous phase
and thus HSO2∗ depends on
pH (Eq. 9). The rates for the hydration of HCHOaq (kh in Table 2) and the acid
dissociations of SO2⋅H2O (Schwartz and Freiberg,
1981) are fast enough and we assume that these reactions are always in
equilibrium.
R16HCHOg↔HCHOaqR17SO2g+H2O↔SO2⋅H2O8HHCHO∗=CH2OH2+HCHOaq/HCHOg=HHCHO1+Kh≅HHCHOKh9HSO2∗=SO2Taq/SO2g=HSO21+Ks1/H++Ks1Ks2/H+2
General model description
We perform global simulations of heterogeneous HMS chemistry using the
three-dimensional GEOS-Chem chemical transport model (version 12.1.0, Doi:
10.5281/zenodo.1553349, The International GEOS-Chem User Community, 2018). The simulations are
driven by the Modern-Era Retrospective analysis for Research and
Applications, version 2 (MERRA-2) reanalysis meteorology from the NASA Goddard Earth
Observing System (Gelaro et al., 2017). The original
MERRA-2 has a resolution of 0.625∘ (longitude) × 0.5∘ (latitude) and is degraded to 5∘× 4∘ for input into the simulations. There are 47 vertical layers in
the atmosphere from surface to the mesosphere. The simulations are conducted
for 18 months starting from March 2015. The first 6 months are used for
initialization and we focus on the 1-year simulation results from September
2015 to August 2016. These months are selected to obtain a continuous boreal
winter. We use the tropospheric chemistry mechanism with detailed reactions
for O3-NOx-VOC (volatile organic compound)-aerosol-halogen
interactions. The time step for species advection, vertical mixing, and
convection is set to 10 min. The time step is 20 min for emissions, dry
deposition, photolysis, and chemistry, as recommended by
Philip et al. (2016). The simulated aerosol species include
secondary inorganic (sulfate, nitrate, and ammonium) and organic aerosols,
primary organic aerosols, black carbon, dust, and sea salt.
Emissions are calculated using HEMCO (the Harvard-NASA Emissions Component,
version v2.1.010) (Keller et al., 2014). The global
anthropogenic emissions of SO2, NOx, NH3, CO, VOCs, black
carbon, and organic carbon are from the Community Emissions Data System
(CEDS) (Hoesly et al., 2018).
Emissions are overwritten by regional inventories wherever available: EMEP
(European Monitoring and Evaluation Programme) over Europe
(http://www.emep.int/index.html, last access: 10 June 2020), MIX over Asia
(Li et al., 2017), DICE (Diffuse and
Inefficient Combustion Emissions) over Africa (Marais and
Wiedinmyer, 2016), NEI (National Emissions Inventory) over the United States
(Travis et al.,
2016), CAC (Criteria Air Contaminants) over Canada
(http://wiki.seas.harvard.edu/geos-chem/index.php/CAC_anthropogenic_emissions, last access: 10 June 2020), and MEIC
(Multi-resolution Emission Inventory) over China
(Zheng et al., 2018). Primary emissions of
sulfate constitute 1.4 %–5 % of total anthropogenic sulfur emissions in
different regions of the world. Aircraft emissions are from the Aviation
Emissions Inventory Code (Simone et al., 2013).
Biomass burning emissions are from the Global Fire Emissions Database (GFED,
version 4) (van der Werf et al., 2017).
Biogenic VOC emissions are calculated by the Model of Emissions of Gases and
Aerosols from Nature (MEGAN, version 2.1) (Guenther
et al., 2012). Mineral dust emissions follow Duncan et al. (2007) and are distributed in one fine- and three coarse-size bins.
Anthropogenic emissions of fine dust aerosols are from the Anthropogenic
Fugitive, Combustion, and Industrial Dust (AFCID) inventory
(Philip et al., 2017). Sea-salt aerosols in two size bins
(fine and coarse) are simulated based on Jaeglé et
al. (2011). Other emissions include volcanic SO2 emissions
(Ge et al., 2016), oceanic DMS emissions
(Lana et al., 2011), lightning and soil
NOx emissions (Hudman et al., 2012; Murray et al., 2012), and
natural NH3 emissions from the GEIA (Global Emissions InitiAtive)
inventory (http://www.geiacenter.org, last access: 10 June 2020).
Because of the importance of acidity for heterogeneous HMS chemistry, more
details are provided for the calculation of cloud water and aerosol pH. The
standard model calculates cloud water pH iteratively with an initial
estimate of 4.5, as described in Alexander et al. (2012). The ions considered in the electroneutrality equation are
NH4+, H+, OH-, SO42-, NO3-,
HSO3-, SO32-, HCO3-, and CO32-.
HSO3-/ SO32- and HCO3-/ CO32- are from
the scavenging of SO2 and CO2. SO42- is assumed to be
the only form of sulfate and is obtained from the cloud scavenging of
aerosols. NH4+ and NO3- are from the scavenging of both
aerosols and gases (NH3 and HNO3). The scavenging efficiencies of
aerosols and gases are assumed to be 0.7 and unity, respectively. The
ISORROPIA II (version 2.2) thermodynamic equilibrium model (Fountoukis
and Nenes, 2007) is used to calculate the inorganic aerosol water content
(m3 H2O m-3 air) and pH, including the following gas and
aerosol species: NH3, HNO3, ammonium, nitrate, sulfate, and fine
sea-salt aerosols.
Sulfur simulation in the standard model
The sulfur simulation in GEOS-Chem has been developed and improved based on
multiple studies (Chin et al., 2000; Park et al., 2004; Alexander et al.,
2005, 2009; Chen et al., 2017; Shao et al., 2019). The simulated sulfur
species include DMS, SO2, MSA, and sulfate. It includes primary
emissions of DMS, SO2, and sulfate (Sect. 2.2). SO2, MSA, and
sulfate can also be formed by chemical reactions. The model contains three
gas-phase reactions of DMS oxidation, producing SO2 and MSA (Reactions R18–R20).
An expanded chemistry mechanism for DMS can be found in
Chen et al. (2018). The oxidation of SO2 to sulfate
occurs in the gas phase by OH (Reaction R21) and in the aqueous clouds. The
aqueous-phase oxidants are O3, H2O2, O2 (catalyzed by
transition metal ions Mn2+ and Fe3+), and HOBr (Reactions R22–R25). The
effect of the heterogeneity in cloud droplet pH on sulfate production rates
is accounted for using the parameterization by Yuen
et al. (1996) and Fahey and Pandis (2001). This
parameterization is restricted over the ocean since the heterogeneity in pH
is believed to be caused by alkaline sea-salt aerosols
(Alexander et al., 2012). The model also includes
the oxidation of SO2 by O3 on sea-salt aerosol surface (Reaction R26)
(Alexander et al., 2005).
R18DMSg+OHg→SO2g+CH3O2g+HCHOgR19DMSg+OHg→0.75SO2g+0.25MSAgR20DMSg+NO3g→SO2g+CH3O2g+HCHOg+HNO3gR21SO2g+OHg⟶MH2SO4g+HO2gR22SO2aqT+O3aq→SO42-+O2aqR23SO2aqT+H2O2aq→SO42-+H2OR24SO2aqT+O2aq⟶Mn2+Fe3+SO42-R25SO2aqT+HOBraq→SO42-+HBraqR26SO2g+O3g+fine
sea salt→SO42-+O2
Control simulation
Based on the standard model v12.1.0, we implement heterogeneous HMS
chemistry and assume that cloud water provides the only aqueous medium,
following Moch et al. (2020). As described in Sect. 2.1, HMS is produced by
dissolved SO2 and HCHO, undergoes decomposition, and is oxidized to
sulfate by aqueous OH. Two other cloud sulfate formation pathways are also
incorporated (Wang et al., 2020), in which SO2 is oxidized by
NO2 and HONO (Reactions R27 and R28).
R27SO2aqT+2NO2aq→SO42-+2HONOaqR28SO2aqT+HONOaqT→SO42-+0.5N2Oaq
Tables 1 and 2 show all the rate constants of aqueous-phase reactions and
the Henry's law constants of the reactants. The solubilities of transition
metals Fe and Mn are reduced following Shao et
al. (2019). Ten advected tracers are added: one is the aerosol HMS species
and the others represent different sulfate formation pathways. Transport and
deposition of these tracers are treated in the same way as the sulfate
tracer as in Moch et al. (2020). In addition, several other changes are made
in the control simulation to the standard model. First, we update the dry
deposition scheme and the reactive uptake coefficients of NO2,
NO3, and N2O5 on aerosols, following
Jaeglé
et al. (2018) and Shah et al. (2018).
Second, this simulation includes some updates developed by Luo et al.
(2019, 2020) in the treatments of wet processes, including spatially
and temporally varying in-cloud condensation water contents, empirical
washout rates for water-soluble aerosols and nitric acid, the cloud fraction
available for aqueous chemistry, and rainout efficiencies for water-soluble
aerosols and gases. Third, more ions are included in the cloud water pH
calculation. We consider Ca2+, Mg2+, NH4+, Na+,
H+, OH-, Cl-, SO42-, NO3-,
NO2-, HSO3-, SO32-, HCO3-,
CO32-, HCOO-, CH3COO-, HMS, and
CH3SO3-.
The Newton–Raphson method is used to find the solution to the cubic
electroneutrality equation, following Luo et al. (2020) and
Moch et al. (2020). Ca2+ and Mg2+ are assumed to
constitute 3 % and 0.6 %, respectively, of the dust by mass (Claquin
et al., 1999; Fairlie et al., 2010; Nickovic et al., 2012; Shao et al.,
2019; Moch et al., 2020). Only Na+ and Cl- from sea-salt aerosols
are considered. HMS and
CH3SO3- are
from the cloud scavenging of aerosols. NO2-, HCOO-, and
CH3COO- are from the scavenging of HONO, HCOOH, and CH3COOH,
respectively. Fourth, HMS,
CH3SO3-,
and Ca2+ and Mg2+ in fine dust are included in the ISORROPIA
calculations. We assume the same hygroscopicity of HMS and MSA as sulfate
(Xu et al., 2020).
We evaluate the performance of the control simulation by comparing it with
the standard GEOS-Chem v12.1.0 (GC12.1.0). Figure S1 in the Supplement shows the horizontal
distributions of surface SO42-
and SO2 concentrations. The global average
SO42- in the control simulation
is reduced by 24 % compared to GC12.1.0. The updates in the treatments of
wet processes by Luo et al. (2019, 2020) are primarily responsible for
this difference. The SO42-
concentrations modeled in the control simulation are consistent with the
improved model results in Luo et al. (2020), which have
been found to agree well with
SO42- observed in the United
States, Europe, and Asia (Luo et al., 2020). Moreover,
since GC12.1.0 was released in late 2018, it is necessary to compare it with
a more recent model version. Accordingly, we conduct a simulation using the
standard GEOS-Chem v12.7.0 (GC12.7.0, released in February 2020,
http://wiki.seas.harvard.edu/geos-chem/index.php/GEOS-Chem_12, last
access: 10 June 2020). We find that the global average
SO42- in GC12.7.0 only differs
little (3 %) compared with that in GC12.1.0 (Fig. S2 in the Supplement).
Below, we provide details on the calculation of cloud sulfur chemistry and
highlight the need for more accurate representations of in-cloud SO2
titration by various reactants, which include O3 (Reaction R22), H2O2
(Reaction R23), O2 (Reaction R24), HOBr (Reaction R25), NO2 (Reaction R27), HONO (Reaction R28), and HCHO (Reaction R8).
Cloud sulfur chemistry is calculated locally in the model grid cells where
aqueous clouds are present. fc (dimensionless, ≤fc≤1) denotes the fraction of aqueous cloud in a
grid cell, and L (m3 H2O m-3 air) denotes the in-cloud liquid
water content. In each chemistry time step (Δt=20 min), the
losses of SO2 in the above reactions (R8, R22–R25, R27, and R28) are
calculated. Reaction (R24) is treated as a first-order reaction of SO2 (O2 is
in large excess), while the other reactions are second order. The first- and
second-order rate constants for the aqueous reaction of
SO2aqT and
Xiaq, k1,aq,i
(s-1) and k2,aq,i (M-1 s-1), are obtained by
Eq. (10) from the kinetic data in Table 1. Xi (i=1:7)
represents the ith reactant with SO2. Raq,i is the
reaction rate (M s-1). k1,aq,i and k2,aq,i
are used to derive the first- and second-order rate constants for the
heterogeneous reaction of SO2g and Xig,
k1,g,i (s-1) and k2,g,i (mol mol-1 s-1) (Eq. 11). HSO2∗ and
HXi indicate their Henry's law constants. fg,SO2
and fg,Xi are the gas-phase partitioning fractions of
SO2 and Xi, respectively (Eq. 12). R is the gas constant. T (K) is
the temperature. P (atm) is atmospheric pressure. The loss of SO2 over
time Δt, ΔSO2g,i, is solved analytically
(Eq. 13). SO2,t=0g and Xit=0g are the mixing ratios (mol mol-1) for
SO2g and
Xig at the beginning of this time
step. The grid-average losses of SO2g from all seven reactions are limited by the availability of
SO2g within the cloud
fraction fc.
10k1,aq,i=Raq,i/SO2Taq and k2,aq,i=Raq,i/SO2TaqXiaq11k1,g,i=k1,aq,iHSO2∗fg,SO2LRT and k2,g,i=k2,aq,iHSO2∗fg,SO2HXifg,XiPLRT12fg,SO2=1+HSO2∗LRT-1 and fg,Xi=1+HXiLRT-113ΔSO2g,i=SO2,t=0g1-exp-k1,g,iΔt,1storderSO2,t=0gXit=0gC-1SO2,t=0gC-Xit=0g,C=expSO2,t=0g-Xit=0gk2,g,iΔt2ndorder
Since multiple in-cloud reactions consume SO2
simultaneously, it is important to allow them to compete effectively and
fairly. As shown in Eq. (13), the contribution of the ith reaction to the
total SO2g loss depends on
its rate constant (k1,g,i or k2,g,i), its
relative abundance (Xit=0g/SO2,t=0g), and
the choice of Δt. Ideally, Δt should be
smaller than the lifetime (τi) of
SO2g for any ith
reaction. τi is the inverse of the pseudo-first-order rate
constant, k1,g,i∼, which equals to
k1,g,i for a first-order reaction and to
k2,g,iXit=0g for a second-order reaction. Figure 3 shows the
probability density distributions of the calculated
k1,g,i∼ and the total rate constant for the
seven reactions, ∑i=17k1,g,i∼, in the lower troposphere for a
randomly selected week in boreal summer. k1,g,i∼ (and thus τi) can vary by several orders of magnitude in
different model grid cells. Notably, there is a > 50 %
possibility that the lifetime of SO2g is smaller than 20 min, the Δt used in this
simulation. The rapid consumption of SO2g is mainly via O3 and H2O2, as shown in
Fig. 3 and Table S1 in the Supplement (statistics of probability distributions). The other
five reactions consuming SO2 (HCHO, TMI+O2, NO2, HONO, and
HOBr) can be considered as minor pathways. This means that using
Δt=20 min for the sulfur chemistry will in general lead
to an underestimation of the contribution of O3 and H2O2 and
an overestimation of the importance of the other reactants such as HCHO. An
example is provided in Text S1 in the Supplement to conceptually explain the effect of
Δt on the competition of different reactions. We conduct a
sensitivity simulation in which Δt is set to 10 min and, as
we expect, the SO42-
concentrations through the cloud O3 chemistry increase significantly
(Fig. S3 in the Supplement). A simple way to solve this problem is to reduce Δt. The possibility of τ<Δt decreases to
only 4 % when Δt=1 min (Fig. 3 and Table S1). Also,
most (> 80 %) of the cases of τ<1 min arise
from the rapid reaction of SO32-
with O3aq when cloud water pH
is high. The remaining cases are from the reactions of
SO32- with
HOBraq and HCHOaq. The other four reactions can hardly lead to τ<1 min. We change the time step to 1 min when calculating in-cloud
SO2 titration in the default simulation (Sect. 2.5).
Probability density distributions of the
pseudo-first-order rate constants with respect to
SO2g for cloud reactions in
the control simulation. The shaded area shows the sum of rate constants for
the seven reactions consuming SO2. The red, green, blue, and orange curves
indicate the distributions for reactions with O3, H2O2, HCHO,
and the sum of rate constants for the other four reactions consuming SO2
(TMI+O2, NO2, HONO, and HOBr), respectively. Data shown are for
the first week of July and in the lower troposphere (13 vertical layers
above surface up to about 800 hPa). Since the chemistry time step
(Δt) of this simulation is 20 min, there are 504 steps in
this week. The total number of data points is 72 × 46 (number of
5∘× 4∘ grids) × 13 (vertical layers)
× 504 ≈2.2× 107. About 1.4 × 107 data points have aqueous clouds (cloud fraction fc>0), accounting for about 2/3. The probability density
distributions are plotted based on these data points. The dashed and solid
vertical black lines indicate the rate constants corresponding to
Δt of 20 and 1 min, respectively.
Another issue in the control simulation is, in a partly cloudy
(<fc<1) model grid, that the mixing of air between
the cloudy fraction (fc) and the cloud-free fraction
(1-fc) occurs in the same timescale as the chemistry time
step of the model (Holmes et al., 2019). In each time
step, the grid-average loss of SO2g from all in-cloud reactions cannot exceed the amount of
SO2g available within the
cloudy fraction and at the beginning of this time step (Eq. 14). This
so-called “cloud-partitioning method” is unphysical as the
entrainment/detrainment rates are affected by the setting of the chemistry
time step (Holmes et al., 2019). Since many chemical
transport models such as GEOS-Chem do not resolve individual clouds,
Holmes et al. (2019) developed a more realistic and
stable “entrainment-limited uptake” method, which accounts for cloud
entrainment/detrainment within the chemical rate expression. We apply this
method to the default simulation (Sect. 2.5).
∑i=17ΔSO2g,i≤fcSO2,t=0g
Default simulation
Three major changes are made in this simulation based on the control
simulation, as mentioned in Sect. 2.4. The first is applying the
entrainment-limited uptake method developed by
Holmes et al. (2019) to more realistically model the
entrainments and detrainments of air in cloudy grid cells. The second is
reducing the time step to 1 min when calculating cloud sulfur reactions to
better quantify the competition of different chemical pathways consuming
SO2. The third is adding the reaction of H2O2 and SO2 in
aerosol water using the kinetic data reported recently by
Liu et al. (2020). The control simulation only
includes the reaction of H2O2 and SO2 in cloud water. Figure S4 in the Supplement shows the horizontal distributions of surface
SO42- and SO2
concentrations in the control and default simulations, and only very small
differences (4 % for SO42- and
1 % for SO2) are found for their global average values.
In the entrainment-limited uptake method (Holmes et
al., 2019), the first-order loss rate of SO2g in a model grid cell due to heterogeneous cloud
chemistry, k1 (s-1), depends on the cloud fraction
(fc), the detrainment rate (kc, s-1), and
the in-cloud total pseudo-first-order rate constant,
k1,g∗=∑i=17k1,g,i∗ (s-1) (Eq. 15). As shown in
Holmes et al. (2019), the entrainment/detrainment
(kc term) limits its reactive uptake. In a completely cloudy
condition (fc=1), Eq. (15) reduces to
k1=∑i=17k1,g,i∗. kc is the reverse of
the in-cloud residence time of air (τc), which varies with
cloud types and ranges from 15 to 120 min for stratus and cumulus clouds
(Holmes et al., 2019). We use τc=30 min in this work since MERRA-2 does not provide this information. A
sensitivity simulation shows that assuming a τc of 60 min
decreases the global average surface
SO42- concentration by 10 %.
Holmes et al. (2019) have pointed out that future
studies are needed to specify the spatiotemporal variability of τc in the global reanalysis data sets. Within the cloudy fraction
of a model grid cell, as shown in Fig. 1 and Eq. (16), the heterogeneous
reaction rates are limited by a series of resistances associated with the
mass transfer processes from the gas phase to the aqueous phase, including
gas-phase diffusion, transfer of the reactants across the air–water
interface, and aqueous-phase diffusion (Ravishankara, 1997; Jacob, 2000).
In Eq. (16), the αSO2 term represents the
limitation due to mass accommodation at the air–water interface and the
Dg,SO2 term represents that due to gas-phase diffusion. A
dimensionless parameter Q, whose expression is given by Eq. (17) (0<Q<1), is used to account for aqueous-phase mass transport
limitations when calculating k1,aq,i and k2,aq,i
(Eq. 10).
151k1=1-fcfckc+1fck1,g∗=1-fcfckc+1fc∑i=17k1,g,i∗161k1,g,i∗=1k1,g,i∼+4AvSO2αSO2+rADg,SO217Q=3cothqq-1q2q=r∑i=17k1,aq,i∼Daq
Here, r is the radius of cloud droplets and is assumed to be 10-5 m. A (m2 m-3 air) is the surface area density of cloud droplets and is
derived using L and r. vSO2 (m s-1) is the molecular mean
speed of SO2 (Eq. 18). αSO2
(dimensionless) is the mass accommodation coefficient of SO2 (Table 3).
Dg,SO2 (m2 s-1) is the gas-phase diffusion
coefficient of SO2 (Eq. 19). q is a dimensionless parameter determined by
r, Daq, and k1,aq,i∼ (the
pseudo-first-order rate constant with respect to
SO2aqT for the
ith reaction). For a first-order and second-order reaction,
k1,aq,i∼ is equal to k1,aq,i and
k2,aq,iXiaq,
respectively (Eq. 10). Daq is the aqueous-phase diffusion
coefficient (10-9 m2 s-1) (Song et
al., 2019a). MSO2 (g mol-1) represents the molar mass of
SO2. ρn,air (molecule cm-3) is the number
density of air. k1,g,i∼ (s-1) is the
pseudo-first-order rate constant with respect to
SO2g for the ith
aqueous-phase reaction, and is equal to k1,g,i and
k2,g,iXig for the
first-order and second-order reactions, respectively. In addition, as
illustrated in Fig. 1, the second-order reaction rate may also be limited by
the mass transfer of Xi. Thus, the in-cloud
pseudo-second-order rate constant, k2,g,i∗, is
given by Eq. (20). vXi, αXi, and
Dg,Xi are the molecular mean speed, the mass accommodation
coefficient, and the gas-phase diffusion coefficient of Xi,
respectively. vXi and Dg,Xi are calculated
similarly to Eqs. (18) and (19). αXi can be found
in Table 3.
18vSO2=8RT/πMSO219Dg,SO2=9.45×1013×T×3.47×10-2+1/MSO2ρn,air201k2,g,i∗=1k2,g,i+MAX4XigAvSO2αSO2+rXigADg,SO24SO2gAvXiαXi+rSO2gADg,Xi
As mentioned in Sect. 2.4, we do not change the chemistry time step of the
model (Δt=20 min) but only the time step (to 1 min)
when identifying cloud SO2 reactions. For each 1 min time step, the
loss of SO2g for the
ith reaction, ΔSO2g,i, is solved analytically
using Eq. (13), in which k1,g,i and k2,g,i are
replaced by k1,g,i∗ from Eq. (16) and
k2,g,i∗ from Eq. (20), respectively. This change
reflects the mass transport limitations. The grid-average first-order loss
rate of SO2g,
k1, is calculated using Eq. (15), in which
∑i=17k1,g,i∗
is replaced by the in-cloud total pseudo-first-order rate constant estimated
from ∑i=17ΔSO2g,i. The grid-average
loss of SO2g and the
contributions of different reactions are then calculated using
k1 and ΔSO2g,i. The mixing ratios of
the relevant chemical species are updated at the end of this 1-min time step
and used as initial condition for the next time step. The calculations are
repeated 20 times in a chemistry time step.
Mass accommodation coefficients on aqueous surfaces.
Speciesα (dimensionless)Reference and noteSO21+exp14.7-3825/T-1Boniface et al. (2000)O30.04Müller and Heal (2002); note *H2O20.23Seinfeld and Pandis (2016)HCHO0.04Davidovits et al. (2006)NO22×10-4Shao et al. (2019)HONO0.09Davidovits et al. (2006)HOBr0.6Shao et al. (2019)
* The α of O3 is very uncertain with the upper limit
approaching unity.
Description of model simulations.
AbbreviationDescriptionGC12.7.0Standard GEOS-Chem version 12.7.0GC12.1.0Standard GEOS-Chem version 12.1.0CTRLControl simulation; major changes to GC12.1.0: adding cloud HMS chemistry and cloud reactions of SO2 with HONO and NO2 and applying some wet process updatesDFLTDefault simulation; major changes to CTRL: improving treatments of entrainment/detrainment and heterogeneous cloud sulfur chemistry and adding aerosol water reaction of SO2 with H2O2; shorter time step for calculating cloud sulfur reactionsAll ten sensitivity simulations are based on DFLT with changes in individual parameters or processes HiKfHigh kf (HMS formation rate constant); the low kf is used in DFLTHiKdHigh kd (HMS decomposition rate constant); kd is increased by a factor of 2HiOHHigh OHaq in cloud water; OHaq is increased by a factor of 10 leading to a faster HMS oxidation in cloudsCWpHCloud water pH; its calculations do not consider Ca2+, Mg2+, Na+, Cl-, NO2-, HCOO-, and CH3COO-AWOHAerosol water HMS oxidation by OHaq; the same OHaq and oxidation rate constant are used with cloud HMS chemistryAWK0Aerosol water HMS formation and decomposition; the same kf and kd are used with cloud HMS chemistryAWKEAerosol water HMS formation and decomposition; the same kd with cloud HMS chemistry is used whereas the kf is enhanced relative to dilute solutions by the same EF for the reaction of SO2 and H2O2 in aerosol waterThe three sensitivity simulations below focus on the region of East Asia HiNH3High NH3 emissions; anthropogenic NH3 emissions in the MEIC inventory are increased by 50 %HiFAHigh HCHO emissions; transportation and residential HCHO emissions in the MEIC inventory are increased by a factor of 5AppHetApparent heterogeneous chemistry for SO42- production; it is applied over East Asia (97.5–152.5∘ E, 16–56∘ N) during the cold season (November–March)
The cloud water pH and rate constants for the heterogeneous reaction of
SO2g and
Xig are calculated only at the
beginning of each chemistry time step. We conduct a sensitivity simulation
that redoes cloud SO2 calculations using the cloud water pH and rate
constants estimated at the end of each chemistry time step. The resulting
change is insignificant (global mean
SO42- concentration decreases by
<2 %). The aqueous-phase sulfur reactions are hard-coded into the
model. Ideally, further model development of cloud chemistry should apply
the advanced numerical solvers generated by the Kinetic PreProcessor (KPP),
which may not only allow a full coupling of gas-phase and cloud chemistry
but also make it easier for the model to incorporate additional aqueous
reactions (Fahey et al., 2017; Viral Shah, personal
communication, 18 December 2019).
The implementation of sulfur chemistry in aerosol water is similar to that
for cloud sulfur chemistry. As shown in Fig. 1, the heterogeneous reaction
rates are also controlled by the mass transfer of reactants from the gas to
the aqueous phase. The difference is that aerosols (and aerosol water) can
be considered evenly distributed in a model grid cell, and it is unnecessary
to include the entrainment/detrainment processes. The major difficulty in
parameterizing the aerosol water sulfur chemistry is the lack of suitable
reaction rate constants. Liu et al. (2020) have
recently found that the high ionic strength of deliquesced aerosols
significantly enhances the rate constants for the reaction of H2O2
and SO2. The enhancement factor (EF) relative to its rate constant in
dilute solutions is derived by fitting the data in
Liu et al. (2020) as a function of the
molality-based ionic strength, μb (mol kg-1) (Table 1). The
water content, pH, μb, and the absorbed water volume fraction of
inorganic aerosols are calculated by the ISORROPIA II model (Sect. 2.2). The
aerosol water volume fraction of 0.25 is used as a threshold for the
occurrence of aqueous reactions as it governs the transition of aerosols to
a liquid state (Bateman et al., 2016).
Sensitivity simulations
In addition to the control and default simulations, we conduct ten
sensitivity simulations to investigate the key factors leading to
uncertainty in the modeled HMS concentrations. As shown in Table 4, all
these sensitivity simulations are based on the default simulation. HiKf,
HiKd, and HiOH make changes to HMS formation, decomposition, and oxidation,
respectively, in heterogeneous cloud chemistry. HiKf uses the high
kf instead of the low kf in the default
simulation (Sect. 2.1.1). HiKd increases kd by a
factor of 2, the upper limit of its estimate (Sect. 2.1.2). HiOH increases
OHaq by a factor of 10, matching its
average value in current multiphase models (Sect. 2.1.3). CWpH considers
less ions, i.e., NH4+, H+, OH-, SO42-,
NO3-, HSO3-, SO32-, HCO3-,
CO32-, HMS, and
CH3SO3-, in
cloud water pH calculations.
AWOH, AWK0, and AWKE examine the potential role of aerosol water in
heterogeneous HMS chemistry (Table 4). Since the rate constants of HMS
chemical reactions in concentrated solutions have not been determined
experimentally, we have to make assumptions about these data. AWOH
implements the oxidation of HMS by OH in aerosol water and assumes the same
rate constant as those for cloud water. AWK0 adds the formation and
decomposition of HMS in aerosol water also using the rate constants for
cloud water. Theoretically, we anticipate that the rate constant of HMS
formation, kf, in concentrated solutions should be enhanced
relative to dilute solutions (Song
et al., 2019a), similar to the situation found for the reaction of
H2O2 and SO2. AWKE arbitrarily increases kf by
the same EF for the H2O2 and SO2 reaction (Table 1). The
implementation of the above chemical reactions of HMS in aerosol water
follows the approach described in Sect. 2.5.
Three sensitivity simulations, HiNH3, HiFA, and AppHet, focus on East Asia
(Table 4). SO2, HCHO, and NH3 emissions may influence the modeled
HMS. Although SO2 emissions are well
understood, recent studies have shown that there may be large uncertainties in emissions of NH3
and HCHO in China (Pan et al., 2018; Kong et al., 2019; Liu et al., 2019;
Song et al., 2019a). An inverse study found that the MEIC inventory
underestimated NH3 emissions by 30 % nationally and by > 40 % in eastern and central regions using observations over the same time
period as our study (Kong et al., 2019). HiNH3 increases
the anthropogenic emissions of NH3 in MEIC by 50 %. Less information
is available regarding the emissions of HCHO due to its sparse observations
and complex chemistry. Model–observation comparisons in Beijing suggested a
strong underestimation of HCHO emissions during winter
(Song et al., 2019a). Mobile and
residential emission sources may be responsible for its underestimation
(Jaeglé et al., 2018; Song et al., 2019a). HiFA increases HCHO
emissions from the transportation and residential sectors by a factor of 5.
Chemical transport models commonly underestimate
SO42- during winter haze
episodes in China (Chu et al., 2020), and thus some studies have
adopted an apparent heterogeneous parameterization for SO2 reactive
uptake in order to compensate for the missing
SO42- (Zheng et al., 2015;
Cheng et al., 2016; Chu et al., 2016; Wang et al., 2016; Liu et al., 2019;
Li et al., 2020). This parameterization is applied in AppHet during the cold
season, in which the reactive uptake coefficient of SO2 increases from
2 × 10-5 to 5 × 10-5 with 50 % < RH ≤ 100 % (Zheng et al., 2015).
Results and discussionSpatial and seasonal distributions in the default simulation
The horizontal distributions of HMS concentration in the surface layer and
the vertical profiles of its zonal average are shown in Fig. 4 (DJF:
December–January–February and JJA: June–July–August) and Fig. S5 in the Supplement (MAM:
March–April–May and SON: September–October–November). The concentration
unit is µgsm-3, where 1 sm3 equals 1 m3 at standard
temperature and pressure (273.15 K and 1013.25 hPa). The molar ratio of HMS
to sulfate, also shown in Figs. 4 and S5 in the Supplement, is a useful metric to assess
the significance of HMS in sulfur chemistry. Higher HMS concentrations and
HMS / sulfate ratios are found over the continental regions in the Northern
Hemisphere. The vertical profiles indicate that most HMS exists in the lower
troposphere. These features are expected because the precursors of HMS,
SO2 and HCHO, are more abundant in these regions compared with
elsewhere (Fig. S6 in the Supplement).
Distributions of HMS concentrations and the molar ratios
of HMS to sulfate modeled by the default simulation. Top and bottom panels
show results for DJF (December–January–February) and JJA
(June–July–August), respectively. (a), (c), (d), and (f) are the
horizontal distributions in the surface layer. (b) and (e) are the vertical
distributions of the zonal averages from surface to 200 hPa. The
concentration unit is µgsm-3, where 1 sm3 equals 1 m3
at 273.15 K and 1013.25 hPa. The color bars are not linear and differ in the
three columns. The same color bars are used for each pair of the top and
bottom panels. The black-outline boxes indicate the three regions selected
for quantitative analysis.
The surface HMS concentrations and HMS / sulfate molar ratios exhibit distinct
seasonal patterns with maxima in DJF (boreal winter) and minima in JJA
(boreal summer), and thus our analyses focus on these two seasons. It is
noted that there are hotspots of HMS in JJA in Siberia that are linked to
massive forest fires in that region in July 2016 (Sitnov et
al., 2017). As highlighted in Fig. 4, three regions with relatively high HMS
levels, East Asia (EA), Europe (EU), and North America (NA), are selected
for quantitative analysis. Figure 5 shows the statistics of HMS levels from
the default simulation with comparisons to other simulations. The average
HMS concentrations in DJF (JJA) are 0.59 (0.09), 0.16 (0.013), 0.055 (0.015) µgsm-3, for EA, EU, and NA, respectively. The average HMS / sulfate
ratios in DJF (JJA) are 0.09 (0.01), 0.06 (0.006), 0.04 (0.009), for EA, EU,
and NA, respectively. The wintertime in East Asia, northern China in
particular, has both the highest HMS concentration and highest HMS / sulfate
ratio. The average HMS concentrations (1–3 µgsm-3) and
HMS / sulfate ratios (0.1–0.2) are found during the winter season in northern
China (Fig. S7).
Comparison of the modeled surface HMS concentrations
(a, c, e) and HMS / sulfate molar ratios (b, d, f) from different simulations for
three regions and two seasons. EA, EU, and NA are East Asia, Europe, and
North America, respectively. DJF and JJA represent
December–January–February and June–July–August, respectively. The solid
and dashed lines indicate the DJF value from the default (DFLT) simulation
and its double and half. The vertical axis differs in the left panels.
As mentioned in Sect. 1, previous studies have suggested that the formation
and existence of HMS in the condensed phase are generally favored under the
following conditions: high precursor (SO2 and HCHO) concentrations, low
photochemical oxidant levels, low temperature, abundant aqueous water, and
moderate acidity (Munger et al., 1984, 1986; Moch et al., 2018; Song et
al., 2019a; Ma et al., 2020). The seasonal variability of HMS does not
follow that of the precursor levels (Fig. S6 in the Supplement). The seasonal variation of the
geometric mean of the two precursors, SO2×HCHO, is weak because of their
opposite seasonality (more SO2 but less HCHO in winter). The cloud
liquid water content (L) in the lower troposphere shows a spatial
distribution with higher values over the ocean and lower values over land
(Fig. S8). There is no consistent seasonal pattern of L between DJF and JJA
over the three regions (EA, EU, and NA). The modeled cloud water pH exhibits
a seasonal difference. The average pH in DJF (JJA) is 4.3 (5.8), 4.7 (5.6),
and 4.7 (5.7) for EA, EU, and NA, respectively. The higher pH in JJA is
related to more abundant gaseous NH3 (Fig. S8 in the Supplement), given the buffer
capacity of NH3 in moderating the acidity of atmospheric condensed
water (Song et al., 2019b).
One of the above-mentioned factors favoring HMS is the moderate acidity.
This term is somewhat ambiguous but is used to represent the pH range that
allows for relatively rapid formation and slow decomposition of HMS. We show
in Fig. 2 that both kf and kd increase with pH.
The lifetime of HMS with respect to decomposition is about 60, 6, and 0.6
hours at pH 5, 6, and 7, respectively, at 298 K, and is even larger at lower
T. For the range of pH in the three regions (its average from 4.3 to 5.8),
the decomposition of HMS is so slow that its chemical equilibrium is
difficult to achieve. Accordingly, the modeled HMS levels are predominantly
controlled by formation kinetics. This is supported by the results from the
HiKd simulation, in which kd× 2 makes little
difference in the modeled HMS compared to the default simulation (Fig. 5).
The higher cloud pH in JJA should lead to faster HMS formation rates than
those in DJF. However, in the default simulation, the modeled HMS levels
show an opposite pattern. This is believed to be linked to the different
photochemical oxidizing abilities in the two seasons. Globally, the two main
aqueous oxidants for SO2 are O3 and H2O2, which compete
with HCHO. The competition of different pathways can be influenced by the
levels of these gases, T (changing gas solubilities and rate constants), and
pH (changing rate constants). O3, H2O2, and HCHO all have
higher concentrations in JJA (Fig. S6). The lower T in DJF favors the
H2O2 reaction most and the O3 reaction least. Notably, the
response of the O3 reaction to pH is essentially the same as that for
HCHO since both react rapidly with
SO32-. The HCHO + SO2
reaction is significant only when the two photochemical oxidants are
inefficient.
Difference between the default and control simulations
Compared with the default simulation, the control simulation realizes very
different spatial and seasonal distributions of HMS concentrations and
HMS / sulfate molar ratios (Fig. S9 in the Supplement). Figure 6 shows the differences in
surface HMS concentrations for DJF and JJA. The corresponding information
for MAM and SON is presented in Fig. S10 in the Supplement. Two features are evident. First, a
weak seasonality is found for the control simulation, but for the default
simulation, HMS is much more abundant in DJF. Second, the control simulation
predicts significantly higher HMS concentrations almost everywhere except in
parts of East Asia and Europe in DJF. Interestingly, the only region where
the default simulation gives higher HMS concentrations is wintertime in
northern China, the focus of several studies (Moch et al., 2018; Song et
al., 2019a; Ma et al., 2020). Specifically, as shown in Fig. 5, the average
HMS concentrations modeled by the control simulation in DJF (JJA) are 0.60
(0.70), 0.22 (0.12), 0.14 (0.11) µgsm-3, respectively, for East
Asia (EA), Europe (EU), and North America (NA). The average HMS / sulfate
ratios inferred from the control simulation in DJF (JJA) are 0.09 (0.14),
0.08 (0.06), 0.09 (0.07), respectively, for EA, EU, and NA.
Surface concentrations of HMS from the control (CTRL) and
default (DFLT) simulations in two seasons. Top and bottom panels show
results for DJF (December–January–February) and JJA (June–July–August),
respectively. (c) is the absolute difference between these two simulations:
b-a. (d) is their relative difference: (b/a-1)×100 %.
Similarly, (g) is the absolute difference between (e) and (f): f-e, and
(h) the relative difference between them: (f/e-1)×100 %. The
color bars in (a), (b), (e), and (f) are not linear.
As described in Sect. 2.5, based on the control, the default simulation
improves the representations of heterogeneous cloud sulfur chemistry in the
model by applying the entrainment-limited uptake method from
Holmes et al. (2019) and by reducing the time step when
calculating aqueous sulfur reactions. These changes allow for a more
realistic simulation of entrainments and detrainments of air in partly
cloudy grid cells and for an effective competition of different aqueous
reactions consuming SO2. In the control simulation, the time step for
calculating in-cloud sulfur reactions is the same as the chemistry time step
of the model, Δt=20 min. But there may be a
> 50 % possibility that the lifetime of in-cloud SO2 is
less than this Δt, as shown in Fig. 3 and described in
Sect. 2.4. Given that the main reactants with in-cloud SO2 are O3
and H2O2, this setting leads to a general underestimation of the
contribution of O3 and H2O2 and an overestimation of
importance of the minor reactants such as HCHO. The bias is larger in JJA
than in DJF, as suggested by the probability distribution statistics for the
in-cloud lifetime of SO2 (Table S1 in the Supplement).
Key uncertain factors
Section 2.6 and Table 4 describe the ten sensitivity simulations we conduct
with an aim to find out the key parameters and processes leading to HMS
modeling uncertainties. All of these simulations are modified based on the
default simulation and can be classified into three groups: heterogeneous
cloud chemistry (HiKf, HiKd, HiOH, and CWpH); heterogeneous aerosol water
chemistry (AWOH, AWK0, and AWKE); and East Asia only (HiNH3, HiFA, and
AppHet). A comparison of the surface HMS concentrations and HMS / sulfate
molar ratios from these sensitivity simulations is provided in Fig. 5,
focusing on three regions (EA, EU, and NA) and two seasons (DJF and JJA).
First, we examine the sensitivity simulations in terms of the formulation of
heterogeneous cloud chemistry. HiKf, HiKd, HiOH, and CWpH make changes in
HMS formation, decomposition, oxidation, and cloud water pH calculations,
respectively. The surface HMS concentrations and HMS / sulfate ratios in the
latter three indicate relative differences of less than ±20 %
compared to the default simulation. However, HiKf shows a very large
increase, by a factor of 2 to 6, in modeled HMS. This is expected since the
high and low kf differ by a factor of about 3 at pH < 2 and by a factor of about 6 at pH > 4 (Sect. 2.1.1). As
described in Sect. 2.1.3, the formation of HMS and its oxidation by OH
represent an indirect oxidation pathway for SO2. The sulfate yield,
defined as the number of SO42- ions
produced due to each attack of OH on HMS, is set to 2 in our simulations.
The small difference between the HiOH and default simulations suggests that
this indirect pathway should be insignificant.
Second, three sensitivity simulations are conducted for East Asia, as it is
found most suitable for the existence of HMS. HiNH3 and HiFA increase the
concentrations for modeled HMS in DJF by 60 % and 20 %, respectively,
whereas the concentrations by AppHet are decreased by about 30 %. The
changes due to HiNH3 and HiFA are much smaller in JJA (Fig. 5). The increase
of HMS in HiNH3 can be attributed to higher cloud water pH, and its decrease
in AppHet should be related to a decrease in SO2 available for cloud
chemistry. Interestingly, HiNH3 increases the HMS / sulfate ratios in DJF by
only 20 %. The higher cloud water pH enhances the formation of sulfate
through the pH-sensitive pathways such as the reaction of SO2 with
O3.
Third, AWOH, AWK0, and AWKE explore the potential role of heterogeneous
aerosol water HMS chemistry. The challenge of modeling aerosol water HMS
chemistry is the lack of its reaction rate constants in concentrated aqueous
solutions. We use the rate constants from dilute solutions in AWOH and AWK0.
The oxidation of HMS by OH in aerosol water leads to losses of 10 %–20 %
(DJF) and 40 %–60 % (JJA) (Fig. 5). The formation and decomposition of HMS
in aerosol water result in negligible changes in the modeled HMS
concentrations, as shown in Fig. 7 (DJF) and Fig. S11 (the other seasons).
Results from AWKE suggest that aerosol water might play a role in the
formation of HMS only when the kf is strongly enhanced in
concentrated solutions like the rate constant of the SO2 reaction with
H2O2.
Difference in surface HMS concentrations in DJF
(December–January–February) between two sensitivity simulations (AWK0 a
and AWKE b) and the default simulation (DFLT). The color bar is not
linear.
Overall, our sensitivity simulations suggest that the key uncertain
parameter in the model is kf. Based on existing experimental
results, the low value for kf seems more reasonable (Sect. 2.1.1). The key uncertain process is modeling the aerosol water chemistry of
HMS in the absence of reliably defined rate constants.
Comparison with prior observations
The quantitative observations of HMS in ambient aerosols remain sparse
(Moch et al., 2020) and we provide here a comparison between
the observations at four sites and two model simulations (control and
default) in Table 5. Since these observations have been collected over the
past three decades while our simulations cover only one year, it is more
appropriate to use the molar ratios of
HMS /SO42- or HMS/MSA rather than
absolute HMS concentrations. The measurement techniques of HMS in different
studies were different (Table 5) and their effects on the reported
results are unclear. Moreover, observations of HMS may be subject to
measurement artifacts that may make quantitative comparisons between model
results and observations difficult (Ma et al., 2020; Moch et al., 2020).
Among the observations shown in Table 5, the highest
HMS /SO42- ratio of 11 % has
been found in winter in Beijing by Ma et
al. (2020). Model results from both default and control simulations agree
well with this observed ratio. Less HMS was observed in other regions,
including New Mexico (USA), Germany, and Osaka Bay (Japan). The default
simulation overestimates the
HMS /SO42- or HMS/MSA ratios by a
factor of 2–3, whereas the control simulation overestimates these ratios by
an order of magnitude.
Comparison between observations and model simulations.
LocationYear and seasonObserved molar ratioDefaultControlReference and noteNew Mexico, USA1997 SummerHMS / SO42-< 0.2 %0.3 %2 %Dixon and Aasen (1999); note aGermany2009/10 All yearHMS/SO42-=2 %5 %16 %Scheinhardt et al. (2014); note bBeijing, China2015/16 and 2016/17 WinterHMS / SO42-=11 %13 %10 %Ma et al. (2020); note cOsaka Bay, Japan1998/99 Spring, summerHMS/MSA = 1320Suzuki et al. (2001); note d
a PM1 (particles smaller than 1 µm) samples of 11 PM2 samples were
collected with each sampled for several days. HMS detection method: ion
chromatography.
b Size-segregated (five stages under 10 µm) daily aerosol samples of
154 data sets were collected at nine sites. HMS detection method: capillary
electrophoresis.
c PM2.5 samples of 77 were collected with 69 daily and eight half-day
samples. HMS detection method: ion chromatography.
d Size-segregated (four stages under 7 µm) aerosol samples of four data
sets were collected with each sampled for 11–25 d. HMS detection method:
proton nuclear magnetic resonance (1H NMR).
A more detailed comparison of the model with observations in Beijing is
provided below (Ma et al., 2020). These
samples from Beijing were stored at -20 ∘C between sample
collection and analysis, had HCHO added to solution during sample
extraction, and were examined by ion chromatography using a more acidic
eluent than normal all in order to limit HMS decomposition and
misidentification. The observations in Ma
et al. (2020) cover 73 d in winter and 11 polluted days in other seasons.
The data for the other seasons is presented only in their discussion paper.
Because of the coarse resolution of global model, we do not expect our
simulations to capture the day-to-day variability that is observed at a
single site. Accordingly, we examine the ability of our simulations to
reproduce the observed relationships between HMS and its influencing
factors. Figure 8 provides scatter plots of HMS concentrations (and
HMS /SO42- ratios) versus two
variables (O3 and RH) and compares the data from observations and model
simulations (control and default). The level of O3 represents
photochemical oxidizing capacity and RH may indicate the abundance of
aqueous water in the lower troposphere.
Relationship between HMS concentrations and O3
mixing ratios (top) and RH (bottom) in northern China. Data from
observations, the control (CTRL), and the default (DFLT) simulations are
presented in (a) and (d), (b) and (e), and (c) and (f), respectively.
HMS / sulfate molar ratios are indicated by the color scale. The observational
data in (a) and (d) were collected in Beijing by
Ma et al. (2020). There were 69 daily (and
8 half-day) samples in the 2015/16 and 2016/17 winter seasons. The model
data are obtained from the grid cell covering Beijing with 366 daily
samples. The vertical axes differ in the panels of observations and model
simulations.
We find a similar relationship between HMS and O3 from the observations
and default simulation (Fig. 8). Significant HMS levels are observed and
modeled only under low O3 conditions (< 20 ppb). However, the
control simulation obtains another cluster of days with high HMS levels when
O3 is abundant (> 40 ppb). This cluster is linked to the
inappropriate representation of heterogeneous cloud sulfur chemistry in the
control simulation. The large time step for SO2 titration excessively
favors the reaction of SO2 with HCHO, as described in Sect. 2.4 and
Fig. 3. It should be noted in Ma et al. (2020) that only 11 daily samples had O3 levels larger than 20 ppb.
There might be a possibility that the days with high levels of both HMS and
O3 were missed in their sampling coverage, but we think it is unlikely
given the rapid oxidation of SO2 by the photochemical oxidants (gaseous
OH and aqueous O3 and H2O2) under such conditions.
The scatter plots of HMS and RH show a similar exponential-like relationship
in the observations and model simulations (Fig. 8). Such an exponential-like
relationship has been interpreted to support the hypothesis that HMS is
produced through aerosol water (Song et al., 2019a; Ma et al., 2020).
This is because the amount of aerosol water also exhibits an exponential
relationship with RH (Song et al., 2018, 2019b). Interestingly, our model
simulations using aqueous clouds as the only medium can obtain a similar
relationship between HMS and RH, which reduces the credibility of this
aerosol water hypothesis and lends support to the hypothesis that cloud
water is a dominant medium for HMS formation (Moch et al., 2018, 2020).
Global atmospheric models, including the numerical weather prediction model
employed in the MERRA-2 reanalysis, are usually not capable of resolving
subgrid cloud processes, and cloud properties are parameterized using an
RH-related statistical scheme (Molod, 2012; Molod et
al., 2015). Thus, it is not surprising to find a relationship between RH and
HMS in the simulations.
Knowledge gained and remaining gaps
The different spatiotemporal patterns of the HMS levels modeled by the
control and default simulations indicate the importance of an appropriate
representation of heterogeneous cloud sulfur chemistry. Our modeling
suggests that photochemical oxidizing capacity is a key influencing factor
for HMS formation because it affects the competition of HCHO with oxidants
(e.g., O3 and H2O2) for SO2. This factor is partly
responsible for the distinct seasonality in HMS modeled by the default
simulation. On a regional scale, the most suitable place for the formation
and existence of HMS is parts of East Asia in the lower troposphere during
the cold season. Aqueous clouds are the major medium for HMS chemistry since
the model simulations can reasonably reproduce both the observed HMS levels
and the relationship between in situ HMS and RH when assuming this as the
only medium. Aerosol water may play a role if the rate constant of HMS
formation is greatly enhanced in concentrated solutions. This finding is
consistent with several studies (Jacob, 1986; Olson and Hoffmann, 1989;
Whiteaker and Prather, 2003; Moch et al., 2018, 2020).
Quantitative observations of HMS are sparse, and more data are required to
validate the model. The quantification of HMS in different seasons and over
different photochemical conditions, with samples analyzed shortly after
collection to minimize potential HMS decomposition, is particularly
valuable.
Two knowledge gaps are identified from our sensitivity simulations. First,
the key uncertain factor in the model is kf, the rate constant
for HMS formation. Large discrepancies exist among existing laboratory
experiments (Fig. 2), and future laboratory studies are required to narrow
its uncertainty. Second, the lack of kinetic and thermodynamic data for HMS
chemistry in concentrated solutions poses a key challenge to modeling HMS
processing in aerosol water, and new laboratory studies are needed. Also, we
did not consider the uncertainty in the meteorological reanalysis. Although
MERRA-2 assimilates extensive observations and represents the atmospheric
states accurately, cloud properties are modeled exclusively. Studies have
shown biases in seasonal and spatial variations of cloudiness when comparing
the reanalysis data with lidar and satellite observations (Kennedy et
al., 2011; Stengel et al., 2018; Miao et al., 2019). Previous work has found
that simulated HMS is extremely sensitive to cloud distributions and
properties, and these biases in MERRA-2 cloud properties have been
identified as a possible source of error for simulation of HMS driven by
MERRA-2 (Moch et al., 2018, 2020).
Recently, the quantum chemical calculations by Chen and Zhao
(2020) suggested that hydroxymethyl sulfite (HMSi), an isomer of HMS, might
also be produced by an aqueous reaction of HCHO and SO2. The laboratory
experiments of De Haan et al. (2020) demonstrated
that HMS was one of the major products from the aqueous processing of
glyoxal monobisulfite (CH(OH)2CH(OH)SO3-), the adduct of
glyoxal and SO2. These new mechanisms need to be considered in future
model studies.
Conclusions
Based on appropriate implementation of heterogeneous HMS chemistry and
assuming aqueous clouds as the only medium, the global GEOS-Chem model can
reasonably reproduce the observations of HMS in Beijing and three other
sites. The modeled HMS concentrations and HMS / sulfate ratios show a clear
seasonal pattern with higher values in the cold period. The spatial
distributions of HMS in descending order are East Asia, Europe, and North
America. Our model simulations find the highest average HMS concentrations
(1–3 µgm-3) and HMS / sulfate molar ratios (0.1–0.2) in northern
China during the winter season. Photochemical oxidizing capacity affects the
competition of HCHO with oxidants (e.g., O3 and H2O2) for
SO2, and is a key factor influencing HMS formation. Aqueous clouds act
as the primary medium for HMS chemistry, agreeing with prior studies (Moch
et al., 2018, 2020), while aerosol liquid water could play a role if the
rate constant for HMS formation is greatly enhanced.
This study identifies future research needs. Laboratory experiments should
reduce the uncertainty in the formation rate constant of HMS and determine
the kinetics for HMS chemistry in concentrated solutions. More field
observations of HMS, especially its quantification in different seasons and
photochemical conditions, are helpful to validate the model. It is important
for future observations of HMS to limit possible HMS decomposition so that
the observations can be compared directly with model results. Limiting HMS
decomposition can be achieved by analyzing samples shortly after collection
and by using analysis methods that are designed to limit HMS decomposition
(Dovrou et al., 2019; Ma et al., 2020; Moch et al., 2020). The coarse
resolution of the global model does not allow it to capture day-to-day
observations at a single site, and we are preparing another paper to
demonstrate the capacities of regional model with a finer resolution to
reproduce individual haze events in northern China.
Code and data availability
The standard GEOS-Chem model is available at:
10.5281/zenodo.3860693 (The International GEOS-Chem User Community, 2020). The code changes made in this study
are available at: https://github.com/shaojiesong/GC1210_sulfchem_Song2020 (Song, 2021). The laboratory and observational data used
in this study were all obtained from published papers and books.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-21-457-2021-supplement.
Author contributions
ShS initiated the study, carried out analysis, and wrote the initial draft.
All authors helped interpret the data, provided feedback, and commented on
the manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank Qianjie Chen, Pingqing Fu, John Jayne, Gan Luo, J. William
Munger, Chris P. Nielsen, Jingyuan Shao, Viral Shah, Xuan Wang, Yuxuan Wang,
Douglas R. Worsnop, Lin Zhang, and Shuping Zhang for helpful discussions.
Financial support
This work was supported by the Harvard Global Institute.
Review statement
This paper was edited by Aijun Ding and reviewed by three anonymous referees.
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